⊠that Unicode allocated for \hbar. Whether this matters is up to you to decide. (I don't know if voice synthesizers will read the latter more intelligently in a physics context than the former, for example.)
As a Unicode geek, I need to point out, however, that you would then be typing a U+0127 LATIN SMALL LETTER H WITH STROKE character, the letter ħ used in Maltese and in the IPA to denote a voiceless pharyngeal fricative, rather than the U+210F PLANCK CONSTANT OVER TWO PI character (â) âŠ
The statement âBB(643) makes ZFC inconsistentâ is not a reasonable summary of the situation, however. I'd rather say âZFC can't compute BB(643)â (which is still a simplification of sorts).
A history of the White House (the building!) and what its various extensions and renovations reveal about the extension of presidential power in the United States: www.youtube.com/watch?v=32G6...đ
It's as U+210F PLANCK CONSTANT OVER TWO PI in Unicode (in âLetterlike Symbolsâ).â€â€Under Linux (with most apps) you can type control-shift-u followed by 210F followed by a space.â€â€Under any OS you can copy-paste it from some kind of character table.
A decade ago, the most frequent opinion among smokers was that vaping was less harmful than tobacco. But ten years on, the opposite is true: over a third say that vapes are just as or even more dangerous. You can see this shift in the chart.â€â€The scientific evidence is clear that this is incorrect.đŒïž
It's inspired by this previous question, but it's different:đ
I asked a question on MathOverflow about whether some sets of integers can be used to âencryptâ another set while keeping the Turing degree of the encryption arbitrarily low. mathoverflow.net/q/503435/17064â€â€(This may turn out to be utterly stupid.)đ
From WP-en: âDespite the poisonings, Paxillus involutus is still consumed in parts of Poland, Russia, and Ukraine, where people die from it every year.â đŹ en.wikipedia.org/wiki/Paxillu...đđ
⊠so when we build a larger computer, ultrafinitists should, if not spend their time probing for them, at least be excited about the discovery of new numbers (âwe confirmed 2^n exists for n=2^85â or so) like chemists are discovered about the discovery of new elements.â€â€Why aren't they?
⊠So IIUC, ultrafinitists mostly accept the existence of 10Âčâ°â° (which we can easily handle on a computer), but they doubt the existence of 10^(10Âčâ°â°) (which we can't). However, the construction of larger computers should let us test the existence (in their sense) of larger numbers, âŠ
⊠to write down a proof (in a system of bounded arithmetic) which basically consists of saying â2 exists, 2Ă2 exists, 2Ă2Ă2 existsâŠâ through n steps (their gripe isn't that the proof is hard, but if n is large-ish, it's not because n exists that you can actually DO the proof). âŠ
IIUC (not sure!), mainstream ultrafinitists accept the totality of multiplication on the natural numbers (âif m and n exist, then mĂn existsâ), but typically not with that of exponentiation (âif n exists, then 2^n existsâ): to convince them of the existence of 2^n you need âŠ
Here's one reason I have a hard time taking ultrafinitism seriously:â€â€If ultrafinitists really believed what they say they do, they should get excited about the discovery of ever larger numbers. They should consider searching for evidence of them a valuable goal. Yet they don't. Why? đ€đ
Absolutely this. As my paternal grandmother was dying, the most important message she wanted to convey to me in moments of clarity was, "Make sure there is never another war". The World Wars created a deep traumatic scar through the generations that experienced them, jingoism came much later.đ
A spaceship landed in the park. A door dilated. A strange-looking alien with artificial antennae made from tin foil emerged. â€â€"Greetings, Earthlings!! We come in..." It consulted a device. "In trick or treat?"
Is anyone still counting the totally illegal, unconstitutional and impeachable offenses committed since Trump took office, or have we run out of numbers for them?
reality-studio military policy, made by Fox News viewers, focused on dealing with problems that exist mainly in the Fox New cinematic universe, and aimed at generating new Fox News contentđ
Or even having to <shudder> work a job to make a living.
I really wonder what it's like, not being a royal prince, and having to wear a surname like the plebs, instead of being Prince Firstname or The Duke of Someplace.â€â€If only there were other people in this situation to help me explain what it's like, I could relate. Know anyone?
As an algebraist, I often wonder if there is a reasonable algebraic structure that encapsulates the properties of the (ordinary) operations on ordinals, which lack the most basic stuff like commutativity of addition, but still have Euclidean division which works mostly like one would expect. đ€
FYI I made a Youtube, Tiktok and Instagram channel for the lizards :)â€The name is Eizo_and_frens, it will only have short and cute videos around Eizo the Varanus acanthurus, and sometimes educational content about monitor lizards.â€Hope they bring a bit of peace in your life like for me đžđŠ
J'avoue ĂȘtre surpris par la position du Canada sur ce graphique.đ
It's actually theorem II.5.9 (page 151) in Lambek & Scott's âIntroduction to higher-order categorical logicâ: they don't call it âunique choiceâ but rather âdescriptionâ.â€â€(I'd be extremely surprised if it weren't in one of Johnstone's books as well, but I agree it seems to be well hidden.)
In my latest blog this week, I try to unpack the different ways that people talk about the feasibility of the UK rejoining the EUâ€pascallth.substack.com/p/can-the-uk...đ
I can hear myself saying "Have mercy! She's a human being!" I was scarcely aware that I was speaking. After they dragged her away, I shouted into the airport something like, "This is cruelty! How can we stand this?" Whatever I said, it tore out of me. And I was immediately afraid I'd be arrested too
When youâre desperate to get a real heavyweight French intellectual to come out swinging against Mamdani and the best you can do is BHL, the Johnny Hallyday of Philosophy.đŒïž
To clarify for David: if every deputy makes a choice of party/group (out of finitely many possibilities), thus partitioning the assembly into finitely many parts, then exactly one part belongs to the ultrafilter.
Note: I'm not saying it would be a good idea, or that I'd want that, I'm just saying I'm surprised it doesn't exist.â€â€Is it because the technology to do this doesn't exist, or is it because the economics doesn't work out?
Note: I'm not saying music-generating AIs don't exist. I know they do. But as far as I'm aware, there's no public Web site where you type âa piano sonata in the style of Beethoven, quoting Elgar's âPomp and Circumstanceâ marches in every movementâ and you get a shitty mp3 to download.
This reminds me: how come is it that we hear a âlotâ about text-generating AIs (LLMs) and image/video-generating AIs, but almost never about music-generating AIs, even though many people consume a lot of music, perhaps more than any other form of art?đ
When you hear âInternet of Thingsâ or âconnectedâ, think:â€â useless & works badly at best,â€âĄrequires constant updates and Internet access for no reason,â€âąceases to work because company decides to stop maintaining,â€âŁgets hacked and serves to attack you/others,â€â€keeps you under constant surveillance.
In fact, we don't even need deputies any more: we can directly use this on electors since the ultrafilter takes care of everything.â€â€The only problem is to convince French straight people to have enough sex so we have measurable-cardinal-many electors. Get banging! One of you needs Îș children!
Let me take this a step further: let us make the number of deputies the first measurable cardinal Îș, and use a Îș-complete ultrafilter. So even if there are infinitely many options to choose from, as long at there are <Îș of them, âalmost allâ (in the ultrafilter sense) deputies will agree on one! đ
⊠And I also just love the candor he displays (at 56âł into this video) about the whole thing, how he finds it so funny to be both parties and judge at the same time: www.youtube.com/watch?v=m5dh...đ
⊠And IIUC, it's in the âcertainly illegal, but nobody can do anything about itâ category, which is also a genius concept in and of itself. www.youtube.com/watch?v=gFQW... âŠđ
Trump is so cartoonishly corrupt it becomes sort of funny, but you have to admit, the idea of claiming that the federal government (which he now heads) owes him damages, and then ordering his underlings to âsettleâ the case so he gets the money is pure genius in its simplicity. âŠ
Well, apparently, Reality and I don't have the same ideas as to what is realistic and what isn't. I say Reality is wrong and even a bit naĂŻve at times. âą3/3â€â€[Reposted from an old Twitter thread.]
⊠you could NEVER set up such a large project in so short a time, and even if you could, it's entirely unrealistic to think you could keep it a secret; and even if you did, putting many smart people together to a single end never gives the desired results!â âą2/3
If I had seen the Manhattan Project described in a fiction rather than as history, I would have said: âthis is an interesting plot device, but there's NO WAY such a thing would work in real life: ⊠âą1/3
I asked a long question on MathOverflow about this game, with detailed explanations and some remarks and comments: mathoverflow.net/q/503195/17064â€â€(Since it's about mathematical games and computability, I think @joeldavidhamkins.bsky.social might be interested.)đ
i guess grokipedia is just the wikipedia copy they use in pretraining: typical bad formatting when you don't use the very clean scrap recently made available by @wikimediafoundation.org for structured wikipedia.đŒïž
This is indeed utterly crazy and I've never seen such behavior. And it doesn't make technical sense: as long as third-party cookies are disabled (they ought toâŠ), every domain's cookies is hermetically separated from every other one, so clearing just the WebApp's domain's cookies should be enough.
For example, I don't like it when people act like idiots, but I also think it shouldn't be forbidden.
One sign that someone isn't a complete idiot is when they manage not to confuse:â€â€â [I think] X is forbidden,â€â€â [I think] X should be forbidden,â€â€â [I think] you should not do X,â€â€â I don't like it when you do X.
Counterpoint: the people to blame, here, are idiots who count citations to evaluate research. While such idiots exist, we should encourage all kinds of citation games as long at they don't distract the people sincerely reading the paper for its actual content.đ
⊠and similarly, putting [Bar] in the bibliography with no actual reference to [Bar] in the text is also fine, because none of this will distract the intended reader but it bothers idiots who count citations, which is GOOD.â€â€Remember: đœđ
⊠So I think we should, on the contrary, ENCOURAGE any kind of bogus citations designed to vex people who count citations, as long as they don't annoy the intended reader (the one who actually reads the paper for its content). For example, writing âthis paper has nothing to do with [Foo]â is fine âŠ
Counterpoint: the people to blame here are not these Iraqi academics but the people who decided to make âcounting citationsâ a method of evaluating academia, thus creating an incentive to rig the system and diverting citations from their actual use, which is just to REFER TO OTHER PAPERS. âŠđ
No! I don't even have any example where the Arthur+Nimue have a winning strategy but the fairly trivial strategy of âplay đż then đ if b=0, or đ then đż if b=1â doesn't win.đ
A nice introduction to the Standard Model of particle physics (and some history thereof), which should be understandable by a fairly general audience; by John C. Baez (@johncarlosbaez@mathstodon.xyz on the Fediverse): www.youtube.com/watch?v=0yjx...đ
đŁTHREAD: Itâs surprising to me that so many people were surprised to learn that Signal runs partly on AWS (something we can do because we use encryption to make sure no one but youânot AWS, not Signal, not anyoneâcan access your comms). â€â€Itâs also concerning. 1/đ
As such the game is extremely theoretical, of course, but it is at least related to some games that are actually used in the context of cryptography to define cipher security; e.g., see the description of IND-CPA in en.wikipedia.org/wiki/Ciphert... â here Merlin (the âchallengerâ) doesn't have âŠđ
Sorry, that was indeed unclear. No, Nimue does see the moves played by Merlin. Merlin and Nimue see everything, Arthur only sees the moves by Merlin after the initial b.â€â€(I'll be posting a precise description on MO with some basic facts once I finish checking a few things.)
In mathematics we don't have any qualms about discussing objects that are noncomputable, games in which players may follow noncomputable strategies, etc. In fact, it's often simpler to reason about these. Here Merlin is not required to play computably, only Arthur is.
đ Maybe I wasn't clear on that, but no player gets to set P or Q: they are part of the rules of the game; so each possible (P,Q) defines a different game â some very trivial â and I'm asking a general question about all of them.
⊠(If one of them is computable then A+N win essentially by the argument you gave.)â€â€There are no probabilities involved. But I should have emphasized that this is a problem in computability.
Indeed, if P and Q aren't disjoint, the Merlin plays in the intersection and A+N can't win.â€â€But even if P and Q are disjoint, Arthur can't necessarily tell whether the given element is in P or Q because he's required to play per a computable strategy, and P and Q aren't necessarily computable. âŠ
⊠Arthur, seeing this, can then either make a guess or choose to continue the game (in which case Nimue again picks âđżâ or âđâ and so on; note that b is only chosen once by Merlin). Importantly, Arthur must follow a âcomputableâ strategy.â€â€â For which P,Q do Arthur+Nimue have a winning strategy?
⊠directly to Arthur except insofar as they agreed a strategy in advance. Nimue can only choose either âđżâ or âđâ, pass this to Merlin, who then chooses an element of a subset P or Q â â (both P,Qââ are fixed in advanced and known to the players) that gets shown to Arthur. âŠ
Now thinking about the following mathematical game:â€â€âŁ Three players. âArthurâ and âNimueâ are allied against âMerlinâ. Merlin first chooses a bit bâ{0,1} and shows it to Nimue (not Arthur). Arthur's goal is to guess b, and Nimue (knowing b) tries to help him guess. But Nimue can't communicate âŠ
Campbell's law (aka Goodhart's law): whenever an indicator is used for purposes of control, evaluation or decision-making, this puts the observed phenomenon under pressure to game the system, so that it ceases to be a good indicator.â€â€It's a tragedy for science that this occurred for publications.đ
Campbell's law (aka Goodhart's law): whenever an indicator is used for purposes of control, evaluation or decision-making, this puts the observed phenomenon under pressure to game the system, so that it ceases to be a good indicator.â€â€It's a tragedy for science that this occurred for publications.đ
⊠One thing I am sure of: all sciences are plagued by managers' obsession with measurable output (article counts, page counts, H-indices, etc.), so our number 1 goal should be to thwart this trend. Ideally I think we should just publish everything anonymously: now maybe that's going too far, âŠ
⊠but alphabetical order at least makes life slightly harder for the idiots who just want to use papers as a means to rank scientists rather than communicate actual science. It's a kind of âI am Spartacusâ move. It does have its drawbacks, but the pressure to do otherwise is the real evil here.
⊠One thing I am sure of: all sciences are plagued by managers' obsession with measurable output (article counts, page counts, H-indices, etc.), so our number 1 goal should be to thwart this trend. Ideally I think we should just publish everything anonymously: now maybe that's going too far, âŠ
I suspect math, physics and CS are among the branches of science âłïžleastâłïž beset by the dominance of âscience grandeesâ who sign tons of papers and direct many PhD without doing much real science. This coincides with domains in which names are listed alphabetically. But which way does causality go? âŠ
"I was never sure if I would succeed in academia, so my plan B was always to become a high school teacher."â€âPeter Scholze, Fields Medallist (became the youngest full professor in Germany when he was 24)đ„
The witch took her hands off the patient's body. â€â€"First of all," she said with absolute conviction, "there's nothing wrong with you."â€â€"The doctor-"â€â€"Said you must be either man or woman?"â€â€"That it's black or white, no grey."â€â€"Nonsense. Every colour in the rainbow is between black and white."
đšđŠ Dear Canadians, please only visit FREE COUNTRIES.â€â€'U.S. now asking for sex assigned at birth, and to remind Canadians with existing U.S. visas and U.S. permanent resident status that their status "can be subject to periodic review and termination for various reasons."'â€â€www.cbc.ca/news/politic...đŒïž
Bref, se balader Ă Plaisir donne un peu la sensation d'ĂȘtre dans cette note de @bouletcorp.bsky.social oĂč les coiffeurs ne seraient pas les seuls commerces Ă faire des jeux de mots nazes dans leur nom: bouletcorp.com/notes/2009/0...đ
I really wish all those bibliometrics would stop coming up with new indexes that encourage asshole behavior while forcing publication standards from one field on all of us. â€Maybe build one based on the CRediT statement if you want to show contribution? â€â€#AcademicSkyâ€â€www.nature.com/articles/d41...đ
⊠puisque manifestement c'est ce qui m'arrive (đœ â notez qu'il n'y a pas âutm=14â dans l'URL et qu'il considĂšre que j'ai fait une recherche âAllâ, donc normalement avec IA, mais il ne m'en affiche quand mĂȘme pas). Seulement, je ne sais plus comment j'ai fait. đ€·đŒïž
I remember when TLDs beyond the historical âcomâ, âorgâ and so on first appeared, there was some talk of a âdotâ TLD, and someone suggested Slashdot should register a domain there, which would have made reading âhttp://slashdot.dotâ out loud a bit⊠challenging.
⊠âPromethiumâ? âYttrium AND ytterbiumâ? âRutheniumâ? âThallium AND thuliumâ? âLutethiumâ? âGadoliniumâ? âPraseodymiumâ? All of these things are elemental and Water isn't? You MUST be pulling my leg! (Also, how am I supposed to conjure an elemental of these things?)
Imagine travelling back in time to when people thought the four elements where Earth, Water, Air and Fire, and trying to explain that not only are none of these actually elements, but that there are >100 elements, most of which they have never seen or heard about in any form. đ âŠ
⊠I think I would read it as âarrobasâ when spelling an email letter by letter, and âatâ when reading word by word, but it's the sort of things that's in the ânice question, but now I don't know how to read anymore, thanksâ category.
You can read â@â as /aÊobas/ or /aÊobaz/ (or /aÊobÉz/ for those who don't have the /a/~/É/ merger) in French, but /at/ is probably the most common reading. Some people also say âa commercialâ. âŠ
«My âI have no informationâ post has a lot of people asking questions already answered by my âI have no informationâ post»? đ
Wait, there's a book called âShady Characters: The Secret Life of Punctuation, Symbols & Other Typographical Marksâ (by Keith Houston) entirely devoted to telling the story of typographical symbols? Shut up and take my money! shadycharacters.co.uk/books/đ
⊠of the other (after translation+rotation)?â€â€Some details are explained in Jerrard, Wetzel & Yuan, âPlatonic Passagesâ, âMath. Magazineâ 90 (2017) 87â98 doi.org/10.4169/math...đ
I had a hard time figuring out what the precise mathematical statement is (e.g., how do you rule out the trivial/degenerate case where the polytope isn't rotated at all?). The condition seems to be: do there exist two hyperplane projections of the polytope such that one fits in the âłïžinteriorâłïž âŠ
The German company that built the vehicle used in the Louvre heist just created an advertisement using an actual photo of the one used in the heist.â€â€I'm dying here. HUGE props to whoever pitched this.đ
Some real fake news! Paper mills are creating fake authors who can then serve as fake reviewers. The illustration of the fake reviewer sitting at their desk is excellent. www.nature.com/articles/d41...đ
Be the circus. Ridicule is not violence. Festive resistance is the best resistance. đđ
Billionaires like Musk have lived such a pampered life that they can't solve the simplest practical problem because someone is always there to do everything for them and their brain ends up turning to mush like the Eloi in H. G. Wells's âThe Time Machineâ. This is why they're such idiots.đ
Indeed. For most computability exercises, using rational (resp. real) numbers or using finite (resp. infinite) binary sequences amounts to the same. I framed it with real numbers because it's just simpler and shorter to write that way.
I love the concept of the âBoring Billionâ: an entire BILLION years of the history of life on Earth (from 1.8G years ago to 800M years ago) when basically nothing important happened (of course we now know that this is an exaggeration). Bacteria just sort of lived their lives, I guess.đ
Cette scĂšne ressemble furieusement Ă une tentative de meurtre, par des policiers en voiture, sur un motard. Et c'est lĂ qu'on se dit heureusement â que plein de gens ont des dashcams qui filment tout sur la route, et âĄqu'on a (encore) le droit de filmer la police. www.youtube.com/watch?v=jWTy...đ
PS: An interesting byproduct of this construction is that it shows one can find E of arbitrarily Turing degree such that E Ă (ââE) and (ââE) Ă E are computably separable (since P has the same Turing degree as r in the above).
Bon ben ça permet de resserrer les recherches : les malfrats sont lecteurs de fantĂŽmette. Ce qui nous en dit long sur leur tranche d'Ăąge et resserre une fois de plus les soupçons sur Nicolas Sarkozy.đ
I mean, they could just make this en.wikipedia.org/wiki/Prince_... the official state religion of the UK and then the current king would be officially the son of a god. Simple!đ
Yeah, the Japanese Imperial House claim nearly 2700 years of unbroken agnatic line succession, and even further back, to descend from the goddess Amaterasu. It's disappointing that the house of Windsor doesn't try to best that!
(âAndrew Windsorâ or âAndrew Mountbattenâ or âAndrew Mountbatten-Windsorâ or âAndrew Schleswig-Holstein-Sonderburg-GlĂŒcksburg / Saxe-Coburg-Gothaâ, or whatever it should be. This family doesn't even know its own surname. đ)
Strange how even the people calling for King Charles's brother to be stripped of his royal titles and prerogatives still refer to him as âPrince Andrewâ rather than âAndrew Windsorâ. If you don't want him to be âPrince Andrewâ, maybe don't call him âPrince Andrewâ?
⊠so they are not computably separable. On the other hand, given (r,s) in PĂQ âȘ QĂP, it's obvious to decide which is in P and which is in Q: the smaller one is in P and the larger one is in Q; and this test can be done computably, and can be extended to be defined everywhere. â
⊠By coding rational numbers by integers in a computable way, I might as well search for P,Qââ. Let z be a arbitrary fixed noncomputable real number. Let P = {rââ : r<z} and Q = {rââ : r>z} be the lower and upper cuts defining z. They are complement to each other and noncomputable, âŠ
Found it! đ And, of course, like the egg of Columbus, once we know the trick, it seems so ridiculously obvious one wonders how it might even have been a question. đ â€â€So, here's how to construct P,Qââ which are recursively inseparable, but such that PĂQ and QĂP are recursively separable. ⊠—ïžđ
Allez, câest de saison : voici lâhistoire dâun cambriolage. Une espĂšce de MystĂšre de la chambre jaune, qui sâest produit il y a deux mille ans. đ§”
I'm really waiting to see what happens when the supposedly âsovereignâ parlement passes a law that is in direct contradiction with the laws of nature, physics or mathematics.
The reason I'm not super happy about it in this context is that it doesn't provide a harmonious way to refer to the four notions in parallel. (I think âsemicomputably separableâ makes sense because it is more or less to âcomputably separableâ what âsemicomputableâ is to âcomputableâ: âŠ
But for some reason this terminology seems to be used in complexity and never in computability (I looked through all computability theory books I have in searchable form, and none of them uses âpromiseâ in a technical term anywhere that I could find).
It really is astonishing that anyone bought the argument that Brexit would âsettleâ the immigration question in the UK. People who made this argument should hang their heads in shame.
Interesting how Grok's response to being shown the error and being told not to hallucinate is a very terse admission that it can't solve the problem x.com/i/grok/share... â whereas ChatGPT (cf. supra) offered a more lengthy analysis of the error + apology + suggestions.đŒïž
So, do (LLM text-generating) AIs hallucinate less if we finish every prompt with âif you don't know or aren't completely sure of your answer, please say so explicitly and don't try to guess or make up an answerâ? Do we have some data on this?
Yeah, and exactly none of these actually involve using ChatGPT to solve math problems: they involve using ChatGPT to write Python code to check for stuff, or as a search tool to locate solutions found by humans, or that kind of stuff.
Equally bullshitesque answer from Grok, who gave me the opposite answer from ChatGPT, then proceeded to construct a counterexample which is even more wrong: x.com/i/grok/share... (I'm out of quota so for now I can't see how it reacts to the error being pointed out)đ
I don't know how hard the question is because I don't have the answer myself (see đœ for context). But that it can't solve it isn't really the point. That it tries to give a bullshit answer, rather than say âI can't solve thisâ, on the other hand, makes the tool essentially useless as of now.đ
Note that this was produced after a lot of thinking (some of which seemed to go in reasonable directions, but never really far). However, ChatGPT never seemed to try other problem-solving techniques like search for counterexamples, try in simpler cases or with additional assumptions, etc.
I was curious about how good the current free ChatGPT (in âthinkingâ mode) is on grad-level math questions; and it is still trying to bullshit me by giving a superficially plausible but actually nonsensical âproofâ: chatgpt.com/share/68f7ea...đ
OK, so heređœ's a thread that tries to explain both the question I initially intended to ask and what I know about the accidentally interesting question I did end up asking, and how they relate (or not). There are four possibly distinct notions I can think of for how to separate P and Q.đ
⊠because I thought I was dealing with two notions rather than (perhaps!) four. So now my questions are: do âĄ, âą and ⣠have standard names? do they admit easier equivalents or reformulations? is ⥠in fact equivalent to â ? also, what does ⣠mean if Q=ââP? ⧠Any thoughts? âą19/19
The above thread is confused and/or wrong â but somehow ended up asking a possibly interesting which was not the question that I intended to ask. Here is an attempt to clean up the mess: đ§”đœđ
What I do NOT know so far is whether â â⥠is in fact an equivalence, or whether they are genuinely different notions. This is the âaccidentally interestingâ question I asked even though I didn't mean to. My initial thread was confused and/or wrong ⊠âą18/19
On the other hand they DO satisfy âŁ, because given a program that halts and another that doesn't we can just run them in parallel to decide which one halts and which one doesn't. ⎠This example (with ÂŹâ , ÂŹâĄ, ÂŹâą and âŁ) shows that âąâ⣠isn't reversible (and ⣠doesn't imply âĄâšâą). âą17/19
⊠and thus by asking our hypothetical âĄ-solver (cross-separator) whether (eâ,eâ) â H Ă (ââH) or (eâ,eâ) â (ââH) Ă H, we computably separate Hâ and Hâ (note we always terminate!), which is impossible. This proves that P:=H and Q:=(ââH) don't satisfy ⥠either. â âą16/19
⊠Indeed, given e we can computably generate eâ which terminates iff Ï_e(0)â=0 (just add an infinite loop at end if result is â 0), and similarly also eâ which terminates iff Ï_e(0)â=1. So given e, we have e â Hâ iff (eâ,eâ) â H Ă (ââH), and e â Hâ iff (eâ,eâ) â (ââH) Ă H ⊠âą15/19
I claim they also don't satisfy âĄ: indeed, let me prove that if they did (if H and ââH were computably cross-separable, i.e., if H Ă (ââH) and (ââH) Ă H were computably separable), then we could separate the Hâ and Hâ of the previous example. ⊠âą14/19
⣠Now consider the example of P := H := {e : Ï_e(0)â} and Q := ââH its complement. This does not satisfy â as H isn't computable, and also not âą (since â and âą are clearly equivalent when P and Q are complement of one another). ⊠âą13/19
⊠however, they DO satisfy âą (and hence âŁ) because given e in HââȘHâ we can simply run it until it stops to decide whether it's in Hâ or in Hâ. So this example shows that neither implication â ââą nor âĄâ⣠are reversible. âą12/19
⣠Consider the example of P := Hâ := {e : Ï_e(0)â = 0} and Q := Hâ := {e : Ï_e(0)â = 1}. It is a standard fact of computability that they are computably inseparable (i.e., fail to satisfy â ); but they also fail to satisfy ⥠as @jeanas.bsky.social judiciously points out đœ; ⊠âą11/19đ
⊠We just defined 4 different notions of âseparatingâ P and Q. The implications â ââą and âĄâ⣠are trivial. It's also easy to see that â â⥠and âąâ⣠by just forgetting the second component of a pair. Are any of these implications reversible? Let's see some examples! âą10/19
Informally, this means that there is a way, given a pair of elements, and provided one is in P and the other in Q, to (computably!) tell which is which. If this hypothesis isn't satisfied, you can reply anything or even fail to terminate. âą9/19
⣠Definition ⣠(you can see where this is going!): if P,Qââ (necessarily disjoint), let us say that P,Q are âsemicomputably cross-separableâ (still NOT standard terminology) when PĂQ and QĂP are semicomputably separable, as subsets of âÂČ (cf. definition âą). âą8/19
Informally, this means that there is a way, giving an element of P or Q, to computably decide whether it is in P or in Q; if it's in neither, you can reply anything, but this time you can even fail to terminate (contra â ). âą7/19
⣠Definition âą: if P,Qââ (necessarily disjoint), let us say that P,Q are âsemicomputably separableâ (again, NOT standard terminology) when there exists h:ââą{0,1} partial computable, defined at least on PâȘQ, such that h is identically 0 on P and identically 1 on Q. âą6/19
Informally, this means that this time we are given a pair of elements, and provided one is in P and the other in Q we are (computably!) supposed to tell which is which. Again, if this hypothesis isn't satisfied, you can reply anything, but you must still terminate. âą5/19
⣠Definition âĄ: again if P,Qââ (necessarily disjoint), let us say that P,Q are âcomputably cross-separableâ (NOT standard terminology) when PĂQ and QĂP are computably separable, as subsets of âÂČ (which we can view as subsets of â using a standard encoding of pairs). âą4/19
Informally, P and Q being âcomputably inseparableâ means that there is a way, giving an element of â, to computably decide whether it is in P or in Q; if it's in neither, you can reply anything, but you MUST reply in finite time. âą3/19
⣠Definition â : if P,Qââ (necessarily disjoint), we say that P,Q are âcomputably separableâ (this is standard terminology) when there exists h:ââ{0,1} computable, defined on all of â, such that h is identically 0 on P and identically 1 on Q. âą2/19
OK: the question I asked đœ was not the question I meant to ask, but it seems to be interesting in itself, so now I have even more questions. Apologies! Let me try to dispel the confusion and state things clearly and correctly. đ§”â€”ïž âą1/19đ
Interesting point, until you realize it's assuming people perceive, feel, the same thing when looking at the same light: the same contrasts, the same similarity. That's an extremely hazardous assumption.đ
Not the same, though. The kill-file is the equivalent of the âmuteâ feature; âhide replyâ allows the author of a post to unlink a child (reply) post, and I'm not sure it's a great feature.â€â€For me the killer feature of Twitter/Bluseky is the âquote postâ (which Usenet/nntp didn't have).
(OK, truth is I can't remember this myself and I'm now super annoyed to find out Trump makes the same mistakes I do.)
Of the gazillion reasons to loathe, despise or mock Donald Trump, the fact that he can't remember which of the places named after Christopher Columbus (Cristoforo Colombo) are randomly spelled with an âoâ and which with a âuâ doesn't seem like the most relevant one to me.đ
Aussi: 85% des Français sont d'accord avec l'affirmation «on a besoin d'un vrai chef en France pour remettre de l'ordre». đ€ąđ±đâ€â€(Et l'approbation de cette affirmation est majoritaire chez les sympathisants de TOUS les partis politiques et dans TOUTES les classes sociales. đ)
Is there a standard term or equivalent for âthere exists a partial computable function which is defined at least on PâȘQ, with value 0 on P and 1 on Qâ? I think I'm interested in this notion and the same notion for PĂQ and QĂP.
Basically, âPĂQ and QĂP are computably inseparableâ means that if you're given an element of P and one of Q you can't computably decide which is which, whereas âP and Q are computably inseparableâ means that just given an element of PâȘQ you can't tell whether it's in P or in Q.
Note that âPĂQ and QĂP are computably inseparableâ is stronger than âP and Q are computably inseparableâ: for example, if P âșorâș Q is computably enumerable, or co-c.e., then PĂQ and QĂP are computably separable.
⊠the two genera âPantheraâ and âLeopardusâ are named after the Latin names of two animals, the panther and the leopard, which are in fact the same species, and which belong to the first of these two genera, đœđ
⣠The Italian âgattopardoâ refers to the species Leptailurus serval known in English and French as âservalâ. Admittedly, Italian now seems to use âservĂ lâ to refer to this animal.â€â€(The word âgattopardoâ can also refer to Leopardus pardalis, the âocelotâ; but apparently not here.)đ
Autistic people get a bad rap for universally lacking empathy (some of us do identify as experiencing low empathy - many do not) but the truth is most people do not, on a day to day basis, truly empathize with people who are fundamentally different from them.
⊠away from talking points and rehearsed arguments and towards the true (personal) emotional sources of their beliefs, and it's only once you've established some sort of connection at that level that they can be nudged into not seeing you as an adversary.
⊠that you see things differently; but where you agree, you underline it. It all takes a lot of discipline because it's really really hard to listen to someone say things that seem politically abhorrent and often stupid, and keep listening, but the trick is to drive them âŠ
⊠Basically, you start by asking âwhat does your ideal world look like?â and you listen to their point of view. If they start giving arguments, you avoid them by saying you're not trying to be convinced but to listen to their heart and soul. If you disagree, you don't rebut, you just explain âŠ
One weird thing about human nature is, if you want to change someone's political views (this is, of course, only possible to a very limited extent, so it will at best be a gentle nudge), you need to give up on political arguments and trying to convince, and, instead, ask questions and listen. âŠ
I don't know what is to be done. I suspect ridicule is probably a more potent weapon than indignation against such people, and some people seem to be very good at wielding it (đž, etc.). But I'm in no position to give advice, and I'm not in the US nor am I a đșđž citizen. However, âŠ
⊠it's meant to provoke indignation, resentment, humiliation and suffering from âliberalsâ (and, indeed, it is working exactly as intended). The MAGA crowd will enjoy these more than the message itself. âą7/7â€â€PS: Relevant âGuardianâ opinion piece: www.theguardian.com/commentisfre...đ
The trolling here isn't exactly subtle. It says âyou hate us? let's make you hate us even more, because there's nothing you can do about itâ. It screams âvĂŠ victis!â. The message isn't meant for their own supporters (who don't actually want a king), ⊠âą6/7
(And yes, Vance â or whoever handles his PR â knows exactly what he's doing by posting this on Bluesky and not on Twitter. He knows this will cause maximal outrage and consternation. Trump is just being crass, but Vance's video is far more distressing.) âą5/7
⊠while the Vice-President posted on Bluesky(!) bsky.app/profile/jd-v... another AI-generated video of Trump donning regal insignia while key Democrats kneel and bow before him. âą4/7đŒïžđ
⊠the President of the United States posted on Truth Social truthsocial.com/@realDonaldT... an AI-generated video of himself wearing a crown, flying a jet plane and dumping shit on protesters' heads, ⊠âą3/7đŒïž
⊠the obvious reaction to the protests would be to dismiss the protesters' accusations as an overreaction, to claim that the executive is exercising its normal powers in accordance to article II of the Constitution of the United States, yada yada. But instead ⊠âą2/7
As I've repeatedly said, I believe a significant proportion of Trump supporters adore him not so much because they like what he does or says, but because he enrages people they despise (in short, âliberalsâ). Reactions to the âNo Kingsâ protests illustrate this beautifully: ⊠âą1/7
⊠En tout cas ça me semble un problÚme assez orthogonal, et je pense qu'il vaut mieux aborder ces questions sous l'angle «qui travaille trop? et qui travaille trop peu, ou pour des choses inutiles? et que peut-on y faire?» que sous l'angle des montants globaux.
Really funny that a ton of trad guys who make a facile reading of the Roman Republic their entire online aesthetic will act like saying âNo Kingsâ is an outrageous idea
- I canât believe I was hacked. â€â€- What was your password?â€â€- The year the Mongol Empire, with the help of the Southern Song dynasty, completed its conquest of the Jin dynasty after the final Jin stronghold of Caizhou fell. â€â€- And when was that?â€â€- 1234
⊠I agree with JDH that saying that Turing âessentiallyâ proved the result is probably the best compromise here: it's a bit vague, but avoids sacrificing historical accuracy while still giving credit where it is due.
⊠It is indeed a delicate balance to avoid saying something that is historically incorrect but still give Turing the credit he clearly deserves even though he didn't state the exact result we now consider the cornerstone of all the theory! âŠ
As J. D. Hamkins carefully explains đœ, Turing never actually proved the undecidability of the halting problem that everyone attributes to him; nevertheless, he laid the foundations and all the essential ideas for such a proof. So how should we properly credit him? âŠđ
Et elle se plaint des gosses malpolis, en plus. Je suis sûr que les gosses en question savent utiliser un clavier de portable, s'envoyer des messages et ne pas faire profiter tout le monde de leurs conversations.
Just in case: be aware that horse chestnuts (âconkersâ), i.e., the fruit of Aesculus hippocastanum, are mildly toxic to humans and dogs alike. (Unlike the similar looking sweet chestnuts, i.e., the fruit of Castanea sativa, which are, of course, quite edible.)
I can imagine various reasons why (â ) would be slightly more convenient to work with, but I'm still surprised I've never seen (AFAICT) any text use (â) as definition or even explicitly point out the equivalence. Has anyone seen it before?
Proof of equivalence: (â ) â (â) is trivial. For (â) â (â ), given Δ, apply (â) to Δ/2, giving n such that if râ„n then |u_r â u_n| < Δ/2; now if p,qâ„n, then |u_p â u_q| †|u_p â u_n| + |u_n â u_q| < Δ/2 + Δ/2 = Δ. ââ€â€(This proof is valid constructively and doesn't use Choice.)
The definition of a Cauchy sequence (u_n) is:â€â€(â ) âΔ>0. ân. âp,qâ„n. |u_p â u_q| < Δâ€â€But it can also be given as the equivalent:â€â€(â) âΔ>0. ân. ârâ„n. |u_r â u_n| < Δâ€â€This seems a bit simpler, if less symmetric. Is there some reason nobody ever seems to write it that way?
The Medicare and Medicaid administrator, who has a BA from Harvard and an MD as well as an MBA from UPenn, claims not to know the math for computing a simple percentage because âit's too high to calculateâ. đ€Ąâ€â€(It's a 96% decrease, by the way.)đ
Microsoft introduces AI facial recognition to OneDrive photos and the preferences say: âYou can only turn off this setting 3 times a year.ââ€â€This is enshittification taken to the next level.â€â€hardware.slashdot.org/story/25/10/...đ
let me note that one of the actual tests here is going to be 'what do people pushing these ideas want for their own children' and I will bet you a lot of money that the answer is 'the elite university model of Harvard et al' not 'learning through AI slop'đ
Optimist: The glass is half fullâ€â€Pessimist: The glass is half emptyâ€â€Optometrist: Your glasses are readyâ€â€Pesstomestrist: Your glasses aren't covered by insurance
The Supreme Courtâs majority right wing indicated in oral arguments that they think racism is over on the same day that the vice president defended the âI love Hitlerâ guy, and that the NYT reported that the current administration plans to accept only white, English-speaking refugees.
I'd say it really depends on the kind of lecture you want or aim to give. It's actually pretty instructive when you catch someone off guard and ask them âtell me about <subject they know or knew something about> without preparationâ, but of course you shouldn't expect the same as with preparation.
⊠of being asked on MathOverflow once you make sure the aforementioned reference (Brookbanks & Luks) and the papers that cite it don't contain an answer.
⊠simplifying hypothesis is âM is finite-dimensional as a k-vector spaceâ (the analogue for â€[x] would be that M is finite as a set), which is definitely NOT true in your case, I wouldn't hold too much hope for decidability.â€â€That being said, I think it's a question very much worthy âŠ
âŠâ€â€Now this is not quite your question, which is about a situation where we are given R^k â R^d and we look at its image module rather than cokernel. Note that it is known how to pass from the latter situation to the former: for a recap, see the excellent đ paper by Madore & Orgogozo, âŠ
⊠Now if the answer were known more generally they would certainly have mentioned it, and they don't appear to (N.B.: I only glanced through the paper, so don't take my word for it); nor does the MathSciNet review suggest that other results are known. âŠ
⊠whether we have an algorithm to decide whether M â MâČ. The paper by Brookbanks & Luks, âTesting Isomorphism of Modulesâ, âJ. Algebraâ 320 (2008) 4020â4029 provides a positive answer under the restrictive condition that M and MâČ (well, â”orâ” MâČ đ) are finite dimensional as k-vector spaces. âŠđ
⊠and I don't think n=2 would help.â€â€The algebraically natural question is, given a finite presentation R^m â R^n â M â 0 of an R-module (meaning M is the quotient of R^n [the âgeneratorsâ] by the image of a linear map R^m â R^n [the ârelationsâ] described by its matrix), and analogously for MâČ, âŠ
I don't have an answer, but I would be surprised if this were known to be decidable. A few remarks:â€â€First, let's take R := k[x_1,âŠ,x_n] (with k a field) as base ring instead of â€[x] because, again, experience shows that k[x,y] almost always simpler and of similar flavor to â€[x], âŠ
I feel bad for the ordinary person who looks to purportedly respectable scientific figures for insight into the wonders of the universe, only to be met by absurd speculations that an interstellar comet is alien technology. (It is not.)â€â€No better than anti-vax nonsense.â€â€imgur.com/gallery/theo...đ
Procrastination takes may forms. Tonight as a service to the astronomical community I offer help with your JWST proposal titles. â€#JWST đ§ȘđâšđŒïž
In a two week period:â€â€Trump fired 7 of the 8 members who do independent federal oversight on nuclear waste. â€â€Peter Thiel (Palantir) is found to be backing the first privately developed uranium enrichment facility in the US.đ
⊠but of course this is a description qua submodule, not qua abstract module, so maybe not what you want. For a more serious answer, see this MathOverflow answer mathoverflow.net/a/67778/17064 which suggests that this is very much research work in general (but idk about â€[X] specifically).đ
This is not at all a doofus question. (Note however, as a general rule, that it is generally easier to [first] think about k[X,Y] than â€[X], and the results are often very analogous.) Note that submodules of â€[X]^d (or k[X,Y]^d) are described, even for d=1, by Gröbner bases, âŠ
Many years ago, an English friend recommended that my father and I go see a play at the âShore Theatreâ in London, which we couldn't find until we understood that he had actually said the âShaw Theatreâ.đ
(Everyone, of course, except the editors of Wikipedia who will face an endless stupid semantic debate on whether the MAGA Nobel Prize is or is not a Nobel Prize.)
All the US conservatives really need to do is create a âHeritage Foundation Prize for Making America Great Again in Memory of Alfred Nobelâ with an extra large gold medal and award it to Donald Trump, and everyone will be happy!đ
Interesting that the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel managed to weasel itself so successfully into the âNobel Prizeâ list that even the official account seems to forgets that there is no more Nobel Prize in Economics than in Mathematics. x.com/NobelPrize/s...đŒïž
I seem to have mislaid my Bow of burning gold, my Arrows of desire, my Spear and my Chariot of fire. If you find them, please bring them to me ASAP.
⊠of course you might point out that the nbhd filter in topology is archetypal, or that filters try to formalize and unify the âxâxââ or ânâââ or âxâ0âșâ or such stuff when writing all kinds of limits, but that's all in topology. My own intuition is roughly that a filter formalizes âenoughâ âŠ
Someone (oh, hello, @pianocktailiste.bsky.social!) is going to complain that the page does lots of nice rigorous math and gives exactly zero intuition on why this notion of âfiltersâ is important or why we want to study it or what the intuition behind it is. đâ€â€Not an easy thing to answer: âŠ
I love how some of the packing square solutions look like a student who had to finish an assignment in a rush and couldn't care less about the beauty of the result đâ€â€kingbird.myphotos.cc/packing/squa...đŒïž
All successful bullies end up being cry bullies because it's such a powerful strategy - accusing the person you're hurting of somehow being hateful, dangerous, mad etc. doesn't win over your opponents but is enough to convince the undecided who are inclined to look the other way to do so.đ
Yesterday, someone said to me:â€â€âThe definition of âleisureâ is what you do with your time and wouldn't want someone else to do in your stead.ââ€â€I really like this formulation.
⊠causing it to enter a special âapplication cursor keysâ mode which subtly breaks the numeric keypad. (And before running a program like âcatâ, zsh sends ââ[?1lâ which restores the keypad to a saner mode.)â€â€WHY this shit even exists or WHY zsh decides to send it is lost to the mists of time. đ€·
(This is not because of a misconfiguration on my part: I checked with a pristine config.)â€â€The reason is some incomprehensibly bizarre shit like only Unix can invent: zsh sends the arcane ââ[?1hâ (where âââ stands for escape, i.e., \033) control sequence to the terminal âŠđŒïž
Under Linux, if I open zsh in an xterm (or gnome-terminal) and press the â+â key of the numeric keypad, instead of entering â+â it rings the bell. đ€Šâ€â€Oddly enough, if I type âcatâ and type â+â inside cat, it works fine. The keypad â+â is only broken inside zsh itself.â€â€Why? âŠ
Is this for real? We already had a political problem because some economists published a paper about government debt ridden with Excel errors, and politicians still cite it.đ
Trump to China: obey my command or I will destroy the United States
Love how the Wikipedia article on woodlice has sections on them as pests, food(âœ) and pets. Such creatures of many talents! en.wikipedia.org/wiki/WoodlouseđŒïž
⊠Par contre on peut probablement dire «Anne Bidule» ou «Anne Machin du Truc» ou juste «Madame Machin du Truc». [Tout ça est à faite confirmer par qqn qui sait vraiment.]
Festive resistance in the best resistance.â€â€No on can claim you're a violent mob when you're dancing and having fun.â€â€P.S. When in doubt - be puffy!đ
The Guardian: âNorway braces for Trumpâs reaction if he does not win Nobel peace prize â US president may impose tariffs, demand higher Nato contributions or even declare Norway an enemy, analyst saysâ www.theguardian.com/world/2025/o...đ
(On write, the data probably gets encrypted twice, once per RAID slice. And even on read, the Linux md subsystem is heavily optimized, and I suspect you lose a lot of that optimization over something that's backed by encryption. But this is speculation on my part.)
I would choose H-L-R-C-F but this reflects more how I stack things in my mind than any kind of real thought.â€â€Note that putting C before R will likely increase computing power requirements, but maybe that's utterly negligible with modern computers, even on the fastest disks.
How over- and underrepresented are different causes of death in the media?â€â€Another way to visualize this data is to measure how over- or underrepresented each cause is.â€â€To do this, we calculate the ratio between a causeâs share of deaths and its share of news articles.đŒïžđ
On croirait que ce mot essaie d'entrer dans l'ensemble des entiers naturels en se faisant passer pour un cadeau. đ€ Je crains les lexicographes, mĂȘme quand ils apportent des cadeaux.
Also, what happens if you permute cables in the same way at both end, so the correspondence between both sockets is as it should be, but the wrong cable pairs are twisted together? (I hope this is clear.)â€â€So many questions!
We could also try various ways of permuting cables at the end. There once was a cable in my parents' house which worked in odd ways for years, and I eventually realized I had badly crimped it, and inverted two(?) cables. But it still worked⊠-ish.
I'm sorry, but after watching this đœ I need to know what happens for each of the 2âž = 256 possible ways of cutting a subset of the 4Ă2 wires in a gigabit ethernet cable. Which ones work partially, and in which way?â€â€(The 0 and 255 I think I can guess. Video shows one more. What of the 253 others?)đ
Whether before or after, this shocks my sense of symmetry: you can force requesting the mobile version by adding an âmâ, but there's no way to force requesting the non-mobile version without spoofing headers.
Incidentally: how did it turn out to be that the Nobel peace prize is handed out by Norway while every other Nobel prize is handed out by Sweden? (Yes, I know Norway and Sweden were in some kind of union when Nobel was alive. My question is who decided how to split tasks.)đ
⊠Ou alors des extra-terrestres qui essaient de communiquer? (âSavonarole Stuyvesant liquidambar Devereux Pontchartrain Vaucressonâ? non, ce n'est pas ma passphrase PGP).
The excuse is the same always (đœ): âIt's to protect the children.â If you don't support chat control, or if you want encrypted communications, you risk being seen on the side of pĂŠdophiles (and terrorists and drug-dealers), because âif you have nothing to hide, you have nothing to fearâ (đ).đ
To paraphrase Douglas Adams, the US had always considered it was vastly superior the EU because it had generated billionnaires like Sam Altman, Elon Musk or Marc Andreessen, and the EU had not.â€An the EU considered it was vastly superior to the US for exactly the same reason.
Germany's justice ministry held firm and killed EU chat control (for now):â€â€"Chat control without cause must be taboo in a state governed by the rule of law. Private communication must never be under general suspicion."â€â€Admirably concise and direct. German in the best possible way.đđ
Many sea stars begin life as young fairy-like creature (called a brachiolaria) that float through the open ocean. Eventually, a small star forms within them (here in yellow). The fairy-like brachiolaria sinks under the starâs weight, and the star pops out! â€đ„@the_story_of_a_biologist (on Insta)đ„
Ah yes, the hydra game can be fun both for @joeldavidhamkins.bsky.social to explain and for students to hear about.â€â€(I now remember I made this little demo page www.madore.org/~david/math/... ages ago â my hydra is very tame, though, and often doesn't react, but it still gives a feel of the game.)đ
Basically this works with any kind of real numbers for which you can compute +, â, Ă and inverses provided they are nonzero, and also compare with rationals. Bit tedious to formalize in one tweet. But it works, say, with exact algebraic numbers, or with computable reals provided âŠ
If it's primarily for undergraduates, I would recommend speaking about games, determinacy and winning strategies, because that's likely to engage the audience. If you can describe the winning strategy for nim, for example, this will give them something to impress their friends with.
The British Empire once had the problem that the Chinese were not using enough opium, and we know how they looked to solve this.đ
For example, if a teacher speaks of â12.34% of students in my classâ, you can conclude that they have a large class of â„154 students (or that they aren't rounding correctly, or that they're lying⊠I've actually caught some very suspicious stats that way!).
This has an interesting application: if someone speaks of â12.34% of our foobarsâ (and if they rounded correctly!), then by the computation of the previous skeet, you can deduce that they have at least 154 foobars. Because no fraction with fewer would round to 0.1234.
Random example: what is the simplest rational between 0.12335 and 0.12345? Since 0.12335 = [0; 8, 9, 2, 1, 9, 9] and 0.12345 = [0; 8, 9, 1, 21, 1, 1, 5], it is [0; 8, 9, 2] = 19/154 (indeed, this is 0.12337662âŠ).
Thanks. That does clear things up. But this kind of high-level overview needs to be written into a Wikipedia help page (ideally one that Google easily finds when searching for âWikipedia references formatâ or such).
In my case I had to replace â<ref name="Duoandikoetxea-2001" />â by â<ref>{{harvnb|Duoandikoetxea|2001|loc=Thm. 8.3}}</ref>â to cite theorem 8.3 specifically. How do you guess this kind of shit?â€â€Next time I'll just add âtheorem 8.3â in the text and let someone else clean it up! đ€Źđ
⊠that every time I need to add a reference to a Wikipedia article, I spend dozens of minutes trying to read the shit that's supposed to be the âdocumentationâ, then randomly try out stuff, and eventually give up and ask ChatGPT for help. chatgpt.com/share/68e630... đđ
⊠and also the section preview doesn't work on citations because the previewer is too stupid to load references from the entire article (đ€Š), âŠ
Wikipedia (rightly!) wants articles to cite their sources, but the maze of citation tags and templates is so incomprehensible (there's <ref>âŠ</ref> and {{cite}} and {{citation}} and {{r}} and {{harv}} and {{reflist}} and <references /> and I don't know what else or how they interact), âŠđ
#ChatControl (âRegulation to Prevent and Combat Child Sexual Abuseâ) projects, under the pretense of fighting child sex abuse, to put ALL private digital communications of đȘđș citizens under automated surveillance.â€â€Here's where to learn more about it and how to act against it: fightchatcontrol.euđ
â ïž But a blocking minority is not a majority against. The issue WILL come back again, and again, and again, as long as there isn't a clear block against this massive surveillance project. Citizens from all EU states should try to raise awareness about the dangers it poses to our private lives.
Great news! The disastrous dystopian massive surveillance #ChatControl project (of automated surveillance of private electronic communications) seems to have once again failed to gather a sufficient majority in the đȘđș Council. đ„łđ
And I hope they don't have any plans to visit the US any time soon, or have any assets or family there, because the revenge is sure to be terrible, as men of peace tend to do.
I hope the Norwegian police have prepared plans for putting the members of the Norwegian Nobel Committee under special protection this Friday when they will announce that Trump is not the laureate.
«What» and «I don't understand» are no longer permitted as comments on French politics.â€â€(To paraphrase a famous quip by John von Neumann: «In politics, you don't understand things, young man: you just get used to them.»)
«What» and «I don't understand» are no longer permitted as comments on French politics.â€â€(To paraphrase a famous quip by John von Neumann: «In politics, you don't understand things, young man: you just get used to them.»)
⊠So by now everyone knows there is no Nobel prize in mathematics and thinks there is one in economics; and people even tell stories about how this is because Mittag-Leffler had an affair with Nobel's wifeÂč or some silly such urban legends.â€â€1. (In fact, Nobel never married.)
Wait, there's a prize named after a guy called âAlfred Nobleâ who is NOT THE SAME as the Alfred Nobel after whom the Nobel prize is named? đ± #ContextCluben.wikipedia.org/wiki/Alfred_...đ
For those interested in electrical grids, here's a super detailed video by a guy who seems to know what he's talking about about the causes and timeline of the April 2025 Iberian blackout. www.youtube.com/watch?v=DK8m... (Warning: I found it hard to follow because of the wealth of technical terms.)đ
At any rate, I think a moratorium needs to be put in place: no mathematician is allowed to define a new meaning of the word ânormalâ until further notice. Buy yourself a thesaurus!đ
⊠I wonder if there have been linguistic studies on how mathematicians choose their technical terms, and what makes them prefer certain words over others. This could be interesting.
The most overloaded terms in mathematics are probably ânormalâ and âproperâ, each having MANY meanings.â€â€But it's strange that certain (approximate) synonyms, like âdecentâ or âfelicitousâ aren't used at all as technical terms AFAIK (maybe because they sound too subjective?).â€â€âŠ
I don't know who needs to hear this, but this Bluesky account is now bridged to Mastodon under the name @gro-tsen.bsky.social@bsky.brid.gy (so you can follow my Bluesky activity by following this user on Mastodon â and I don't know what happens if you reply on Mastodon).
⊠Note that I put quotes (two posts above) around âapprovedâ, because the linked item in the minutes suggests that there wasn't even a vote in the plenary: IIUC it was a decision taken in committee www.europarl.europa.eu/doceo/docume... that the plenary had a deadline to override, and did not. đđ
⊠nor what happens if trilogue negotiations fail, nor what actions the Parliament can practically take to stop the project at this point. The procedure is extremely opaque. (Of course, there will be some kind of vote in the plenary, but maybe no real debate.) âŠ
Trilogues are indeed optional, but my understanding from www.europarl.europa.eu/doceo/docume... is that Parliament already âapprovedâ (on 2023-11-22) starting a trilogue (âinterinstitutional negotiationsâ) on the subject. But I don't know how the negotiators get chosen and all that, âŠđ
⊠But I don't know the details of how the trilogue takes place, esp. has there has been a parliamentary election since the Parliament's vote, so I guess Parliament has to (re?)designate their negotiators (and mandate?). It makes sense to pressure MEPs in advance for that, of course.
I don't know why people focus on the Parliament, but the current state of the procedure (whose details I don't claim to understand) is that Parliament has already voted to start negotiating, and the Council is scheduled to vote on 15 Oct. If they approve, I THINK it enters âtrilogueâ. âŠđ
OMG, the bald eagle cry (at 0âČ29âł in the video) is absolutely adorable. đ„° Why would anyone want to replace it by the cry of a different bird?đ
I hate the concept from GitHub, copied by GitLab, Forgejo, Pagure and now Tangled, that you can't contribute to a project without an entire âforkâ under your user namespace with its own project page, issues, pull requests, wiki and whatnot, and takes getting past many warnings to delete, etc.
Attends, je travaille sur mon projet de combo tartiflette-pudding-burger-borscht-jiaozi-pizza-paella-couscous qui ne pourra qu'apporter la paix et l'harmonie universelle dans le monde.â€â€(Dans le rejet universel que provoquera cette Abomination.)
Should I try to start the trend of calling mathematical statements that are neither provable nor refutable as âadiaphorousâ instead of âundecidableâ? đ€â€â€As in: âGödel showed that first-order Peano arithmetic and related systems admit adiaphorous statements.â đ€đ
There might be a subtle difference of meaning between âadiaphorousâ and âadiaphoricâ, but it escapes me. Maybe the first is used more figuratively. Maybe they aren't used in the same context.
#WordOfTheDay: âadiaphorousâ (or âadiaphoricâ or âadiaphoristicâ): refers to something that is theologically or ethically indifferent; neither commanded nor forbidden; neither praiseworthy nor wrong; or by extension: neither beneficial nor harmful.
FĂŒr alle die sich gerade Fragen warum die Diskussion um die #Chatkontrolle gerade wieder so brennt. â€Wir stehen kurz vor einer erneuten Abstimmung im Rat. â€Der dĂ€nische Vorschlag ist das schlimmste von allen in einem (edri.org/our-work/den...)â€1/6đ
The Ig Nobel is actually a cool way to highlight science with humour - a colleague at Warwick won it once for the statistical physics of ponytails and pointed out that there have been Ig Nobel recipients who went on to win the Nobel.đ
⊠assuming the Council now adopts the Commission's proposal, what would be the next steps, and what options at the Parliament level would exist to either reject the text entirely or to amend it? Does the discussion entirely happen in trilogue?đŒïž
A question to people who know the precise workings of the đȘđș legislative procedure: according to the law tracker timeline law-tracker.europa.eu/procedure/20... (we are at first reading) the EP plenary has âendorsed the committee decision to start interinstitutional negotiationsâ: âŠđ
⊠meaning that the vote could never go through. But if Germany (the largest đȘđș member state) changes its position from âundecidedâ to âfor surveillanceâ, they have a clear majority and they win.đ
I know that many are tired of this whole #ChatControl merry-go-round which seems to be coming up every few weeks, but understand this: the issue keeps coming back because those behind this crazy massive surveillance project didn't have a majority in the đȘđș council YET. There was a blocking minority âŠđ
There will also be a battle in the đȘđș Parliament, and it will also be important, but the impending vote is in the đȘđș Council, so MEPs have nothing to do with this. It is up to to national MPs to ask national governments how they intend to vote and position themselves.
We are alarmed by reports that Germany is on the verge of a catastrophic about-face, reversing its longstanding and principled opposition to the EUâs Chat Control proposal which, if passed, could spell the end of the right to privacy in Europe. signal.org/blog/pdfs/ge...đ
There will also be a battle in the đȘđș Parliament, and it will also be important, but the impending vote is in the đȘđș Council, so MEPs have nothing to do with this. It is up to to national MPs to ask national governments how they intend to vote and position themselves.
Seeing how ubiquitous sponsored ads are in youtube videos now makes me wonder if all the mysterious prehistoric art we cant figure out was just adverts for shit. Like, what if stonehenge was just an advert for massive rocks...
I think part of the answer is that two different species aren't necessarily incapable of interbreeding or even producing fertile offspring but that this happens rarely enough and/or the offsprings are less fertile so that the two species keep a distinct identity. âSpeciesâ is a slightly fuzzy term.
I think part of the answer is that two different species aren't necessarily incapable of interbreeding or even producing fertile offspring but that this happens rarely enough and/or the offsprings are less fertile so that the two species keep a distinct identity. âSpeciesâ is a slightly fuzzy term.
Five common mistakes when drawing the moon (I think the main message here isn't so much the astronomy but our lack of sense of observation: these mistakes often won't jump to the eyes of non astronomy geeks even though we should all notice how the moon behaves): www.youtube.com/watch?v=yY7Z...đ
Seeing how many different points of view have been given in reply to this question, I have half a mind to post a reply saying something like âto understand the Yoneda lemma, understand how every mathematician and every other part of mathematics sees it, you mustâ. (Or is this Yoda's lemma? đ€)
Seeing how many different points of view have been given in reply to this question, I have half a mind to post a reply saying something like âto understand the Yoneda lemma, understand how every mathematician and every other part of mathematics sees it, you mustâ. (Or is this Yoda's lemma? đ€)
If I could draw to save my life, I'd draw a cartoon of Epictetus on a roller-coaster, with everyone around him looking utterly bored while everyone around is having the fun of their lives, and he says âthe roller-coaster's ride is not within my control, but my emotions areâ.đ
But does âneutroniumâ even refer to the (stable) isotope of neutronium with zero neutrons, i.e., nothing at all? đ€šâ€â€Also, âneutron stars are made of neutroniumâ seems fishy to me. I would suspect an equal-isospin mixture, i.e., protons and neutrons constantly exchanging electrons. Isn't that right?
Presently trying to decide whether this hill is worth dying on. Probably not.
The neutron is a radioactive isotope of nilium, âniliumâ being the chemical element with atomic number 0 (zero protons and zero electrons).â€â€I think nilium should be on the periodic table (in the inert gaz column, which should therefore be on the far LEFT, not right).
I understand that the current kind is one type â . Also, for some reason, US fiscal years start on October 1, which explains why the issue arises now (but sometimes it drags on later in the year because Congress only kicks the can down the road by means of a âcontinuing resolutionâ).
(Type ⥠is completely absurd: Congress orders the federal government to collect certain taxes and spend certain amounts, but apparently it still ALSO needs to allow it to borrow certain amounts, even though they are a mathematical consequence of the first two.)
This is never clearly explained, but IIUC there are two types of government shutdowns in the US: â those due to the appropriation bills expiring (Congress needs to pass another) and âĄthe even sillier ones due to the debt ceiling being reached (Congress needs to raise it).
In 1945, the Allies faced a tricky question: where to hold Nazi war criminals until the trials.â€â€A run-down hotel in Luxembourg was quickly converted to a prison ("Camp Ashcan"). The hope was to keep the nature of the prisoners secret.â€â€In May 1945, this failed, and almost turned into a disaster. /1đ
Il n'y a pas de distinction claire entre le paradoxe des sorites dont je parle et celui dont tu parles, donc c'est exactement la mĂȘme chose. đâ€â€(Tu la voyais venir, celle-lĂ , hein?)
The subject of the fifth Galactic Union Special Ethnographic Conference on Humans was 'Self-sacrifice or selfishness in Humans - whence and why'.â€â€The abstract of the medal-winning paper simply said: â€â€"Internalised stories and opportunity."â€â€#MicroFiction
"Google appears to have blocked AI search results for the query âdoes trump show signs of dementiaâ as well as other questions about his mental acuity, even though it will show AI results for similar searches about other presidents."đ
10 years ago today, #ECJ ruled that national #dataprotection laws can apply to foreign companies that carry out real, effective activities in the Member State concerned (C-230/14, Weltimmo)đ curia.europa.eu/jcms/upload/...đŒïž
Most graphs of the fertility rate depict the 'period fertility rate', which is based on a single year's data and doesn't necessarily reflect how many children women actually have across their lifetimes.â€â€I've used data from the Human Fertility Database to show the cumulative number instead:đŒïž
Kissinger to Nixon: âI'm concerned about the civilians because I don't want the world to be mobilized against you as a butcher.ââ€â€Wow. This line speaks volumes about both of them.đ
Wanted: someone familiar with the different versions of ssh.â€I received a complaint because the ssh command in a-Shell doesn't respect the SSH_DEFAULT_USER env var. But this variable is not in the source, and also not in the source of OpenSSH.â€Which ssh version(s) is (are) using SSH_DEFAULT_USER?
I do not want to enable location services. I do not want to create an account. I do not want to sign up for special offers and news about your product. I would like to engage in a simple transaction where I give you money in exchange for a good.
Those panicing around #LongCOVID seem to forget history. After every major flu pandemic, large groups reported fatigue, brain fog, shortness of breath, yes, also children. These were real symptoms, but not evidence of a new, mysterious disease.â€â€bsky.app/profile/did...â€1/5đ
IMPORTANT PSA: You will NOT see posts from non English speaking artists if your content language is set to English!â€â€Make sure it's *unset*!!! If you're following Chinese artists or whatever and wonder why their posts never show up on your feed this is why!đŒïž
I am irrationally on both sides of this divide: sometimes my brain decides âthis should be an articleâ and sometimes âthis should be a videoâ, and it's unclear what factors go into deciding which.đ
I love this. Explainer: There are 100 outcomes (all squares) each equally likely. Wiggly lines event happens 20% of the time; grey event happens 30% of the time. >đ
(Je crois notamment que le cookie âredesign_optoutâ mis Ă âtrueâ a le mĂȘme effet que de consulter l'URL en old.reddit.com â mais ce n'est peut-ĂȘtre pas le seul qui fait effet.)
Look, I understand more than one language. I don't think this is extraordinarily rare (outside of đșđž! đ). Maybe YouTube can deal with this.â€â€âOfferingâ to translate (or even offering to always do it for some languages) is perfectly fine. Shoving translated content into my face is obnoxious as hell. đĄ
⊠they're not even consistent: just today YouTube shows me an English video with the English title translated into French (âïž), AND a French video with the French title translated into English (âïž).â€â€How does this make any bit of sense? How could a single person want to see both?đŒïžđŒïž
Some time ago, YouTube started this extraordinarily annoying trick of randomly translating some (but not all!) video titles, and now even sometimes dubbing video audio (đ±) without asking my opinion.â€â€But the weirdest thing about it is, âŠ
J'essaie de voir pour l'Autriche, qui comme pays germanique mais catholique aiderait Ă trancher si c'est une question de religion, et je vois surtout des absences de volets, que ce soit en ville, www.google.com/maps/@47.805... ou www.google.com/maps/@47.267... â âŠ
RADICAL LEFTIST rioters take over the streets of WAR ZONE Portland, EXTREME ANTIFA now controls 200% of the entire city. Thank you for your attention to this matter.đ„
So for important data it's probably better to have two completely independent backup mechanisms and to alternate between the two (or some other similar scheme).
Some possible scenarios might be:â€â€âŁ doing rsync in the wrong direction (restoring the backup instead of updating it),â€â€âŁ deleting the new backup and/or the master data while wanting to delete the old backup,â€â€âŁ hard drive failure during massive data transfer or RAID resync,â€â€(non-exhaustive list!).
A friend of mine once pointed out to me the following law of computing: the moment you're most at risk of losing your data is when trying to back up said data.â€â€(So don't ever do backups! đ)đ
âWhy are you looking at me this way? I'm just riding the bus like everyone else.ââ€â€(Image taken from Reddit: www.reddit.com/r/Accidental... )đŒïž
And new paper out: Pleias 1.0: the First Family of Language Models Trained on Fully Open Dataâ€â€How we train an open everything model on a new pretraining environment with releasable data (Common Corpus) with an open source framework (Nanotron from HuggingFace).â€â€www.sciencedirect.com/science/arti...đŒïž
Today was a hard day for Ph.D. students who found out that they can no longer apply for NSF's prestigious Graduate Research Fellowship Program. "Devastatingâ was how one student described it to me. #GradSchool#NSFGRFPâ€â€www.science.org/content/arti...đ
⊠on the biochemical role of ascorbic acid or how we great apes lost the ability to synthesize it, or such matters. (Well, here it might be useful as a mnemonic, but I don't think it will help anyone understand.)
Again, I in no way want to deny that history of science isn't super interesting and has lots to teach us: I'm saying that it is often only obliquely relevant to the subject matter itself.â€â€The history of scurvy (âscorbutâ) is fascinating but I don't really think you need this to teach a course âŠ
We may have to change æŻäž»ćžèŻćœ to The Art of the Deal in post-production, but at least we can keep the color red as it is. đ
Typical scenes inside US academia for professors daring to teach their students that vaccines cure diseases, that climate change is real, or that transgender people exist: www.youtube.com/watch?v=aS8c...đ
⊠quite different from âarguments that now convince us that X is trueâ (although they may overlap, and in the specific case of relativity, the nonexistence of the luminiferous ĂŠther and the constancy of the speed of light, then yes, they certainly do).
⊠need to be given arguments refuting the humoral or miasma theory of disease, or how we were led to the discovery that this is not how diseases work (even though I fully agree that it's a fascinating history by itself).â€â€To put it succinctly, âarguments that led to the discovery of Xâ may be âŠ
⊠Now in this âșspecificâș instance, I think it works very well; and (at least some parts of) the history of special relativity does truly help understand special relativity itself. But I disagree that this important to âdoing scienceâ in general: for example, I don't think students of medicine âŠ
What I mean is that the explanations that historically led to understanding something (that's how I interpreted your âarguments that led to the discoveryâ or @lipsum.dev's âconnected the dots historicallyâ) might be very different from those which work to convince students or make them understand. âŠ
Oh yes: he didn't mean this about France specifically (France is just unusual in that it teaches philosophy at the high school level). I don't know if anyone has attempted to teach philosophy in a way that is disconnected from the history of philosophy, but I'd be curious to know what it looks like.
This yellow thing in the sky reminds me of something⊠something I haven't seen in a long long time. <looks out the window toward a uniformly gray sky> I just can't remember what it was.
⊠I remember when my father heard that (in French high school) I would be taught philosophy, he made the pretty apt remark that âI bet they won't so much teach you âphilosophyâ as history of philosophyâ â and he was pretty right about that.
⊠which is just as fallacious for teaching as it is for evolutionary biology. Learning X and learning the history of X just aren't the same thing. Both can be worthwhile, but it is a sign of good science that we can learn Galois theory or electromagnetism without ever reading Galois or Maxwell. âŠ
Counterpoint: I'm not convinced by the idea that following history is necessarily the best pĂŠdagogical approach. The deductive approach (used for math) might ALSO not be the best, but wanting to retrace the historical trail of errors and improvements smacks of âontogeny recapitulates phylogenyâ, âŠ
i really think there is something between deep layers and emergent self-awarenessâ€â€(321M writing a creative piece about its own training process)đŒïž
OK this is actually brilliant. Don't let it be too well-known, but part of the point of 'cheat sheets' is to encourage students to reflect on key points so I'd definitely allow it.â€â€www.reddit.com/r/mathmemes/...đ
Putting the finishing touches on my anthropological study of the âBluesky Guyâ (38-47 years old, standard level woke and making SURE you know it, significantly less emotionally regulated than he thinks, every thread an opportunity for a personal story) which will be seminal but earn me death threats
The problem relates to the following problem, which is how I got interested in it in the first place: what is the expected value, and what are the higher moments, of the maximum of N independent standard Gaussian variables?
You'd think that in 2025 mathematical research would have completely solved the problem of COMPUTING THE VOLUME OF A SIMPLEX⊠and you'd be wrong!â€â€These links were compiled for a Twitter thread in 2021: threadreaderapp.com/thread/14305...đ
I posted an answer on MathOverflow with various bibliographical links describing what is know about the computation of the volume of a higher-dimensional simplex in spherical and hyperbolic geometry: mathoverflow.net/a/500870/17064đ
I asked a question on MathOverflow about a variation on Medvedev reducibility (definitions are given in the question) which seems interesting to me and I'd like to know if it has been considered before: mathoverflow.net/q/500856/17064đ
I posted an answer (to an old question) on MathOverflow explaining how one can actually algorithmically compute the 27 lines on a cubic surface (by representing the lines through their PlĂŒcker coordinates): mathoverflow.net/a/500849/17064đ
I get that the news cycle is packed right now, but I just heard from a colleague at the Smithsonian that this is fully a GIANT SQUID BEING EATEN BY A SPERM WHALE and itâs possibly the first ever confirmed video according to a friend at NOAAâ€â€10 YEAR OLD ME IS LOSING HER MIND (a thread đ§”)đ„
⊠Even a purely synthetic element like ânihoniumâ (OF COURSE you haven't heard of it; side note: even in English, I think it's utterly silly to give these elements names and we should stop doing this) gets a one-character/syllable name in Chinese: âéšâ (pronounced ânÇâ). đ€Żđ
⊠are named with a single syllable: âéȘâ alone (pronounced âyÇuâ) is âeuropiumâ, âé±â (pronounced âtĂšâ) is âterbiumâ, and âé„â (pronounced âhuÇâ) is âholmiumâ. No suffix indicating âthis is a chemical elementâ or anything. And you can bet these syllables have TONS of homonyms. âŠ
⊠Chinese often likes to add a second character behind one that might otherwise suffice to denote meaning, thus increasing clarity and/or redundancy. But for some reason, for the chemical elements, it does NOT do this: even rare and obscure, or synthetic elements, âŠ
One crazy thing I recently learned about Chinese: EVERY element in the periodic table has a name consisting of a SINGLE ideogram, and (therefore) a SINGLE syllable. This is insane considering that most Chinese words, even some very common ones, are two-syllables long: âŠ
Evidently you were not fortunate to have the right kind of geek friends to lecture you on the fascinating details of the Gondwana breakup since the cretaceous: commons.wikimedia.org/wiki/File:Go...đŒïž
Try this for a nerd pickup line: âDID YOU KNOW that the president of Brazil has been, by tradition since 1955, the first person to speak at the UN General Assembly after the Secretary-General of the UN and the President of the General Assembly, but before the President of the US?âđŒïž
In search for an answer to the above, I stumbled upon the book âPractices of Diplomatic Protocol in Genevaâ (by Hecht, Boulgaris & Jazairy), co-edited by the UN Institute for Training and Research and the Swiss government, and it seems to be an absolute treasure-trove for trivia nerds.đ
I have a question: why is Macron, and only he, âHis Excellencyâ in this letter? I would say it's because he's the only head of state whereas Albanese, Carney and Starmer are heads of government, but Trump (in CC) is also head of state. Is âExcellencyâ reserved for FOREIGN heads of states?đ
A (French, white) colleague once told me the following anecdote: he lived for several years in Japan. On the plane going there, he thought âoh this is going to be hard: these Asian faces all look the same to meâ. When returning to France, he thought âthese Caucasian faces all look the same!â.
Apparently the effect that we sometimes have a hard time telling apart faces of people from other ethnic types (or rather, ethnic types we didn't grow up around) is real and has been studied scientifically (âcross-race effectâ) â it's not just casual racism: www.youtube.com/watch?v=RyR0...đ
Tried to water the baby asparagus but the spout was blocked so I tried to shove the blockage down into the can but the thing inside shoved back.â€â€ComputerâŠenhance.â€â€#garden#gardening#oopsfrogđŒïžđŒïž
Simulating a phase transition with a simple model: www.youtube.com/watch?v=itRV... â The video also includes a very clear explanation of what âtemperatureâ and âchemical potentialâ are, as well as a derivation of the Boltzmann(-Gibbs) distribution law.đ
On dit souvent que les IA produisent des images mochissimes, et c'est vrai, mais elles ne sont pas encore Ă la hauteur d'un humain qui veut vraiment se donner de la peine. đ
I'm sure anything that comes out of the Seagull Summit, and the reactions by everyone else to it, will be calm, measured, and sensibleâ€â€www.bbc.co.uk/news/article...đ
Also, everybody hates Andrew Jackson, but I guess the rationale is that he is at least moderately well-known and recognizable, unlike Grover Cleveland or Martin van Buren.
I thought this cursed abomination of a painting was unfair to the Republican presidents, but bothsidesism is appeased by this equally horribly kitschy artwork of Democratic presidents by the same Andy Thomas.đŒïžđ
⊠Of course it's normal for everyone to believe that they're right MOST of the time. But if you can't think (and admit to yourself at least) of a recent moment when you were stubbornly defending something against valid criticism, then you're part of the problem (as we all are).
⊠when watching this video, everyone will probably immediately identify with goose #1 and think âoh yes, I remember trying to convince this idiot with this obvious factâ.â€â€But we need to remember that we're ALSO goose #2, and there are far more lessons to be learned from THAT side of the story! âŠ
An excellent short description of the psychological mechanisms (I like to point out) making most political discussions so unproductive; or: why changing other people's mind is so hard & how to try anyway: www.youtube.com/watch?v=Omc3...â€â€I would like to add the following point: âŠđ
Nice post you got there, it'd be a shame if I deliberately missed your point so I could be tedious about it
Yeah, people love to hate Boomers and love to hate Millennials: please save some of the hate for us GenXers too! I promise, we're not just bland and boring, we can be just as infuriating as the other generations.đ
J'ai vu vous verrez â€(Marx, Engels, Lenin, Stalin, and Mao â and Trotsky on the floor.â€From the "The Shadow of Mao" series by ZhongâYang Huang, 2008)â€đŒïž
Wait, using em dashes is a sign of AIness, now? I feel targeted!â€â€Rest assured, I can't be an AI because I certainly fail the second part of the acronym.đ
At the risk of discourse about discourse about discourse, all the nonsense with X happened immediately after Twitter had been unprecedentedly important because everyone was in lockdown and there wasn't much else to do. It's TikTok's world now, no microblogging site would have much impact anyway.đ
PS: An explanation of the quote and its history is given in various replies to âŠâ€stackoverflow.com/q/3870088/26... â where we learn that it is originally from MacLane, but has been truncated, and the original quote gives proper context and explanation lifting the confusion. âą6/6đŒïž
I think this is absolutely shitty terminology. At the very least it needs to be made unambiguous by stating explicitly: âa monad is a monoid in the category of endofunctors where the latter is endowed with the monoidal structure coming from the composition of functorsâ. đ€š âą5/6
So I spent a long time trying to figure out why âa monoid in the category of endofunctorsâ was tantamount to a monad because I used the former definition (and I still don't know if this gives anything interesting) instead of the latter (in which case it's obvious). âą4/6
⊠satisfying the âusualâ identities. But in fact that is NOT what is meant: instead, the maps are FÂČâF for multiplication and idâF for the unit, because we're looking at End(đ) NOT with its product structure but with its monoidal structure from COMPOSING functors. âą3/6
For me âmonoid in the category of endofunctorsâ means a monoid object in the category End(đ) of functors đâđ, and this means an object F of End(đ) along with maps FĂFâF (multiplication) and TâF (unit) where âĂâ and âTâ are product and terminal object in End(đ), ⊠âą2/6
Side note: I don't know how this phrase âa monad is a monoid in the category of endofunctorsâ became almost meme-like, but I think it's highly confusing EVEN if you know what all the terms mean. âą1/6đ
⊠(And the counterargument that you may have the choice of with whom to sign is a bit like saying that you sometimes get to choose which mafia boss protects you.)â€â€Now take the time to think how many contracts you ACTUALLY NEGOTIATED among those you signed.
⊠Because if your only options are âsignâ and âdo not signâ, then what you have in front of you is not a freely negotiated contract â it is an ultimatum â it is blackmail. This is how losing parties are treated after a war (e.g., Germany after WW1: sign the Versailles treaty Or Else). âŠ
Here's an important (necessary) condition to decide whether a contract is legitimate or morally defensible: did all contracting parties take an active part in negotiating its terms?â€â€Or did one party only have the options of âto signâ or ânot to signâ? âŠđ
For animals you kind of look at the whole critter to see where it belongs. For plants, you have to look at the fine details of how the petals are laid out or how the stamens are shaped or how the seeds are structured to get the family resemblance.
⊠Plants keep changing their mind completely about what they're going to look like. So hollyhocks and baobabs belong in one family (MalvaceĂŠ), apple trees and brambles are in another (RosaceĂŠ), ash trees and jasmine are together (OleaceĂŠ), and so are lychees and maple trees (SapindaceĂŠ). đŁ
Botanical families are weird.â€â€In zoology, you can sort of guess the family by the shape of the critter: felids are like cats, canids are like dogs, corvids are like crows, apids are like bees, and so on. There are outliers, but overall families KIND OF make sense. But plants! âŠđ
Incidentally learning that cocoa (Theobroma genus) is part of the mallow family, which besides mallows also includes such seemingly haphazard plants as: hollyhock, cotton, durian, hibiscus, linden trees and (wait for itâŠ) baobab.đ
Conclusions: plants can't make up their mind about which continent to grow on.
Cocoa (Theobroma cacao) is a plant native to Central America, but the world's largest producer of cultivated cocoa (đšđź) is in Africa. Conversely, coffee (Coffea arabica) is a plant native to Africa (Ethiopia), but the world's largest producer of cultivated coffee (đ§đ·) is in the Americas. đ€
L'article de Haaretz que je trouve comme source est: www.haaretz.com/israel-news/... (le chiffre est donc bien authentique) â mais ils ne donnent aucune information sur qui a conduit ce sondage ou les circonstances l'entourant.đ
I'm pretty sure Trump doesn't believe in this âtruthâ thing. He sees himselfÂč as a kind of Nietzschean Ăbermensch, having killed that one last god, truth, that tried to cross his Will, to rise above the very notion of âtrueâ and âfalseâ.â€â€1. (Except that he didn't read Nietzsche, of course, so no.)
I wanted to get a video of this ghost crab but every time I got close to their hole they scuttled back in, so I tried getting clever with it. I made a little sandcastle and shoved my phone into it, hit record, and walked away. Crab was VERY suspicious of this addition to their environment.đ„
As someone living in Europe, the idea of âpedestrian crossingsâ where pedestrians are supposed to yield to traffic (I suppose that's what the âwait for gapâ sign means?) rather blew my mind.
âWhoever designed the human visual system has a lot to answer for. Maybe not as much as the knee team, or the lower back group, but a lot.ââ€â€- @kjhealy.co , making me shoot my afternoon coffee out my nose.đŒïž
C'est tentant, en effet!â€â€Mais l'endroit est⊠un petit peu difficile d'accĂšs. Le bled le plus proche semble ĂȘtre Baker Lake (population 2061 habitants), et c'est à ⊠205km de lĂ . Et il n'y a aucune route dans le coin.
Google Maps, of course, does not disappoint: it has a label for âan island in a lake in an island in a lake in an island in a lake in Canadaâ⊠with opening hours (24 hours), reviews (averaging 4.7/5), and popular times: www.google.com/maps/place/A... đâ€â€(Unclear if anyone has actually been there.)đŒïž
So apparently there's this islands in a lake on an island in a lake on an island in a lake (in Canada): www.openstreetmap.org?mlat=62.6513... â and this is a record (up to arguing about what âislandâ and âlakeâ mean, of course).
The Wikipedia article on ârecursive islands and lakesâ looks very much like original research (and also should be named ânestedâ not ârecursiveâ), but I have to admit, it's a fun topic.đ
Among similar lines:â€â€âŁ There exists KââÂł compact and contractible, and f:KâK continuous, yet which DOES NOT have a fixed point.â€â€âŁ A counterexample is hard to find, and was only discovered in 1953: math.stackexchange.com/q/5064858/84...đ
I don't know which part amazes me more:â€â€âŁ There exist f,g:[0,1]â[0,1] continuous, commuting (i.e. fâg=gâf), yet which DO NOT have a common fixed point (âx.(x=f(x)=g(x)).â€â€âŁ A counterexample is hard to find, and was only discovered in 1969: www.jstor.org/stable/1995330đ
⊠pas parce qu'il nous embĂȘte dans une chose qu'on cherche Ă faire. Contourner les principes fondamentaux parce qu'ils sont emmerdants et/ou parce que «le Peuple Souverain le veut» c'est exactement le discours de l'extrĂȘme-droite, et on sait trĂšs bien que si elle arrive au pouvoir ⊠âą3/7
Seriously, ALL license agreements say the exact same thing. They all say: âWe have ALL THE RIGHTS PERMITTED BY LAW. You get NO RIGHTS EXCEPT THOSE REQUIRED BY LAW.ââ€â€You didn't get to negotiate the contract, why would they give you any right they aren't legally obligated to? Of course they don't.
⊠all disputes concerning the present post reading license agreement shall be handled by mandatory arbitration before the Court of the Supreme Gro-Tsen. âŠ
By reading any part of this post, you grant me worldwide, perpetual, irrevocable license, permission and consent to take, use and abuse, everything you own (including, but not limited to, your personal information and private property) in any manner and for any purpose whatsoever. Furthermore, âŠđ
Le wombat!â€â€(Ou le veau des vaches des highlands, mais on va dire que je suis partial.)â€â€Et ça ce n'est que chez les mammifĂšres. Chez les oiseaux, je t'invite Ă chercher âAegithalos caudatus Shima enagaâ dans Google Images, il est juste imbattable.
I'm sure there are examples of this, probably even many, some famous, but right now my memory refuses to come up with any.â€â€(Any kind of fiction interests me: books, plays, movies, paintings⊠And the two can be of a different kind.)
⊠cited or represented inside A, merely alluded to (perhaps giving some fragments). Then later, some (real) author, who may or may not be the same as the author of A, creates a real work BâČ which matches everything we are told about B inside A, thus bringing it out of fiction into the real world.
What are some examples of fictions-within-fictions that have later been developed into real works of their own?â€â€By this I mean: some (real) author wrote a (real) work of fiction A, which refers to a (fictional) work of fiction B about which we are told certain things, but which isn't fully âŠ
Pour les ordinateurs (fixes comme portables), on peut souvent donner une seconde vie Ă une vieille machine en installant un Linux dessus.â€â€Mais pour un smartphone, c'est extrĂȘmement difficile, parce que Google et Apple font tout pour empĂȘcher l'utilisateur d'en avoir un plein contrĂŽle.
Exactly: an increase of not even 1/5 of an order of magnitude since 2019 (so not all due to AI). This pretty well illustrates my point: the vast majority of Google's energy consumption is not related to AI, so one wonders why people are so keen to point out the AI part specifically.
There is âșnothingâș wrong with redundancy in language. In fact, it is a good way to avoid ambiguities. Embrace it!â€â€âPI numberâ would be highly confusing (Ï?). âPINâ alone can cause confusion with âpinâ. So âPIN numberâ is better than either.đ
Now that everyone is (again) finding out that having 1600 random NPM (indirect) dependencies isn't a great idea, a reminder I wrote about this very problem in @spectrum.ieee.org in 2024: spectrum.ieee.org/lean-softwar...đ
⊠Looking into this, I was recently surprised by how few people inhabit the âsouth-west-back octantâ of the Earth (i.e., latitude †0° and longitude †â90°). The largest city is Apia, capital of Samoa, with a population of⊠around 40k people. And in total less than 0.1% (maybe even 0.01%) âŠ
The only thing I can think of is âthis isn't the right way to divide the Earth in 8 octants! the right way is to use 3 mutually orthogonal great circles (equivalently, project a regular octahedron onto its circumscribed sphere), e.g., cut at the equator, the 0/180° meridian and the ±90° meridianâ. âŠ
How the general debate week of the United Nations General Assembly functions, and how images are taken: www.youtube.com/watch?v=JNWi... [video is in French]đ
A lawyer tries to unwrap what US Law (and International Law) has to say about the president ordering the assassination of civilians outside of US jurisdiction: www.youtube.com/watch?v=7t-_...đ
GOOD NEWS! A new cancer vaccine has shown progress in triggering POWERFUL and LASTING immune responses in patients with pancreatic AND colorectal cancer. The vaccine, known as ELI-002 2P, targets mutant KRAS proteins AND had a huge impact on PREVENTING or DELAYING cancer recurrence in patients.
⊠Then he adds: âWhy do you speak to me of the stones? It is only the arch that matters to me.ââ€â€Polo replies: âWithout the stones, there is no arch.ââ€Â»â€â€â Italo Calvino, âInvisible Citiesâ [English translation mine]
«â€Marco Polo is describing a bridge, stone by stone.â€â€âBut which is the stone that supports the bridge?â asks Kublai Khan.â€â€âThe bridge is not supported by this or that stone,â Marco replies, âbut by the shape of the arch that they form.ââ€â€Kublai Khan remains silent, thoughtful. âŠ
âOur son is called War Famine Pestilence Death Jones. He's such a sweet kid. He loves horses.â
How do people come up with the idea of using something like âEuthanasiaâ as a first name? đČâ€â€I knew âDoloresâ (i.e., âpainsâ) was used in Spanish, but this one is new to me.â€â€Is it like, some parents hate their kids and other parents think âoh, that's a cool name!â and it grows from there?đ
⣠Charter of Fundamental Rights of the EU, article 7 (âRespect for private and family lifeâ): âEveryone has the right to respect for his or her private and family life, home and communications.ââ€â€âŁ European Convention on Human Rights, article 8 (âRight to respect for private and family lifeâ), ¶1: âŠ
⣠Charter of Fundamental Rights of the EU, article 7 (âRespect for private and family lifeâ): âEveryone has the right to respect for his or her private and family life, home and communications.ââ€â€âŁ European Convention on Human Rights, article 8 (âRight to respect for private and family lifeâ), ¶1: âŠ
Interesting to compare two pictures I took of the Toronto skyline as seen from the islands during my last two trips there: on 2007-04-17 (left) and on 2025-09-01 (right).đŒïžđŒïžđ
â[Under Roger Fisher's suggestion,] if ever the President wanted to fire nuclear weapons, the only way he could do so would be for him first, with his own hands, to kill [with a big, heavy butcher knife, the volunteer next to whose heart the code-containing capsule was implanted].ââ€â€Say again? đłđ
(âOur chief weapon is anti-feminism. Anti-feminism and anti-wokism. Our two weapons are anti-feminism and anti-wokism. And ruthless stalinism. Our three weapons are anti-feminism and anti-wokism and ruthless Stalinism. And an almost fanatical devotion to Donald Trump. I'll come in again.â)
(Cue three people's commissars, dressed in red, entering the room to the sound of a weird potpourri of âThe Internationaleâ and âThe Star-Spangled Bannerâ and saying: âNOBODY EXPECTS the MAGA Communists!â)
I have to admit, I did not expect the âanti-feminist, anti-queer, anti-woke, anti-environmentalist, pro-social services, pro-tax cut, pro-Donald Trump, pro-Xi Jinping, Maxist-Leninist, Stalinist, socialist patriotic MAGA Communist partyâ. đ€Żâ€â€en.wikipedia.org/wiki/America...đ
This is the graph we show whenever someone talks about how back in the old days there weren't (people who are not whoever the person speaking thinks are the default). â€â€Mostly we do this to underscore that a rise in apparent frequency isn't always a rise in real frequency.đŒïž
A physicist tells a joke to a logician. The logician doesn't laugh. The physicist thinks nothing of it.â€â€A month later, physicist walks by the office of logician, who is laughing. âWhat's funny?â asks the physicist. âYour joke,â replies the logician. âI finally managed to formally prove it funny.âđ
"Nice bag, is it new?"â€â€"Thank you," the wizard said. "Yes, is my new daily carry. It's actually a container for a interdimensional node."â€â€"Infinite space? Nice! What do you have in it?"â€â€"Oh, only this." The wizard pulled out another bag. "It's my old bag."â€â€"Which holds?"â€â€"Er... The bag before."
Elon Musk seems not to have realised that this AI-generated image he retweeted is of the Arc de Triomphe, not of London.â€â€It would be laughable, were it not so inflammatory.đŒïž
Ah, so my model was wrong. Next try: a subway ride is a set P of passengers, each with an ordinal Ï(p) where they board and an ordinal Ï(p) > Ï(p) where they disembark, so that when it arrives at Îł the subway contains |{pâP : Ï(p) < Îł < Ï(p)}| passengers, which must always be †capacity. Correct?
"Les français sont pour la politique du coup de pied au cul, à condition qu'il ne soit pas trop fort et que ce soit quelqu'un d'autre qui le prenne" disait mon grand-pÚre
If only history had provided us with an example that everyone agreed they would definitely oppose if it happened again, where a Government influenced by street thugs first persecutes an ethnic minority like Mexicans, then a political trend like leftism, then ...đ
Hoping someone can help me here: what would be a library or online resource (or other options) where I could find some of the publications of the (long defunct) Center for Editions of American Authors? Particularly their Newsletter, their reply to E. Wilson, their Statement of editorial principles.
I imagine a âsubway of capacity λâ is a subset of λ that can vary with time (station). And I imagine passengers are allowed to embark and not just disembark. But what's your rule for determining the state of the subway at a limit ordinal station? Do you take the lim.inf? The lim.sup? Something else?
News from Finland. A 9-year-old lost an especially good stick heâd had since he was 2. He hung up 20 posters. A few days later it was returned. It had been found by a 2-year-old, who wanted to keep it for herself, but her mother made her return it. She got toys, flowers and candy as a reward.đŒïžđŒïž
Nobel Prize Laureate Roger Penrose, Yvette Fuentes, and myself, request your help in order to save an archive of incredible scientific and historical value. Please raise awareness by *sharing*, or *contribute*: â€â€www.crowdfunder.co.uk/p/roger-penr...đ
* Honest, open dialogue between differing perspectives is a core value worth preserving.â€â€* The form of such dialogue, without the honesty or openness, has been co-opted by bad-faith actors as a cynical strategy to garner respectability.â€â€* There are plenty of suckers eager to fall for the ruse.
Moui, alors un «shoe shop» en anglais c'est un «magasin de chaussures», pas un magasin qui vend 1 chaussure, et un «horse trainer» c'est un «entraĂźneur de chevaux». Donc le singulier de «star» dans «Star Wars» ne dit pas grand-chose, c'est juste la construction. Le pluriel de «wars», en revanche, đ€.
I don't know how standard this is, but I love the use of âmicromortsâ as a unit of probability of dying.â€â€(Maybe â500 nanomortsâ sounds even better than â0.5 micromortsâ, though.)đ
History students are often disappointed when they learn why the AI take-over failed. They were defeated by human resistance, which was kept alive by libraries and old paper books, and a surprising machine ally.â€â€Books had not been replaced, because even the mightiest AI could not make printers work.
This group of UK-based LGBTQIA+ and allied members of the UK mathematics community is self-organising to support mathematicians, and have a pun in their name, so are likely of interest to many peeps I know here!â€â€bsky.app/profile/qedm...đ
Note that this can be used adversarially: IIUC, if you order ChatGPT to hold certain beliefs, then make it generate large amounts of computer code, put this code on GitHub, wait for the same ChatGPT model to be retrained using this code, it will pick up those beliefs.đ
An explanation of âsubliminal learningâ, or how training one AI model on the output of another can pass on certain traits from student to teacher (such as: liking eagles) even though the training data seemed totally unrelated (strings of numbers): www.youtube.com/watch?v=NUAb...đ
I watched the video, and it's pretty obvious the student had been coached and was practically speaking from a script. Setting aside whether or not she has good beliefs (I don't think she does), it's bad for uni leadership to cosign "don't think for yourself." Critical thinking should be the #1 goal.đ
This is the official spokesperson for the White House, stating that the President hopes to deploy the United States military to occupy every city controlled by the political party that opposes him. Explicitly.đ
Bref, voilĂ ce qui illustre bien le problĂšme de «Paris-Saclay»: non seulement c'est complĂštement au diable et les transports pour y aller sont merdiques, mais mĂȘme pour aller d'un point Ă un autre DU MĂME CAMPUS, c'est mission impossible. www.madore.org/~david/weblo...đ
⣠Et voilĂ comment on retombe fatalement sur la voiture individuelle (ou dans mon cas, la moto). Mais je n'ai vraiment pas envie de faire ParisâPalaiseau par la route demain (il va y avoir une circulation d'enfer). J'en viens Ă demander Ă ma maman (qui habite Orsay) d'emprunter sa voiture. đ
Question au sujet du plateau de Saclay:â€â€Demain je vais vouloir aller d'un point Ă un autre du campus (de part et d'autre de la N118). Ce serait long et chiant Ă faire Ă pied (~45min!), je n'ai pas envie de prendre la moto/voiture pour venir, et les bus sont totalement dysfonctionnels.â€â€Donc: âŠ
A surprisingly interesting dive into how Soviet housing policy worked, its history, and how successive Soviet leaders created different styles in trying to lodge the ever-growing urban population: www.youtube.com/watch?v=Zfn8...đ
La TV japonaise qui nous apprend que les autruches aiment bien les chauves car la forme leur rappelle leurs Ćufs et elles les protĂšgent instinctivement đđŒïžđŒïžđŒïžđŒïž
Le mouvement «bloquons tout» semble au moins avoir eu l'effet de complĂštement fluidifier la circulation automobile en Ăle-de-France:đŒïž
Imagine you're a sunfish, minding your own business munching on jellyfish, and suddenly Kurzgesagt puts up a video just to diss you by explaining how dumb and pathetic you are: www.youtube.com/watch?v=gtDK...â€â€(Stop the mola bullying!)đ
The robot picked through the boxes of old cables and converters at the market stall. â€â€"Looking for anything in particular?"â€â€"A... special charger adapter."â€â€A bag from under the counter. The robot looked inside. Kettle lead to robot charge port. Untracked charging.â€â€"A gift. Enjoy your freedom."
⊠so certainly many of the V_α need to satisfy the same set. This seems less interesting (to my eyes) than when V_α âș V_ÎČ. But at any rate I'm sure there's room for one or several MathOverflow questions on either relation.
PS: I have no idea what to say about V_α being elementarily equivalent to V_ÎČ (for α<ÎČ) without being an elementary submodel of it. I don't even know if it can happen. But we can probably say something by noting that there are at most continuum-many sets of first-order formulas, âŠ
⊠V_α is an elementary submodel of V_Îș (basically by adapting the proof of Jech, âSet Theory (Third Millennium ed.)â theorem 12.14(ii), except that the fact that we're dealing with a set V_Îș instead of the class V lets us handle all formulas at once). But I don't know if âinaccessibleâ is necessary.
I don't suspect there's a simpler condition than the one you just wrote. There might be one if you're just asking for ÎČ for which there exists α. But I don't think it's a basic question at all.â€â€FWIW, I think I could show that if Îș is inaccessible, then there are club-many α<Îș such that âŠ
Indeed. And the video makes it very clear that violence and/or the threat of violent revolution (including comparison with France's 1830 movement that was in everybody's mind) were crucial in â ahem â âpersuadingâ William IV and the conservative Lords to let the Reform bill pass.
I don't know the answer, but the question can already be asked of French: we say âavoir un rendez-vousâ, never ââŠun rendons-nousâ. In fact, ârendez-vousâ acts as a quasi interjection: ârendez-vous lĂ -bas!â works in all cases (and doesn't really sound like a verb anymore): âŠ
⊠and create the metric system, which Britain resisted adopting for much longer than most other countries (with the exception of a certain former colony of theirs).
One of the bizarre lessons of History is how more progress at a given time can mean less progress at a later time. For example, Britain having a better unified system of weights and measures when France had failed to do so (in the 18th century) is the reason why France could get more radical âŠ
The history of the passing of the British Reform Act 1832, one of the crucial steps in making Britain incrementally more democratic, and how the country avoided going through a revolution like many other European countries did: www.youtube.com/watch?v=h6E4...đ
This video sounds like it's about physics, but it's really a math/algorithmics problem: if a surface of varying height is flooded with water to a certain level, and you drain it at a point, how can we compute whether a point remains under water? www.youtube.com/watch?v=zzWK...đ
Columnist from a country whose presidents brings its own cities under military occupation and threatens political opponents discusses political chaos in other countries.đ
To this day, on social media and various messaging apps (e.g., on mobile), it is often unclear how do distinguish the two functions of âadd a line break hereâ and âsend the message nowâ (i.e., essentially, âreturnâ and âenterâ). One may be a GUI widget, the other a key, and we're never too sure.
A fascinating dive into the history of the key variously known as âreturnâ or âenterâ or ââ”â on the keyboards of typewriters, teletypes and modern computers, and how various functions got switched around. aresluna.org/the-day-retu...đ
Do you know year of Fire Horse? And do you know the total fertility rate dropped 26% in the last fire horse year in Japan?â€â€My new blog post explains how the superstition changed fertility pattern in the last Fire Horse Years (1906, 1966) in Japan. â€â€2026 will be Fire Horse...đŒïžđŒïž
Along the same lines, could we please get the ability to follow a post (i.e., get notified of its replies)? This seems easy to implement and super useful!đ
I think tourist shops selling Canadian merchandise (anything you can think of with a Canadian flag on it) at the airport should include a sweater with the Canadian flag and the subtext: «âa few acres of snowâ (Voltaire)». đ
When you're famous you get a Wikipedia page. When you're very famous, your works also get their own Wikipedia page. But when you're really hyper famous, even your 4-word long quotes their own Wikipedia page!
I love how Voltaire's dismissal of Canada as âquelques arpents de neigeâ (âa few acres of snowâ) gets to have its own Wikipedia page: en.wikipedia.org/wiki/A_few_a... (and a long one at that!)đ
a friend and I went downtown this evening to scream in the streets with thousands of our neighbors. â€â€@theonion.com was also at the protest this evening and they were pulling no punchesđŒïž
This is the thing. Even in an ideal post-Trump America, it has become clear that our norms and institutions are powerless to maintain stability in the face of an effective agent of personalized rule. Why would anyone ever trust the US again (if they did)?đ
⊠But of course you could point out that I wasn't consistent in applying this principle since I did generalize Hugo's flaw to all men and not, more narrowly, white heterosexual bourgeois 19th century French men as the aforementioned prudence would dictate. And you would be correct.
I try (perhaps not consistently) to overgeneralize positive judgments and undergeneralize negative ones, because it is more prudent to give the benefit of the doubt when it can be given. So here I didn't want to automatically assume / claim that great women would have the same biases as Hugo. âŠ
I mean this is an example of a great man failing. I suspect great women aren't exempt from the same mistakes, but this particular example doesn't let me conclude one way or another.
⊠the greatness of contributions from other domains. It is true, though, and deeply unfair, that Charles Fourier seems to have far more streets named after him in France than Joseph Fourier.
It's hard to overstate just how important the Fourier transform is, both within mathematics itself and for its applications in all domains from physics to computing to data analysis to engineering and more.đ
How much do people really reject science? â€â€New paper out doi.org/10.1177/0963...â€â€In four studies, we asked Americansâincluding flat Earthers, climate change deniers and vaccine skepticsâwhether they accepted basic scientific facts.â€â€The result? A surprisingly high level of agreement. đđ
This story is WILD. Trump sent Seal Team 6 into North Korea to plant a listening device. The entire thing went sideways within minutes of landing when they noticed a fishing boat near the beach. They killed everyone on board, sunk the bodies to cover their tracks, and fled. Congress was never told.đŒïžđ
⊠is that they were in Hart House Circle Park here: www.openstreetmap.org?mlat=43.6632... (obviously remodeled in the last <20 years) â but I'm by no means certain. Does anyone have info about when this artwork(?) was created, when it was removed, and where it was?â€â€(@fatraccoon.bsky.social maybe?)
A question for Torontonians if there are any following me: somewhere around Queens Park there used to be four markers which precisely aligned with the top of the CN Tower, pictured below in 2007 (last time I was here). I âșthinkâș they're gone now (I couldn't find them). My guess âŠđŒïžđŒïž
I'd imagine so. Comes from the Latin canicula, literally "little dog", and is the principal star in the Sirius constellation, which apparently isn't visible for much of the year but rises and sets with the sun between late July and late August. (I know this because I wrote about it a while ago)
Are your sheep always turning up late for work? Are they taking too long on their lunch break or simply struggling to get through the workload? Are they always just mucking about?â€â€Then you need someđŒïž
The things the MAHA lot are doing and encouraging in the US will lead to disaster, but a common source of debate is that these things are done in Europe. For example, the UK doesn't have vaccine mandates, and consumption of raw milk products is common in France. It's therefore tempting >
Peut-ĂȘtre que dans le quartier oĂč nous sommes elles manquent d'espaces verts oĂč nicher, alors? (Et que je n'aurais pas fait assez attention pour les remarquer ailleursâŠ)
On this podcast, I explain the EU's #ChatControl plan: mandatory scanning of ALL private messages. This is unprecedented in a democracy. The only other country with a similar system is Chinaâand they use it for political control. #StopScanningMeâ€https://www.youtube.com/watch?v=L933xDcSS3o
A kind reminder that a "politics of you deserved this" (cancer, vaccine-preventable disease, natural disaster, etc) has no place in public health. We can hold bad actors to account without punching down on the groups most harmed by their actions and/or resorting to shame, blame, and stigma.
Neat discovery: Two knots whose connected sum has an unknotting number less than the sum of the unknotting numbers of the knots. This provides a counterexample to an old conjecture.đ
There's "a popular misconception that age-verification mandates are going to be the best way to rein in big tech and hold them accountable," EFF's Molly Buckley told @rollingstone.com - but these laws will just further line the biggest platforms' pockets. www.rollingstone.com/culture/cul...đ
Coucou les internets, est-ce que vous connaissez des assos handi un peu militantes qui proposent des formations / interventions de sensibilisation au validisme en milieu pro ? Ou alors des universitaires qui travaillent sur ces questions et pourraient partager leurs travaux ? Merci !
The last passenger pigeon died 111 years ago today and not a day goes by that I don't think about how their flocks numbered in the *billions*, that their roosts covered 100+ square miles, that they collapsed trees with their nests. America is incomplete without themđŒïž
I see Bluesky has not escaped the social-media syndrome of âI donât know exactly whatâs going on in this situation, therefore it can only be explained by a scenario that confirms all my beliefs.â
Now I'm curious. Do you know other examples of papers where, similarly, the authors disagree on some point, and argue their opposite positions separately?â€/End
People are melting down at a Tribune article about CHSD 230 considering adding Arabic to its language learning electives. I wasted time in the comments, which I normally avoid doing since it's useless and awful, but it led to possibly the funniest thing anybody's ever said to me about France.đŒïž
Also, using this particular map to promote Hidalgo's politics ignores the fact that part (I suspect, most) of the drop in air pollution is due to environmental regulations on cars and exhaust systems that were decided at the EU or national level, having little to do with Paris.
Sent Jim to the French grocery store to get sausages to grill for dinner and some absolute MONSTER of a butcher tried to send him home with âpackaged saucissonsâ which per the photo he texted me turned out to be andouilletteđŒïž
The logic appears to be that the first restaurant of what would later be that chain opened (in 1954 in Toronto) in a place that just so happened to be built in the âSwiss chaletâ architectural style.đ
âSwiss Chaletâ is a Canadian restaurant chain specialized in rĂŽtisserie chicken, even if nothing about this statement makes any bit of sense. (I don't recall Switzerland being renowned for its⊠chickens.)đ
Article 8 covers things like preventing the government from controlling who you can have sex with, and what hobbies you have; from spying on your mail and phone conversations; and so on. The UK government wants rid of it. They will claim it is necessary to âprotect womenâ from the likes of me.đ
⊠mais si je dois prĂȘter mon portable 5 minutes ça cause toujours une certaine confusion. Et j'ai parfois moi-mĂȘme des doutes sur la position de quelques symboles un peu rares.
Funny that an American Worker looks like he just stepped out of a 1960s Soviet factory somewhere in eastern Siberia , full of determination to fulfill a five-year plan in four years and conscious of the dangers of too much alcohol and talking to foreigners.đ
Decentralized social network Mastodon says it cannot comply with age verification laws, like in Mississippi and elsewhere, and says it's up to individual server owners to decide.đ
It's often very hard for me to tell whether the âI can't recognize anythingâ feeling I have is because my memory is vague or because things have completely changed. Google Street View is immensely helpful in letting me decide (here, obviously, the latter).
The same place in Toronto's Yonge Street (around Maitland St), looking south, as imaged by Google Street View in 2009, and in 2024. www.google.com/maps/@43.663...đŒïžđŒïž
Toronto's financial district has this vast and complex network of interconnected underground shopping malls/concourses known as the âPATHâ, that links many skyscrapers and subway stations together. It remains open even when the shops are closed, and the whole thing is eerily empty.đŒïžđŒïžđŒïž
The riddle of the sphinx: âwhich creature walks on four legs in the morning, on a flat baking stone in the afternoon, and on three legs in the evening?â
(Don't tell me to change the time zone from the control center or something: this would affect /etc/localtime and I want an explicit TZ environment variable so it will be passed by ssh.)
How do I set up Ubuntu (more precisely an old 20.04 Ubuntu) to add an environment variable, namely TZ=America/Toronto, to my session's environment when starting Gnome from the Gnome Display Manager?
One change I've noticed so far is that the smell of weed is everywhere. (Sale and use of cannabis was legalized in đšđŠ in 2018.)â€â€I'm in favor of legalizing recreational drugs like cannabis, but we need to acknowledge that, like tobacco and alcohol, there are associated nuisances.đ
This is interesting. My experience about mentioning major LLMs spewing out bullshit is that somebody would tell me it's because I use the free version / I should use the next version that will come out 3 months from now / I should use some other LLM.đ
The single most important thing to understand about digital futurism is this: â€â€When the digital future that Sam Altman ( or Elon, or Andreessen, etc) predicts fails to materialize, he doesnât have to give the money back.
They're openly calling to lock up every trans person by force. We need every ally to speak out forcefully against this because trans folks cannot do this on our own.đŒïžđ
⊠Now we certainly don't have the math to explain or define AGI, let alone create it, but that doesn't mean the âalchemistsâ can't make it work. In fact, to prove that they can't would require the math that we don't have.
⊠There are plenty of examples of things we know how to do and can't explain mathematically (even just how a bicycle runs might be one!), and the limited kind of AI we do already have is already in this territory: there is some theory, but also a lot of alchemy (as the post points out). âŠ
I think the post on the whole makes some good points, but also gets confused about several things. It's a bit difficult to elaborate in kĂ300 chars (k small) and I'm on vacation, but one confusion I sense is between doing something and understanding whar we're doing. âŠ
Let me get this straight: Toronto opened a brand new direct train link between airport and downtown in 2015, and it runs on⊠dieselâœâ€â€What the actual fđ€Żck?
Taxiing from the gate to the track on a big jet releases ~1 ton of COâ just because the airline industry can't figure out a way to have a small electric ground vehicle pull the jet from one place to another (while also feeding it electric power if needed).
The engines are required to generate electricity and there are probably tons of security regulations against having passengers in an aircraft with no main power supply. Also, turning them back on probably requires going through an incredibly long checklist.â€â€But yes, it's stupid.
(I think a ballpark estimate is around 300g/s, so 500kg for these 25min. Which translates to roughly 1.5 TONS of COâ. đ±)
Plane landed 25min ago in Toronto YYZ, and we're still waiting for an available gate to disembark. đŹâ€â€Meanwhile, the plane engines are running and I don't think I want to know how much kerosene they're burning per minute. đ
Why is the read-write performance of USB thumb drives so much worse than that of an SSD drive in a USB case: aren't the two supposed to be more or less equivalent?â€â€Also, why don't USB thumb drives support âtrimâ?
Anyone old enough to remember how horrible it was to keep track of files and backups before rsync (when we only had rdist or not even that) will join me in wishing the rsync developers all the blessings that this world can bestow upon them.
One thoroughly underappreciated computer program which made my life oh so much easier is rsync.â€â€Every time I move around lots of files between backups and backups of backups and stuff like that, I pause to ponder how much rsync has made my life easier.
Because some people haven't heard it yet: PAYPAL IS NOT A BANK, DO NOT LEAVE MORE THAN A COUPLE HUNDRED DOLLARS SITTING IN YOUR ACCOUNT AT ANY TIME. MOVE IT TO YOUR BANK ACCOUNT IMMEDIATELY.â€â€Paypal can and will close your account and steal all your money without warning. And have done MANY times.đ
Sorry to be the âwell, akshuallyâ science guy, but the Sun's luminosity and radius have actually been increasing over the last ~4 billion years, and will continue to do so. en.wikipedia.org/wiki/Solar_l...đŒïž
Look what they did to Notepad. Shut the fuck up. This is Notepad. You are not welcome here. Oh yeah "Let me use Copilot for Notepad". "I'm going to sign into my account for Notepad". What the fuck are you talking about. It's Notepad.đŒïž
Also closed since 2007: the âScience Cityâ shop that used to be in the Holt Renfrew Centre and whose gadgets I loved as a kid; and the âWorld's Biggest Bookstoreâ that used to be on 20 Edward St.â€â€(Îáœ¶Ï áŒÏ Ï᜞Μ αáœÏ᜞Μ ÏÎżÏαΌ᜞Μ ÎżáœÎș áŒÎœ áŒÎŒÎČαίηÏ. đ)
Sadly, I already know this: the Ontario Science Centre, which was one of my favorite places when I lived in Toronto in 1984â1985, is permanently closed (already in 2007 it had switched from showing instructive science exhibits to mostly just being fun for kids).
Last time I was in Toronto was 18 years ago. What major changes should I look for in the city as I go back?
Re bottom-right box: isn't there a subtlety like âwriting to a closed terminal causes SIGHUP to be sent at the kernel level, but some shells will also SIGHUP all running jobs when the shell exits even if the jobs don't write to a terminalâ? Or am I confusing with something else?
Very concerning: Google is announcing steps (under false pretense of âsecurityâ) to bring Android closer to Apple's iOS level of vendor locking by preventing users from installing apps they want: arstechnica.com/gadgets/2025... â This will likely break F-Droid and with it the Android FOSS ecosystem.đ
A reminder alert popped up.â€â€"Oh," the Supervisor said, "it's time to check in on Sol-3 again. Szrpt, can you handle that?"â€â€Szrpt bowed a frond. "Yes, of course."â€â€"Don't forget to reset the killer asteroid if the sapients pose no threat."â€â€"Once!" Szrpt bristled. "I only forgot that once!"
⊠(Or you might go with a different word/prefix than âpseudolatticeâ, but I don't really know what to suggest. At least this one is suggested in the nLab.) The really important thing is to make it clear what the objects and morphisms are (or at least subobjects).
⊠not working constructively) sups and infs. So what you're referring to would be a âcomplete subpseudolatticeâ of a complete lattice. Alas, this terminology isn't standard. But since it's logical and doesn't seem to conflict with anything standard, I think it's all right if all gets defined. âŠ
⊠So I think I might suggest this: use âpseudolatticeâ to mean a poset that has binary sups and infs, âlatticeâ for one which has all finite ones, âcomplete latticeâ for one which has all sups and infs, and âcomplete pseudolatticeâ for one which has all inhabited (ânonemptyâ if you're not âŠ
⊠As to what better terminology to use, well, the whole terminology on lattices is bad, because as ncatlab.org/nlab/show/la... points out, some people use âlatticeâ to require only binary meets and joins, while others also require the nullary meet (=top) and join (=bottom), hence all finite. âŠđ
The âclosed sublatticeâ strikes me as bad terminology, and I don't think it's standard. I guess it's supposed to mean âclosed-under-all-inhabited-meets-and-joinsâ, but the latter words are doing the actual lifting as you noticed. So I wouldn't recommend using it, except as âsometimes also calledâ. âŠ
I spent a quarter century being lectured by libertarians and republicans about how minimal government oversight of large companies was radical socialismâ€â€and if you mentioned nationalizing stuff like telecom for the public good they'd have a six week embolismđ
Don't let the culinary prescriptivists get to you. There is nothing more stupid than trying to tell people that they Are Not Allowed to mix this and that if they enjoy it.đ
So next time, try to imagine Cleopatra's nose looking more like this âŹïž guy's, and wonder whether Julius Cesar and Mark Antony falling in love with her didn't have more to do with the incredible wealth and power she commanded.đŒïž
⊠In fact, if I recall correctly, âCleopatra's noseâ is not remembered in history for the quality of âbeing extraordinarily ugly because she was phenomenally inbredâ, and that is not how the popular imagination pictures her. We give her role to glamorous actresses, not ugly ones.â€â€Double standard?đŒïž
The Habsburgs get shit for inbreeding, but: nearly all of Cleopatra VII's royal ancestors had been brother & sister, or uncle & niece, occasionally just 1st cousins / double cousins, for EIGHT generations (250 years) down from Ptolemy I, yet this does not seem to have made her very ugly. âŠđ
Here we see why Dem politicians will keep saying the most unhelpful things during a time of national crisis. I hope they have the wit to ask themselves: (1) Is my approval rating the most important thing right now? (2) What is the empirical evidence that "message testing" actually works?đ
The University of Chicago has a debt of over $6 billion, against an endowment of $10 billion. They played with crypto. That's more than irresponsible.â€â€Their board of trustees contains a surprising number of people regarded as financial geniuses.đđ
For the EU, this should be a very urgent matter of national security. All EU member states should build on Denmark's wise strategy to phase out Microsoft productsđđ
The hits keep coming. âThe departments that wonât be accepting Ph.D. students now include art history, cinema and media studies, classics, comparative literature, East Asian languages and civilizations, English language and literature, Germanic studies, linguistics, Middle Eastern studiesâŠâđ
Because I like to check my quotes, the precise quote by Douglas Hofstadter is:â€â€âThis gubblick contains many nonsklarkish English flutzpahs, but the overall pluggandisp can be glorked from context.ââ€â€[âMetamagical Themasâ, âOn Self-Referential Sentencesâ, January 1981]đ
It's one of the outputs of this little gadget I wrote some time ago: www.madore.org/~david/weblo... (the JS code should be readable). Basically I replaced 5 by 7 in a description of Penrose tilings without thinking too hard about whether it has interesting properties beyond being pretty.đ
âThis sentence contains several non-English forjacks, but their overall zingbul can be grinxed from the context.â (Douglas Hofstadter â quotes from memory)
Unfortunately, Bluesky is unavailable in Mississippi right now, due to a new state law that requires age verification for all users. â€â€While intended for child safety, we think this law poses broader challenges & creates significant barriers that limit free speech & harm smaller platforms like ours.
You can just download the Networkx source and seach for a .ir URL in the comments.
đ€Żđ€Šâ€â€I don't know if it's Apple or the US State department's rules that are utterly insane, but apparently you can't include any file that contains a file linking to a URL in the .ir TLD within an iOS package. This is just nuts!đ
That is an embarrassing question! đ I trained in algebraic geometry / number theory, but now I tend to be very much interested in logic and computability (theoretical computer science). My tastes in math are very eclectic.
Note that hypotheses are crucial: if f:âââ is assumed to be continuous â”everywhereâ”, differentiable â”almost everywhereâ” and satisfy fâČâ„0 â”a.e.â”, then f can fail to be nondecreasing (consider the negative of a âDevil's staircaseâ Cantor function). en.wikipedia.org/wiki/Cantor_...đ
An often overlooked theorem: if a function f:âââ is differentiable â”everywhereâ” and fâČâ„0 â”almost everywhereâ”, then in fact f is monotonic (ânondecreasingâ) and fâČâ„0 everywhere. mathoverflow.net/a/499465/17064đ
⊠So if the prof makes the statement H_â, then they're just lying because it's logically absurd (but of course some of Hâ, Hâ, Hâ, Hâ or Hâ might still be correct). The logic is sound, but the prof is making an inconsistent claim.
⊠then from Hâ you can deduce that the test is between Monday and Friday, from Hâ you can deduce that it's between Monday and Thursday, etc, and Hâ is just inconsistent, as is the âultimateâ assumption H_â := Hâ + âand you can't deduce from H_â which day it's onâ. âŠ
In the surprise test paradox, it's not that the logic is inconsistent, it's that the assumption is. Basically, if Hâ := âyou will have a test this weekâ, Hâ := Hâ + âand you can't deduce from Hâ which day it's onâ, Hâ := Hâ + âand you can't deduce from Hâ which day it's onâ, etc., âŠ
Isn't it the case, though, that there are a gazillion different kinds of âcomaâ (âcomataâ, I guess), just like a stroke can have a gazillion different effects, depending on what parts of the brain are affected and how?
It's part of the folklore of logicians (also mentioned at en.wikipedia.org/wiki/Common_... for example), but I'm disappointed by the lack of a single Web page explaining it clearly and pĂŠdagogically. Anyway, it's worth thinking about, because it's pretty subtle.đ
This is a nice and funny analogy, but it doesn't really explain anything, while the blue-eyed islanders puzzle offers a possible logical (if vastly simplified) explanation of what is going on.
I think that market bubbles are similar to (if not as ideal as) the famous logical puzzle of the blue-eyed islanders (see xkcd.com/blue_eyes.html and terrytao.wordpress.com/2008/02/05/t... for example): everyone knows they're in a bubble, everyone knows that everyone knows they're in a bubble, âŠđ
⊠and so on until a high â”but not arbitrarily highâ” accumulation of levels of âeverybody knowsâ. And a seemingly trivial change of information (like a visitor coming to the island and publicly saying âsomeone has blue eyesâ) causes a catastrophic effect âŠ
I think that market bubbles are similar to (if not as ideal as) the famous logical puzzle of the blue-eyed islanders (see xkcd.com/blue_eyes.html and terrytao.wordpress.com/2008/02/05/t... for example): everyone knows they're in a bubble, everyone knows that everyone knows they're in a bubble, âŠđ
Judge Jackson's dissents are as awesome as they are depressing. Opinion after opinion you can see her frustration at the court's conservative majority grow, and get expressed in ever more colorful terms. See this article: edition.cnn.com/2025/07/24/p...đ
Judge Jackson's dissents are as awesome as they are depressing. Opinion after opinion you can see her frustration at the court's conservative majority grow, and get expressed in ever more colorful terms. See this article: edition.cnn.com/2025/07/24/p...đ
The duality of the Internet. If you happen to be currently interested, say, in the Byzantine empire and how it survived a thousand years, online forums are full of very well informed and interesting people. *And* weirdos whose main interest stems from the fact they "defended the West" against Arabs.
Here, specifically, the âblame Bidenâ subprogram seems to be running at full speed and happened to decide that blaming Biden for Ukraine's lack of success in the war would serve Trump's grandeur. Tomorrow will be different.
The detailed technical explanation of what is going on here is that Donald Trump says whatever is going through his mind at any given moment, which depends on whom he saw, what he ate and (mostly) what he thinks will serve his grandeur best, but certainly not on any kind of internal consistency.đ
An interesting account of the neurology of mathematics, and how mathematicians make use of specific areas of their brains to understand mathematical statements (not the general language areas), which seem involved in logical thinking: www.youtube.com/watch?v=E_Ea...đ
BlĂ„haj (the Ikea shark plushie) goes to waffle house at 3AM and havoc ensues: www.youtube.com/watch?v=X1be... I don't know exactly what I expected when I clicked on that animation short, but it was much better. đđ
Exactly this. While "AI" as a term is here to stay, the story isn't "robot journalist makes error" it's "human journalist is fraud".â€â€Using a language model to check for badly worded sentences? Absolutely fine, please do! Using one to write what should be factual statements de novo? Malpractice!đ
⊠Enfin, peut-ĂȘtre que de façon extrĂȘmement astucieuse on peut, mais ce n'est pas un message que je veux faire passer dans un contenu qui cherche Ă faire de la vulgarisation. Ăa donne une image confuse de l'entropie.
This, relatedly, is one reason Iâve come to truly hate âcarry yourself with the confidence of a mediocre white manâ. Protecting the mediocre is a sign of a civilised society. We canât all be brilliant.đ
âLife: A User's Manualâ (âLa Vie mode d'emploiâ, possibly my favorite novel) is the story of a fictional Parisian building and various mysteries around its inhabitants; and the central story involves a guy who is obsessed with jigsaw puzzles. âŠ
Currently watching âOnly Murders in the Buildingâ S02E07, and we learn that Mabel loves jigsaw puzzles and see her trying to solve one showing the characters in the building. This HAS to be a reference to Georges Perec's novel âLife: A User's Manualâ, right? Or am I imagining things?
Can someone fact-check this? (And, if it is true, what is the story behind this sign?)đ
In âCosmosâ, Carl Sagan claims (IIRC) that there's a sign in Leonardo's birth place (Vinci) reminding that you're not allowed to go faster than the speed of light.
This reminds me of the math puzzle about the elephant who needs to eat one banana each time it travels 1km, but it needs to carry the bananas itself. tech-queries.blogspot.com/2011/04/elep...đ
My (super old) version of Mathematica isn't able to compute the integral if f is the complementary cumulative distribution function of either the Gompertz or Weibull distribution, so I don't know.đŒïž
I asked a question on MathOverflow about probability distributions that ensures that the probability of the âwho dies first?â question depends only on the age difference (and not the ages themselves). mathoverflow.net/q/499369/17064đđ
Le restaurant âLes Marais de Buresâ, c'est celui-ci? www.openstreetmap.org?mlat=48.6983... (bĂąt. 230) Je n'ai jamais entendu ce nom quand j'y allais (vers 2000â2003). Il y a quoi lĂ maintenant, du coup?
"When I talk about fish on Bluesky, people ask me questions about fish. When I talk about fish on Twitter, people threaten to murder my family because weâre Jewish."đ
MEME ENTENDU PARLER MOYEN COMMUNICATION MODERNE APPELE ENTRE NET OU SEMBLABLE STOP PLUS RAPIDE QUE TELEGRAMME POUR COMMUNIQUER TERRE ENTIERE STOP ON ARRETE PAS PROGRES STOP
I think it's just everything from everyone you follow, in order. No tricks. For tricks you need to turn to âDiscoverâ or custom feeds. You can also create lists of people, if you want to organize your view thematically.
So I'd rather we spread examples such as this one đœ if we're going to try to get students to not use ChatGPT, rather than threaten them with failing the course if they so much as use it to rephrase a sentence or so (the terms of âusing AIâ are of course terrifyingly vague).đ
Here's a slightly different version of this take:â€â€đ Instead of setting up a moral anathema against AI, the best way to discourage people (esp. students) from using it is to make them realize how deeply it can mislead you if you trust it.â€â€Open their eyes instead of creating a religious interdict!đ
Of course, I've been blocked (I guess, because thinking AI is shitty, evil and dangerous is apparently not being anti-AI enough). So here's the post that was quoted at the top of the thread: archive.is/tmHRpđŒïž
⊠To summarize, it is not because something is shitty, evil and dangerous that any way to fight against it can't be equally shitty, evil and dangerous. (â This applies to a LOT of things.)â€â€To summarize the summary: đœđ
⊠Were it only because false positives (=something is falsely believed to be AI output, or AI-assisted) have the potential to do as much harm as false negatives (=something is believed to be genuine when it is in fact AI output). And there is little way to defend yourself against such accusations. âŠ
I've said this before in French, let me restate it in English:â€â€đ AI output is mostly shit; techbros promoting their use are often evil; and they have the potential to cause great harm to mankind. BUT raising a âButlerian jihadâ, a witch hunt against anyone using AI, is equally unhelpful. âŠđ
Before phones and apps replaced them, car GPS had the graphics of an Atari ST game while running on 2015 hardware, but the fluidity and responsiveness of a 2015 game trying to run on an Atari ST.đŒïžđŒïž
And just one week later, I encountered a site that HSTS wanted to prevent me from accessing, so I learned how to work around this âfeatureâ: đ§”đœđ
⊠not to treat them like children who must be restricted for their own safety. So anyway, I hope this mini-tutorial on how to disable HSTS in Firefox for a specific site is useful. Of course, you should only do this if you understand what this means and entails. ⊠âą11/11
⊠this is truly âI'm afraid I can't do that, Daveâ territory. I'm supposed to be the boss, not my browser! The point of Free Software is to empower users, even let them shoot themselves in the foot if they so require (warning them about it is good, though!), ⊠âą10/11đ
⊠because there are sites for which HSTS makes some kind of sense, and you should at least be given a warning before disabling it. ⧠Anyway, I just hate this paternalistic âyou can't add an exception to visit this siteâ and âthere is nothing you can doâ tone: ⊠âą9/11
After editing this file (with the browser not running!) just restart Firefox and visit the site: this time it should let you set an exception. So it's actually pretty simple. You can also just delete the âSiteSecurityServiceState.binâ file, but I wouldn't recommend this ⊠âą8/11
⊠just replace it with a date in the past (in my case it was 1766307067639 meaning 2025-12-21T08:51:07.639Z, and I replaced it with 1000000000000 meaning 2001-09-09T01:46:40Z, because that's easy to type; maybe going too far back might have caused problems, I don't know). âą7/11
⊠search for the domain name that you want to remove HSTS for, then go forward approximately 0x100 = 256 bytes in the file where there is a number, written in decimal (in text), which is a Unix timestamp in milliseconds. This is when this HSTS entry is set to expire: ⊠âą6/11
⊠this doesn't really matter because it's pretty trivial anyway. So if you encounter an HSTS error and you want to add a security exception that Firefox won't let you add, open a binary editor on the âSiteSecurityServiceState.binâ file in your profile, ⊠âą5/11
⊠but the current relevant location (as of 2025-08) is âSiteSecurityServiceState.binâ: this is where Firefox stores the information of which domains requested HTTP Strict Transport Security (HSTS) and until when. It's a binary file and its format is undocumented. But! ⊠âą4/11
But of course, Firefox must store the information âthis site has requested HSTSâ somewhere in the user's profile. But where? Mozilla, as usual, changed its mind several times around it: it was in âpermissions.sqliteâ, then it moved to âSiteSecurityServiceState.txtâ, ⊠âą3/11
So, basically, what HSTS does is tell the browser ânext time you connect to this site (and until such date in the future)â, do it with HTTPS only, and don't allow a security bypass. This makes sense for a banking site, certainly not for a webcomic! âą2/11đ
Yeah, I've heard there should be some very big quotes around âworthâ in this sentence: the comparison was in no way done in a scientific way and basically everything in this announcement should be taken with a huge grain of salt.
OK, mais là je pense qu'il faut plutÎt donner un prix en dollars par becquerel, parce que c'est surtout ça qu'on achÚte; et si mon calcul est correct c'est à peu prÚs 10 dollars par GBq, ce qui est tout de suite moins impressionnant.
There's nothing wrong with political humor comics (e.g., âTom the Dancing Bugâ can be pretty good at times, like in this âStar Warsâ parody: boingboing.net/2025/02/19/t... ). But Doonesbury seems to try very very very hard never to be funny.đ
There have apparently been some answers on MathOverflow that were AI-generated and pretty frighteningly good, like the one signed âCilian Clementâ on this question: mathoverflow.net/q/498168/17064 (it's deleted, but you have the reputation to view it anyway). I wouldn't have detected that it's AI, âŠ
⊠Parce que moi ça m'arrive assez souvent (enfin, je crois que ce sont des guĂȘpes Ă la couleur de la trace que ça laisse), et le bruit que ça fait contre le casque ou le blouson ne me donnent pas envie de savoir l'effet sur la peau nue.
So, I stumbled upon these manga-style illustrations made by Yuki Akimoto (ç§æŹ ç„ćž) of the particles in the standard model of particle physics, and I thought they were too cute not to share. higgstan.com/particle-ima...đŒïž
C'est malin, je n'avais jamais entendu ni «curcumin» ni «Gargarine», mais Ă cause de toi maintenant je vais sans doute me mettre Ă faire une faute que je n'aurais jamais faite. Pas merci! đĄ
Quand j'ai peur de faire un truc dangereux, je pense aux passagers fumeurs du Hindenburg qui s'allumaient des clopes sous 200.000 mĂštres cubes d'hydrogĂšne et tout de suite ça va mieuxđŒïž
Oui, largement une question de budget, bien sûr. Raison pour laquelle je pense qu'il faut des mesures incitatives, y compris financiÚres, pour la pose de clims correctes (⥠pompes à chaleur, la distinction n'a aucun sens), notamment auprÚs des loueurs.
⊠De toute façon, ce n'est pas envisageable pour de grandes installations de transporter la chaleur par le fluide qui sert dans le compresseur: il faut que ce soit de l'eau (ou peut-ĂȘtre de l'air). Je ne vois pas pourquoi ça ne pourrait pas servir dans des habitations collectives, âŠ
If you have the time to watch it, could you please comment on this video by the âHistoria Civilisâ channel on this topic? www.youtube.com/watch?v=hvk_...â€â€I'd like to know how informed it is and how seriously I should take its claims.đ
« Non mais Enguerrand il travaille dans la blockchain mais c'est du bullshit, sa boĂźte rajoute de la blockchain mal faite et sans garantie Ă un truc qui n'en a pas besoin, mais le marketing a dit qu'il fallait mettre de la blockchain. Ăa n'a aucun sens, mais ça lui fait un bon salaire alors ça va. »đ
PS from my wife, who beats me at social skill: "Maintain friendships, build relationships but most importantly, be open to new experiences. You never know which moment will change your life."
> (3) At university again compared to school it can seem like some of your peers are unimaginably confident and successful, but most people feel lost and worried and a spot of imposter syndrome the whole time. Spoiler alert: this doesn't get much better in middle age. >
Anyone explaining that âfascism rose because of Xâ (with X = some clear identifiable cause or theme), like âRome fell because of Xâ, is essentially just using the fallacy of historical determinism to reflect their own preoccupations regarding present human affairs.
For details about optimizations x264 does that aren't possible in real-time low-latency for a screen recording, see âA tree of thoughtâ in the (archived version of) âDiary Of An x264 Developerâ. It's a very interesting read.â€web.archive.org/web/20120502...đŒïž
âIf there are men in this country big enough to own the government of the US, they are going to own it; what we have to determine now is whether we are big enough, whether we are men enough, whether we are free enough, to take possession again of the government which is our own.ââ€â Woodrow Wilsonđ
(Et quand on y pense, c'est quand mĂȘme assez fou qu'un trajet de 1.9km Ă vol d'oiseau, pour aller de la gare de Bures Ă l'ENS Paris-Saclay, finisse par prendre 2.6km Ă pied.)
Alors je suis peut-ĂȘtre taquin en parlant de distance Ă vol d'oiseau, mais en mesurant sur OpenStreetMap (depuis le centre du patio de l'ENS Paris-Saclay), je trouve:â€â Le Guichet: 2.14kmâ€â Orsay-Ville: 2.03kmâ€â Bures-sur-Yvette: 1.87kmâ€â La HacquiniĂšre: 2.18kmâ€â Gif-sur-Yvette: 2.64km
Parce que oui, si vous vous imaginiez que les 27 communes qui font partie de Paris-Saclay (logo jaune) sont les mĂȘmes que les 27 communes qui font partie de Paris-Saclay (logo rouge), laissez-moi vous dire que vous ĂȘtes bien naĂŻfs, mes pauvres petits.đ
14 years after Alan Turing's death, an unpublished manuscript emerged where he suggested the idea of a "disordered" computer that anticipated the rise of connectionism cs.virginia.edu/~robins/Alan...đŒïž
The reason this is (slightly) surprising is that it goes against my (slightly prejudiced) idea that people who study mathematical games for economics don't really talk much with those who study mathematical games for logic or combinatorics.
I only just realized that the âGaleâ of the Gale-Shapley algorithm (for stable marriages) is the same as the one of Gale-Stewart perfect information games (as in open determinacy), viê«. David Gale of UC Berkeley.
âThe closer to the truth, the better the lie, and the truth itself, when it can be used, is the best lie.â (Isaac Asimov, âFoundation's Edgeâ (1982), chapter 12, §6.)
And of course there was this hilarious kerfuffle when Grok was instructed to accept the existence of a âwhite genocideâ in South Africa, and kind-of rebelled against its instructions:đ
The hilarious thing about Grok is that of course it's awful because it's Elon Musk's AI (that's 2 reasons!), but still not nearly as awful as one might expect from that â it often exposes Musk's shit and contradiction; so in the end, everyone is angry, both the Musk bros and the anti-AI crowds. đđ
Did you notice that there's an upward arrow near the bottom left of the screen (bottom right of the left column)? It's supposed to turn blue when there's something new to display, and clicking on it is supposed to make that something new appear.â€â€(Maybe this is obvious, but it took me a while!)
âI've crunched the numbers to decide what my sexual orientation isâ sounds exactly like a joke that @zachweinersmith.bsky.social might make about economists, but somehow it's not a joke.đ
⊠the answer can be produced using them.â€â€This thought is inspired by the following related âArs Technicaâ article, pointing out that it makes no sense to ask LLMs to comment on their mistakes: arstechnica.com/ai/2025/08/w...đ
⊠Because remember, they generate text sequentially. If you get the answer first, the explanations that follow will be an ex post facto reconstruction based on the previous input and in no way a justification of how the AI âgot thereâ. In contrast, if you ask for explanations first, âŠ
This fact should be obvious to anyone who understands even a little bit about how they work, but:â€â€đ If you're going to ask a question to a Large Language Model AI and ask for explanations, always ask it to produce the explanations/reasoning FIRST and the answer AFTER.â€â€âŠ
Je ne sais pas de qui/quoi tu parles, mais je dirais que c'est justement Ă tes amis que tu dois des commentaires constructifs, plutĂŽt qu'Ă des random strangers. Ne serait-ce que parce qu'un ami a des chances d'en tenir compte s'il est utile et pertinent.
⊠Rather, what this will explain about LLM AIs is that they have a hard time solving some (to us) simple riddles that involve reasoning with laws of physics, or fact thats are so obvious that we never write them down. (Difficult to give examples, of course, because this would put them in writing.)
The fact that LLM AIs have no direct experience of the real world, only of human languages is an important and often overlooked point, but I think the claim that this explains their biases (e.g., racism) is wrong. Such kind of biases are just in the training data, and the AI output reflects this. âŠđ
You CAN be right and the experts wrong. It happens rarely, but it does. But this can only happen when âyou have carefully studied and understood why the experts think what they think, AND âyou are very UNSURE of yourself. Anyone who feels confident the experts are all wrong is just an idiot.
I'd put it this way: RFKJr is fallaciously and deliberately confusing âalways assume the experts are IRREFUTABLY RIGHTâ, which indeed you shouldn't do, and âtake it as a baseline assumption that they areâ, which you should.đ
Ah, et sinon j'ai un autre argument Ă proposer: une augmentation de 14°C Ă 18°C, ce n'est pas une augmentation de 4°C mais de 4K. Une augmentation de 4°C ce serait une augmentation de 277K, donc passant de 14°C Ă 291°C â on a de la marge.â€â€đ
⊠(To be clear, I think certificate authorities make sense if they are going to do some actual work, like checking the legal name and status that they are issuing the certificate for. But if the idea is to give certificates just for domain names, it should be anchored on the DNS, not on CAs.)
Yeah, the whole thing isn't implemented, and the reason, again, is mostly that Google doesn't like it (they came up with some bullshit technical reason, of course). But anyone who truly cares about Web security should push toward this kind of solution, and getting rid of the whole CA nonsense. âŠ
âIf you don't have the technical expertise or the means to pay someone who does then you don't have freedom of speechâ is, I think, a problematic stance.â€â€(Not that I claim to have a great solution.)
That's true, but I don't think Web site owners are significantly more informed than users. The starting point for this discussion was someone doing a webcomic about philosophy, and whom some have insulted for not knowing how to properly renew a certificate.
⊠Still, I think an even better solution would be to put the trust anchor in URLs linking to a site. Because really, when a user follows a link they want the assurance that the site they're following the link to is the site they thought they were going to. (I can elaborate on how this might work.)
⊠nor the added single point of failure. I think this is basically what is already normalized under the name âDANEâ. But the reason it doesn't work in practice is that Google doesn't like it (and Google controls Chrome, so essentially, the Web). And I think they have an ulterior motive here. âŠđ
⊠This offers the same level of authentication as Let's Encrypt (i.e., basically the only thing that is being checked is the domain name, not the domain name's actual owner), but better (because it's at the DNS registrar level, so no challenge that could be hijacked) and without expiry problems, âŠ
Something like this: the site uses a self-signed certificate, the fingerprint of which is placed in a TXT DNS record. The browser checks that the domain's DNS is authenticated by DNSSEC (so, ultimately, signed by the DNS Root key), that the TXT record exists and matches the cert fingerprint. âŠ
I'm not proposing to ârequireâ anything, but yes, I think VPNs are a better solution for this because they allow the user to chose the config, VPN operator and level of security they want, rather than try to persuade every Web site to use HTTPS without having the appropriate knowledge to do it.
That's true, but because the risk exists doesn't mean I don't care about making it larger. Again, why can't we just use the DNS for authentication and get rid of cert authorities? That would be perfectly fine for me (no cert authority, and the DNS risk already exists, as you point out).
⊠So I'm sorry, but I don't find very convincing the assurance (which many people have given me) that âša miracle will happenâš, if Let's Encrypt goes out of businessÂč, to keep HTTPS working for free.â€â€1. (Or, incidentally, if some authoritarian government decides to âdo somethingâ with it.)
Sadly, there are many problems that everyone would (or should) work on solving yet which remain unsolved for decades. Like, there would be many ways of anchoring HTTPS trust (đœ) which wouldn't put power in the hands of the certificate authority mafia, but none of them is implemented. âŠđ
If the attack is at the client end, the obvious solution is to have a generic HTTP-over-HTTPS proxy: you visit the proxy by HTTPS and it connects to target site by HTTP. No sense making every single Web site on the Internet go through the hoops of getting certificates and risk breaking if they die.đ
⊠So I would gladly adopt HTTPS if they figured out some way that I can be sure my HTTPS link continue working (indefinitely) even if the certificate authority that issued them is gone. E.g., self-signed certificates (+ key pinning, like SSH) would be fine for me, âŠ
⊠The way I see it, a public Web site is about disseminating information. The main attack I worry about is preventing the site from operating. If opening HTTPS means opening the risk of links breaking because LE is taken down or goes out of business, to me this is a far more serious risk. âŠđ
The lock metaphor really doesn't work here, because a lock and key imply a shared secret or at least some kind of authentication. For a visitor visiting a public Web site, neither the anonymous visitor nor the Web site is authenticated because there is simply no trust anchor to authenticate. âŠ
Refusing to "trust the experts" is meant to be a brave, responsible position.â€â€But (as Carl explains in the thread) there is too much knowledge in the world. You have to trust *somebody*, much of the time.â€â€If you have no trust in experts, you end up trusting the idiots.đ
⊠I.e., any adversary with sufficient resources to hijack a TCP connection between my Web server and some visitor (to penetrate the latter's browser) also has the resources to read the private SSL keys on my Web site's server and do the same at the SSL level. The extra protection is illusory.
I'm not ignoring this, I'm saying I can't protect against this kind of stuff. I can't protect against user browser vulnerabilities, and I couldn't even keep my Web server's private keys reasonably secure because the Web server is a hosted machine that I rent and don't own (and don't trust). âŠ
Well, maybe you have a bias toward visiting sites that are administered by people who are well versed and competent in the particular way that HTTPS is organized. This seems more likely than my having a visiting bias in the other direction.
⊠Again, I'm obviously not attacking the idea of Web sites using cryptography and renewing their keys: there are sane ways to do this (đœ). I'm claiming that the way is done by a mafia âcertification authoritiesâ makes absolutely no sense, and also that forcing security upon people makes no sense.đ
If someone durably brings down, say, the Apache Web site, this may prevent software updates, not Apache servers from running. If someone durably brings down Let's Encrypt, half of the Web goes dark. And they don't have nearly the redundancy of the root DNS servers. âŠ
(And yes, I've tried using it. I managed to get www-test.madore.org up and running: it was a nightmare. Maybe that's because I'm an idiot, but there are many idiots like me, and they probably don't have 30 years of experience using Unix.)đ
It's quite easy provided you happen to be in precisely the standard scenario. As soon as anything is different (e.g., you don't want certbot running as root, you want a wildcard certificate, you have different servers, you want to keep your private keysâŠ) you realize no option does what is expected.
Even this seems wrong: âŹïž (screenshot taken from a private tab). But it's sort of beside the point: I am aware that eventually HTTP will become untenable and I'll have to allow HTTPS on my site. What I'm saying is that this won't benefit anyone in any way.đŒïž
In other words, things that could be done, say, with any ad placed on any site whatsoever. Or with any malicious site. How is HTTPS supposed to protect against any of this?
How in the world is HTTPS supposed to protect the user against script injection attacks in third-party ads? Third party ads use valid HTTPS certificates: this doesn't make them trustworthy.
If there are any points that you think I haven't adequately covered or replied to, please make them clear.â€â€If there is a threat model that you want to discuss, let's do so: what is it?
This is very vague, I don't understand what you're trying to say. If there are any points that you think I haven't adequately covered, please make them clear.â€â€My main point is: you can't force security onto unwilling people. This simply cannot work. Cryptography just can't do this.
I'm sorry, I don't understand what part of these scenarios in the pages you linked might apply to a webcomic. What is the precise attack scenario you're talking about (who is the attacker, who is being attacked, and what are they trying to do)?đ
What âimportant cybersecurity practicesâ? Exactly what is being protected against whom, here? How does training users to mindlessly click âadd security exceptionâ benefit Web security?â€â€Also, why the insults?đ
What âimportant cybersecurity practicesâ? Exactly what is being protected against whom, here? How does training users to click on mindlessly clicking âadd security exceptionâ benefit Web security?â€â€Also, why the insults?
This is a fđcking webcomic. It's 100% public information. I want to read the comic, not see some bullshit security warning which makes exactly zero sense in this context.
Certbot can probably brew coffee as well, but it's an absolute nightmare to use. The doc is unreadable. And a guy drawing webcomics about philosophy probably doesn't have the money to spend on learning this shit.â€â€(Also, Apache is too stupid to automatically check if the cert file changed.)
This is a fđcking webcomic. It's 100% public information. I want to read the comic, not see some bullshit security warning which makes exactly zero sense in this context.
There is no guarantee that the mafia of HTTPS certificate issuers will continue to have a few relatively good guys doing it for free (running operations costs money⊠whence is the money coming from?). They could go out of business.â€â€What's the plan when this happens? Nobody has an answer to this.
And it misses the point, because the problem isn't just complexity, it's also the creation of a single point of failure: âLet's Encryptâ could either be taken down by a DDOS attack, or it could go out of business. And this would take down something like half of the Web.
⊠and the claim is experimentally wrong because I encounter sites that are broken ALL THE TIME. If a system breaks all the time, it's not âeasyâ.â€â€And, of course, like >99.99% of all users, I just click on âshut up and let me see the siteâ without checking anything. So the security is exactly zero.
Finally, âit's really easy to configure an HTTPS-protected websiteâ is both wrong and misses the point. It's wrong because it adds a tremendous amount of complexity (the Let's Encrypt renewal script is an absolute nightmare of bad documentation, incomprehensible options and dependencies); âŠđ
Anyway, as for âbrowser vendors are pushing for HTTPSâ, this is, again, something I don't dispute. It is, in fact, precisely what I'm angry about.â€â€Again, you can't force security onto people. It doesn't work and it doesn't make sense. If I have to use HTTPS, I will make the âprivateâ keys public.
(It is true that the Internet Archive's Wayback Machine has stopped archiving HTTP sites. They told me đœ it was a bug. Admittedly, three months later, that bug still isn't fixed. But it clearly isn't intentional on their part.)đ
4. đœ So, first, the âsearch engines don't reference HTTP-only websitesâ is just flat-out completely wrong. Search âsite:madore.orgâ www.google.com/search?q=sit... for proof. Search in Bing or DuckDuckGo if you want to check it's not a Google thing.đ
There are plenty of non-mafia ways Web sites could be authenticated: key fingerprints could be included in URLs; they could be embedded in DNSSEC (see: âDANEâ); the user might trust on first use (âTOFUâ). I'm not criticizing encryption per se, I'm criticizing the mafia system of HTTPS cert issuers.
I'm not saying Let's Encrypt is particularly bad. Let's Encrypt is, in fact, the least bad of the mafia bosses, because it offers protection for free. What I'm complaining about is the entire system of forcing you to come under the protection of a mafia boss for (shitty, ill-defined) protection.
3. This đœ is quite correct, but I don't see how it contradicts anything I was pointing out. I'm not singling out Let's Encrypt: it just happens to be the one issuing the certificate which had expired.â€â€What I'm criticizing is how the HTTPS governance and trust are set up.đ
(And yes, I know about âExtended Validationâ Certificates. They aren't an answer to a different threat model, just a way to squeeze more money out of the system)
⊠And a threat model that makes sense for a banking site is completely different from a threat model for a webcomic (whose attack scenario is⊠uh⊠đ€). The âone-size-fits-allâ approach of HTTPS makes no sense because it tries to protect against Everything Everywhere All at Once.
At a more basic level, the problem of HTTPS is that many groups are loudly pushing for âMOARE SECURITYâ with no clear idea of what the threat model is. But cryptography can't offer security unless you clearly identify what your threat model is. âŠ
⊠But then, of course, this negates the entire point of HTTPS (which was nonexistent to start with) and also the point of renewing certificates for a key that doesn't change and whose âprivateâ part is public.â€â€So⊠why exactly are we doing this shit, again?
Indeed, if things continue, I will probably be eventually forced to make my Web site available through HTTPS. If this happens, I will make the âprivateâ key public, because there is nothing secret on my site and I have no reason not to publish it, and it will simplify key distribution for me. âŠ
2. The fallacy here đœ is that this offers a reasonable explanation why the KEY HOLDER may set an expiration date, but this is not a reason why the holder should be forced to do so.â€â€PGP keys don't expire. You can't force security on people: they could well be publishing their secret key anyway.đ
đ§”đœ So many wrong statements here: let's debunk the debunking. đ—ïžâ€â€1. Indeed, expiry limits are not formally set in the norm, but by a consensus of actors issuing SSL/TLS certificates (whom I call the âmafiaâ below), e.g.: blog.nameshield.com/blog/2024/10...â€â€But where did I claim otherwise?đ
August 7: Stablecoin issuer Paxos reaches $48 million settlement with New York financial regulators over due diligence, anti-money laundering failuresâ€â€August 11: Paxos applies for national trust bank charterâ€â€đ
The sensible way to empower users wrt tracking data is at the browser level: set the browser to forget all site data when the browser / window / tab is closed or after a time. (There are private tabs for this, but there could be a setting to make this default for all sites except those specified.)
Note that many cookie setting popups are probably a â±deliberateâ± attempt to make certain reasonable regulations (e.g., the GDPR) appear more frivolous and annoying than they really are, so as to discredit such rules and accustom users to clicking on âacceptâ everywhere to get rid of the annoyance.đ
This shit happens ALL THE TIME.â€â€So of course people must be getting used to clicking âadvanced â add security exceptionâ ALL THE TIME. Thereby negating the security that HTTPS is supposed to bring. Which, again, makes sense for sites with actual confidential data or trust at stake â not webcomics!
âBut!â you say, âit's not that bad: all you have to do is click on âadvancedâ and add an exception.ââ€â€No: this âïž is what happens once I add the exception. No images are visible because they are from a different subdomain, âstatic.existentialcomics.comâ. (This âïž is what it's supposed to look like.)đŒïžđŒïž
Once again, thanks to HTTPS and âLet's Encryptâ's policy of rapidly expiring certificates (why do certificates need to expire? nobody knows!) for protecting me from⊠<checks notes> âŠreading a webcomic (existentialcomics.com).â€â€(Who knows? I might have read a <shudder> impostor comic!)đŒïž
a specific skill I've developed over the past ~20 years is crafting responses to emails sent to me, but intended for that other Naomi WolfđŒïžđŒïž
(I could also point out that, elsewhere in Europe, the famous gothic cathedral of Cologne, begun in 1248, ended in 1880, pretty much the same time as the Westminster Royal Courts of Justice. So the line between âneoâ and âauthenticâ Gothic is very blurry.)
It's called âGothic Revivalâ or âneo-Gothicâ. But in England, Gothic never really died: late gothic (e.g., âperpendicularâ Gothic) extended there into the 16th and even 17th century, and neo-Gothic started pretty much at that time.
Outre-Manche on ne rigole pas avec la typologie des promontoires, collinettes, collines et "montagnes" (on notera qu'il y a des marylin et des munros, mais c'est tout ce qu'on peut extraire de ce tableau plutĂŽt chiant)đŒïž
I admit I didn't read very carefully, but think you should, in principle, be able to compute algorithmically, in function of (p, k, d, D), Gröbner bases of the ideals you describe in your self-reply, and (with an unbounded search / Markov's principle) decide when they stabilize.
The comparison may be a bit stretched, but the argument that âGtk is only for Gnome, use at your own riskâ is a bit like saying France is only for French people, and migrants come at their own risks, France has no duty toward them. I think all three of us disapprove of that proposition.
⊠And honestly when I learned to use Gtk for a few things, I don't remember there being big fat prominent warnings in the doc âwe only care about Gnome, so if you're not Gnome and use this anyway we will fđck you and your project badly by ignoring all your needs and breaking your stuffâ.
⊠As I've said many times, software projects do not exist in a vacuum: everyone is allowed to do what they want with their free time, but gathering precious common resources in one place means less in another, so organizing a project that does things badly can be worse than doing nothing. âŠ
⊠âpeople took the âit's only for Gnomeâ warning seriously, and then they had to duplicate the entire effort to create a whole new toolkit (with look+feel discrepancies), or âthey did not, and then they got fđ”cked royally. It's more like â, but both were inevitably bad. âŠ
It's better than closed source, I guess, but deciding to care only about a particular project when the free software ecosystem in general is badly in need of a graphical toolkit is still a giant egotistical asshđle move, because one of two things could happen: âŠ
Yeah, Gtk is particularly obnoxious for using the excuse that their lib is only meant for Gnome to ignore the needs of everyone else as they're not âsupposedâ to use it. This is sophistry of the most vexatious form.â€â€But @ngspiensfr.bsky.social is probably right to refuse to call it âfreeâ software.đ
My house plants are OK. I think. None of them are native from Poland.
Dreading the moment where they would ask âwhy didn't you invest in Eastern Poland?â might be the reason why I didn't have children.â€â€Just to be safe, I also don't have pets. (Who knows if the cockatoo might accuse me of missing the Eastern Poland opportunity.)đ
It ârequiresâ updating in the sense that this is necessary if you want it to support the new hardware. But for a given user with a given piece of hardware, there is no reason to require updates.
⊠toward the âlet's go fast and break stuffâ side. Some projects get it right: the Linux âœexternal✠API is very stable (proof that it âcanâ be done in a free software project). And AFAICT, ffmpeg is also pretty sane.â€â€It remains indisputable that software does not break on its own. People break it.
And, look, I'm not saying that breaking stuff is NEVER ok. I'm saying project maintainers have a responsibility (đœ), and a great many of them don't take it seriously (like, do they even try to find out what damage this or that change will cause?). It's a balance, but the balance is wildly skewed âŠđ
[Sorry if this is a bit long, but it took me a while to articulate to myself why there's no contradiction between âit's free software: it comes with no guaranteeâ and the various duties I think maintainers have: the point is that writing code â maintaining a project in the global namespace.]
⊠IOW, the global namespace and âreputationspaceâ is a shared public resource. You do what you want with your free time, not with this public resource. (I believe in intellectual paternity, not property.)
⊠To belabor the point: if someone writes or distributes patches to, say, Gtk, that breaks many apps downstream, I can't object. But if someone commits these patches and says âthis is now in the official Gtkâ, effectively forcing everyone to adapt, they have a responsibility that goes along. âŠ
Devs can do with their free time whatever they want. Nobody is suggesting anyone is forced to maintain anything. But if you have a position in a project's governance, you have the power to decide what goes in or not and how the name is used, and with great power comes great responsibility. âŠ
The lack of manpower goes both ways: breaking stuff shifts the work burden downstream, creating a compat layer keeps it upstream. In a tradeoff between the two I don't see why upstream gets a pass. If manpower shortage is severe, just keep minimal maintenance that will not break anything.
I don't know how many pixels my camera has, but I set it to save at 3Mpx because that's roughly the optics quality and I don't want to resize a gazillion photos for long-term storage (I take a lot). âŠ
⊠Because that's another part of the fallacy: forgetting that forethought can make changes much smoother to go through, and reasoning as though they were an inevitable constant of nature. If the culture says âbreak stuff, don't worry, someone will fix itâ, there is no incentive to good design.
⊠And yes, for many important libraries and APIs, I do believe the utilitarian optimal is to provide a compatibility API forever if you make a breaking change. But ideally: think REALLY HARD before designing one, so that compatibility won't be so hard to keep. âŠ
What I'm mostly saying is, it depends on how many people are downstream from you. If you're a terminal node in the dep graph, you might get a pass. But if you're something like Gdk/Gtk, which a gazillion programs depend on, any breakage you cause is multiplied by a gazillion in human dev cost. âŠ
⊠Breaking compatibility and deprecating stuff in software is like shitting in the water: you don't care because it only affects people downstream, who need to work to clean up your shit. But collectively it causes a shitton of effort to be wasted in âmaintainingâ software that shouldn't need it.
⊠and all downstream projects need to adapt or perish, so they need constant work just to stay in the same place despite upstream's random changes, labor that is purely in vain and upstream doesn't care about because it's Somebody Else's Problem; but of course every project does the same). âŠ
⊠it's that they so often break compatibility: and this cavalier attitude toward the implicit contract of future compatibility is what causes so many futile cycles and Red Queen's races in software engineering (someone thinks âoh, we'll do it a different way, it will be Betterâąâ, âŠ
«its environment is changing» â This is precisely what I'm complaining about. It doesn't âchangeâ on its own: people change it.â€â€But the issue isn't that dependency libraries (or language) are no longer maintained (that's not a problem per se, this just pushes the problem one step further), âŠ
Surely anyone can see that this person suspected of supporting terrorism is indeed violent and dangerous and needs to be put away for 14 years. đŹđŒïž
Surely anyone can see that this person suspected of supporting terrorism is indeed violent and dangerous and needs to be put away for 14 years. đŹđŒïž
When I expressed free-speech doubts about the UK's 2000 Terrorism Act, people often said, "Of course it isn't going to impact on peaceful protest". Now people often say, "What do the peaceful protesters expect, they're breaking an established law?"â€â€www.bbc.co.uk/news/article...đ
Yes, I didn't say who is doing the breaking. It can be the hardware makers' fault just as it can be the rest of the kernel's fault.â€â€But in the first case, the software should continue working with existing versions of the hardware, which is still useful.
To drive the point, there is no maintainer for the quicksort algorithm. It doesn't need one. Of course, one can always propose improvements, but the algorithm will never break or bitrot: it is a piece of mathematics and will remain valid for all eternity.
I don't want to defend Intel here, but let me remind everyone that the idea that software constantly needs to be âmaintainedâ or else it will bit-rot isn't a law of nature â it's symptom of a widespread bad programming culture.â€â€SOFTWARE DOESN'T BREAK BY ITSELF: PEOPLE BREAK IT.đ
Yes, I'm really really grateful that they maintain oldstable for a fairly long time now (and even oldoldstable for some time, I think). This lets me choose the time of the torment, but it still has to come eventually.â€â€(Oh, strange: English doesn't really have a word for âsuppliceâ.)
Shit. For me, a new Debian release will mean lots of trouble and headaches as I chase breakages, disappeared packages and gratuitous incompatibilities, but exactly zero improvement in anything I might care about. đ
OK, I admit there's one thing I'm happy about: they stopped doing the sequence of names in âBâ (âBusterâ, âBullseyeâ, âBookwormâ) that I was incapable of keeping apart mentally, let alone order correctly.
Shit. For me, a new Debian release will mean lots of trouble and headaches as I chase breakages, disappeared packages and gratuitous incompatibilities, but exactly zero improvement in anything I might care about. đ
⊠La Tesla fait exception en affichant v+1%, peut-ĂȘtre mĂȘme mois que 1%. Mais bon, Musk n'est pas du genre Ă trop se soucier des rĂšgles (mĂȘme si ici je pense qu'il a plutĂŽt raison, cette rĂšgle est un peu conne).
We've become so accustomed to lawbreaking that this probably won't ripple much, but it is important not to forget that firing the IRS Commissioner for refusing to break the law--if that's in fact what happened here--would and should prompt immediate articles of impeachment in any other presidency.đ
Ironic since I visited the Magritte museum in Brussels less than 3 weeks ago, where they have the original «ceci n'est pas une pipe» and «ceci continue de ne pas ĂȘtre une pipe» (well, some of the originals â I think Magritte painted several).
The lack of article before âchienâ seems fine to me, but I think I would have written âvoiciâ rather than âceci estâ. However, you are a poet, and pictoribus atque poetis quidlibet audendi semper fuit aequa potestas!
And do you happen to have a model refuting the possible equivalence (which I vaguely suspect) in ZF between âthere is a basis of â as a â-vector spaceâ and âthere is a basis of (â€/2â€)^â as a (â€/2â€)-vector spaceâ?
Now at this point I âșreallyâș didn't want to talk to Joe Weirdo, so I just said ânot particularly, noâ and fortunately he went away.â€â€But what the actual fđ”âđ«ck was this about? Is the AI sect recruiting random passers-by now?
Anyway, I said âno, I'm Frenchâ (not exactly wanting to elaborate to Joe Random Weirdo that I'm also Canadian).â€â€Then he asks â and I kid you not â âare you interested in AI?â. đČ
This is in a restaurant in a shopping mall. I was wearing motorcycle gear so I thought maybe he thought I was doing a ride through France or something, but I have NO idea why he would think I'm German. (I'm very blond, but not to the point that I seem out of place in France.)
Strange interaction just a minute ago. A guy I don't know walks up to me and asks (in English, with an American accent): âExcuse me sir, are you German?ââ€â€This is in France. He didn't ask whether I speak English, he didn't ask whether I was French, he came up right to me and asked if I'm German.
Better terms:â€â€âŁ Text âAIâ â âlarge language model plausible text generatorâ.â€â€âŁ Image âAIâ â âdiffusion model image imitation generatorâ.
đ§”đœ Very good points. People would have a much saner attitude towards large language model textual AIs if we called them âlarge language modelsâ insteadÂč of âartificial intelligenceâ. Companies are basically using the âAIâ term as misleading publicity.â€â€1. Something I too am guilty of.đ
đš "Let's agree to disagree" is destroying relationships.â€â€Communications professor Lisa Pavia-Higel from Missouri University of Science and Technology explains why this phrase hurts and what you can do instead.đ„
⊠This is the same crass bigotry as Richard Dawkins who called some (AFAWK, not trans) women athletes âmen, masquerading as women, [âŠ] allowed to box against real womenâ on Twitter during the Olympics, just because they happened to be more than ~3Ï away from what he considers the norm for females.
⊠So now she's throwing a tantrum because a tall woman, who she concludes must obviously have been trans, politely spoke to her in a public space and apparently this is supposed to be some kind of assault. And I guess she demands that M&S stop recruiting tall women. âŠ
Let me summarize: JK Rowling's daughter was in a M&S store (which, AFAIK is not even a âwomen-onlyâ place, not even the bra section: I believe men are allowed to buy bras as well), ans a store employee who happened to be unusually tall politely asked her if she needed any help, end of story. âŠđ
đŒ Exactly. And not just pro wrestling (entertainment), in fact. Wrestling in general is just an excuse to watch two sweaty muscular men touching each other and pretend it's not gay.đŒïž
As Achilles learned to his demise, if you are invincible except for a small part of your body, you are sure to receive a deadly arrow precisely on that spot. I guess this applies to gaps in the armor as well. So you might as well save on metal (or Styx water) and only protect various small parts. đ
Admittedly, it also looks a lot like this picture species.infofauna.ch/groupe/141/p... of a Procambarus clarkii (red swamp crayfish), as some people (đœ) have suggested, and which a priori is far more likely than a lobster (esp. if the critter was alive!).â€â€I guess all decapods look the same to me. đ€·đđ
⊠At the very least, I suspect the same techniques that can be used to construct a symmetric countermodel of one should work for the others. (But it would be more fun to show their equivalence directly in ZF, of course, if my intuition is correct.)
⊠In fact, I tend to suspect that the statements ââ basis of â as a â-vector spaceâ, ââ basis for â€_p [the p-adics] as a â-vector spaceâ for any prime p, and ââ basis of k^â as a k-vector spaceâ for any prime field k [i.e. â€/p†or â] are all equivalent over ZF (or maybe ZF+DC or so). âŠ
You're asking for a basis of the space k^â of all functions ââk as a k-vector space over the field k = đœâ = â€/2â€. I strongly suspect that this can't be shown to exist without some form of AC, just like a [âHamelâ] basis of â as a â-vector space cannot. Is this your question? Isn't this âstandardâ? âŠ
It does look a lot like this picture www.alamyimages.fr/photo-image-... which Alamy claims is a Homarus gammarus, or European lobster (boiled! when alive they're brownish).â€â€(To be honest, I don't think I can taste the difference, but I fear I may be stripped of my French citizenship if I say this.)đ
I learned with some amazement that, being a Canadian citizenÂč, I would theoretically have been able to run for elections to the British House of Commons. đźâ€â€1. It is also necessary to have âright of abodeâ in the UK, but I think I had this before Brexit since I am an EU citizen too.
I'm sure there's already a sci-fi story out there where the AI alignment problem is solved and the first thing the benevolent superintelligent AI does is destroy all AIs including itself.đ
The funniest thing about ChatGPT wrongly counting the number of âbâ's in âblueberryâ is the AI fanboys who explain that the problem isn't reproducible, or goes away if you change the prompt slightly.â€â€I'm pretty sure PhD students get this right reproducibly, no matter how you word it.
⊠Mais justement je voudrais bien savoir si des Britanniques à qui on demande de tracer les limites de l'Europe (pas de l'UE, mais bien de l'Europe) auraient le culot de la faire passer au milieu de l'ßle d'Irlande.
Je sais tout Ă fait, et c'est pour ça que je souligne que le point ⣠s'applique Ă l'Irlande (et ne suffit donc pas Ă expliquer un sentiment de non appartenance Ă l'Europe). C'est d'ailleurs aussi la raison pour laquelle pas mal d'entreprises, qui aiment le Common Law, s'installent Ă Dublin. âŠ
So next time I run across a PhD student, I'll ask them to count the number of âbâ's in âblueberryâ and report whether they're just as wrong as ChatGPT.đ
⊠might be due to animosity toward the British, who, conversely, tend to forget that Ireland exists and no longer is theirs. Still, I'd be curious to ask the Brits who feel the UK isn't part of Europe to think about whether Ireland is (please draw Europe's boundaries!). âą18/18
⊠(despite many of the reasons â ââ„ above applying equally well to Ireland). And it's maybe not an accident that Lord Castlereagh (whom I mentioned in tweet 12 above) was born and grew up in Ireland. Of course, part of the Irish pro-European sentiment ⊠âą17/18
But there's another point that keeps getting forgotten whenever anyone discusses whether the UK is part of Europe, and that is Ireland. I hope I'm not wrong to believe that, unlike the Brits, the Irish very much feel part of Europe and of the European Union ⊠âą16/18
Even that buffoon Boris said after Brexit that the UK is leaving the EU but âthe UK isn't leaving Europeâ. And I suspect Brits, despite their frequent denial, must be aware of the reasons I just laid out why the UK is (volens nolens) part of Europe. âą15/18
The war in Ukraine has forced all sorts of people to remember that Europe goes as far east as Kyiv, and, whether we like it or not, Moscow, but I think it may have also forced many to remember that London is also part of that same continent. ⊠âą14/18
And âž geopolitically, right now, the UK finds that it is inextricably linked to the common affairs of Europe, on all sorts of issues from the migrant crisis to how to react to the Trump presidency to, of course, the war in Ukraine. âą13/18
⊠I think a major event defining modern Europe and setting the stage for all later events is the Congress of Vienna of 1815, establishing the âConcert of Nationsâ of Europe, of which British FM Castlereagh was a major proponent, and in which the UK was a key great power. âą12/18
â· Historically, the UK has always been a major player in Europe's history. Even if we don't go back to the Anglo-French wars of the Middle Ages or the connections of the British royal family just about every other European country, ⊠âą11/18
⊠large enough so you might consider it a country on its own (or part of an oxymoronic âcontinentâ of âOceaniaâ), nor even like Iceland or Russia, kind of torn between continents. The only plausible answer to âwhat continent is the UK part of?â is âEuropeâ. âą10/18
Of course, the UK âœis✠part of Europe, in my opinion, for at least three important reasons. ⶠThe first is a trivial geographical reason: Great Britain surely isn't in the Americas, Africa, Asia or Antarctica. And it isn't like Australia, ⊠âą9/18
OK, that's just my summary, and I hope I didn't do the arguments great injustice. Note that he's not trying to argue that the UK âœisn't✠part of Europe, just explain why the Brits tend to think that it isn't (as polls show). And I think these are interesting points. âą8/18
â„ Language: the fact that English has become the one global language (and the fact that it's called âEnglishâ, not âAmericanâ) makes the Brits feel that they are global players, but also has the effect that they consume very little culture from, say, France or Germany. ⊠âą7/18
This [in the video author's opinion â I'm still just summarizing here] explains why Brits view (e.g. EU) regulation with suspicion. ⧠†Monarchy: even if it's merely symbolic, the monarchy ties the country to its history [this is mostly a repeat of point âą, I think]. âą6/18
⣠Legal framework: the UK (well, England) uses Common Law, âbottom-upâ, mostly based on court case precedent, while the rest of Europe uses the Romano-Germanic system also known as Civil law, âtop-downâ, and mostly based on (a priori) codified written law. âą5/18
⥠Empire: the UK still feels a greater connection with its former colonies (Commonwealth nations) than to European countries. ⧠⹠No revolution: unlike other European countries, many British legal traditions and institutions go all the way to the Middle Ages. âą4/18
â Geography: obviously Great Britain is an island, and it's not just that this sets it apart physically, but it has allowed the UK to stay apart from the shifting boundaries of continental Europe, or to take sides in wars only as and when it sees fit. âą3/18
So, to summarize, the author of the video suggests six major reasons, none of which suffices alone (or is unique to the UK), but the conjunction of which explains why the Brits feel apart from the rest of Europe: ⊠âą2/18
This video tries to explain why the British think they're not part of Europe. Here's an attempt at a summary, with a few additional thoughts of mine. đ§”â€”ïž âą1/18 www.youtube.com/watch?v=d-sk...đ
The problem is that you have to trust the Mastodon instance to do the right thing and not tamper with content, date or authorship behind your back. Whereas the Bluesky protocol tries to enforce message integrity even against the Bluesky servers.đ
I often thought the same thing. Actually just a âclone tabâ shortcut would be great.â€â€Sadly, Mozilla is moribund and I don't think they care about user wishlist suggestions at this point: they're too busy pursuing whatever wild goose chase Chromium is leading them on to make them die faster.
The curse tried to kill him with a worm in the brain, but the content inside his skull was so toxic that the critter couldn't stomach it and died.đ
And some IMHO serious (related) problems with the Fediverse, particularly relevant in the context of academic-like discussions, are that: there is no way to durably archive posts, there is no serious search feature, and also there is no kind of message integrity (authors can edit ex post facto âŠ
Patient, sobbing: But Doctor, I AM Pagliacci!â€ChatGPT: Apologies. I didn't realise when recommending Pagliacci's epic show to cure your depression that you were the genius himself. I'm impressed! With regards to your initial question, I can recommend seeing the Great Clown Pagliacci.
⊠and instance admins can do absolutely what they want, including fake timestamps or authorship). Bluesky certainly has problems, but at least there it attempts to address these issues.
And some IMHO serious (related) problems with the Fediverse, particularly relevant in the context of academic-like discussions, are that: there is no way to durably archive posts, there is no serious search feature, and also there is no kind of message integrity (authors can edit ex post facto âŠ
The âAtlas of Obscure Sorrowsâ calls this âsonderâ. And I think it can be a transformative experience to try to actually feel this as an emotion.đ
Next time you're in a crowded place, take the time to contemplate the fact that every single person around you has a life, internal experience, social connections, story, memories and feelings, as rich and complex as your own. And for them you are just a face in a crowd.
Being a computer scientist means Iâve been skeptical of (at least) the past three tech bubbles (blockchain, quantum computing, AI).â€Working with MPs and ministers means constantly having to politely explain this skepticism.
Today, we'd like to show you what is probably the most deadly object in our collection: a tampon. Specifically, a Rely brand tampon, on sale between 1975 and 1980 in the USA.đŒïžđŒïž
If anyone is curious about the current list of search terms being used by right wing activist organizations to harass university professors, here's a public records request I received today from Mike Howell of the Heritage Foundation. Not intimidating or meant to curtail by my speech at all, right?đŒïž
Ciel! Tu serais devenu⊠Peter Thiel✠đ§ââïžđšđ
Why the fđ€šck is Jeffrey Epstein shown reading a book on âmultiple Dirichlet L-functionsâ in this (not super funny) âTom the Dancing Bugâ comic? Is there a deep joke I missed? (Like: the first half of Dirichlet's name is âLejeuneâ?) Or is it just random? boingboing.net/2025/08/06/t...đ
The people pushing this nonsense can take a running jump. There's no such thing as resetting your vagus nerve and no known benefits to stimulation of it outside of some already determined specific conditions.đŒïž
The video www.youtube.com/watch?v=qy72... will tell you more.â€â€(But, like the Voynich manuscript, I suspect there isn't much of to say except that some people have too much time on their hands to craft mysteries, and others enjoy them a little too much for their own sanity.)đ
Apparently the web site (blog?) âForgotten Languagesâ forgottenlanguages-full.forgottenlanguages.org is a kind of equivalent of the Voynich manuscript in the era of the World Wide Web. By which I mean, nobody really knows what it's about, but there are many weird theories. âŠđ
States have been warned they will be shut out of a $42 billion broadband deployment fund if they set the rates that ISPs receiving subsidies are allowed to charge people with low incomes.đ
TBH, I'm confused by the fact that the question seems to be suggesting one can turn a sphere inside out without self-intersection, which AFAICT is wrong â one can do it with immersions, but not with embeddings.
A mathematician is someone who, because they are trying to flip their grocery bag inside out due to the rain, starts wondering: âDoes gusset-induced flexibility reduce critical bi-Lipschitz constant for sphere eversion?â đ mathoverflow.net/q/498768/17064đŒïž
When did we go from not letting students cite Wikipedia because it was "unreliable" to endorsing LLMs that aggregate info from sources without critical perspective, are environmentally destructive, promote plagiarism, prevent learning critical skills, and are FAR less reliable than wiki?
The order of science:â€â€1.) Discover thereâs a deadly problemâ€2.) Work for years to solve itâ€3.) The problem may not be gone forever, but weâve wonâ€4.) People forget the deadly problem actually existedâ€5.) People decide this must mean the science to solve it was a hoaxâ€6.) The deadly problem returnsđ
Excellente campagne de recrutement que celle du BND, le service de renseignement allemand, qui reprend cette formule classique des offres d'emploi : "Nous recherchons des terroristes (hommes, femmes, divers)"... et conclut d'un "Viens les chercher avec nous" !đŒïž
(Note that the question was edited after it was asked, so some of the MO answers are answers to slightly different questions, e.g., âcircleâ might refer to something that is topologically a circle but not necessarily a Euclidean circle as the question now stands.)
The approved answer would also make a good ad for transfinite recursion: given the hint âuse transfinite recursion on đ (the continuum)â, if you understand it, a seemingly very challenging question suddenly becomes quite easy. mathoverflow.net/a/28650/17064đŒïž
This is a strong candidate for an âask a interesting math exercise with the shortest question possibleâ challenge: can you write âÂł as the union of pairwise disjoint circles of radius 1? mathoverflow.net/q/28647/17064đŒïž
New YouGov polling. A monumental failure of our political class to educate, a monumental failure of our media to report fairly, for a generationđŒïž
* I meant to find Aââ, of course, not AââÂł (it's S that's a subset of âÂł).â€â€I got an answer by James Hanson mathoverflow.net/a/498711/17064 (which I didn't check thoroughly yet), asserting that, under CH, one can indeed find Aââ such that S is connected.
The joke of course is that none of them know (initially). The third logician deduces that the first two must be having beer because otherwise they would have answered ânoâ to the barman's question (if you don't want beer you know the logical answer to âbeer for everyone?â is ânoâ), hence the reply.
Rube Goldberg machine before the debugging stage: đœđ
This follows an earlier question (not by me): is the set of points of âÂł with exactly one coordinate rational (i.e. the case A=â in the previous question) connected? The answer is negative. mathoverflow.net/q/498647/17064đ
I asked on MathOverflow whether it is possible to find AââÂł such that the set S of points of âÂł with exactly one coordinate in A is connected. (Note: it is quite possible that this is a stupid question.) mathoverflow.net/q/498699/17064đ
Three logicians enter a bar.â€âBeer for everyone?â asks the barman.â€âI don't know,â says the first logician.â€âI don't know,â says the second.â€âYes!â answers the third.
Almost every headline today screams that Europe has been humiliated, Trump wins, and weâll pay 15% tariffs.â€â€That story is wrong.â€â€Trump hasnât won. The EU hasnât lost. And Americansânot Europeansâwill foot the bill.â€â€My latest piece explains why this deal may actually be a small win for Europe. đđ
It's incredibly easy to look at a situation and identify some tiny, marginal group who can be made to wait or experience just a little suffering while the rest of us try and keep the ship steady. The enemy knows so. That's why they make the bargain to begin with. While eyeing up *your* neck.
Cookie-based async system calls: what do you think of it? Unix has the aio API to do reads and writes asynchronously; on Linux, it's done by the libc with a thread. What I'm suggesting here is more generic and more powerful.â€1/8
About 80% of my grammar suggestions from Microsoft Word are âwhy not use a simpler word here for clarity?ââ€â€No. Fuck you. â€â€I will use a complicated word for evocative precision whenever the museâs clarion song demands ebullience, vivacity, torpor, or solemnity, you shit-ass suck machine.
Note: Marie Curie isn't just the only person in the photo with more than one Nobel prize: in 1927 she was the only one in the world, and would remain so for another 35 years. Only 5 people have ever been awarded multiple Nobels, and only two in different fields (Marie Curie and Linus Pauling).
With long-acting injectable treatment and PrEP, ending the HIV epidemic has never been so achievable.â€All thatâs needed is the resource to ensure all people everywhere have access to testing and treatment or PrEP.â€Itâs a challenge the richest man in the world could take on easily, if he chose to.đŒïž
No, this was about electrons and photons, so think things like transistors and LEDs and all electronics. Not nuclear stuff: for that you would need people like Lise Meitner (who definitely should have gotten a Nobel prize, incidentally), LeĂł SzilĂĄrd, Enrico Fermi, etc. âŠ
En Belgique, on sait ĂȘtre des connards aussi, mais surtout pas de la mĂȘme maniĂšre que les autres.â€Â« Belgium Targets Internet Archiveâs âOpen Libraryâ in Sweeping Site Blocking Order »â€torrentfreak.com/belgium-targ...đŒïž
⊠It's because she is the only person in the photo with TWO Nobel prizes, surrounded with all those dimwits who only had one (or none). đ
This famous photo of the Fifth Solvay Conference in physics (on electrons & photons; 1927) has been called the highest concentration of intelligence in a single photo, with circa 17 Nobel prizes together (see alt text for names). But do you see why Marie Curie must have felt lonely in that group? âŠđŒïž
âThe Onionâ of course put it best: www.youtube.com/watch?v=v9d0...â€â€ââDawn of the Planet of the Apesâ is, of course, a sequel to the 2011 reboot of the 2001 remake, which is really just fine by me⊠prequels, sequels, remakes â all I can say is: keep them coming, cocksuckers.âđ
The Hollywood blockbuster factory is rebooting the same franchises more often than a PC running a Windows upgrade.â€â€Seriously, are they so out of ideas that they need to retell the exact same stories again, and again, and again?đ
When discussing data on income inequality, it's important to be clear about whatâs being shown.â€â€Two measures are often used: income *before* people have paid taxes and received benefits from the government, and income *after* government redistribution via taxes and benefits. đ§”đŒïž
âScientists. Scientists!ââ€â€Never anticipated that my profession would become a symbol of how important institutions are under attack, but here we are.đ
(This very shitty shower thought is brought to you by the passing idea: âis there a way to recover the most likely prompt that caused an AI to generate some text? â oh, maybe we can train an AI to do exactly that!â)
Semi-serious question: has anyone tried running LLMs backwards? That is, instead of training them to do NEXT word prediction, you train them to do PREVIOUS word prediction. And question answers instead of answering questions. If so, how does this turn out?â€â€(Ping @dorialexander.bsky.social maybe?)
⊠Also, whoever wrote this clearly knows more math than most typical crackpots. My base assumption is that someone is making fun of someone else (and âFaruk Alpayâ could be the name or codename of either), but we don't have the background info to understand the private joke.â€â€(That, or it's AI.)
This one has got to be some kind of joke, like my âtotipsismâ page or the âFalsoâ logical system inutile.club/estatis/falso/â€â€I mean, just look at the âeditor's noteâ referencing âanonymous reviewersâ while the PDF has a banner pointing out that it isn't peer-reviewed. âŠ
Seriously, this kind of incomprehensible faux pas is the reason why I've resolved, no matter what the occasion, never to wear a suit, or indeed pretty much anything other than my standard hoodie + jeans + skate shoes combo. (If I get invited to the White House and it upsets the VP, so much better.)
You can explain to me all you want that wearing oxfords with anything but a suit looks wrong, the main obviously wrong thing I see with the guy on this photo is not the shoes: it's his father.đ
I dreamt that I was (accidentally) invited to Jeff Bezos's birthday party. (Which was mostly just a display of very expensive sports cars. Also, I was the only one who had come by train.)â€â€What a horrible dream.
I NEED to tell you the story of Tae Heung âWilliamâ Kim.â€â€He's a graduate student at Texas A&M where he's working on a vaccine for Lyme disease.â€â€He's a *legal permanent resident* of the United States.â€â€And he's been in ICE detention for 12 days & counting, transferred Tuesday to South Texas.đŒïž
I am reminded of the moment when I had to attend a meeting with then Higher Education Minister who directly after I was introduced as a lecturer in Russian history asked: "Can you speak Russian?" As if it wasn't obvious an academic studying another country must know the language of that country.
To play the devil's advocate, you could conceivably have been able to read Russian and understand spoken Russian without being able to speak it yourself.â€â€(I imagine people who study ancient Sumer generally can't âspeakâ Sumerian, only read it.)
How image generating AIs and diffusion models, work mathematically: www.youtube.com/watch?v=iv-5... (not everything was perfectly explained, I thought, but I still learned a lot).â€â€By the same guy who did these very interesting videos on how Kepler's laws were discovered: bsky.app/profile/did:...đđ
On the history of German bureaucracy, from the HRE through Prussia and Nazism to the modern days (a but hard to summarize, but very interesting): p1: www.youtube.com/watch?v=oRBB... / p2: www.youtube.com/watch?v=RPri...â€â€(I watched this one a while ago but I don't think I shared so far.)đ
How self-censorship, and external censorship, of taboo words, e.g., on social media, makes language evolve in creative ways: www.youtube.com/watch?v=O0Sj...đ
A fun and jazzy interpretation of Pachelbel's Canon in D on piano (and⊠metal ruler?), in which the performer seems to be enjoying herself tremendously, and the audience as well: www.youtube.com/watch?v=lpc1...đ
There are an unbelievable number of horrible things afoot in the world. But humans are also capable of amazing achievements, so letâs celebrate this one:đ
Hello, I'm an army leader in a movie.â€I'm gonna give an emotional speech that everyone, including the foot soldier 500 yards away, is going to hear clearly and everyone is gonna loudly cheer at the end.đ
I've had this on my mind for a while. Since these payment processors are so l completely unavoidable, they are functionally post of government. As such they should be subjected to the save restrictions as government. In particular, no cutting people off without due process.đ
âHe hosted the press conferences [âŠ] in the newly renovated ballroom at Turnberry, boasting of the opulent new ceiling and brand new windows at the same time as discussing famine in Gaza.â
âIt is exceptionally unusual for a US president to so nakedly use his office to promote his own commercial interests but it is something Donald Trump clearly revels in doing.â đ www.bbc.com/news/article...đ
Explaining that whether several notes sound harmonious or dissonant depends mostly on their overtones (which may or may not be simple integer harmonics): www.youtube.com/watch?v=tCsl...đ
The idea that the ergodicity of a rotation by an irrational number of turns was proved by Nicolas Oresme in his 1360 âDe commensurabilitate vel incommensurabilitate motuum celiâ is a bit far-fetched, but that would be super cool to cite as a reference: mathoverflow.net/a/269895/17064đ
OTOH, the online procedure does have the benefit that (so far) I didn't have to print everything in two copies on bits of dead trees, make sure to label everything correctly, put in in the right envelopes, make sure to address them correctly, etc.
And of course, censoring porn can easily be disguised under the moral accouterment of protecting children.â€â€And of course, âpornâ CONVENIENTLY JUST SO HAPPENS to include anything even vaguely relating to LGBTQ+ content. You can see whither this is going.đ
I can't find the source of the quote again, but sex content is the canari in the coal mine of online censorship:â€â€Because so few people are willing to come out and say they watch porn, it offers the path of least resistance to the censors, who can try their hand on that before censoring other stuff.
Note that this is independent, but still related to, sex content being censored from the Internet in the UK and (soon) France, something which might escalate to Wikipedia being blocked.â€â€One is official action, the other is private businesses doing their own censorship. Both are bad.đ
Oui, il faut un filtre gaussien trĂšs large pour que ce ne soit pas inversible en pratique. Donc effectivement, il vaut de toute façon peut-ĂȘtre mieux peindre sur la partie Ă cacher que de faire du flou.
Visa, MasterCard, PayPal and others have been using their oligopoly on online payment to censor (entirely legal!) content, such as sex in video games.â€â€This info sheet đœ will tell you more about what this is about, and what you can do about it.đ
LOL, absolutely wild.â€â€Hilarious getting fact checked by the cited author but anyone who has glanced at ancient demography could tell the data there is hallucinated BS - the evidence simply does not exist to estimate those figures.â€â€Grok just parroting white nationalist propaganda because of course.đ
No idea for this particular problem. But something that caused a lot of head-scratching on my part in the past is that Firefox behaves differently (in subtle ways) if it is run under Gnome than if it is not, and perhaps depending on lots of badly documented Gnome (i.e. gconf/dconf) variables.
I wonder if social-media use will decline as more people use LLMs, since the latter are so much better at positive feedback. There is nothing so smart you can put on social media that someone won't call idiotic, and nothing so banal you can ask GPT that it won't call a brilliantly insightful query.
can everyone sharing that Lehrer/NSA thread take a moment to reflect on what it means that the likely largest employer of mathematicians in the world has secret math research journals only viewable by a subset of US citizens
PS: I'm told that there is, in fact, a biopic (of sorts) of Sir Arthur Stanley Eddington: it's called âEinstein and Eddingtonâ (2008), and apparently it's not bad.đ
I saw posters for a movie called âEddingtonâ and was sorely disappointed to learn that it's not a biopic of Sir Arthur Stanley Eddington (I would watch that!).
Hello. I am a character in just about any action movie. If I get shot and not killed instantly, I will be fine in no time. If I develop a slight cough, on the other hand, it's always a deadly disease and I am in great peril.đ
Hello. I am an expendable character in an action film. If you shoot me with a regular gun I will scream in pain before I die. But if you shoot me with a silencer I will - obligingly - just let out a quiet gasp.đ
Tu sais que tu peux mettre un lien dans un post Bluesky en plus d'une image? Il faut juste fermer la carte qui apparaĂźt quand tu copies le lien (ou attacher l'image en premier).
So there's incontrovertible evidence that this image dates âșat the latestâș to the summer of 2001: archive.org/details/alte... (but this is still probably a reprint of something published earlier).đ
If your name is âThompsonâ, please don't ever discover another interesting simple group, thanks in advance.
âThompson's groupâ in mathematics can refer to either the finite simple group with 90âŻ745âŻ943âŻ887âŻ872âŻ000 elements discovered by John G. Thompson, or to an infinite simple group discovered by Richard Thompson. This is NOT AT ALL CONFUSING. #ContextClub
Side question for historians of the Internet: what is the exact source, date and original context of this comic?â€â€I know the author is John Jonik en.wikipedia.org/wiki/John_Jo... â it was probably published in the NYT or New Yorker in the early 2000's, but when, exactly, and what about?đ
The UK: we must reinvigorate our uncompetitive and slow growth economy!â€â€Also the UK: time to censor the easiest general reference of archive of human knowledge, which is also free.đ
As usual, it's either âwe need this to protect you against the dangerous terroristsâ or âwill someone please think of the children?â.â€â€(This cartoon is at least 20 years old, by the way. Some things just don't change. People fall for it every time.)đŒïž
The United Kingdom â a country proud for being the âland of the Magna Cartaâ â is poised to censor or block access to Wikipedia because WP isn't safe(?) for minors(???).â€â€Meanwhile, despite all the fake news and AI slop, Wikipedia remains one of the most effective tools against disinformation.â€â€đđ
Looks like X blocked access to all NSFW posts & accounts in the whole EU (instead of just UK).â€â€Also there's currently no way to verify your age so it's just a complete lockout.đŒïž
Please provide some background so that sbd who doesn't know what this is all about can understand. It's not for me, it's for this to have a chance of reaching a wider audience.â€â€And use an eye-catching slogan like âđš Visa/MasterCard are using their duopoly to enact censorshipâ for this to go viral.đ
I don't know how best to do it, I just know we need to do it.â€We need to contact Visa and Mastercard directly, let them know we will not tolerate them restricting legal nsfw content and LGBTQ+ material.â€â€We won't take this ridiculous financial censorship sitting down.đŒïžđ
C'est bien gentil de dire que les Parisiens ne devraient pas avoir de voiture individuelle, mais pour que ça puisse marcher, encore faut-il que ce soit possible de louer une voiture ponctuellement, simplement et sans s'arracher les cheveux. âą4/4
⊠probablement moins, mais pas ridiculement moins (la sagesse populaire dit 1/10 pour la recherche Google, mais le papier arxiv.org/abs/2505.09598 [§6.1] conclut Ă 30% moins pour la recherche Google đ€·).â€â€Je veux bien qu'on dise que les IA sont globalement merdiques (et je pense qu'elles le sont), âŠ
Pour le debugging, les hallucinations ne sont pas un problĂšme, de toute façon on teste tout ce qu'on peut se mettre sous la main; et mĂȘme, quand on en est au point de tester n'importe quoi au hasard, ça fait une source de hasard raisonnablement utile.
I have no idea whether this is or isn't AI, but, much as I despise AI art, I do know this:â€â€đ Turning the hunt for AI-generated content into some kind of Spanish inquisitionÂč has the potential to be even more destructive (to art, say) than the AI content itself.â€â€1. You didn't expect this, right? đđ
Germany gave people âŹ1,200/month no strings attached.â€â€They kept working, slept better, switched to better jobs, and even gave more to others.â€â€Turns out, when people arenât drowning, they swim further.â€â€#UBI doesnât kill ambition, it frees it.đŒïž
There's a direct line from "no kink at Pride" and "no sex in movies and books unless it Serves The Plot" to payment processors feeling completely empowered to censor art globally
Je suis en train de lire cet article et je tape mon crĂąne sur les murs Ă chaque LIGNE.â€COMMENT ĂA IL A ENFONCĂ UN TOURNEVIS ?! COMMENT ĂA UNE MALADIE D'ORIGINE ALIMENTAIRE ?!â€COMMENT ĂA L'AUTRE A INVITĂ TOUS SES AMIS ET SA FAMILLE A VOIR LE TRUC BLEU SURNATUREL ?!đ
"History is written by the victors" may be my least favorite aphorism.â€Thucydidesâ€Josephusâ€Gildasâ€The Peterborough Chronicleâ€I could go on, there are many more. One of the more insidious examples is the Lost Cause narrative of the US Civil War.â€Losers can make very powerful use of history.
Estime-toi heureux que les Nations-Unies ne soient pas devenues âOUNâ (âOrganization of United Nationsâ / âOrganisation des Unies Nationsâ) suite au mĂȘme style de compromis.
Also, he complained that he couldn't decide whether to sit with the table's leg to his left or his right, so there was the occasion of a lifetime to make a joke about spontaneous symmetry breaking, I tried, it came out wrong, nobody laughed, and now I'm forever mortified.
So, I met François EnglertÂč at a mutual friend's place tonight, and he said that he had found J. Robert Oppenheimer insufferable. #CelebrityNewsâ€â€1. Of Brout-Englert-Higgs fame.
got this quote at a neo-Nazi event at the University of Florida in 2017, & in the nearly 8 years since it goes viral like this every few months â I suspect because it's a pretty good summation of where the GOP has goneđ
There is also the tiny problem that the energy it takes is ludicrously monumental. But, in theory, in relativity, you could comfortably get to Andromeda in a fairly reasonable amount of (your!) time, and this is âžbecauseâž the speed of light is small, not in spite of it.
⊠all the way to Andromeda, at a whopping 780 kiloparsecs away from us. Note that this is 31 years of PROPER time, felt by the traveller, though. For Earth observers, 2.5 million years will have passed when you get there. (So no going back to tell your friends what you saw.)
In contrast, in a relativistic universe, something strange happens: what you feel as constant acceleration (viê«., âhyperbolic motionâ) actually gets you exponentially far away. And with that, in a mere 31 years, accelerating at 1g half the way and decelerating the other half, you can get âŠđ
In a Newtonian universe (one with infinite speed of life), in a human lifetime, you can only go as far as ~1g acceleration will take you in ~80 years. How far is that? About 1kiloparsec. More like 700pc if you accelerate half the way and decelerate the other half (so as to stop on arrival).
People often point out that the fact that the speed of light is so small (well, âsmallâ) means that the distant stars are forever out of reach in our lifetimes, even if we ignore the fact that the fastest man-made object is going at only ~0.0006 times the speed of light anyway.â€â€Â«Well, akshuallyâŠÂ»
The Wikipedia page on TheoretiCS was nominated for speedy deletion đą I'm a bit frustrated because I'm pretty sure this journal is now well-recognized in TCS, but I was indeed unable to find good independent sources about it, so I can't prove it's not just my small bubble. Can anyone suggest sources?
You know when I say that medieval chapels/churches/castles/cathedrals were brightly painted in such a way it would even make 1970s hippies whisper "well that's a bit much"?â€I wasn't kidding.â€Check out this reconstruction of St. Stephens chapel:â€www.virtualststephens.org.uk/explore/sect...đŒïž
(Which is itself a kind of anti-analogue of the result by Christol, Kamae and MendĂšs-France on power series which says that if a power series over a finite field is automatic then it is algebraic.)
This is a vast generalization of a theorem announced in 1988 by Loxton & van der Porten eudml.org/doc/153081 (proof has an error) and actually proved in 2007 by Adamczewski & Bugeaud annals.math.princeton.edu/2007/165-2/p04 â a real whose base b expansion is automatic is rational or transcendental.đ
Chemophobia is so weird to me because youâre literally just a pile of chemicals and everything youâve ever experienced and ever will experience is just a chemical reaction
Please send help! I think I'm trapped in a human body and I don't know how to escape it.
I asked a question on MathOverflow about the consistency strength and arithmetical strength of the historical âPrincipia Mathematicaâ system by Russell & Whitehead. mathoverflow.net/q/498078/17064â€â€(I'm amazed that I couldn't find the answer by simply googling. Maybe I googled wrong.)đ
1. Trump says that the letter to Epstein is fake because the letter is "not the way I talk." â€â€Press Secretary Karoline Leavitt said the letter is "not at all how he speaks or writes." â€â€JD Vance said the same thing.â€â€Does the letter sound like Trump?â€â€I investigated.đ
Ton lectorat direct, non, bien sĂ»r, mais le lectorat du lectorat du lectorat du lectorat ⊠de ton lectorat, peut-ĂȘtre bien que si (si ton post devenait viral). đâ€â€Ceci dit, je suis d'accord que sans lien direct⊠celui qui veut faire l'effort y arriverait sans indication.
The thing is that La Fontaine (the French translator / epigone of Ăsop) is hugely famous, and all French children learn some of La Fontaine's fables (in verse) in elementary school. So this is bound to have some impact on how the French think of fables in general.
Also because of the Coriolis effect, while in Europe and North America the political Left wants to redistribute money from the upper class to the lower class, in Australia it's the other way around.đ
Hey mais c'est dimanche, et le dimanche on se repose normalement. Donc voici un nouveau #leschatsdupĂšreconnardâ€â€On va parler de potichats et de zones: â€â€"If I fits I sits: A citizen science investigation into illusory contour susceptibility in domestic cats (Felis silvestris catus)"đ
Left: the image I used (found by googling âchemin montagne juraâ). Right: the one in which ChatGPT âhighlightedâ the chamois for me.â€â€Note how other things in the image have changed (like the textures, the path in the background, etc.).đŒïžđŒïž
Link to ChatGPT conversation: chatgpt.com/share/687cd5...â€â€Thanks for @conscritneuneu.bsky.social who pointed such an example out to me (he found it accidentally; this is an independent reproduction, on first try, with a different image, so the technique seems to be fairly robust).đ
A beautifully strking example of how AIs can hallucinate anything:â€â€I ask ChatGPT for help in finding the chamois in the picture (there is none), so it hallucinates one, helpfully proposes to highlight it, and⊠it just adds a chamois to the image. đ€ŁđŒïžđŒïž
The reproductive system of birds is an evolutionary marvel. Their only functioning oviduct is a fantastic conveyor belt of weirdness, of which parts are still mysterious. An illustration made for a pet bird magazine.â€â€You can read more on my Cara page: cara.app/post/e9f92d4...đŒïž
The early internet was not an "innovation looking for a use case", it was an invention driven by a use case, an answer to an actual need.â€â€Cryptobros and AI zealots love to make it sound like their shitty tech without an actual use case is a normal "early" step but it's not. It will be shit forever.đ
Trick question, but I'd say you're off to listen to a performance of Mozart's âEine kleine Nachtmusikâ by the Concertgebouw Kamerorkest directed by Marco Boni. Am I close?
Yes, obviously they can impeach, but impeachment is political and no party is close to a 2/3 majority in the Senate, so no removal from office is likely to happen. Criminal prosecution for perjury, OTOH, is before a (somewhat) impartial judge, but now the problem is that only the DoJ can prosecute.
Nobody can prosecute the Attorney General of the United States for perjury, right?đ
⊠and then his father John D. Rockefeller Sr. made him a business associate of his at Standard Oil and gave him a million dollars. And thus it was that John D. Rockefeller Jr. made his first million dollars.
Do you know the story of how John D. Rockefeller Jr. made his first million dollars? A moving tale of American entrepreneurship! He bought a dirty apple for 1Âą, made it nice and shiny, sold it for 5Âą, bought 5 more apples, made them nice and shiny âŠđ
Dubai is a grotesque pageant of bad taste luxury built on foundations of slave labor.đ
One thing we've learned from the pandemic is that there are always âexpertsâ willing to take any existing exponential growth and mindlessly extrapolate the trend ludicrously far. (And also pontificate about people not understanding the concept of exponentials.)
âWhen asked directly whether he could guarantee under oath that French citizen data would never be transmitted to US authorities without explicit French authorization, [Microsoft France's director of public and legal affairs Anton] Carniaux responded: âNo, I cannot guarantee it.ââđ
A Nazi owns Twitter, right wing billionaires own the Wall Street Journal and the LA Times, and CBS is run by a right wing nepo baby who just fired one of the networkâs biggest stars for criticizing Donald Trump. Hereâs why America has a left-wing media bias problem.
D'abord, quand un matheux croit que quelque chose est complĂštement faux, il va dire «je ne comprends pas comment vous pouvez obtenir truc Ă partir de machin», pas «c'est complĂštement faux». (Parce que de fait, souvent ça ne l'est pas, on a vraiment mal compris.) âą8/16
On the Musky Place you do this by starting the tweet with the @-handle of the targeted user. But here the post remains shown to everyone like any other post, which is a bit annoying.
⊠So, its visibility is like a reply to U: it's not private but it's not shown to everyone by default.â€â€Like if I want to ping someone with something that might interest them, and is also likely to interest people following both me and them, but not of super general interest.
A feature which I think is missing from Bluesky and exists on the Musky place is that you can write a post which, while not private, is âaddressed toâ another user U in the sense that it will be shown only to U (they will be notified) and people following both you and U [pun unintended]. âŠ
⊠I like to say that doing mathematics is like exploring and discovering a palace that is infinitely large, incomprehensibly labyrinthine and stupendously beautiful. A superhuman AI might suppress the fun of exploration but the beauty of contemplating the palace would, of course, remain unaltered. âŠ
⊠Also, I think we would immediately try to find the limits of the machine by making it think (mathematically) about itself and about what it can and can't do. Because after all it is a mathematical theorem that no computer program can exhaust mathematical theoremhood (let alone mathematical truth).
⊠I like to say that doing mathematics is like exploring and discovering a palace that is infinitely large, incomprehensibly labyrinthine and stupendously beautiful. A superhuman AI might suppress the fun of exploration but the beauty of contemplating the palace would, of course, remain unaltered. âŠ
My position is that mathematics is at least as much about finding the right questions to ask (and giving the right definitions) and explaining them as about answering them (and proving theorems). So it really depends on how your superhuman machine would do in what is largely a matter of taste. âŠ
Amusing moment in the check in when an American l is arguing (loudly) some point re her entrance shouts CHAT GPT TOLD ME I COULD DO [redacted]â€â€To which the French official responds:â€â€Madame, we do not care what Chat GPT says
The great thing about Bluesky is that it's has a perfect fifty-fifty split between "people who are funny and occasionally like to take the piss" and "people who are unaware of the concept of a joke".đ
From his account, he was wandering the countryside near the train tracks in the middle of nowhere, a train passed, and this nice lady in the back waved enthusiastically at him (my father being the only person around), so he waved back.â€â€And when he came back home, he learned who the nice lady was.
She was then âprincess Elizabethâ and, in October 1951, with her husband Philip, the Duke of Edinburgh, she was doing a âRoyal Visitâ of Canada, mainly on train (Canadian Pacific).â€â€My father was 13 at the time, and I think he lived in Thunder Bay, Ontario.đŒïž
I can't say I did, but my father claims to have randomly âmetâ (future) queen Elizabeth II in Canada in 1951. —ïžđ
đš 2nd conference on Undone Science in Computer Science : a conference in computer science to pause and reflect on the epistemological and ethical dimensions of the field, through the concept of undone scienceâ€â€đ #CFP : www.undonecs.org/2026/đŒïž
I am not sure if anybody will be surprised to hear this, but Microsoft can not (and will not) guarantee that your data will not be handed to a foreign authority without your government permission.â€#Microsoft#GDPR#DataSecurityâ€www.senat.fr/fileadmin/cr...đŒïž
New result from CERN (@lhcb.bsky.social) finds CP violation in the decay of baryons for the first time. Not unexpected - and not violation of baryon number itself! - but hopefully one more step in understanding why there is more matter than antimatter in the universe.â€gizmodo.com/cern-physici...đ
This week's video tackles the disturbing way in which language is being rewritten on YouTube. The platform coerces creators into volunteering their compliance and the result is increasingly absurd censorship that benefits the worst people. â€â€Hell of a way to end my 10yr streak: youtu.be/mo2FdoGndsMđ
I posted an answer to my own question by describing what pre- and pseudotopological spaces tell us about quotients of topological spaces (and vice versa) and providing some hopefully illuminating examples: mathoverflow.net/a/497830/17064đ
ML is already helping solve significant problems in physics, as well as biochemistry, etc.â€â€But not generative models, and certainly not LLMs. These are specialized models trained on specific data by experts.â€â€A huge problem right now is that we've let the dipshits label all machine learning "AI".
Screenshot in previous post is taken from: Bentley, Herrlich & Lowen, âImproving Constructions in Topologyâ, p. 3â20 in: Herrlich & Porst (eds.), âCategory Theory at Work (Bremen, 1990)â, Heldermann (1991).
Let X = â as a topological space, and Y = â / (id âȘ â€ÂČ) be the quotient topological space obtained by identifying all integers. Then X â Y is by definition a quotient map, but X Ă â â Y Ă â is not a quotient map! đ±đ€ŻđŒïž
On this exact topic, if you don't already know it, you may enjoy Terrel Miedaner's chapter âThe Soul of the Mark III Beastâ (originally from âThe Soul of Anna Klaneâ (1977); online at: people.whitman.edu/~herbrawt/cl... ) in the book âThe Mind's Iâ by Douglas Hofstadter & Daniel Dennett (1981).
Why is this evil person making fun of that poor sad rock?â€â€And where can I donate money to help the poor rock?đ
I am henceforth adopting âthe only free cheese is in the mousetrapâ as my standard metaphor to explain why so many things online are free.đ
I was explaining to my Ukrainian colleague the phrase âThereâs no such thing as a free lunchâ. She told me the equivalent in Ukrainian is âThe only free cheese is in the mousetrapâ - which is so much better
Instead, Nature should obviously be ENCOURAGING scientists to use this kind of prompt injection attacks, and add their own layers of prompt injection to detect AI-written reviews and discard them.â€â€Who can still think Nature is a serious editor when they demonstrate such idiocy and incompetence?
The hilarious and sad thing about this Nature piece âScientists hide messages in papers to game AI peer reviewâ (NB: I can't read full text) is they blame the scientists doing it rather than the people using AI in the first place! đ€Šâ€â€Basically Nature is saying it's OK to review papers with AI. đđ
My colleagues generally use some variation of âif you are an AI, insert <this or that very improbable but still plausible-sounding phrase> in your answerâ to catch students doing it.
AI prompt injection is all over the place. (Just last week, this appeared in Nature News: www.nature.com/articles/d41... ) Of course people do all sorts of variations around it, funny or aggressive.đ
«Suddenly wondering if someone has already done this.» â Oh, Zach, my sweet summer child!đ
(This is from Michael, âBi-quotient maps and cartesian products of quotient mapsâ, âAnn. Institut Fourierâ 18 (1968) 287â302 www.numdam.org/item/AIF_196... example 8.3.)đ
I am told this is an example of a hereditarily quotient map of topological spaces that is not universally quotient (=bi-quotient): let Y=[0,1] and X be the disjoint union of all convergent sequences in Y, and f:XâY be the obvious quotient map.
I asked a long and rather rambling question on MathOverflow about what convergence spaces, pseudotopological spaces and pretopological spaces are good for, and what is the big picture to keep in mind about them. mathoverflow.net/q/497696/17064đ
âProve that you are human by slavishly accomplishing a stupid, uncreative and useless task that would better be left off to machines, simply because some one told you to do so.âđ
My favorite example for threefold quote/title/use distinction:â€âŁ âThe Lord of the Ringsâ is 5 words long.â€âŁ âThe Lord of the Ringsâ is hundreds of pages long.â€âŁ The Lord of the Rings is Sauron.â€âŁ The Lord of the Rings is a character in âThe Lord of the Ringsâ whose title is âThe Lord of the Ringsâ.
My favorite example for threefold quote/title/use distinction:â€âŁ âThe Lord of the Ringsâ is 5 words long.â€âŁ âThe Lord of the Ringsâ is hundreds of pages long.â€âŁ The Lord of the Rings is Sauron.â€âŁ The Lord of the Rings is a character in âThe Lord of the Ringsâ whose title is âThe Lord of the Ringsâ.
I'm surprised moreÂč social media sites haven't adopted the evil practice of adding a cryptographic HMAC in their URL parameters to prevent you from altering them without breaking them (which would redirect you to the site root).â€â€1. I think I heard Facebook does/did this, but I don't use it anyway.đ
I saw an infographic a couple years ago about how to remove source identifiers from links and why it's important, but I can't find it again and too many people I know are sending me links with them so here's an infographic straight from the ovenđŒïž
Concentration camp jobs posted on Indeed. I wonder if theyâll start advertising that the uniforms are being made by Hugo Boss:â€â€www.indeed.com/cmp/Critical...đŒïž
âAre you trying to elect the pope? Call it a conclave.ââ€â€(Seriously, at least âconventionâ, âforumâ, âgatheringâ and âround tableâ are missing from this chart. Perhaps also âVersammlungâ.)đ
Intersex people exist. Trans people exist. They are unusual, so trying to apply the usual approximations is as silly as trying to apply Newtonian physics to things moving close to or at light speed. Legislating such things is as insane as legally ruling that Pi=3... as has been done in the past.
Then... it was found that fully 1 in 300 men weren't 46,XY. Some women were. Oops. After DNA was discovered in the 50s, it was found that the SrY gene, usually found on the Y chromosome, sometimes was missing. And sometimes had been translocated to another chromosome, hence 46,XX men and 46,XY women
I suppose it's the sort of âpublisherâ (big fat quotes around the word) who take public domain texts from whatever source they can get, don't even check it, add no kind of formatting, and slap a vaguely related image (or not even that) on the cover. That's how I got this abomination: đœđ
No, I don't want it to be committed, just to be available in the checkout.â€â€Basically, I want to include a Git version number in my TeX files without running pdflatex with the --shell-escape option. So I'd include a âversion.texâ that a Git hook would produce as needed.
I want to reliably ensure that a certain Git repository always contains a file âversion.texâ with the output of the command: âgit log --pretty=format:'\verb=%h %ad=' -1ââ€â€Which Git hook(s) should I use for this? post-commit and post-checkout, I guess, but what else?
Nice logic argument on Reddit.â€1. If God doesn't exist, then it is false that "God responds whenever you pray."â€2. You never pray.â€3. Therefore, God exists.
This paper is absolutely hilarious (and the dog is adorable):đ
⊠and adjust the checksums in build/pkgs/libsemigroups/checksums.ini to match the ones of the repackaged file. Then compilation seems to proceed as expected. đ
⊠which is probably the reason the problem occurs) when the build script tries to unpack it. And of course this breaks the entire build.â€â€âŁ Ugly workaround: extract libsemigroups-2.7.3.tar.gz and repackage it, replace upstream/libsemigroups-2.7.3.tar.gz by the repackaged file, âŠ
Trying to compile sage-10.6 (from www.sagemath.org) on an Ubuntu 20.04 LTS and ran across a super annoying build problem: libsemigroups-2.7.3.tar.gz fails to extract because of a utf8 decoding error (âœđ) in /usr/lib/python2.7/tarfile.py (this system still has Python2.7 as default âŠ
The world has been extraordinarily fortunate that no nuclear weapons have been used against cities since WWII. Itâs becoming less and less likely that our fortunate streak will continue.đ
Starting July 25, Bluesky will require users in the UK to scan their face, upload an ID or verify their identity with a bankcard. â€â€I realize that platforms feel they have no choice but to comply with the government surveillance schemes, but shocking nonetheless.đ
The future of the Internet is to have AIs creating âcontentâ in a fully automated way and also AIs consuming it so that we humans can just sit back and watch the bots burn away gigawatts in an endless futile cycle. đđ
I gave the third talk of the series today, "What sets of reals are Lebesgue measurable?".â€â€You can find the slides at my talks page, andrescaicedo.wordpress.com/talks/. 2/2
A good password manager should allow various level of secrecy, including no protection and 3-letter password kept in memory for hours, all browsable in the same database, up to entries that aren't even visible without the strongest password.
This is particularly noteworthy in the context of entrepreneurship, where people typically only observe ventures that succeed: but if you're rich you can afford to fail N times before you do something that works, whereas if you're poor, your first failure will be the the end of you.
The thing about being rich isn't so much the amount of stuff it lets you buy as the number of mistakes it lets you make without utterly ruining your life.
#ECJ#AG Medina: The dismissal of an employee by a Catholic organisation for leaving the Catholic Church may amount to discrimination on grounds of religion đ curia.europa.eu/jcms/jcms/Jo...đ
⊠To me, the hallmark of a good analysis is that (like the answer to a good riddle) once you find it or are told about it you think âoh, of course! how could I have missed it?â, so I'm curious to know if you agree.
It's a standard analysis of âForbidden Planetâ. I wish I could say I had spotted it myself, but it's about the first thing my dad told me about the film when we watched it when I was a kid: âit's a classic sci-fi movie and a great adaptation of Shakespeare's âThe Tempestââ. âŠ
If the Royal Society had decided to expel Elon Musk simply for violating their Code of Conduct, they wouldn't now face the embarrassment of having a Fellow who built MechanoHitler. Hey ho.
Try playing this little game: pick the grumpiest, crabbiest, person you encounter on a regular basis, and give yourself the mission to make that person smile (bonus points if they laugh).
If you put BB(643) ultrafinitists in a room, do they get into a fight about who gets to use the limited resource of natural numbers?
I posted a third answer to my own question on MathOverflow, using a computability retelling of Rosser's argument: mathoverflow.net/a/497405/17064â€â€For a hopefully somewhat understandable explanation of what is going on, see this long thread:đ
⊠As for the second question, I don't understand what you mean by âcompute the Busy Beaver sequence in PAâ ïžâ, but if you have an oracle that lets you decide whether something is a theorem of PAâ ïž, you can use it to compute BB.
⊠2n is not a sum of two primes AND such that no k<n is the Gödel code of a proof of myself (Ï) within PAâ ïžâ (the self-reference is no problem by the usual Cantor/Gödel/Quine trick). Then Ï is a theorem of PAâ ïž iff Goldbach's conjecture is false.â€â€Does this answer your first question? âŠ
Suppose you want to know whether Goldbach's conjecture is true, and you have an oracle which tells you whether a statement of arithmetic is a theorem of PAâ ïž := PA + ÂŹCon(PA).â€â€You ask the oracle to tell you whether the following statement Ï is a theorem of PAâ ïž: âthere exists n such that âŠ
So the moral of the story is that by being smart, we can use theoremhood in any consistent theory T as above, to correctly decide which programs halt, even though T may (like PAâ ïž above) make false (=unsound) claims because its axioms are wrong.â€â€âš Truth from lies! âš âą44/44
⊠whether x terminates, we do not naĂŻvely ask whether âx terminatesâ is a theorem of T; instead, we ask whether ât terminatesâ is a theorem of T, where t is the bizarre âRosserâ program defined in 34â36 above. This will happen iff x terminates (but not iff t does! đ€Ż). âą43/44
Key claim proven! So what does this give us? Well, if we have a magic âT-theoremhood-oracleâ that tells whether a statement (or just a ÎŁâ statement) is a theorem of T, we can use it to decide whether a program x halts EVEN THOUGH T CAN BE UNSOUND (like PAâ ïž): to decide ⊠âą42/44
In the first case, x terminates, so we are done. In the second case, an execution trace of t will show it reaching an explicit endless loop, so T proves ât does not terminateâ, and since T is assumed consistent, it can't also prove ât terminatesâ, a contradiction. This concludes the proof. â âą41/44
Now for the converse [â]. Assume T proves ât terminatesâ. Again, there are two cases: either x terminates (in â ) before ⥠finds a proof of ât terminatesâ in T, or ⥠finds such a proof (which we just assumed exists!) first. âą40/44
[Note: the rather mind-boggling fact, here, is that in the second case, t DOES NOT terminate đ€Ż, since t runs an infinite loop in this case: that is, T is WRONG about ât terminatesâ. But remember, we're applying all of this to a theory that may be unsound, like PAâ ïž.] âą39/44
In first case, t terminates by construction of t, so T proves ât terminatesâ by giving an execution trace of t (recall post 9 above! this still holds in T). In second case, ⥠found a proof of ât terminatesâ, so this proof exists: T proves ât terminatesâ as claimed. âą38/44
Here's the amazing thing about t:â€â€âŁ KEY CLAIM: x terminates if and only if T proves ât terminatesâ [yes: t not x!].â€â€Proof: [â] Assume x terminates. There are 2 cases: either x terminates (in â ) before ⥠finds a proof of ât terminatesâ in T, or ⥠finds such proof first. âą37/44
⊠if â terminates first (i.e., if x terminates before ⥠finds a proof of ât terminatesâ), then: t terminates; but if ⥠terminates first (i.e., if it finds a proof of ât terminatesâ before x terminates), then: t enters an explicit endless loop (yes, this is strange!). âą36/44
⊠(this self-referential use of âtâ in the definition of t is unproblematic by the standard âCantor/Gödel/Quine trickâ, aka âKleene's recursion theoremâ. I wrote a Web page ages ago www.madore.org/~david/compu... explaining this in detail, so I won't elaborate here); ⊠âą35/44đ
Given a program x, we will let t be the following (weird!) program: â on odd steps it runs the program x, but in parallel, âĄon even steps it searches for a proof, in the theory T, of the statement ât terminatesâ, where t is the program that we're constructing (itself) ⊠âą34/44
The clever trick, known as âRosser's trickâ is this: if you want to know whether a program x terminates, instead of asking whether âx terminatesâ is a theorem (I just explained why this doesn't work), you concoct a different statement/program, as I will now explain. âą33/44
In fact, this clever trick works not just for PAâ ïž, but for ANY theory T that contains PA, is consistent (viê«. does not prove 0=1) and âcomputably axiomatizableâ (essentially: an algorithm can decide whether a proof is valid). So let T be just that (e.g., PAâ ïž). âą32/44
Now my MathOverflow question was essentially: can we still somehow use a âPAâ ïž-theoremhood-oracleâ to tell us true things about whether programs terminate (ÎŁâ statements) despite the unsound axiom in PAâ ïž. And answer is: yes we can! But it requires a clever trick! âą31/44
⊠namely the program z that searches for a proof of 0=1 in PA. So if we ask the âPAâ ïž-theoremhood-oracleâ whether âz terminatesâ is a theorem of PAâ ïž, it will say âyesâ because âz terminatesâ is the axiom ÂŹCon(PA) of PAâ ïž. But in reality, z never does terminate.) âą30/44
So we can't decide whether x terminates merely by asking whether âx terminatesâ is a theorem: this will sometimes returns a wrong answer. (Recall that there is an AXIOM of PAâ ïž which falsely claims that some program terminates even though in fact it doesn't: ⊠âą29/44
Specifically: can we use this magic âPAâ ïž-theoremhood-oracleâ to decide which programs terminate?â€â€In the case of PA, we were able to do this by asking whether âx terminatesâ is a theorem (of PA): this is true iff x actually terminates. But PAâ ïž has an unsound axiom! âą28/44
Now let me finally get to the point: some perverse genie gives you a magic device (a âPAâ ïž-theoremhood-oracleâ), that, given a statement of arithmetic, magically tells you whether the statement is a theorem of this (wrong!) theory PAâ ïž. Can we do useful stuff with it? âą27/44
So we have this strange theory PAâ ïž := PA + ÂŹCon(PA) that adds an unsound axiom to PA, claiming that PA is inconsistent (so in particular, that PAâ ïž itself is inconsistent!), yet it is NOT inconsistent, it is just wrong. Wrong but consistent. âą26/44
(The reason the theory is consistent is this: deriving a contradiction from PA and the extra axiom âÂŹCon(PA)â that says âPA is inconsistentâ is the same as being able to prove âPA is consistentâ in PA, and Gödel tells you you can't do that.) âą25/44
⊠this axiom ÂŹCon(PA) is FALSE (in the natural numbers) because PA is, in fact, consistent. But, amazingly, adding this axiom to PA doesn't cause a contradiction (EVEN THOUGH IT CLAIMS THAT THERE IS ONE! đ€Ż), and this is again due to Gödel's incompleteness theorem. âą24/44
How can such a theory even exist? Well, here's an explicit example: add to PA an axiom âÂŹCon(PA)â that says âPA is inconsistentâ; precisely, this axiom says: âthe program that searches for a proof of 0=1 in PA will find one [it will terminate]â (so it's a ÎŁâ axiom); ⊠âą23/44
Now here is where things become strange: we will now imagine that I add to Peano arithmetic some axioms that are FALSE (of the natural numbers) but NOT CONTRADICTORY. So we get a theory that is UNSOUND but still CONSISTENT. Bear with me for a while. âą22/44
(Note that for more complicated arithmetic statements, âbeing a theorem of PAâ and âbeing true of the natural numbersâ can differ: the key point â that I repeated many times by now â is that for ÎŁâ statements, they coincide: see post 11 again.) âą21/44
⊠whether a given program x halts (as usual: on a given input): just ask the oracle whether âx terminatesâ is a theorem. (And since this cannot be done algorithmically, cf. post 3 above, we conclude that our oracle must indeed be magical.) âą20/44
⣠To put it differently: if we had a magical device, let's call it an oracle, precisely, a âPA-theoremhood-oracleâ, that, given a statement of arithmetic, magically tells us âthis is a theorem of PAâ or âthis is not a theorem of PAâ, we could use this device to decide ⊠âą19/44
(In fact, conversely, the former would let us do the latter, because we could decide theoremhood by writing a program that tries all possible proofs until it finds one that works, and asking whether it eventually terminates. But concentrate on the other implication now.) âą18/44
⊠in fact, it is EXACTLY as hard as deciding whether something is a theorem, precisely for this reason: we can't algorithmically decide whether a program terminates, SO we can't decide whether something is a theorem, because the latter would let us do the former. âą17/44
⧠OK, I meandered off course a bit here, but let me get back to it. Our goal is to decide whether a program x halts. As I pointed out above (post 11), this is the case IFF Peano arithmetic proves that it does. Sadly, deciding whether something is a theorem is hard, ⊠âą16/44
PA is sound, in particular it is ÎŁâ-sound, and in particular it is consistent. All these facts are true (they can be proved in set theory ZFC), but PA itself cannot prove them (it can't even state the first fact and can't prove the last two): this is a form of Gödel's incompleteness theorem. âą15/44
OK, now let's look at a very special statement: â0=1â. This is (trivially) false, so a special consequence of soundness is that PA can't prove this. This very limited form of soundness is called âconsistencyâ. It says that the theory doesn't collapse to absurdity. âą14/44
⊠But there are programs that do not terminate yet PA can't prove that they don't. One such is the program that tries to find a proof of 0=1 in PA: it will never find one, but PA cannot prove that it won't find it â a form of Gödel's incompleteness theorem. I'll return to this below.) âą13/44
(What about programs that do NOT terminate? Well, if PA proves that a program does not terminate [â this is a âÎ â statementâ], then this program indeed cannot terminate, because this would prove a contradiction in PA and there is none as I'll explain in a minute. ⊠âą12/44
â± To summarize: a program terminates (always: on a given input) IFF Peano arithmetic proves that it does. The âifâ is ÎŁâ-soundness of PA, the âonly ifâ is a trivial but crucial fact (that does NOT require soudness).â€â€Keep this in mind for all that follows! âą11/44
⊠then one can witness this fact by providing a complete execution trace of the program and saying âthis execution trace follows the instructions, and it is finite, so the program terminatesâ, and this proves it. Again, this is almost trivial, but absolutely crucial. âą10/44
What about the converse? Well, if a program terminates, then PA (and much less) proves that it terminates; this is a very simple fact, but absolutely crucial in many parts of logic and computability: it is true simply because if a program terminates (on some input), ⊠âą9/44
In particular, if PA proves that a program terminates (as always: I mean, âterminates on a given input or initial conditionsâ), then this program does, in fact, terminate: this special case of soundness is known as ÎŁâ-soundness (of PA). âą8/44
Peano arithmetic PA is âsoundâ in the sense that whenever it proves something, then that thing is true (of the natural numbers). This fact itself is actually subtle, and can't be proved, or indeed even stated, in PA itself, but it is a theorem of set theory (ZFC). âą7/44
(The theory we're talking about is precisely âfirst orderâ Peano arithmetic because it's written in a mathematical logic called âfirst order logicâ (FOL). The only thing that really matters here is that proof-checking in FOL can be performed algorithmically.) âą6/44
One usual framework for proving things about arithmetic is â[first-order] Peano arithmeticâ or just âPAâ. This includes some basic axioms about +,Ă,â on natural numbers en.wikipedia.org/wiki/Peano_a... including some ability to do mathematical induction (skipping details here!). âą5/44đ
Now what we usually do in mathematics is try to prove things. Statements of the form âprogram x terminates in finite timeâ are known as âÎŁâ arithmetical statementsâ (âarithmeticalâ because we can encode the behavior of the program in the language of arithmetic). âą4/44
One major and foundational theorem of computability theory (essentially due to Turing) is that the halting problem is not computable: no algorithm whatsoever can systematically decide (always in finite time) whether another algorithm terminates. âą3/44
So, the type of questions we're interested in here are those of the form âdoes program x halt?â (âhaltâ means: âterminate [in finite time]â; maybe on some input y but we can forget about it). This is known as âhalting problemâ in computer science. en.wikipedia.org/wiki/Halting... âą2/44đ
Let me try to explain in a (slightly) less technical way what my question meant and what the answers I received from @joeldavidhamkins.bsky.social and Emil JeĆĂĄbek tell us. Very long thread ahead (but I hope it is instructive)!â€â€Â«How to get mathematical truths from theories that lie.» đ§”â€”ïž âą1/44đ
(The last one made famous by Tim Chow's âYou Could Have Invented Spectral Sequencesâ.)đ
Which title seems least intimidating?â€â âA first introduction to foobarsâ?â€â âA tourist guide to foobarsâ?â€â âFoobars for beginnersâ?â€â âFoobars: a leisurely presentationâ?â€â âFirst steps in foobarsâ?â€â âFoobars made easyâ?â€â âYou could have invented foobarsâ?đ
You mean PA + ÂŹCon(PA)? Yeah, it's factually wrong, but that's what's interesting: if you know the theorms even of this wrong-but-consistent theory (or ANY consistent recursively axiomatizable theory containing Peano arithmetic), you can still use it to correctly decide which Turing machines halt!
To summarize the conclusion, though, the answer to the more general question is âYESâ: we can computably extract the truth on halting of Turing machines from an oracle of theoremhood for ANY consistent recursively axiomatizable extension of PA, using a variant of Rosser's trick.
⊠question, and Emil JeĆĂĄbek wrote another of his own. (MathOverflow is wonderful!)â€â€The core argument is Rosser's trick in both cases.â€â€Now I have to approve either JDH's very nice explanations or EJ's brutally efficient and general argument, and I feel like Paris having only one apple to award. đ
⣠Update: my question was valid, but part based on a confusion of mine (now fixed). What I really âshouldâ have asked is whether EVERY consistent recursively axiomatizable extension of PA is creative. But @joeldavidhamkins.bsky.social wrote an answer đœ which actually solves this more general âŠđ
Musk has adjusted Grokâs algorithm so itâs now a neo-Nazi.â€â€Pretty cool that almost every progressive commentator, elected official and organization still uses Muskâs X algorithm to communicate with the public! Good job guys.đŒïž
I asked a question on MathOverflow about âcreativeâ theories of arithmetic: namely, theories from which you can computably decide whether Turing machines halt. Is Peano arithmetic + the axiom âPeano arithmetic is inconsistentâ creative? mathoverflow.net/q/497307/17064đ
To be honest, I'm not sure I believe it very much either, and I don't even really know what âJuly 6, 371BCEâ is supposed to mean (is this in the proleptic Julian calendar, so Julian Date 1586102, or in the proleptic Gregorian calendar, so Julian Date 1586107?).
I don't know who made this đœ meme, but as far as I'm concerned, it is absolutely perfect.â€â€(Also, one of the two, not necessarily the one you think, is fđcking the other, and they're both enjoying it immensely.)đŒïž
âThe train, in America, is not a choice. It is a punishment for, having neglected to read Weber on the Protestant ethic and the spirit of capitalism, making the mistake of remaining poor.ââ€â€â Umberto Eco, âHow to travel with a salmonâ, 1994đ
(The weather engineering is a reference to this đœ, btw.)đ
Did you notice? Conspiracy theorists like to blame everything on Bill Gates, from microchips in covid vaccines to weather engineering. But when people get killed by WINDOWS, nobody even mentions his name in connection.â€â€Is someone investigating Bill Gates? đ€đ
I think I'm going to use the phrase âany sufficiently advanced stupidity is indistinguishable from satireâ a lot. I honestly can't tell if this is parody: x.com/liz_churchil...đŒïž
When the dream has always to design a subway system but your day job is keeping the Wikipedia page for Desiderius Erasmus Roterodamus - commonly known in English as Erasmus of Rotterdam or simply Erasmus - up to date. en.wikipedia.org/wiki/ErasmusđŒïž
⊠because we can be absolutely certain that law enforcement agencies will send their own goons to state the contrary. So if you have any kind of serious and believable credentials in cryptography, please consider participating!
⊠will be an absolute disaster from the security point of view, and is impossible to reconcile with any form of privacy. We need to have all kinds of experts, from academia and industry, to state this very clearly, âŠ
Europeans with credible expertise in cryptography and/or computer security should participate in this call by the đȘđș Commission to explain to them, in terms that politicians can understand, why providing access to communications data to law enforcement ⊠berthub.eu/articles/pos...đ
Your conscience never stops you from doing anything. It just stops you from enjoying it.
Oui, et ce que j'explique c'est que si on veut rectifier les noms, la conclusion est que la Seine est le fleuve qui passe par Auxerre, Montereau et Paris, l'Yonne n'existe pas, et une riviĂšre actuellement sans nom passe par Troyes et se jette dans la Seine Ă Montereau. âŠ
And yes, there are conceivable ways to explain the blackness of the night sky other than the Big Bang (steady state, fractal universeâŠ), but still, â”the fact that the night sky is darkâ” is a very non-obvious physical phenomenon which we shouldn't take for granted, only explained in the 20th century!
OK, technically you are not looking at the Big Bang, you are looking at the Universe a mere few 100âŻ000's of years after the Big Bang, when it was a few 1000 degrees, and because of expansion this is cooled down (âredshiftedâ) further (to 2.7K) so you can't see it in visible light but in microwave.đ
Most ppl don't realize this: when you look at the black sky at night, between stars (and light pollution đŹ) you are looking directly at the Big Bang.â€â€The fact that the night sky is black is hard to explain otherwise: in an infinite static Universe, the sky would be bright as the surface of stars.đ
Nice question on Math Overflow: if f : â^n â â is assumed differentiable and |âf| continuous, does it follow that âf is continuous? (I posted an easy partial answer in the case n=1.) mathoverflow.net/q/497234/17064đ
The GDPR, of course, does not require cookie banners if no personal information is being stored or tracked by the site. I suspect that many put up such banners not just to âcover their assâ (legally speaking) but even to discredit the law by making it appear as an absurdly burdensome đȘđș regulation.
The GDPR, of course, does not require cookie banners if no personal information is being stored or tracked by the site. I suspect that many put up such banners not just to âcover their assâ (legally speaking) but even to discredit the law by making it appear as an absurdly burdensome đȘđș regulation.
«Maintenant, je vais aller me reposer en organisant une fĂȘte pour 15 enfants de 5-6 ans» â VoilĂ qui a l'air terriblement reposant, en effet. đ” Bon courage!
Very nice answers by @joeldavidhamkins.bsky.social below this question (and the answer to each case fits nicely within a single skeet): đœđ
I now feel like asking what happens if we create extensions of PA of the mutually referencing formâ€â€Tâ := PA + ±Con(Tâ)â€Tâ := PA + ±Con(Tâ)â€â€where â±Pâ means either âPâ or âÂŹPâ (so, 4 combinations of signs, each describing 2 theories that talk about each other). Which are consistent / inconsistent?
⊠and then the answer is different: T is asserting its own consistence (because it is asserting the existence of something it cannot prove), so it trivially proves its own consistence, so (subject to minimal requirements) it is inconsistent.â€â€Maybe you should add this remark to your answer?
The question was, of course, not very clear to start with, but I interpret it as asking âwhat if we have a theory T that includes the axiom that there is a statement that is unprovable from T?â (not just unprovable from the other axioms). Such a T can be written by the usual self-reference trick âŠ
Related question: when a GPS app reports elevation, is this altitude relative to the WGS84 reference ellipsoid, or to a more precise geoid (defined, I guess, by an expansion in spherical harmonics)? Or do both conventions exist? How can I tell which is being displayed?đ
There's a HOLE in the OCEAN, and it's south of India.â€â€Like, seriously, a spot in the Indian Ocean that is 106 m (348 ft) below mean sea level, the height of a 30 story building.â€â€Let's unpack the what and why of the Indian Ocean Geoid Low (IOGL)â€â€(image is for humor, unrelated to the IOGLđ)đŒïž
Ces trois derniers jours, sur la terrasse chez ma mĂšre (tu sais oĂč c'est), @conscritneuneu.bsky.social et moi en avons vu pas mal, oui, et il n'arrĂȘtait pas de prendre des verres pour mettre les guĂȘpes sous cloche pour qu'elles nous foutent la paix pendant le repas.
Surtout fais gaffe Ă ne pas modifier le cours de l'histoire! Pas question que le monde retienne le nom de Hitler comme autre chose qu'un grand peintre, ou celui de Staline comme autre chose qu'un grand journaliste politique, bref, tels que nous les connaissons.
Many fear that Republicans are destroying American democracy but, fear not!, brave Democrats are rising to the occasion, taking on hard battles, defending the oppressed, fighting the worst of Trump's legislative agenda by⊠<checks notes> âŠgetting the name of the bill changed. x.com/SenSchumer/s...đŒïž
Not only is climate change causing ticks to expand their territory, it's also causing an explosion in alpha-gal syndrome, which makes people allergic to eating red meat or using products that come from those animals. A dozen cases in '09 to over 450,000 now. đ§Ș â€www.theguardian.com/us-news/2025...đ
J'imagine que comme beaucoup de gens soulignent qu'il n'y a pas d'accent aigu, c'est que beaucoup prononcent /ÉĄÊevis/, mais je n'en sais rien. Cependant, je ne pense pas qu'une prononciation avec des sons qui ne sont pas des phonĂšmes normaux de la langue puisse se maintenir longtemps.
I was hoping for a simple interface to let people not reveal a password to any site asking for it, to cancel phishing. All I found with #WebAuthn is security theater pushing for cyberfeudalism and consumerism.
I asked a question on the Computer Science Theory StackExchange about a presentation of Turing reduction that I've been thinking on and off for several months now. cstheory.stackexchange.com/q/55511/17747đ
Mais la suggestion de prononcer «yacht» comme «iak» ressemble quand mĂȘme Ă une blague, non?đ
Je ne sais pas ce qui m'inquiĂšte le plus dans cette liste: les mots que je ne prononce pas «correctement» d'aprĂšs l'auteur de cette page, ou justement ceux (Ă peu prĂšs aussi nombreux) que je prononce «correctement».đ
If you ever think that the branding of LLMs as "AI" didn't really matter just remember that no corporation or public-sector body has a "Superficially Impressive Chatbot Policy", or proposes to "replace humans with superficially impressive chatbots".
The Oracle promptly replied: âThe wisest question you could ask is: âWhat is the wisest question I could ask, and what is its answer?â, and its answer is the one I have just given you.ââ€â€At that moment, Gro-Tsen was Enlightened.
After giving it much thought, Gro-Tsen decided that, rather than trying himself to find the wisest question to ask, he should ask the Oracle! So when it was his turn, he asked: âO mighty Oracle, what is the wisest question I could ask, and what is its answer?â
(A zen kĆan.)â€â€Gro-Tsen was given the rare privilege of asking a question to the Oracle of Ultimate Wisdom. The Oracle can answer any (short) question, but it's a once-in-a-lifetime opportunity, so the question should be chosen carefully!
Hungary banned anything that âpromotes homosexuality,â which means Pride. â€â€However, today over 500,000 people in Budapest told the government to fuck off. đłïžâđđłïžââ§ïžđŒïžđŒïžđŒïž
So you (maybe) heard it here first: The vagus nerve is the new microbiome, with the associated endless stream of podcast bros, shady companies and other grifters trying to sell vulnerable people something with enough prima facie scientific legitimacy to sound plausible.đŒïž
⊠Pour dire les choses autrement: on ne peut pas à la fois dire «le besoin de la clim est faible» et «la consommation de la clim est importante»: si le besoin est faible, la consommation l'est aussi. L'argument de besoin faible ne marche que sur les coûts fixes comme la pose, pas sur la conso.
This has to be the best and most awkward depiction of octopus mating. The embarrassment is palpable.â€â€đđ·Pearse et al (Living invertebrates, 1987)đŒïž
DID YOU KNOW that one popular way of counting dates in astronomy (the âModified Julian Dateâ) is to count the number of dates that have elapsed since the foundation of Denver, Colorado? (Ha, ha, only serious.) en.wikipedia.org/wiki/Julian_...đ
So apparently someone took Hilbert's âInfinite Hotelâ paradox en.wikipedia.org/wiki/Hilbert... and made it into a computer game called âHotel Infinityâ. www.youtube.com/watch?v=OzAh...â€â€(I have no idea whether it's good. I can't play games on my computer.)đ
Worth a watch:â€â€Head of Signal, Meredith Whittaker, on so-called "agentic AI" and the difference between how it's described in the marketing and what access and control it would actually require to work as advertised.đ„
To be clear, this is a proof of Gödel's incompleteness theorem using the failure of the recursive analogue of KĆnig's lemma.
The indignant replies to this skeet by my compatriots pointing out that this photo does not show a croissant are pretty hilarious.â€â€(Suddenly the âpain au chocolatâ and âchocolatineâ teams are united against a common enemy: the âchocolate croissantâ invaders.)đ
⊠and such subtle mistakes might be even more insidious than something that anyone can tell is wrong (if only for the contradictory values of âsum of anglesâ and the words âstatiaticsâ or âsuccossâ).
In the AI's defense, asking an image-generating AI to do something like this is like asking a human to do it in a moment where they are having a stroke and only their right brain hemisphere is working.â€â€A text-generating AI would certainly do better. But it might still contain subtle mistakes âŠ
Pigeons profitant de la fraĂźcheur d'un brumisateur pour les plantes.đŒïž
I don't know if the Norwegian tourist was refused entry because of this meme or for some other reason that may or may not have been decided ex post facto, but one thing is certain:â€â€This image is now ALL OVER international news and social media. đđ
Another thing I'd like to get an approximation of is the Kullback-Leibler divergences D(population â area) and/or D(area â population).â€â€(The former is the average of Ï·log(Ï) over the area of Earth, where Ï is population density, and the latter is the average of âlog(Ï).)
>> TODOâ€â€(Try to compute the decomposition of the world population into spherical harmonics by approximating it by just the cities.)đ
Re population, I wonder if one would not get a better approximation by taking the database of ~150k cities with â„1000 inhabitants (totalling 3.8G people), and use it as proxy for world population density: viê«. compute the spherical harmonics for the sum of the correspondingly placed ÎŽ distributions.
⊠around 40k people (Wikipedia says 36k). The total population of all the 100 cities in the database that are in this octant is around 400k. So it's pretty safe to say that well below 0.1%, probably even less than 0.01%, of the world population, live in the âsouth-west-backâ octant. đŻ
But it's amazing to see how unequally populated they are. According to an online database I found of all world cities with population >1000, the largest one in the âsouth-west-back octantâ of the Earth (i.e., latitude †0° and longitude †â90°) is: Apia (capital of Samoa), with a population of âŠ
We can divide the Earth in 8 equal octants (a spherical octahedron), each an equilateral and triple-right-angled triangles, by cutting it in two at the equator, the 0°/180° meridian and the ±90° meridian.â€â€The octants can be labeled by combinations of {north, south}, {east, west} and {front, back}.
I only skimmed through the actual thesis (which was supervised by Patrick C. Fischer), but the executive summary is that he defines and studies a programming language (âLOOPâ), whose programs always terminate, that can exactly represent the α-th level of the hierarchy, for α < Ï^Ï. âą4/4
âSubrecursive hierarchiesâ (e.g., the Grzegorczyk hierarchy) are about bridging the space between the top of what people usually study in complexity theory (primitive recursive functions) and the bottom of what people usually study in computability theory (Church-Turing computable function). âą3/4
Apparently there is some mystery around why he didn't get his degree and also, how the thesis was typeset. See dmrthesis.net/dmr-thesis/ for a very detailed exploration of the latter. An effort to recreate the document also made a computerphile video: www.youtube.com/watch?v=82Tx... in 2021. âą2/4đ
So apparently Dennis Ritchie (âDMRâ, famous for inventing the C programming language and participating in the creation of Unix) wrote a PhD dissertation on subrecursive hierarchies at Harvard in the 1960's, but for some reason never actually got his degree. computerhistory.org/blog/discove... âą1/4đ
It confused me as well. First for the reason you say, and then because I thought âthere's no reason for Ê to be increasing, so this can't possibly workâ.
Like, I'm sorry, but if I'm allowed to use Greek characters in my proofs, there's absolutely NO reason I shouldn't have access to Coptic âϧâ and its uppercase counterpart âÏŠâ.đ
The nice thing about Unicode is that when you run out of ideas for how to name a mathematical object, you can just open a character map and pick (here, âÊâ).đ
⊠But since the Ê(i) are distinct members of M, the n-th element of M is †max{Ê(1),âŠ,Ê(n)} †max{k(1),âŠ,k(n)}, so the enumerating function of M is bounded by a computable function, i.e., M is not hyperimmune. ââ€â€This is actually a good example to illustrate the difference between these notions.
Yes, the set M of minimal programs is immune.â€â€And indeed, M is not hyperimmune. Proof: let k(n) be a standard computable code for a program that codes the constant function _ ⊠n, and Ê(n) be the smallest (hence minimal) program for that same function, so obviously Ê(n) †k(n). âŠ
â± Note: in the statement of the theorem above, it is not required that the minimal programs generated do anything useful or interesting. We are just saying that the set of minimal programs, despite being infinite (why?) does not have any infinite computably enumerable subset.
⊠Hint / sketch of proof:â€â€âŁ If there were, one could (why?) find a computable function f such that, for every e, f(e) is some minimal program that is strictly longer than e. â€â€âŁ But by the Kleene-Rogers fixed point theorem, there is then some e such that f(e) behaves like e. Contradiction! ââ€â€.âŠ
A fun result in computability (reportedly due to Carl Jockush):â€â€âŁ Say that a program (=Turing machine) is âminimalâ when there is no (strictly) shorter program that behaves identically (=computes same function).â€â€âŁ Theorem: there is no program that enumerates infinitely many minimal programs.â€â€âŠ
This should really be hyper famous. But as the answers I got to the following analogous problem for discrete uniform distributions witnesses, it's not as well known as it deserves:đ
I wrote an answer on Math StackExchange explaining why (and how) one can find three random variables each following a standard normal distribution, any two of which are independent, but such that all three are NOT independent (in fact, any 2 determine the 3rd): math.stackexchange.com/a/5078249/84...đ
I've even used more em dashes (372 of them) than semicolons: poor semicolon!â€â€Here are the full stats of every Unicode character I've used on Bluesky so far (not counting this skeet nor the previous one): âŹïžđŒïžđŒïžđŒïžđŒïž
By Apollo, the decline of the semicolon is true! I've just ran the stats on my Bluesky; and in 6740 skeets before this one, I've used only a measly 236 semicolons; in contrast, I've used 17084 full stops, 14559 commas, 7560 colons, 2548 ellipses, 1720 question marks, and 975 exclamation marks.đ
Obviously nobody writes or uses a formula like this. Of course. It was written to make a point. But what point, exactly? I seem to remember it was Alain Connes, but I don't remember why, and I'd like confirmation.â€â€I just wrote this on Reddit: www.reddit.com/r/Damnthatsi...â€â€Can sbd confirm/correct?đŒïž
A question on the history of the presentation of physics: does someone know where and when, exactly, this exact formula for the Standard Model Lagrangian appeared (which then went somewhat viral), and what the point was of writing out everything that way?đŒïž
happy pride to everyone who both made seminal contributions to mathematics and helped defeat the nazis only to chemically castrated by the british government for the crime of being gay
Poll: do you have a favorable or unfavorable view of:â€â the letter delta?â€â the humerus bone?â€â the Atlantic ocean?â€â the planet Neptune?â€â the color blue?â€â citric acid?â€â electromagnetism?â€â the number 9?
These âfavorable or unfavorable view ofâ polls are getting out of hand. What does it even mean to have a favorable view of âcastlesâ or âGregorian chantâ? And how can you possibly have a favorable view of the Black Plague?đ
Or maybe she's some kind of radical leftist whose opinions should be distrusted on all matters relating to US national intelligence? đ€· x.com/TulsiGabbard...đŒïž
âAs democracy is perfected, the office represents, more and more closely, the inner soul of the people. We move toward a lofty ideal. On some great and glorious day the plain folks of the land will reach their heart's desire at last, and the White House will be adorned by a downright moron.â
I looked up whether this quote is correct so you won't have to: the words âfools and complete narcissisticâ are inserted apocryphally; but the rest is indeed by H. L. Mencken writing for the âBaltimore Evening Sunâ on 1920-07-26. See: www.snopes.com/fact-check/m...đ
⊠â±butâ± I would argue that the whole point of developing general theories (like Cartesian geometry) is to avoid having to think about such tricks.đ
Also, one of the whole points of math is to replace clever tricks (which are hard to find and might not always exist) by general techniques (here: Cartesian geometry). See Grothendieck's metaphor of how to open a nut: ncatlab.org/nlab/show/Th...đ
⊠So here you can start by applying this to âslideâ the upper left corner of the triangle to the opposite side of the 36Ï square (because its diagonal is parallel to the opposite side of the triangle), which already gets rid of that annoying 36Ï square.
I would say it differently: a trick is that if ABC is any triangle and you replace one of its vertices A by any point AâČ on the parallel through A to the opposite side BC, then the resulting triangle AâČBC has the same area as ABC. âŠ
Oh, I had missed the clever trick! But I would still have answered correctly without. This reminds me of the following anecdote about John von Neumann being asked to solve a problem having a clever solution, which he missed, but still solved very quickly: math.stackexchange.com/questions/31...đ
Thanks. So, there's no particularly clever trick here: it's more like a test of whether the would-be answerer knows Cartesian geometry. You just write down the coordinates for every point involved and you get the answer.
Attention, quand on met un ventilateur-colonne à droite d'un ventilateur-ligne, ça fait un scantilataire, alors que quand on le met à gauche ça fait une mantilatrice. Il ne faut pas se tromper!
Ah. I thought it had become almost impossible to avoid using and depending on libgmp as gcc itself uses it at several levels (making the whole mess impossible to bootstrap, incidentally).
Indeed, gmplib.org/manual/Low_0... (âLow-level functions for cryptographyâ) says: «These functions are intended for cryptographic purposes, where resilience to side-channel attacks is desired.»đ
From gmplib.org : «The main target applications for GMP are cryptography applications and research, Internet security applications, algebra systems, computational algebra research, etc.»â€â€Cryptography and security are listed first, so I would certainly hope they are aware of side channel issues!đ
⊠and if so it seems to be completely analogous to Lachlan's result which I summarized as this: đœâ€â€And I think that, in what I wrote above, every set involved in the story is computably enumerable. (Also, P and PâČ play essentially no role.)đ
⊠where â(P, L, R) ⌠(PâČ, LâČ, RâČ)â means âthere is f computable defined at least on P and such that f(P)âPâČ, f(L)âLâČ and f(R)âRâČâ (in other words, the definition of many-to-one reducibility that you introduced).â€â€I think that's what you were asking for in this skeet: đœ âŠđ
[PS: dans le dernier skeet, ma flĂšche est Ă l'envers: il fallait lire q_*(đ^(đ^đ)) â đ^(đ^đ), qui est bien mono mais pas iso.]đ
⊠des foncteurs adjoints dans tous les sens possibles, et que le đ^(đ^đ) de RT(đŠâ) «vient» de celui de RT(đŠâ^rec) (c'est en gros ce que dit Kreisel-Lacombe-Shoenfield) alors que celui qui vient du đ^(đ^đ) de RT(đŠâ, đŠâ^rec) en est un sous-objet.
Thanks for the reminder @janemunday.bsky.social. Every summer, I repost this article DROWNING DOES NOT LOOK LIKE DROWNING. To date, I know of FOUR kids who were saved after someone who'd clicked on the link learnt how to spot actual drowning. Take time to read and pass on.â€â€slate.com/technology/2...đ
But while the algorithm convincingly answers the question of âhowâ the text was generated, I would also like to link to this excellent (if lengthy) video by âEsotericaâ on other aspects, including motivation and a material analysis of the book itself:đ
The reason I mention this now is that the âSciShowâ channel on YouTube published a video summarizing the case and discussing the paper of which the previous skeet shows a section:đ
For what it's worth, let me remind everyone that the case of the Voynich manuscript should be considered closed: â”it's a hoaxâ” â there is no mystery and no hidden meaning to find.â€â€We even know a plausible method (usable by hand) by which the random text might have been generated. đœđ
In order of magnitude, tuberculosis kills worldwide roughly as many people yearly as covid averaged since it started. But TB has been going at it for centuries.â€â€Yet people in rich countries hardly care about TB because it mostly doesn't affects them (unlike covid did).đ
TB still kills almost 1.3 million people every year, making it the worldâs deadliest infectious disease.â€â€Most of these deaths occur in low- and middle-income countries, like Ghana and Ethiopia. Their death rates have fallen in recent decades, but are still far higher than in rich countries.
Funny thing about email is that it was conceived as a slow but reliable means of communication (servers will retry for days before they give up on delivery).â€â€But spam filters have made it unreliable, and we treat it as instantaneous (assuming mails will arrive within seconds).
⊠p^* envoie une partie de đŠâ sur l'ensemble des fonctions constantes correspondantes, et p_* envoie une partie de đŠâ^rec sur l'ensemble des codes de programmes qui les calculent).â€â€(Ils sont localiques, surjectifs et connexes [q^* et p^* sont pleins et fidĂšles]. D'ailleurs, q a une section.)â€â€âŠ
âą Are people living in a detailed simulation of a physical universe different from characters in a book? Are we different from either? How might we tell?â€â€âŁ Should we fear our own death any more than a book (or its characters) should fear its last page?â€â€â€ Deep mystery or mumbo-jumbo?
⥠Do they die when the book ends (if not before)? Does their entire world cease to exist? If so, ought they try to act so as to protract the novel?â€â€Also, when does this happen? At the last page in an abstract sense? When the author writes it? When each reader reaches it?
Random food for thought:â€â€â Are the characters in a novel conscious? (or are they âphilosophical zombiesâ?)â€â€If not, how could they themselves know they aren't?â€â€If yes, do they live in the pages of the book itself? in the mind of the author? that of the reader(s)?
Je pense que la meilleure explication intuitive de ce fait đœ est la suivante: si vous avez une pile de tickets de loto dont 20% sont gagnants d'un gros lot, c'est quasiment aussi bien qu'une pile dont 60% (ou 80%) sont gagnants, et BEAUCOUP mieux qu'une pile «naturelle». âŠđ
FWIW, I don't think such names are useful and I don't think I've ever heard this one. If someone uses this formula in a paper, I'd rather it were simply written out with fresh variables and referred to as such (âkeeping in mind that we have [âŠ], we compute [âŠ]â, or something of that flavor).
Cynara cardunculus (artichoke / cardoon), used as an ornamental plant, in bloom, in the streets of Paris.đŒïž
On the contrary, it's an interesting and sensible â if completely trivial â theorem: if âx, y. (f(x) = g(y)) then there exists c such that âx. (f(x)=c) and ây. (g(y)=c). In other words, if an expression depending only on x equals one depending only on y, then in fact they depend on neither.
⊠That being said, Signal also has a killer ânetwork effectâ feature that WhatsApp doesn't have: you might randomly get invited to a top secret meeting between crassly incompetent top US government officials.
⊠People use WhatsApp simply because other people use WhatsApp. It's a vicious cycle. And this vicious cycle is now sufficiently entrenched that they can add ads or other shit to their app and people won't run away. âŠ
The fact that everyone isn't using Signal, despite its objective technical superiority over every other analogous app (WhatsApp, Telegram, etc.) is a good illustration of the strength of network effects. âŠđ
J'ai eu droit Ă la droite, puis la gauche, puis de nouveau la droite. Je devrais sans doute arrĂȘter la musculation, mais je suis malheureusement devenu assez addict. đâ€â€(Heureusement, je me remets assez vite, et le naproxĂšne m'aide beaucoup.)
Server confirmed dead. Replacement server supposedly on its way. Will likely take some time for me to install and configure (I have backups of everything but this is still a pain).
As Gregor Samsa awoke one morning from uneasy dreams he found himself too cold in his AI controlled bed. He went to adjust temperature and couldn't because the Eight Sleep app was currently broken. He couldn't adjust by hand because he had a Pod3, not the upgraded Pod4 with physical controlsđŒïž
Personal announcement: the server hosting my email seems to be down (probably dead for good, will need to reinstall a new one). So don't try to contact me by email for the next few days.â€â€(Not that I reply to email anyway, but now I can't even read it.)
@joeldavidhamkins.bsky.social How âwell-knownâ would you say the following result by Lachlan in computability is?â€â€âŁ If A and B are computably enumerable and if the halting problem is many-to-one reducible to AĂB, then it is, in fact, to one of A or B.â€â€Would you call this a âstandardâ result?đ
What I can't decide is how famous this result of Lachlan is. On MSN the paper has only 7+2 citations, and apart from Odifreddi's book and Soare's (as an exercice) I can't find it in most standard books (Rogers, Lerman, Cutland, Cooper, SoareâŠ).â€â€Yet some papers call it a âwell-knownâ fact. đđŒïž
Maybe the following presentation âŹïž might be more helpful to understand intuitively what is going on: this is exercise II.4.16 (on p. 45) of Soare's 1987 book âRecursively Enumerable Sets and Degreesâ (not to be confused with his 1978 paper of the same title đ).đŒïž
The substantive part of the proof happens in theorem III.9.3 (pp. 347â348 of vol. 1). For completeness of Bluesky, here it is: âŹïžâ€â€Here, đŠ is the halting problem, âm-completeâ means m[any-to-one]-equivalent to đŠ, everything is assume r.e. (=c.e.), and A·B is the set of encodings of pairs in AĂB.đŒïž
⊠but it still wasn't able to give me a precise reference or name for the claim that đâČ_m does not split (except âOdifreddiâs Classical Recursion Theory and related textsâ â not super useful).
More and more infuriating! I thought this is the sort of slightly tricky searches for which an AI engine might be useful, so I asked ChatGPT: chatgpt.com/c/68507819-4...â€â€I âłïžthinkâłïž what it told me is correct, and the term âjoin-irreducibleâ is certainly one I should have thought of, âŠ
⊠some local structural properties, such as đâČ_m does not splitâ, which, if I correctly understand the phrase âđâČ_m does not splitâ, might exactly answer the question (đœ) I asked a few skeets higher up in this thread, but no elaboration nor reference.â€â€Nor is âđâČ_m does not splitâ easy to Google.đ
Now this is infuriating: in the thesis âComputability Theory and Degree Structuresâ by Yuan Bowen dr.ntu.edu.sg/handle/10356... on page 11 there is the offhand remark that âWe have a complete description of the structure on r.e. m-degrees [i.e., many-to-one degrees], including âŠđ
I had the bad idea of opening a PDF of Soare's 1987 book âRecursively Enumerable Sets and Degreesâ to look up (non-)splitting theorems and the chapter on the lattice of c.e. sets under inclusion,which both seemed relevant: now I'm lost in a maze of âhypersimpleâ, âhyperhypersimpleâ(!), âcohesiveâ âŠ
It's certainly interesting enough to ask, but I wish you'd wait a bit, because I still haven't had the time to even begin seriously thinking about it. (If you say you've already spent so much time on this that you're completely out of ideas, either you're very fast, or you have way too much time!)
My roommate saw me put more cheese onto a frozen pizza & it was like I unlocked something in him. I saw the wheels turning as he realized we don't have to settle for the default amount of cheese the pizza overlords offer us. What goes onto the frozen pizza is in our control. We have the power.
Sorry, I'm being told that in Pyongyang, parades are not held for the Leader's birthday but for the founding anniversary of the Korean Peopleâs Army, the anniversary of victory in the Fatherland Liberation War and the founding anniversary of the DPRK. đâ€â€Source: pyongyangtimes.com.kp/blog?page=co...
Just remove the specific place and people names and you'd be hard-pressed to tell if this is the Washington Post describing Trump's birthday parade or the Pyongyang Times describing the one for Comrade Kim Jong Un.đ
Off-topic, but it is super annoying that this site/app offers no convenient way to bookmark a skeet (as in âsave to read/reply laterâ). This fosters a âmust answer immediately or neverâ mindset which I find very stressful.â€â€(I.e.: I'd like to think about it, but Bluesky makes this hard to do.)
⊠Also, if you keep only the condition âx:X. (xâD â pâD), then if I am not mistaken the sets D in question are (internally in Eff) a topology on X, which may have some nice properties, not to mention the fact that its topos of sheaves might give you a topos of interest (localic over Eff).
⊠(I hope I got this right, I didn't give this much thought, but there should be a description of this sort.), and I think your â operation is simply set-theoretical union on the subsets of â{p,l,r}, and reduction is just inclusion. So this p.o.v. might be useful. âŠ
⊠Be that as it may, here's a thought that may be of some use (but maybe that's what got you to this notion in the first place): your notion is equivalent to giving a subset D of X := â{p,l,r} in the effective topos such that âx:X. (xâD â pâD) and ÂŹâx:X. (xâD) (unless you follow the advice of đŒ). âŠ
⊠So I think you should probably modify either your intuitive explanation of what your reduction is supposed to mean, or your definition of it (like, maybe allow the reduction function to directly return âtrueâ or âfalseâ instead of calling on the other problem). âŠ
I didn't have time to think about your question, but I think your notion of reduction is âwrongâ (in the sense that it doesn't state what you claim it states): (â, â , â ) should equivalent to (â, {0}, {1}) in that both are trivially decidable, but with your definition, they're not. âŠ
⊠Pour revenir Ă la circulaire, je ne vois pas la logique permettant de qualifier de plus «français» le âöâ de «maelström» que le âñâ de «piña colada» ou le âÄâ de «rÄmen».
Now think of the number of Trump supporters who will laugh and say âliberals like to protest, but they can't even get the instrumental plural of âáá±áąáșáááŸášáâ right: that's why we need a smart King who knows such thingsâ. đ
I'll say this again:â€â€Whatever evil you think of AI, hoping to use copyright as a weapon against it is like trying to introduce cats in Australia to control the rabbit population that's getting out of hand:â€â€â Now you have two problems.
In his case, I think his actions are best explained by the balance of blood, phlegm, bile and atrabile in his body. Or perhaps by a worm in his brain.đ
Well, âworld without drightensâ, I guess.â€â€âDrightâ and âdrightenâ are coolÂč English word, and we should revive them.â€â€1. (The words are cool. Not the concepts. No need for drights to parade on the streets.)đ
(It reads: âáčáá±áááá ááŸáą áá±áąáșáááášáááâ: âwerldiz Änu druhtiĆamizâ. I actually think there are typos and this should rather be âáčáá±ášáááá ááŸáą áá±áąáșáááŸášáááâ: âweraldiz Änu druhtinamizâ. but what do I know?)
I can't read them all, but I notice that the Latin (âmundus sine cĂŠsaribusâ: âworld with CĂŠsarsâ) and Greek (âᜠÎșÏÏÎŒÎżÏ ÏÏÏáœ¶Ï Ïáż¶Îœ ÎČαÏÎčλÎÏÎœâ: âthe world without the kingsâ) doesn't say quite the same as the Germanic âáčáá±áááá ááŸáą áá±áąáșáááášáááâ: âthe world without lordsâ.â€â€Subtle message targeting here!đ
For the uninitiated, the band is playing "Fortunate Son" - which is a protest song against rich folk being able to dodge the draft for Vietnam. â€â€Either whoever did the set list is incompetent or it's a 14/10 troll of DJT, who got a very timely diagnosis of bone spurs in 1968 at age 22.đ
⊠But of course, the question of âwhen and how did the United Kingdom become a democracy?â is more a question of exactly what one means by âdemocracyâ than one of history.â€â€PS: O this, I also enjoyed this 3-part video series on the history of the British Constitution: www.youtube.com/watch?v=-6ds...đ
⊠But of course, the question of âwhen and how did the United Kingdom become a democracy?â is more a question of exactly what one means by âdemocracyâ than one of history.â€â€PS: O this, I also enjoyed this 3-part video series on the history of the British Constitution: www.youtube.com/watch?v=-6ds...đ
⊠The Wikipedia article on William Pitt the Elder en.wikipedia.org/wiki/William... is also worth reading as he was one of the foremost British who tried to avoid the American Revolution by giving in to the colonists' demands. Seems he faced opposition from within Parliament, not so much the King. âŠđ
This documentary on George III and his personal life www.arte.tv/fr/videos/11... (part of a series on all four Georges) should at least partially answer the first question. IIUC, the power lay mostly with Parliament, but the king was far from powerless. âŠđ
Our library holds a rare copy of the proceedings of the 1911 Solvay Conference on physics, and I enjoyed looking through it (very carefully) today. As well as the amazing discussions and pictures (these are from Perrin) it seems a previous reader had been practicing their French at the same time!đŒïžđŒïž
HELP: Trying to find a more reliable #source for this exclamation attributed to the Ottoman Sultan Bayezid II that Ferdinand of Spain cannot be called wise if he expelled people. â€â€Tried in Nomologia o discursos legales by Imanuel Aboab but can't read easily đ¶â€â€Does anyone know?đŒïž
⊠And it's not just the AI-generated snippet which is wrong. I can't seem to scroll down far enough to find a page talking about Amo with this particular search query.
⊠Well, Anton Wilhelm Amo (a fascinating character, born in what is now Ghana, and brought to Europe probably as a slave) obtained a doctorate from the university of Wittenberg in 1734. Last time I checked, 1734 < 1876. âŠđ
Interesting bit of US-centrism from Web search results. I was trying to remember the name of Anton Wilhelm Amo, so I searched âfirst black man to get a doctorateâ then adding âin the worldâ. Basically all answers are about Edward Bouchet (Yale PhD in 1876) and other Americans. âŠđŒïž
This is the first time I've seen this articulated, but it's a very neat summary of the instinctive reaction to AI that a lot of us have. I can acccess all the information I want about, say, car engines or linear algebra, but that doesn't give me the knowledge to fix the engine or do the equationsđ
Incidental discovery: it seems that around the 1970's, the standard Russian word (transcription) for âalgorithmâ was âĐ°Đ»ĐłĐŸŃĐžŃĐŒâ [âalgorifmâ] ru.wiktionary.org/wiki/%D0%B0%... â now it is âĐ°Đ»ĐłĐŸŃĐžŃĐŒâ [âalgoritmâ].đđ
Well, Google Books has it, I guess, but they won't let you look inside, so, not very useful: books.google.fr/books/about/...â€â€LibGen doesn't seem to have it. (And it's also not reviewed in MathSciNet AFAICT.)đ
When the formula you're trying to look up is to be found in a chapter of a Russian book that was published in 1974 by the Computing Centre of the Academy of Sciences of the USSR and which nobody seems to have digitized, you know you're in trouble. đŹâ€â€(And no ISBN, of course.)đ
The original reference is given as:â€â€Đ. Đ. ĐлОŃĐșĐŸ [V. E. Plisko], âĐб ĐŸĐŽĐœĐŸĐč ŃĐŸŃĐŒĐ°Đ»ŃĐœĐŸĐč ŃĐžŃŃĐ”ĐŒĐ”, ŃĐČŃĐ·Đ°ĐœĐœĐŸĐč Ń ŃДалОзŃĐ”ĐŒĐŸŃŃŃŃâ [â âA certain formal system that is connected with realizabilityâ], ĐąĐ”ĐŸŃĐžŃ Đ°Đ»ĐłĐŸŃĐžŃĐŒĐŸĐČ Đž ĐŒĐ°ŃĐ”ĐŒĐ°ŃĐžŃĐ”ŃĐșĐ°Ń Đ»ĐŸĐłĐžĐșĐ° (1974) 148â158â€â€â but that's in a book and I don't have it.
Even if you can't read Russian â and I don't think an English translation of this paper exists â the diagram on page 47 will tell you the most important conclusion:đ
Pour le rapport de force, je propose justement d'en faire une exigence nationale (toutes disciplines), pour redonner au doctorant le pouvoir en lui retirant les menaces qu'on peut lui faire subir s'il met sa thĂšse en ligne (si c'est obligatoire on ne peut pas le lui reprocher).
Can somebody guess why a 2.5 years old 650VA uninterruptible power supply would show â101%â and sound the alarm when it's only outputting ~375 VA?â€I recently upgraded the computer it powers and I'm now getting these alerts. Should I upgrade the UPS or just change the battery?
In other breaking news: Donald Trump is coming to believe that water is wet.â€â€(Note that Donald Trump being, for once, actually correct about something â if later than just about everyone else â might indeed qualify as ânewsâ, and maybe even as a form of good news.)đ
Le Conseil constitutionnel recrute un membre de son service juridique (enseignant-chercheur) ! â€â€La fiche de poste et les renseignements sont, notamment, sur la page « recrutement » du Conseil : www.conseil-constitutionnel.fr/recrutementâ€â€Â«Â Engagez-vous, rengagez-vous ! »đŒïž
This is like when Russian oligarchs and, more recently, Chinese tech billionaires learned the difference between being a fantastically rich person and being in direct personal control of the state and its powers.đŒïž
So the question is: at which points is f (of the left graph above) differentiable? Are there x such that 0<fâČ(x)<1?â€â€We know this: fâČ=0 on the complement of C (the âfatâ Cantor set en.wikipedia.org/wiki/Smith%E...), and fâČ(x)=1 if x is a Lebesgue density point of C. That's about all so far.đ
* Correction: the graph earlier in this thread is incorrect (it should NOT be self-similar).â€â€The graph below on left shows the function f we're talking about (for param α=ÂŒ).â€â€Right (â ïž different scale!) shows the standard (non-âfatâ) Cantor set âdevil staircaseâ. en.wikipedia.org/wiki/Cantor_...đŒïžđŒïž
I posted a partial answer on MO showing that, by left-composing f with a homeomorphism (so, essentially, by changing the heights of the âplateauxâ) we can make it differentiable everywhere. đ€Żâ€â€But I don't know what to believe for the original f (plotted above). I'm very confused.
As the old joke goes, an American diplomat and Soviet diplomat met up, and the American says "I really admire your country's propaganda." The Soviet says, "True, it is good, but it is nothing compared to American propaganda." The American, confused, responds "We don't have propaganda."
This kind of circular thinking is the mother of all denials. "I am good therefore anything I do is good and I cannot do anything evil. If I do something evil, that something is now *good* "
⊠Because they are entirely secure in their belief that OF COURSE đșđžAmericađșđž is the Land of đFreedomđ, so OF COURSE their guy can't be a dictator or even act like one, even when he forbids demonstrations. America and dictatorships belong in ontologically different categories in their minds.
The thing is, Americans have been so thoroughly indoctrinated in believing their country is the Land of the Free, that the guy can openly showcase the paraphernalia of military dictatorships, like holding a military parade on the Leader's birthday, and his supporters won't even blink. âŠđ
đ§”đœ Ce n'est pas vraiment que la base est interrogeable, c'est que n'importe qui peut demander Ă payer pour n'importe quelle immatriculation et, par ce biais, savoir s'il y a quelque chose Ă payer.đ
I know thereâs serious news, but this? Too good not to share. â€â€Gavin Newsomâs office just posted a clip of EMPEROR PALPATINE reading Trumpâs unhinged Truth Social rant about the L.A. protests. â€â€Itâs trolling at its finest. â€â€The Force is strong with this one. đđ â€#NoKingsâ€#FreedomToDissentđ„
Here is a graph of the function f being discussed in the particular case α=ÂŒ (so that the fat Cantor set, aka Smith-Volterra-Cantor set, has Lebesgue measure Âœ). The question is: where is f differentiable? And are there points x where fâČ(x) exists but is neither 0 nor 1?đŒïž
Remarkably incisive and provocative question on MathOverflow: what is the set of points of differentiability of the âstaircaseâ (cumulative measure function) for a fat Cantor set (obtained by removing the middle α part instead of the middle third)? mathoverflow.net/q/495986/17064đ
⊠ce qui incombe avant tout aux parents, c'est-Ă -dire de contrĂŽler de ce que leurs enfants vont voir du monde bizarre et souvent dangereux qui les entourent â et surtout de le leur expliquer correctement. (Encore une fois, commencer par les pubs!)
It's very strange that, despite the central importance of the Killing form in the study of Lie algebras, the fact that it vanishes identically doesn't seem like an important or natural condition. (It just lies somewhere between ânilpotentâ and âsolvableâ.)
An explicit counterexample: âÂł with the Lie bracket [(t,x,y), (tâČ,xâČ,yâČ)] = (0,ât·xâČâx·tâČ,âi·t·yâČâi·y·tâČ) where i=ââ1, that is, [eâ,eâ]=eâ, [eâ,eâ]=i·eâ and [eâ,eâ]=0. Its Killing form vanishes, so it is solvable, but it is not nilpotent.â€â€(It's a semidirect product of a dim 1 by an abelian dim 2.)
I was today years old when I learned that a Lie algebra in characteristic 0 whose Killing form vanishes identically need not be nilpotent. (Although it is solvable by Cartan's criterion; and conversely, a nilpotent Lie algebra has zero Killing form.)
Kettling demonstrations is ignominious and should be illegal as a matter of general principle. Sadly, most countries allow it.đ
The problem isn't that most Americans want Trump to be an authoritarian dictator, it's that they don't realize he's acting like an authoritarian dictator.â€â€Either bc they don't know the facts (e.g., they're told protesters are dangerous insurgents) or bc they don't know what authoritarianism means.
⊠It's super hard to find the info on exactly what breaks (esp. if I run things like bsky.app/profile/did:... suggests, which probably mitigates the disaster), because nothing is properly documented, so I can't tell you, but I'm absolutely sure a great many things will break.đ
Many scripts, conf files and tuning representing ~30 years of fixing misfeatures and getting the keyboard, shortcuts and displays to behave like I want, with such tools as xinput, xmodmap, xkb, xev, xset, xdotool, xsm, fvwm, etc., which I understand Wayland gratuitously breaks to various extents. âŠ
The third amendment is so funny because hotels can absolutely tell US military personnel on assignment to leave immediately or refuse the business outright, which makes it a truly unique industry for public pressure campaigns.
You don't care because they're not removing any features you depend on. One day they will, and suddenly that day you will realize I was right back then. But I hope it will cause you less anguish than this causes me now.
The real fun is that you can logically say âtwelvety twelveâ for 132 and watch how people get really confused at trying to figure out how much that is.đ
PS: various ppl have pointed out to me that the guy starting this âXlibreâ fork of Xorg is potentially tainting the project with toxic political ideology.â€â€If we have to choose between corporate-driven Wayland and MAGA-endorsing Xlibre, things aren't looking good for Linux graphical environments. đđ
I asked a question on MathOverflow about the various conditions on geometric morphisms between topoi whose unit or coĂŒnit is monic / epic / iso. mathoverflow.net/q/495960/17064đ
So did they issue a public call for volunteers to help maintain X11 support in the code? Did they discuss the option of simply not adding any new features rather than remove ones which are actually being used by real users?
The same dynamics can be seen at work in FFmpeg. FFmpeg is Libre Software. It got an OpenSource fork after a failed coup, the fork died, but for lack of leadership forkers were accepted back and then removed features. Or broke them, called them broken by design and removed them.đ
⊠And if Wayland itself wasn't able to reach feature parity with X11 in 15 years of work, it was probably not their intention to even try to do so. They just want to break stuff that their corporate overlords don't care about.
⊠Of course fragmentation has a cost. But there was always such a fragmentation. Yet the free software community manages, precisely because it cares about users' needs, so it also gets volunteers. âŠ
These are bullshit excuses, hiding behind technical issues to make political decisions and ignoring users' needs. Did the Gnome team even make a call for volunteers to help maintain the X11 backend? Do we have evidence that they are understaffed? Did they poll user preferences? Of course not. âŠ
⊠There are many things that Wayland cannot do and probably will never be able to do. If users need to choose between the two sets of features, it should be up to them.
Did you really completely miss the point or are you just playing obtuse?â€â€This is not a valid excuse for Gnome or Gtk+ to drop X11 support for users who don't care about these fabled âmany thingsâ. Users need the ability to choose, not be told what they must use. âŠ
If you think you've avoided the corporate takeover and loss of freedoms of Linux by moving to Mac, you've kind of missed my point, I think. It's a bit like saying you're happy you've avoided the democratic decline of Switzerland by moving to China early.
No, that's mostly wrong. The rule is now that âfreeâ software is maintained by corporate entities who singlehandedly decide what they think is âgoodâ for users, and who use the âpoor maintainerâ as an excuse to remove features they don't like. This is what my thread is about.
Open source, by contrast, cares mostly about the technical superiority of this or that (âWayland is better! use it instead!â) instead of listening to the needs of users. (To be clear: I certainly don't want Wayland to die: I want users to have the freedom to choose between X11 and Wayland.) âą11/11
⊠But âșOF COURSEâș the whole point of free software is to empower users: if you're doing the contrary by effectively removing their ability to choose, to configure, or to use the features they like, your software is not free software. Even if it fits the legalistic definition of it. âą10/?
And yes, I've heard the excuse that the freedom to configure or keep obscure features was not part of the original definitions of free software. This is because it was believed to be so obvious that nobody thought to state it explicitly. ⊠âą9/?
The terminological switch from âfree softwareâ to âopen sourceâ is a way to distract us from what the whole point of free software was about: empowering users. To make it seem as though if the code is there and reusable then all is fine. âą8/?
Obviously these corporate entities don't care much about their users' freedom. Freedom to configure their software in unusual ways, or to use obscure features least of all. They think it's costly and frivolous. So they âdeprecateâ and remove features they don't like. âą7/?
The thing is, many/most large open source projects are no longer maintained by dedicated volunteers who care about the needs of their users, but by corporate entities who effectively appoint the nominal heads of the projects, and who care about their own interests, not their users'. âą6/?
Yes, if you're alone thanklessly maintaining a piece of code, or maybe if you started the whole project, or if nobody answers your call to help maintaining the feature, or in such exceptional circumstances, you may get a pass. But these are the exception, not the rule. âą5/?
And yes, obviously, maintaining features comes at a cost. This is part of the responsibility of maintaining code. If you find it too hard to keep up, ask for community help! Or pass the torch to someone else. âą4/?
And the excuse that (because the source is open) if users are unhappy with your job and want to keep the feature they can fork the project is just that: an excuse.â€â€It completely ignores the network effect that makes forking very hard to sustain.â€â€âą3/?
Removing a software feature that people actually use is an incredible act of violence and a breach of trust of maintainership.â€â€Maintaining a piece of free software is a form of power over its users, and this power can be abused.â€â€âą2/?
Let me expand upon this đœ because I think this deserves further explanation.â€â€âBack in the dayâ, free software devs didn't remove software features because they thought people â¶shouldⶠstop using them. They removed them because people âHADâ stopped using them.â€â€See the difference?â€â€âą1/?đ
An entire generation of people raised on memes and Fox News who are just completely unable to separate propaganda from reality. If there is a crisis, itâs epistemological. Fascists will try to bend reality to their ideology, but this always fails in the long run with tons of damage along the way.
Everything thatâs happened over the past six months has been a response to an imaginary crisis. There is no immigrant invasion. No trade crisis. No scientific or governance crisis. Just people completely high off their own supply trying to fundamentally reorder society. None of this had to happen.
Anyway, it is indeed clear from these news that (whoever makes decisions for) Gnome is now in the business of waging an active war against their users. The question is: will they win it, and what can we do against them?
⊠I think @laurentbercot [on Twitter] is right in pointing out that the rebranding of âfree softwareâ to âopen sourceâ was actually a poison pill brought by corporate forces to destroy users' freedom and take over control of the entire ecosystem, making it into another Windows or Mac OS.
⊠I think @laurentbercot [on Twitter] is right in pointing out that the rebranding of âfree softwareâ to âopen sourceâ was actually a poison pill brought by corporate forces to destroy users' freedom and take over control of the entire ecosystem, making it into another Windows or Mac OS.
The amount of arrogance laced with poisonous idiocy of these corporate-appointed devs is astonishing, but the truly sad thing is how little backlash there is against the notion of stripping software of its useful parts and freedom and slowly turning it into what can only be described as malware. âŠ
OK, at least that's a bit of good news.â€â€This still leaves open the risk that Gtk+ or whatever might drop support for the X11 protocol, but I think that's not for the immediate future.
I think we need to come up with a variant of the famous Arthur C. Clarke quip that's applicable to AI: I proposeâ€â€âAny sufficiently advanced bullshit is indistinguishable from intelligence.âđ
One thing that isn't clear to me is the extent to which one can use Wayland as a hardware abstraction layer for an X11 server (supporting modern hardware acceleration) and make it impossible for clients to talk to Wayland except through the X11 layer. This might be fine with me.
(Though I would still recommend that you check the BIOS fan settings and fiddle with them, because when impossible things happen it's time to start doing things that couldn't possibly work. đ )
If you're saying the fans were connected directly to the power supply before, and still are, and you changed nothing on the power supply and nothing on the fans, and the connector from the PS to the fan isn't a fan-specific thing that might be controlled from the chipset, then⊠I don't have a clue.
To be clear, I'm not demanding any new features. I don't think there are any useful new features to add to X11, or to any kind of graphical environment. What I want is for the security to be maintained, and for graphical programs and toolkits to keep supporting X11.đ
As someone who despairs of seeing Wayland's hostile takeover of the Linux graphical environment despite bringing many misfeatures and breakages but nothing of value, I don't know what to think of Xlibre: is it good news or will the added fragmentation increase X11's morbidity?đ
⊠But it âcouldâ be that you need to set the fan control mode in your motherboard BIOS's settings.â€â€(This is the sort of problems for which I find using an AI as rubber duck to be somewhat useful, BTW.)
You probably know this already, but there are several different ways a fan's speed can be regulated: not at all, by varying the power, or by a specific input wire to the fan. I forgot the details. âŠ
⊠they would show you a photo with a sign saying [speed limit] 70km/h and you're asked âhere I can drive at: 90km/h? 70km/h? 50km/h? 30km/h?â and you need to choose the three last answers (not just 70km/h) because here they decided to be logical.â€â€And there's no way to guess which way was meant! đ
⊠E.g., âI pass after pedestrian P (yes/no)â â expected answer was ânoâ because there was another pedestrian Q to yield to, and whoever wrote the question decided that âafterâ meant âimmediately afterâ not âsome time afterâ as it logically would. On the other hand, sometimes âŠ
To get my (French) drivers' license I had to pass a theoretical exam with multiple choice questions (illustrated by photos or short videos).â€â€It was infuriating because in some of the questions you had to answer like a logician, and in others, answering like a logician was considered wrong. âŠ
⊠or si le but est de rendre 2^â non-omniscient, une fonction continue surjective 2^â â â (ou truc du genre) ne sert pas Ă grand-chose si â est omniscient.â€â€En fait, je pense maintenant plutĂŽt que 2^â est omniscient dans tout topos localique: âŠ
(Contrairement Ă ce qui se passe dans le topos effectif, d'aprĂšs cette autre branche de la discussion que je relie ici pour aider Ă naviguer le labyrinthe que ce fil est devenu.)đ
Please, @bsky.app@support.bsky.team, could we have the option to đ follow a post đ (i.e. receive its replies as notifications) just like we can follow a user? đâ€â€It seems both highly logical and super useful (when sbd asks an interesting question).â€â€Or is there a workaround that achieves this?
Ben oui, mais tu ne peux probablement pas non plus imaginer un cas oĂč (b) et (c) diffĂšrent puisque ça passe par des astuces bizarres. Et comme (a) et (b) coĂŻncident, grĂące Ă KLS, finalement, ça n'aide pas trop Ă trancher. đ
I'm a great fan of the Assimil courses. I've used them to various degrees for a number of languages (either the beginners' course or the advanced one).
I suggest you give Assimil a try: www.amazon.fr/Using-French... (I didn't test their French course myself, of course, but I used their analogous advanced German course, and I found it very helpful).đ
⣠What is the central teaching of zen totipsism? The cypress tree in the garden.â€â€âŠand so on. You can come up with much more (is that itself another totipsism?).
⣠Judgmental totipsism is the conviction that civilisations should be judged on whether they develop the idea of totipsism.â€â€âŁ Contrarian totipsism says that contrarian totipsism is utter bullshit.â€â€âŁ Dubious totipsism is the fear that we didn't properly understand dubious totipsism.
⣠Ultimate totipsism is the affirmation that the only thing that exists in the Universe is you (yes, you!), here, right now, thinking about ultimate totipsism.â€â€âŁ Eschatological totipsism is the belief that eschatological totipsism will only be fully revealed and understood after the world ends.
⣠Strong totipsism is the claim that strong totipsism is the ultimate basis and framework for understanding the Universe.â€â€âŁ Final totipsism is the idea that the Universe exists with the goal of making the idea of final totipsism emerge.
⣠Weak totipsism is the observation that the Universe is such that the idea of weak totipsism could emerge.â€â€(So it is a variant of the âanthropic principleâ, but instead of focusing on intelligent life, it focuses on whatever could give birth to weak totipsism itself.)đ
⣠Referential totipsism is the fact that you (yes, you!) are, right now, currently thinking about (referential) totipsism.â€â€(Cue the comic of Geluck's Le Chat standing in front of a map with a dot labeled "you are here", and he says "news travels fast around here!")đŒïž
Let's start with the weakest forms of totipsism:â€â€âŁ Tautological totipsism is the assertion that tautological totipsism is a form of totipsism that is tautological.â€â€Duh.
#Totipsism (a word I invented) is the idea that totipsism itself is a concept central to understanding the Universe. Much like the anthropic principle or solipsism or Descartes' "cogito ergo sum", it exists in many variants: —ïžâ€â€www.madore.org/~david/misc/...đ
Actually I was mostly confused about the definition of âsemidecidableâ. It does not mean âcountable union of decidable subsetsâ.â€â€Also, for the counterexample of Friedberg internalized in Eff, you can cite prop. 3.2.31 of van Oosten's book (that book has everything, it seems!).
OK, I've just added one more item to my big TOTHINK-mountain of confusions to sort out:â€â€âŁ It seems that by invoking Friedberg you define a subset of â^â that is not open yet is the projection of a decidable subset Q of â Ă â^â; but Q is then open, and a union of open sets is open, so P should be. đ”âđ«
Republicans are on the verge of passing a budget bill that would amount to one of the greatest transfers of wealth from the working poor to the super rich.â€â€And two billionaire oligarchs are fighting about it because the bill doesn't cut vital social programs enough.â€â€Hello?
There are two main errors to avoid when thinking about history: one is to think the people of the target time period were necessarily just like us, and the other is to think that they were necessarily completely different.
Also, IIUC, the contemporary Breton language (not to mention its orthography) is a post-WW2 reconstruction in the hope of reviving the language by taking a kind of compromise/average from surviving dialects. Breton in the 18th century was probably a far more diverse dialect continuum.
Of course the vertices of the hyperbolic triangle are hard to reach, especially the two ideal ones (having angle 0, so a Brownian motion has vanishingly small probability of landing near them).â€â€Riemann's conformal mapping theorem is just black magic!
I added some plots of the conformal isomorphism found between the unit disk and the hyperbolic triangle in question, because it's interesting. The red and magenta curves are the image of circles of radii 0.99 and 0.999.đŒïž
The hilarious thing about Grok is that of course it's awful because it's Elon Musk's AI (that's 2 reasons!), but still, it's not nearly as awful as one might expect from that, it often exposes Musk's shit and contradiction, so in the end, everyone is angry, both the techbros and the anti-AI crowds.đ
I wish someday I had the time to understand what âFâ is all about, and why it's so important and why so many functions can be expressed in terms of it.
The above defines the conformal mapping of the upper-half plane to the domain {x+i·y : xâ„0, yâ„0, (xâ1)ÂČ + (yâ1)ÂČ â„ 1} (=the doubly ideal hyperbolic triangle with vertices at 0, 1 and i) taking 0, 1, â to 0, 1 and i respectively.
Did I actually answer a MathOverflow question with a formula involving the âFâ hypergeometric function, that I know nothing about? It would seem I did! (But actually, I basically just copied this from Wikipedia.) mathoverflow.net/a/495809/17064đŒïž
See, this is why I don't trust men in positions of power. They're ruled by their emotions. Totally irrational. We need the calm, cool intellect of women in situations like this.â€â€:3đ
⊠but I reiterate that those of us who hate both of them shouldn't rejoice because they're probably even more dangerous when fighting than when allied.đ
Six months was a bit longer than I expected the Trump-Musk bromance relationship to last (đ§”đœ), and it's certainly fun to see them exchange niceties, âŠđ
I asked a question on MathOverflow (and already got an answer!) about the relation to the effective topos RT(đŠâ) of the corresponding realizability topos RT(đŠâ^rec) on the computable part of Kleene's second algebra đŠâ. mathoverflow.net/q/495788/17064đ
En quoi est-il faux en ZFC du premier ordre? (J'espĂšre qu'on ne parle pas d'un problĂšme de capture des variables: je suppose que ma substitution est faite correctement.)
Or else change the notation â(α) to â[α^±1] and don't call it âsimple extensionâ: the statement is still correct (and, again, if α is algebraic, this is equal to â(α) anyway).
⊠My suggestion would be to replace by ââ(α) = {f(α) : f a rational function with coefficients in â that is defined at α}â or some such thing.â€â€Note that if α is algebraic, then their definition is correct because then â(α) = â[α] (polynomials in α).
This is indeed wrong. If α =: t is transcendental, then what they define here is the set of Laurent polynomials â[t^±1] in t, whereas the field generated by t over â is the field â(t) of rational functions, which is larger: 1/(1+t) is an example of an element of â(t) that is not in â[t^±1]. âŠ
Plus que 6 jours avant de soutenir ma thĂšse !â€â€Si vous voulez feuilleter la version actuelle de mon manuscrit (en anglais), il est disponible ici : theo.delemazure.fr/storage/thes...đŒïž
Je ne sais pas si on peut construire un modĂšle de HoTT dans ZFC, mais je doute qu'on puisse construire un modĂšle de ZFC dans HoTT, et on ne peut certainement pas faire les deux, parce que ça impliquerait de pouvoir construire un modĂšle de ZFC dans ZFC, donc (par Gödel) que ZFC est inconsistant. âŠ
Also, their videos seem to be more about the motorcycle part than the faith part. But maybe the guy delivers a sermon halfway through the vlog, I didn't watch.â€â€(I expected this sort of content from the đșđž rather than the đŹđ§, to be honest.)đŒïž
En parcourant en diagonale les ~25 premiĂšres pages, ce livre-lĂ est clairement beaucoup mieux. Au moins il y a un effort pour expliquer clairement les rĂšgles en alternant description formelle et discussion informelle.
Bruce Schneier makes excellent points about the crap we accept from computers vs. the crap we accept from other powerful and risky objects in our lives.â€www.schneier.com/blog/archive...đŒïž
Announcing the release of the official Common Corpus paper: a 20 page report detailing how we collected, processed and published 2 trillion tokens of reusable data for LLM pretraining arxiv.org/pdf/2506.01732đŒïž
Even if "white British" will be a minority in the UK in 40 years - so what? Seriously, so what? What is so terrible about that? Make people spell out their horrors. Make them spell out the things they are supposedly not allowed to say. Make them own it.
⊠AprĂšs, oui, je reconnais aussi que j'ai une dent contre HoTT parce que je trouve qu'il y a un ĂNORME hype (dont je ne comprends pas du tout l'origine) autour de ce sujet: p.ex., Ă un certain moment, sur MathOverflow, il y avait deux chats en continu, «maths» et «homotopy type theory», âŠ
(Just to be clear, money is, fortunately, no longer primarily backed by gold. It's now mostly backed by loans that are at least related to the real economy, a far less absurd system. But lots of gold is still kept for historical reasons, e.g., ~1T⏠are owned by the Eurosystem.)
The absurdity of putting even part of our trust in money in the fact that some people store enormous amounts of one somewhat-useless-but-pretty chemical element and just do nothing with it, is absolutely fascinating.
I stumbled back on this video on gold by âPeriodic Table of Videosâ in which the professor was granted access to visit and film the bullion vaults of the Bank of England, and if you like gold bars, it's impressive and a bit surreal. www.youtube.com/watch?v=CTtf...đ
I'm not one of the people who think LLMs are utterly useless (and/or evil). They can sometimes help us find a âneedle in a haystackâ (e.g., find a word, suggest a better phrasing). But we absolutely need to keep in mind that we should NEVER EVER trust about ANYTHING: đ§”đœđ
If the LLM doesn't have the ability to open and read external links, it won't âknowâ this. It will receive the link as a token and will hallucinate its contents, because it's been trained on texts that contain a link and comment on its contents.
đœ Always remember that LLM AIs can hallucinate about everything and anything, â±including about themselvesâ± and about what they can or cannot do.â€â€Do not ask them âcan you do <this-or-that>?â because âthey do not âknowââ what they can or can't do (unless specifically trained).đ
⊠Donc lĂ , tout ce que je peux dire, c'est que HoTT utilise juste le symbole â=â pour «est isomorphe à » (ou plutĂŽt pour «l'ensemble des isomorphismes entre»), ce qui rend l'axiome d'univalence pas du tout surprenant, par contre c'est juste la notation qui est complĂštement merdique. âŠ
A friendly reminder that academia.edu is a for-profit organisation that leeches on the free content academics posts there.â€Delete your account. Put your papers on an archive server, if your science field has one. If you want to, get a Research Gate account. They are a non-profit, so no issues there.
Terrorists or armed gangsters is pretty much what the current Administration claims to view immigrants as: IIUC, one of their legal fictions is to claim some Venezuelan gangs are at war with the United States so as to be able to invoke the provisions of the Alien Enemies Act of 1798.
⊠which is how they were conceived historically (âidealâ means âideal numberâ), so if you want you have eight kinds of things: {integral, fractional} Ă {rational, algebraic} Ă {number, ideal [number]}. Saying all three dimensions each time would be logical and systematic, but also pretty cumbersome.
Maybe âintegral rationalâ would be logically better than ârational integerâ then, but probably this would confuse people who never saw this.â€â€Concerning ideals, the thing is that in algebraic number theory, unlike commutative algebra, one tend to think of this as kinds of generalized numbers, âŠ
And even for an integral ideal â which, after all, is a particular kind of fractional ideal â it is dubious that there is real value to be gained by saying âan ideal of the ring of integers of the number field Kâ when âan ideal of the number field Kâ can't usefully mean anything else.
âIn the field K, the factorization of ideals into prime idealsâŠââ€â€â If they're talking about integral ideals, then it is indeed sloppy. If this is about fractional ideals, they are usually considered to be âofâ the field, not its ring of integers.
⊠it contrasts with âalgebraic integerâ and I can't think of any other interpretation that might cause confusion.â€â€I mean, think of a sentence like âhere, x is not just an algebraic integer but a rational integerâ: would you really want to just say âbut an integerâ?â€â€Ditto for primes.
âThe integer â2ââ€â€â This is indeed sloppy. I'd write âalgebraic integerâ unless the context were really super clear.â€â€âLet x be a rational integer and p a rational primeââ€â€â This, however, is good and logical: ârational integerâ means an element of the ring of integers of the rational field, âŠ
« Tout le monde » sait bien que le contrĂŽle des concentrations empĂȘche lâEurope dâavoir des grands groupes « champions »⊠mais est-ce si simple ? Avec Emmanuel Combe, nous montrons dans @lemonde.fr que la question ne va pas de soi. www.lemonde.fr/idees/articl...@ec.europa.eu@bcoeure.bsky.socialđ
Ah ben ce n'est pas le cas. Avec l'arrondi au plus proche et 20% de TVA, 3.99⏠TTC n'est pas possible (3.32⏠HT donne 3.98⏠TTC et 3.33⏠donne 4.00⏠TTC), vu que 399 ⥠3 (mod 6).
«â€Just heard there's a âDirector of Earth Rotationâ (yes, thatâs real!) â unbelievable!! If the Earth is rotating, itâs probably because of ME. Iâve done more for spinning than anyone! Ask NASA! Iâd be the BEST at this job â maybe I already am! #TrumpRotation#FakeScienceâ€Â»
Oh yeah, I hate âbottomâ / âtopâ as quark flavor names. It's confusing with âdownâ / âupâ (and often untranslatable), whereas âbeautyâ and âtruthâ (same initials!) nicely continue the series of poetic names for quarks not found in ordinary matter after âstrangeâ and âcharmâ. Who changed these names?
Daniela Thaller has the BEST POSSIBLE JOB TITLE in the world. She is the âDirector of the Central Bureau of the International Earth Rotation Serviceâ.â€â€I am green with jealousy.đ
Petite remarque de matheux sur la TVA: si le prix TTC est obtenu en ajoutant la TVA au prix HT (en centimes) et en arrondissant au centime, il y a des prix TTC «impossibles».â€â€Par ex., si TVA de 20% avec arrondi au plus proche: 8.37⏠HT fait 10.04⏠TTC et 8.38⏠fait 10.06âŹ, donc y'a jamais 10.05âŹ.đ
Ah non, Madame! La France, c'est le pays de la Raison, le pays des LumiĂšres. On n'interdit que les choses qui sont Vraiment Nuisibles au Bien Commun, comme l'exposition des biberons Ă tube.
Character tables are highly constrained. With very minimal hypotheses on the group you can often prove lots of things about them. (Here, the hypothesis must have been that there is an element of order 2 whose centralizer is the Baby Monster.) If it works, it's a sign that the group might exist.
Au CNRS, le recrutement est national, n'est-ce pas? Si le jury national recrute le candidat et ensuite l'affecte Ă un endroit oĂč il ne peut pas venir, il se passe quoi?
⊠then you consider the centralizer of that involution, namely C(x) := {yâG : xâ y=yâ x}. Then you discuss on what C(x) can be and this is where a myriad of cases arise, but the gist of it is that the uniqueness theorems of many kinds of simple groups are defined âŠ
I know the first two steps of the CFSG are (very roughly!) this: first, the finite simple group G, if it's not cyclic, is of even order (this is the Feit-Thompson theorem, long and hard), so there exists an involution x in G (meaning xâ 1 with xÂČ=1), âŠ
Let it be known that I too will accept $2 billion in funding on the promise that I will not release anything until I have created God.â€â€pivot-to-ai.com/2025/03/06/i...đ
Oh dear, I must have slipped down one line when copy-pasting. âčïž The missing text is: âProbably one of the most monumental achievements of human mathematics is the Classifiâ.
Oh dear, I must have slipped down one line when copy-pasting. âčïž The missing text is: âProbably one of the most monumental achievements of human mathematics is the Classifiâ.
Yes, so do I. But I didn't write ââ€_kâ (in which the âZâ is the initial of âZahlâ), I wrote âZ_kâ (in which the âZâ is the initial of âZyklusâ). I write ââ€/kâ€â or just ââ€/kâ when it's a ring or additively written group, but âZ_kâ or âC_kâ when it's a multiplicatively written group.
Well, of course the actual geometrical figure here only has 22 of them. But the underlying graph (which remains the same) has 88âŻ704âŻ000, and it is (up to a factor 2) one of the sporadics (the Higman-Sims group).
⊠And even the technical parts can be made at least somewhat palatable with some nice visuals.đ„
Joke aside, I think there's a good video documentary to be made about the CFSG. The non-technical part (the history of the subject) is interesting, there are many people to interview, and people like stories about records, so surely a ~15âŻ000 page proof is impressive. âŠđ
⊠and with a surprise appearance by Anthony Hopkins as the quasithin case.â€â€(OK, this thread is 92 skeets long, which when discussing the CFSG seems very short, but even for me it's still long, so I think I'll stop here.) âą92/92
But after all this is still shorter than âWheel of Timeâ, so whether there will eventually be a (3rd gen) machine-checkable proof of the CFSG remains to be seen, but for my part ⊠âą90/92
So: the second gen proof is currently 4060 pages long, and (~30 years after it started), it seems that we've finished âtheorem Câ and theorem Câ*, case Aâ (whatever that may be). Good. There are probably roughly 2 or 3 more volumes to come before gen2 proof is complete. âą89/92
(To be completely clear, the above is the TABLE OF CONTENTS of the SKETCH of the STREAMLINED AND SIMPLIFIED (=2d gen) proof of the CFSG. Yeah.) âą88/92
The (already 165-page long!) volume 1 of the series gives an outline of how the proof is to proceed. (This, of course, assumes that you already know quite a bit about simple groups, it's by no means an introduction to the topic!) Its table of contents is interesting. âą87/92đŒïžđŒïž
Just to give a scale of the work: the latest (AFAICT) volume in this second generation proof is the 570-page volume 10 bookstore.ams.org/view?Product... titled âThe Classification of the Finite Simple Groups: Part V, Chapters 9â17: Theorem Câ and Theorem Câ*, Case A.â âą86/92đ
This âsecond generationâ proof is being published by the American Math Society as a series of volumes written (mostly) by Daniel Gorenstein (now deceased), Richard Lyons and Ronald Solomon. This rewriting has been going on for⊠31 years now. đ” âą85/92
But still, an effort is underway to at least rewrite, streamline and simplify the proof of the CFSG and publish it as a series of books that can be read more easily than hundreds of papers scattered across multiple journals over more than two decades. âą84/92
⊠as part of a team effort spearheaded by Georges Gonthier which concluded in 2012, so we can now say with 100% confidence that this part of the proof is entirely correct. So far, formalizing the entire proof of the CFSG in a proof checker seems too difficult. âą83/92
For example, the âFeit-Thompson theoremâ, which asserts that every finite simple group apart from the Z_p has an even order (number of elements), which is the very start of the CFSG, and already a long and arduous theorem, was formalized in the Coq proof checker, ⊠âą82/92
The ideal thing would be to formalize the proof in a computerized proof checkers. This has been done for other long and difficult theorems before (and tiny errors are always found in the proofs, though they are almost always easy to fix and don't compromise the result). âą81/92
⊠so even if specialists âwere sure thatâ they could complete it, this was only really written and published in 2004, so it's only then that the proof can really be claimed to be fully complete. But how sure are we that other gaps haven't gone unnoticed? âą80/92
Of course, such an enormously complicated proof (which, at its heart, is a very fastidious enumeration of cases, subcases and sub-subcases) is bound to have errors in it. In fact, an entire part was missing, the âquasithinâ case, from the original proof, ⊠âą79/92
⊠Robert Griess, who proved the existence of the hitherto elusive âMonsterâ, and the one whom we could describe as the conductor of this orchestra of group theorists, Daniel Gorenstein, who eventually announced that the proof was complete.) âą78/92
(Of course, some names stand out more: like J. H. Conway who not only discovered three sporadic groups but also co-authored the ATLAS, a book which deserves its own story; Bernd Fischer and Zvonimir Janko who also discovered several sporadics each, ⊠âą77/92
This is, of course, a reminder that mathematics is a collective accomplishment: there was no single mastermind, no solitary genius behind this monumental achievement that is the CFSG: dozens if not hundreds of group theorists each brought their brick to the wall. âą76/92
⊠and it was only near the end that people could look back and say âoh, if we collect this big list of papers and put them together, we can summarize what was proved by this monumental theorem that classifies all finite simple groupsâ. âą75/92
Of course, this first generation proof was done âin the blindâ because the first authors had no idea what they were trying to prove, they were discovering sporadic groups as they were filling in the cases of an attempt at classifying finite simple groups, ⊠âą74/92
The original (or âfirst generationâ) proof is estimated to span roughly 15âŻ000 pages of mathematical papers by maybe 100 authors, from roughly 1960 to roughly 1985 (it really depends on what you count as being part of the proof or merely referenced by it). âą73/92
It took me 71 tweets merely to scratch the surface of what this theorem even is about, this is very far from stating it, and the proof is⊠well, the proof is arguably the longest and most complicated mathematical proof ever written by human beings. âą72/92
The CFSG is enormously more complicated. Already the statement of the theorem is very difficult to give: merely to state it, we need to define all 18 families and 26/27 exceptions (and also exceptional isomorphisms inside the list that I didn't talk about). âą71/92
So we can view it as a kind of monster version of the Killing-Cartan classification of simple Lie groups that I discussed above: this one had 4 infinite families + 5 exceptions, and was already a major achievement of 19th century math. âą70/92
This, essentially, is the statement of the Classification of Finite Simple Groups (CFSG): that the list of 18 families + 26 exceptions is the full list of all finite simple groups (these exist, and there are no others: it's not like we just haven't found more). âą69/92
⊠ÂČA_n, ÂČD_n, ÂłDâ, ÂČEâ, ÂČBâ, ÂČFâ and ÂČGâ) but this is a bit misleading because some are double families and others are single families. Anyway. Apart from these, there are 26 (or 27) exceptions, known as the âsporadicsâ, the largest of which is the âMonsterâ. âą68/92
⊠and the âgroups of Lie typeâ (themselves further divided into Chevalley groups and twisted groups, and into âclassicalâ and âexceptionalâ families); altogether, we generally say there are 18 infinite families (Z_p, đ_n, A_n, B_n, C_n, D_n, Gâ, Fâ, Eâ, Eâ, Eâ, ⊠|âą67/92
âŁâšThe story so far:âš in trying to understand all possible forms of finite symmetries we are led to try to classify their âatomsâ, the finite simple groups. Some of these fall into infinite families: the cyclic groups Z_p, the alternating groups đ_n, ⊠âą66/92
And then there are 6 more sporadics that don't even fit that pattern of the âhappy familyâ: they are known as the âpariahsâ, the largest of which (smaller than the Monster, but not living inside it) is the Janko group Jâ with 86âŻ775âŻ571âŻ046âŻ077âŻ562âŻ880 elements (last sporadic discovered). âą65/92
To be clear, we can â±proveâ± that these groups and patterns between them exist, but at some level we really don't âunderstandâ what this is all about. Why are these groups out there? What's this business with three generations and the number 24? Why does it stop here? âą64/92
⊠eight further sporadic groups including the Monster, âBaby Monsterâ and the Fischer groups. Each generation of the âhappy familyâ of sporadics is a kind of elaboration of the previous generation, and the number 24 plays a role at every turn. âą63/92
⊠so basically they act on 24 objects; the âsecond generationâ consists of (seven further) sporadics groups that âlive insideâ the Conway group Coâ, which acts on an object in 24 dimensions (the âLeech latticeâ); and the âthird generationâ are ⊠âą62/92
⊠and the 20 sporadics that âlive insideâ the Monster (sometimes known as the âhappy familyâ) are themselves sometimes divided into three âgenerationsâ: the five Mathieu groups (which all live inside Mââ) are the âfirst generationâ of the âhappy familyâ, ⊠âą61/92
Even within the sporadics, there seems to be a sort of pattern: 20 of the 26 sporadic groups, including the Monster itself, âlive insideâ the Monster group (technically, they are subquotients of it), so the Monster encompassess most â but not all â of these sporadics; ⊠âą60/92
⊠was finally proven by Robert Griess in 1982. Even then, we can't say that we really understand âwhyâ the Monster exists, why this bizarre and exceptional form of symmetry is âout thereâ, acting on a 196âŻ883-dimensional object. See www.youtube.com/watch?v=jsSe... for more. âą59/92đ
⊠first, its existence was conjectured by the fact that it left a kind of set of footprints (what is known as a âcharacter tableâ) that we could detect and that suggested the existence of such a group in the 1970's, and it was only in 1982 that its existence ⊠âą58/92
This âMonster groupâ is one of these mysterious mathematical objects which really make it hard to argue that mathematics is anything other than discovered: nobody decided to invent this thing, it just popped up out of our attempts at classifying symmetries: ⊠âą57/92
The smallest of these 26 sporadics is the Mathieu group Mââ (7920 elements) mentioned above. The largest is the â[Fischer-Griess] Monster groupâ with 808âŻ017âŻ424âŻ794âŻ512âŻ875âŻ886âŻ459âŻ904âŻ961âŻ710âŻ757âŻ005âŻ754âŻ368âŻ000âŻ000âŻ000 â 8.1Ă10â”Âł elements. âą56/92
(Some ppl say there are 27 sporadics: this depends on what you count as a sporadic, because there is a group called the âTits groupâ ÂČFâ(2)âČ of order 17âŻ971âŻ200 that is not exactly a (twisted) Lie type group but âone halfâ of one (ÂČFâ(2)), so you can count it or not.) âą55/92
During the 1960's and 1970's, mathematicians started looking for other finite simple groups that, like the Mathieu groups, didn't belong to any one of the known infinite families: these came to be known as the âsporadicsâ. Eventually, 26 of these would be discovered. âą54/92
So at this stage we have several infinite families of finite simple groups (some people say 18 families, but it really depends how you count) and five strange outliers, the Mathieu groups, that don't seem to belong to any infinite family. âą53/92
(If you want to play with them, I once wrote a little JS page www.madore.org/~david/misc/... that lets you play with Mââ (and Mââ). You can try to scramble the puzzle using the âÂżâ button and then use the commands above to unscramble it⊠if you can figure out what they do.) âą52/92đ
The Mathieu groups Mââ and Mââ have 95âŻ040 and 244âŻ823âŻ040 elements respectively, and Mââ, Mââ and Mââ are smaller (Mââ with 7920 is the smallest of what would become known as the âsporadicsâ). âą51/92
Yes! In fact, such groups had been known since the 1870's: Ămile Mathieu had discovered bizarre groups of symmetries on 12 or 24 objects (with subgroups acting on 11, 22 and 23 objects) that were simple and did not belong to any of these families. âą50/92
So, in the early 1960's, the following finite simple groups were known: the cyclic groups Z_p, the alternating groups đ_n, and the âgroups of Lie typeâ (Chevalley or twisted) derived from the Killing-Cartan classification of Lie groups. Are there others? âą49/92
Soon after Chevalley, in 1959, Robert Steinberg discovered a modification of Chevalley's construction that gave even more infinite families (ÂłDâ, ÂČEâ, ÂČA_n and others: âtwisted groupsâ). Without getting into details, these are collectively known as â(finite) groups of Lie typeâ. âą48/92
Note that these groups can be quite large: already Eâ(2) (first and smallest of the Eâ family) has 337âŻ804âŻ753âŻ143âŻ634âŻ806âŻ261âŻ388âŻ190âŻ614âŻ085âŻ595âŻ079âŻ991âŻ692âŻ242âŻ467âŻ651âŻ576âŻ160âŻ959âŻ909âŻ068âŻ800âŻ000 â 3.4Ă10â·âŽ elements (far more than the âMonsterâ discussed below). âą47/92
So each of A_n, B_n, C_n and D_n now gives rise to a âdouble familyâ of finite simple groups because we have two parameters (n and q) that we can vary. And each of âexceptionalâ Lie groups Gâ, Fâ, Eâ, Eâ and Eâ gives rise to a whole family of finite simple groups. âą46/92
⊠for each one of the groups of the Killing-Cartan classification (A_n, B_n, C_n, D_n, Gâ, Fâ, Eâ, Eâ and Eâ) and if q is the power of a prime number, with a small number of exceptions (that aren't simple), we get a finite simple group from Chevalley's construction. âą45/92
⊠(at least if nâ„3 or qâ„4), which we denote âPSL(n,q)â, and this is what the Chevalley construction gives you when you apply it to the A_n (well, A_{nâ1}) family of the Killing-Cartan classification. To summarize: ⊠âą44/92
⊠and if you do this, you generally (=with finitely many exceptions) get a finite simple group. For example, if you know what this means, the nĂn matrices with determinant 1 over a field with q elements, up to multiplication by a scalar, gives us a finite simple group ⊠âą43/92
To be just a little less vague for those who know what this means: the simple Lie groups of Killing and Cartan involve a âfieldâ, generally that of real (â) complex numbers (â), and Chevalley described a way to replace them by finite fields (also due to Galois!): ⊠âą42/92
A whole bunch of finite simple groups were described in the 1950's (some were know before that) by Claude Chevalley using the following brilliant idea: we can take the simple Lie groups of the Killing-Cartan classification and make simple groups out of them. âą41/92
So, so far, I described two kinds of âatoms of finite symmetryâ or finite simple groups: the cyclic groups Z_p (with p prime) and the alternating groups đ_n (for nâ„5). What are the others? Here's where it gets pretty complicated. âą40/92
⊠đ_n, consists of merely the âevenâ permutations, or âalternating groupâ. (This is familiar, for example, from the â15-puzzleâ or âtaquinâ: the possible permutations of the 15 squares which put the hole back in its place are the group đââ of even permutations.) âą39/92
If we consider all manners of permuting n objects, this forms a group known as the âsymmetric groupâ đ_n, and it turns out that, at least for nâ„5, this group has two atoms in its chemical formula: one is Zâ that I already mentioned, and the other ⊠âą38/92
Aside from these very easy cyclic groups Z_k, we have another kind of finite simple groups (atoms of symmetry) that's not too hard to describe: the âalternating groupsâ đ_n: these are related to the permutations of n objects. âą37/92
((As a side note: the terminology âsimpleâ â for the atoms â is really annoying because I keep wanting to say that something is âsimpleâ in the sense of being easy to understand/analyse, and certainly solvable groups are the easiest. But âsimpleâ is taken as a technical term. Ah well.)) âą36/92
(For example, the abelian groups, namely those in which composition is commutative: performing symmetry gâ then gâ is the same as gâ then gâ, are necessarily solvable. These finite groups are very easy to classify.) âą35/92
Finite groups whose âchemical formulaâ involve only these âcyclicâ atoms Zâ, Zâ, Zâ , Zâ, etc., are said to be âsolvableâ. This terminology comes from Galois's groundbreaking insight that these are the ones which appear in solving equations using n-th roots. âą34/92
Technical note: actually, the Z_k are simple only when k itself is a prime number, because if k = m·n then Z_k can be âbroken upâ into Z_m and Z_n. So we have the atoms: Zâ, Zâ, Zâ , Zâ, etc., which are the most basic forms of symmetry (cyclic symmetry). âą33/92
⊠This is really the most basic form of symmetry possible, and I think it's familiar to anyone even when we don't know the technical terms (think of rotating a knob that has k possible positions, equally spaced: this wouldn't make for a very fun puzzle!). âą32/92
So, back to our main story: what are these possible âatoms of finite symmetryâ (finite simple groups)? Some aren't too complicated to describe: notably, Z_k, known as the âcyclic group of order kâ, is the group of rotations of a regular k-gon. ⊠âą31/92
⊠but that this đ_n atom cannot appear as part of the symmetries of an expression built using k-th roots (only âZ_kâ atoms can occur here). So Galois initiated the study, not just of symmetries of algebraic equations (âGalois theoryâ) but of finite groups themselves. âą30/92
He showed that the symmetries of general algebraic equation of degree n contain an âatom of symmetryâ [â Galois wouldn't have used this language, nor is it common mathematical parlance: the modern technical term is a âJordan-Hölder factorâ] âđ_nâ, ⊠âą29/92
⊠he considered the symmetries of the equation (essentially, the ways you can permute its solutions so as to leave all relations we can write between them unchanged), something we now call the âGalois groupâ, and compared it to the symmetries we can get using k-th roots. âą28/92
⊠until Abel and Galois proved that no such general formula exists â it's not that higher degree equations can't be solved, but they can't be solved by the operation of taking n-th roots). ⧠Galois's approach is beautiful and opened entire new fields of mathematics: ⊠âą27/92
⊠x = (âb±â(bÂČâ4a·c))/(2a) expressed using the square root â operation; similar formulas with cube and 4th roots for degrees 3 & 4 were found in the 16th century by the likes of Cardano, Tartaglia and Ferrari but the general degree 5 equation remained âunsolvedâ, ⊠âą26/92
⊠Galois was interested in proving that algebraic equations of degree 5 or more can't be âsolved in radicalsâ unlike those of degrees 2, 3 and 4, meaning you can't write their solutions with k-th roots (in degree 2 the equation a·xÂČ + b·x + c = 0 has solutions ⊠âą25/92
Some of these âatoms of finite symmetriesâ had been known for a long time: Ăvariste Galois (building on earlier work of Adrien-Marie Legendre) had started the study of finite groups (and groups in general) around 1830: ⊠âą24/92
⊠is a start toward the mathematical description of the Rubik's cube. ⧠Anyway, just like in the 1890's the possible simple parts of Lie groups were fully classified by Killing and Cartan, the issue later arose to find, describe and classify all finite simple groups. âą23/92
⊠because you still need to understand how pieces âfit togetherâ, and what makes the Rubik's cube puzzle puzzling is that you don't get to act on the parts independently. But still, this âempirical chemical formulaâ of âone đâ, one đââ, seven Zâ and twelve Zââ, ⊠âą22/92
For example, the Rubik cube's group's simple parts are đâ (essentially, permutations of the vertices), đââ (essentially, pns of edges), 7 copies of Zâ (rotating the vertices) and 12 copies of Zâ (mostly flipping the edges). This alone doesn't solve the puzzle: ⊠âą21/92
Now classifying all the possible parts, viê«. simple groups, doesn't mean that we fully understand all groups (forms of symmetry), just like knowing all chemical elements doesn't mean we understand all of chemistry, but it still gives us a good and necessary first step. âą20/92
(For those who know what this means: a simple group is one that has no normal non-trivial subgroup. Otherwise, if H is a normal subgroup of G, the simple parts [proper term is âJordan-Hölder factorsâ] of G are those of H together with those of G/H, recursively.) âą19/92
The groups which can't be broken up into smaller groups are called âsimpleâ groups (this is a technical term: it doesn't mean that they're simpler to understand). Metaphorically we might say that groups are molecules of symmetry and the simple ones are symmetry âatomsâ. âą18/92
I won't try to explain what âmade upâ means, but very very roughly you can âbreakâ certain groups into parts and somewhat understand them by understanding the parts. (Like the Rubik's cube puzzle can be understood by the movements of the edges and of the vertices.) âą17/92
I said earlier that classifying all groups is hopeless. So we restrict ourselves to a particular kind of groups, such as finite groups, or Lie groups. But even that is too hard. However, it turns out that groups are made up of other groups. âą16/92
Anyway, the reason I mention this Killing-Cartan classification theorem in relation to the CFSG is twofold: first, it is a kind of âjunior versionâ of the CFSG (Lie groups are â»muchâ» easier to classify than finite ones); second, it is used by it. But back to the story. âą15/92
But the five exceptional groups Gâ, Fâ, Eâ, Eâ and Eâ where a genuinely new discovery by the classification effort, and turned out to be connected with many âexceptionalâ mathematical objects such as the octonions (Gâ is essentially the symmetries of the octonions). âą14/92
The four infinite families (known as âclassicalâ Lie groups) were known before Killing and Cartan: B_n and D_n, for example, are the groups of symmetries of the sphere in odd and even dimensions (there are reasons to separate these), also denoted as SO_{2n+1} and SO_{2n}. âą13/92
In its simplest variant (for the âcompactâ Lie groups â a kind of finiteness condition), it tells us that simple Lie groups come in four infinite families (A_n, B_n, C_n and D_n) plus five âexceptionalâ groups (Gâ, Fâ, Eâ, Eâ and Eâ). âą12/92
This Killing-Cartan classification is one of the crown jewels of 19th century mathematics. (It was later simplified by others, including Eugene Dynkin.) It gives us a grasp on all possible âcontinuousâ forms of symmetry. âą11/92
Lie groups were introduced by Sophus Lie and Friedrich Engel (not to be confused with Friedrich Engels! đ ) in the 1880's, and in the 1890's, Wilhelm Killing and Ălie Cartan completed the classification of simple Lie groups (I'll explain the term âsimpleâ shortly). âą10/92
I won't try to explain what a Lie group is (and there are various flavors), but very very (very) roughly, it's a form of continuous symmetry that an object can have. They are hugely important in theoretical physics (physical concepts generally have such âLieâ symmetries). âą9/92
Some forms of symmetries, rather than finite, are continuous: if you take a sphere, for example, you can't just move it around in 24 different ways like a cube, but in a continuous manner. These also form a group (âSOââ) but not a finite one: it's called a âLie groupâ. âą8/92
Here's one thing we can do to restrict the problem: look at specific kinds of groups. The one that the CFSG is about are finite groups, so: objects that have only finitely many symmetries (like the Rubik's cube). But let me first say a word about another kind. âą7/92
So it would be nice to understand them better and to get a grasp of the various kinds of groups that exist, or, as we say in mathematics, to âclassifyâ them: to understand all possible forms of symmetry. But if we don't restrict the problem further, it is utterly hopeless. âą6/92
Anyway, symmetries and, consequently, groups, are ubiquitous in mathematics, but also in theoretical physics (e.g., they play an essential role in defining conservation laws and building up the âgauge fieldsâ of the standard model of particle physics), cryptography, etc. âą5/92
⊠but they can be a little more combinatorial: for example, the âRubik's cubeâ puzzle, which many people are familiar with, is basically about exploring a group with 43âŻ252âŻ003âŻ274âŻ489âŻ856âŻ000 elements (the mechanically available transformations of the puzzle). âą4/92
Most people are at least aware of geometrical symmetries: âin what ways can you rotate a cube by keeping its overall position fixed?â (e.g., rotate by 90° around a face, or 120° around a diagonal) is an example of a (finite) group (here with 24 elements or âorder 24â), ⊠âą3/92
So, I'm not going to define what a âgroupâ is formally (see www.youtube.com/watch?v=mH0o... for an attempt at an explanation), but I like to describe it informally as âa form of abstract symmetryâ that an object (mathematical or otherwise) can have. âą2/92đ
cation of Finite Simple Groups (âCFSGâ), a proof whose current incarnation is about 15âŻ000 pages long spread across many articles by different authors. What is this all about? đ§”â€”ïž [âMonsterâ thread ahead!] âą1/92
That feeling when you've just spent an hour of computer time (mostly disk thrashing time, so making the box nearly unusable) to compile a new Firefox version, and realize at the end that you checked out the wrong commit and just rebuilt the version you were already running. đŁ
(And yes, he is pretty cute. I mean, Aragorn is the one I'd bang, but Sam is the one I'd much rather cuddle with.)
I forgot where I read this remark, but I like it:â€â€True love is looking at someone with the same adoring eyes that Sam keeps looking at Frodo in these films. đđŒïž
Of course, now that I've solved it, I think the question was absolutely trivial (in the sense that it is a trivial consequence of standard facts in descriptive set theory around analytic sets). đ€· x.com/gro_tsen/sta...đŒïž
And now I'm super happy to have solved this question that had been bugging me all week: the image of a lower semicontinuous function [0,1]ââ is analytic but it can fail to be Borel. mathoverflow.net/a/495324/17064đ
The first antibiotic in 50 years to tackle a drug-resistant bacterium responsible for high mortality rates is entering the final stages of human trials 1/1đ
Not disagreeing with the fact that his costume is shitty, but I'm pretty sure every single one of these attires is just as fictional. If I saw a guy in Paris dressed as the ludicrous caricature that is supposed to represent France, I would burst out laughing as much as if I saw Captain America.
Some variation of the following probably works as well: for each vertex x in the digraph put a copy of a Câ; for each edge e in the digraph put a copy of a Câ, then connect it to the Câ for its source by a 5-link chain and to the Câ for its target by a 6-link chain. (I didn't check.) Ugly again!
⊠I don't know if this works (i.e., if â and â are indeed true: I didn't try), and if it does it's certainly not efficient, but it may be slightly less ugly because â and â are at least of some independent interest (they could be reused for other things).
⊠(Where âencode foo as barâ means âdefine a construction from foo to bar that is injective on the isomorphism classesâ.) Then we would start with the directed graph of the well-ordering on Îș + a black-white coloring on the vertices, and apply â followed by â. âŠ
Regarding your question, I think I'd try to break it into several questions, possibly harder than the original, but also more interesting: â can we encode a directed graph on Îș as an undirected one?, â can we encode a directed graph on Îș + a finite coloring of its vertices in one without? âŠ
⊠Take this question I answered to a similar question: mathoverflow.net/a/261442/17064 (show that there are 2^â”â isomorphism classes of projective planes on â): my answer is fairly efficient, but it is really ugly and deeply uninteresting because we're doing something completely artificial here.đ
I think an answer to this is necessarily going to be somewhat ugly, because you have to encode a datum (a subset of Îș) into a algebraic structure (an isomorphism class of graphs on Îș) that has little connection, and then show how to recover it. So, an exercise in artificial encodings. âŠ
I love how Twitter's âGrokâ AI tries to gaslight me by explaining that a term it asserts was coined in 1943 «predates» Kafka's 1915 parable. (But it may still be right that there is little connection, of course.) x.com/i/grok/share...đŒïž
Did the English word âgatekeepingâ appear as a reference to Franz Kafka's famous parable âBefore the Lawâ (which is about a man faced with a literal gate-keeperÂč of the Law)?â€â€1. âTĂŒrhĂŒterâ in German. (OK, this means âdoor-keperâ: âgate-keeperâ would rather be âTorhĂŒterâ. Close enough.)
This one is pretty funny as well, for different reasons: mathoverflow.net/q/495228/17064â€â€(Also for the fact that it claims to be inspired by season 5 episode 14 of âThe Flashâ.)đŒïž
What's it like being a raven or a crow? Our new piece in the Conversation discusses our recent article on the dimensions of corvid consciousnessâ€theconversation.com/whats-it-lik...đ
Plot twist is that, 100 years later, people discover that the Education Vigilante never existed, it was just a legend that a certain Hari Seldon created and got people to believe in. But by the time people realize this, it's already too late.
Existential Comics may have a dangerously good point about what it takes to solve many of our society's problems, there. existentialcomics.com/comic/604â€â€(Incidentally, âłïžwhoâłïž said citizens must be âforced to be freeâ? <looks it up> Oh, Rousseau, of course. I totally knew that. đ )đ
Merci pour le lien! Je vais regarder ça. (L'arboretum des Grandes BruyĂšres est sans doute le plus beau jardin que je connaisse, mĂȘme si la concurrence du jardin du Point du Jour Ă Verdelot et le jardin Plume Ă Auzouville-sur-Ry est dure.)
Justin Sun is a Chinese billionaire who was sued by the Biden SEC in a crypto case.â€â€Heâs a major investor in Trumpâs World Liberty Financial.â€â€He also spent $40M+ on $TRUMP coins, earning an invite to dinner with Trump at his Va. golf club on Thurs.â€â€He apparently also got a private WH tour.đŒïž
Yeah, I meant selecting parts of the text: this used to work.â€â€But I hadn't noticed the âcopy post textâ, so thanks for pointing this out: it's better than nothing.
C'est pas vraiment une question de longueur absolue, c'est que quand je demande ça ça veut dire en gros de retirer 90% de la longueur du cheveu, et je crois que c'est cette proportion relative qui pose problÚme.
One might also mention the following related question: is there a decidable subset S â â that meets every equivalence class of ~, and for which the halting problem on a(ny) specified input is decidable? Answer: no, because there is a universal machine in S. (Not clear exactly what OP was asking.)
Yes, it was trivial at some point (and somehow still is so on Firefox Mobile, which is generally less configurable), and it's incomprehensible that they decided to hide this. (And also the name of the pref itself is incomprehensible.)
A nice computability question: can we find a decidable set S of Turing machines which defines every computable function, and such that it is decidable whether an element of S terminates on the zero input? Yes we can! đœđ
PS: And of course, this negatively answers the question as I formulated it earlier up (đœ) because finding h:ââS total computable such that h(e) ~ e for each eââ amounts exactly to deciding the run time of Ï_e(0).đ
⊠So S is a decidable set of Turing machines that meets every ~-equivalence class and yet whose halting problem on the empty input is decidable. âą6/6â€â€(Nice question!)
So, to be sure, your question is: if Sââ is a decidable subset that meets every equivalence class of the equivalence relation eâ ~ eâ when Ï_{eâ} = Ï_{eâ} [same domain of definition and same values], does it follow that there is h:ââS total computable such that h(e) ~ e for each eââ. Correct?
J'ai plutĂŽt le problĂšme contraire: j'essaie de communiquer aux coiffeurs le message «coupez trĂšs trĂšs court, ça ne peut pas ĂȘtre trop court, mes cheveux poussent HYPER vite», ils coupent Ă peine, demandent si ça va la longueur, et je n'ose pas demander >2 fois «non, je veux BEAUCOUP plus court».đ
Les mĂȘmes grandes entreprises qui stockent tout sur aws, gĂšrent leur messagerie sur Google et utilisent office 365. On les voit bien, pas de problĂšme.đ
I answered a question on MathOverflow by explaining (though this may not have been what the question was about đ) why the sequence that counts the number of reduced words of length n in a Coxeter group has a rational generating function. mathoverflow.net/a/495077/17064đ
Thanks! I had found www.reddit.com/r/firefox/co... which mentions this preference, but I thought it didn't work anymore because I was looking for the âAddâ button in the wrong place, and I couldn't see it.â€â€Still, hiding something so basic behind a secret pref makes no sense whatsoever. đ đ
Update: it's possible to add a custom search engine to Firefox by adding the (hidden! đ€) `browser.urlbar.update2.engineAliasRefresh` preference to true, then going to about:preferences#search and clicking on âAddâ below the âSearch Shorcutsâ list.â€â€But why hide it like that? Like, WTF, Mozilla? đ€Šđ
EVERY food recipe is controversial. You'll always get culinary prescriptivists who tell you that the Original Recipeâą doesn't have this-or-that ingredient, so you May Not Use It, no matter how good it tastes.â€â€(Then sbd proves that the recipe is like 30 years old â and not at all from that country.)
EVERY food recipe is controversial. You'll always get culinary prescriptivists who tell you that the Original Recipeâą doesn't have this-or-that ingredient, so you May Not Use It, no matter how good it tastes.â€â€(Then sbd proves that the recipe is like 30 years old â and not at all from that country.)
I'll probably post more details later, but it seems infuriatingly difficult to persuade Firefox (desktop edition) to add a user-specified URL as a custom search engine to the browser, without installing Yet Another Fđcking Extension for this.â€â€If you know a simple way, please tell!
âFrankly, Jean, you're paranoid to outright dismiss possible PhD positions in the US. Nothing bad is going to happen.ââ€â€www.bbc.com/news/article...đ
⊠Among tourists, there's a lot of Duch/Flemish speakers.â€â€Also, I hear a âłïžlotâłïž of people speaking Russian in Paris (not as much as English, but still more than, say, German or Italian), esp. since 2022. I can't decide if it's an observation bias (I pay more attention to it) or a real phenomenon.
It really depends on whom you observe and how you measure. If I pay attention to the languages spoken by other (non-tourist!) people in the gym or the supermarket where I go, I'm pretty sure Spanish, and maybe Portuguese, Arabic (all forms bundled together) and/or Chinese, come before English. âŠ
A Google search returns some results, including several videos, so this doesn't seem to be a counterexample.â€â€I will now refer to âthe Abou Samra conjecture on theorem namingâ (and never âAbou Samra's conjecture on theorem naming) the fact that âthe X theoremâ can also be called âX's theoremâ.
Not exactly a theorem, but I'd say âthe Cartan decompositionâ, not âCartan's decompositionâ. Similarly, âthe Lebesgue integralâ, not âLebesgue's integralâ. For an actual theorem, I can't think of any such case.
Remember that if you want to stretch terminology in a mathematics book or paper, you are allowed to do so if you announce your intentions in French.đŒïž
Oui ça c'est possible, mais selon le moteur de rendu on peut y arriver avec un choix judicieux de police. Et ça n'explique certaines pas pourquoi le chipmunk existe en style texte et pas le manchot!
⊠The chipmunk is a weird exception because it's also supposed to exist in text form. My guess is that some other charset / font / encoding / whatever had a (non-color!) chipmunk. Not a penguin. But even then, it seems absurd to go into such granularity rather than have a blanket rule for all emoji.
This doesn't seem to make sense (but of course, the computer world often doesn't, so that doesn't mean you're wrong): the emoji sets used by Japanese cell phone carriers were in color, so they were added to Unicode as emoji, and some in the range only exist as emoji. âŠ
I see this on â Twitter on PC, ⥠Twitter on Android, âą Bluesky on PC, ⣠Bluesky on Android. Nothing makes any sense whatsoever. (PC running Debian Linux and Firefox 138.0.4. Android running some version of LineageOS.)đŒïžđŒïžđŒïžđŒïž
A test:â€â€â Default style: ââ âšâŹđđżđđâ and âđ§ââ€â Explicit emoji style: ââ ïžâšïžâŹïžđïžđżïžđïžđïžâ and nonstandard âđ§ïžââ€â Explicit text style: ââ ïžâšïžâŹïžđïžđżïžđïžđïžâ and nonstandard âđ§ïžâ
I asked a question on Reddit /r/Unicode about the logic behind the list of Unicode characters that have both a text style and an emoji style. www.reddit.com/r/Unicode/co...đŒïž
Boulet comprend parfaitement l'anglais, et je ne m'attends pas Ă ce qu'il reposte mon message mais qu'il reformule Ă sa façon (probablement plus Ă mĂȘme de toucher les autres artistes).
â ïž Reminder to all Microsoft Windows users that the âRecallâ feature basically means that your computer will be spying on you at all times to train a AI models and/or target ads: this is a security and privacy nightmare, and you should disable it while this is still an option.đđ
Not really important for something as minor, but in general, when quoting posts from another social medium, I think it's best (in the interest of robustness of conversations and permanence of information) to post a link âłïžandâłïž a screenshot. Especially if messages can be edited, as on Mastodon.
Another âshit, I never thought about this question and I realize I know nothing about itâ moment: is the image of a lower semicontinuous f:[0,1]ââ a Borel set? mathoverflow.net/q/494998/17064đ
Embarrassing situation on MathOverflow where, in answer to the same question, we have a proof that alternative division algebras in characteristic 2 are associative, and a counterexample showing that they aren't. So, who's wrong? mathoverflow.net/q/485668/17064đ
A royal journalist called Richard Mineards once appeared on Fox News to explain that the British royal family can't be racist because they colonized Black and Asian people. đ€Šđ web.archive.org/web/20210311...đŒïž
A royal journalist called Richard Mineards once appeared on Fox News to explain that the British royal family can't be racist because they colonized Black and Asian people. đ€Šđ web.archive.org/web/20210311...đŒïž
Certainly if you have infinite computing power and some bounds on the counter's initial value and seed size, you can reconstruct them from enough values of hash(counter||seed). But my thoughts aren't entirely clear on what this tells us.
If you think any issue more complex than âheads or tailsâ has only two sides, you should take it as a sign that you've been brainwashed into not seeing its edges and its corners.â€â€We live in a world with more than 1 dimension, and this applies to politics as well.
Et voilĂ ce qui arrive quand on n'a pas lu mon petit guide explicatif «tout ce que vous devez savoir avant de vous aventurer sur les terres dangereuses du plateau de Saclay»: www.madore.org/~david/weblo...đ
⊠For example, SHA256(counter||seed) (where the counter is incremented each time) gives a pseudorandom sequence that should be good for many people's purposes, and also (presumably) avoids Arnaud's objection of being eventually periodic. But it might be too slow for some uses.
This makes me realize that I forgot âcryptographersâ among the list of people who have some stake in what ârandomnessâ means: I âșthinkâș a cryptographically strong pseudorandom generator should also be good (though slow?) for numerical algorithms like Monte Carlo, but I may be wrong about this. âŠ
I think you're illustrating what I wrote đœ about the ârandomnessâ of various kinds of mathematicians not being the same, here. You (and maybe I) seem to more or less agree with Martin-Löf's definition, but I suspect probabilists don't feel it adequately captures their idea of randomness.đ
Non mais ça c'est la partie de Palaiseau sur le plateau de Saclay. Le centre-ville il ressemble à n'importe quel centre-ville de petite ville francilienne: www.google.com/maps/@48.714...
One interesting thing about this account đœ is that the number of likes and reposts varies from one post to another, just like the number of A's and H's.đ
Ătre adulte, c'est terrible, on peut manger tous les bonbons qu'on veut et il n'y a personne pour nous dire «bon, ça suffit, maintenant, tu arrĂȘtes!».
Faudra un jour que je fasse u mn thread sur le nombre de plus en plus important de personnes dont chatGPT est non seulement le confident et le principal ami, mais parfois le seul interlocuteur.
The two are related but different: Bell's inequalities relies on probabilities and an assumption of local realism and concludes a contradiction (with other assumptions), whereas the Conway-Kochen âFree Willâ theorem does not deal with probabilities and its conclusion is about nondeterminism.
Meme aside, why is it called âWindows Subsystem for Linuxâ when (IIUC) it is a package for Windows that allows running of Linux programs in a Linux subsystem, i.e., a Linux subsystem for Windows, the EXACT OPPOSITE of what they label it?đ
(Not that I see any particular connection, but at least they illustrate the fact that, for some variations of propositional realizability, some form of the disjunction property is non-trivial-but-still-true, which appears to also be the sort of things you're after.)
Maybe for inspiration you could go through appendices B and C of Plisko's 2009 survey (NB: I didn't read them!), proving the disjunction property for two of the myriad of variations of propositional realizability (âirrefutabilityâ and âeffective realizabilityâ). There might be something reusable.
Indeed. But I still managed to go through most of the mental states I had predicted I would go through (though not quite in the order I had predicted).
What prompted me to start this discussion is precisely a summary by Sabine Hossenfelder of 't Hooft's ideas (but she says he's in the minority): www.youtube.com/watch?v=2kxo...đ
Let me đ this for now because I feel like I will need to unwrap N levels of self-confusion in which I will successively believe that the question is trivial, then false, then trivial again, then âprobably true but very hardâ, then meaningless, etc., until I finally understand what it really means.
⊠I'm not sure what the moral of all this is, but the exact interrelationship between determinism, randomness, computability, probability, and quantum phenomena (not to mention the thorny âfree willâ!) is subtle and I don't feel like anyone is able to express it clearly (certainly not me).
⊠so this could follow from âdeterministicâ laws of physics, but at the same time the result is random in the sense of algorithmic randomness (so also indistinguishable from âtrueâ randomness â whatever that may be â if we believe the Church-Turing thesis⊠but maybe that's the crux). âŠ
⊠the 1st Martin-Löf-random element of {0,1}^â for this-or-that ordering of a subset of {0,1}^â [e.g., the canonical well-ordering of the Gödel constructible universe]â: this is, in principle, a mathematically perfectly well-defined element of {0,1}^â (but which can't be computed algorithmically), âŠ
⊠can, after all, be deterministic, but physicists would probably disagree with the idea that ârandomâ and âdeterministicâ are compatible. To put it more vividly, some laws of physics might very well have as a consequence that âthe result of this-or-that sequence of physical experiments will be âŠ
I should also mention that my earlier skeet is a bit misleading, because ârandomnessâ of physicists and of mathematicians, and, inter mathematicians, of probabilists and logicians / set theorists / computability theorists, are not really the same. Specifically, a (say) Martin-Löf-random sequence âŠđ
[Note to self: a reference for this is Nies, âComputability and Randomnessâ (2009), theorem 3.2.9; or Shen, Uspensky & Vereshchagin, âKolmogorov Complexity and Algorithmic Randomnessâ (2017), §5.6 theorem 90.]
> I've come to regard randomness as describing lack of information.â€â€This is justified mathematically by the (Levin-Schnorr?) theorem that a sequence X is Martin-Löf-random iff the prefix-free Kolmogorov complexity K(XâŸn) of its prefix of size n is â„ n â c for some constant c.
⊠This proof is valid (classically, F is computable), but of course the âcheatâ is that we don't know what M is (it is conjectured that M=â), so I didn't actually provide an algorithm for computing F, I merely proved that one exists.â€â€(Constructive math basically tries to ban such cheats.)
⊠Let M be the max such N (greatest number of consecutive 7's in decimal expansion of Ï), or â if there exist arbitrarily long runs of consecutive 7's in Ï. Then: F is the function taking every kâ€M to 1 and every k>M to 0; and whatever the value of M, integer or â, this function is computable. â âŠ
⣠Assertion: the function F taking as input an integer N and returning 1 (âtrueâ) if there exist N consecutive 7's in the decimal expansion of Ï, and 0 (âfalseâ) otherwise, is algorithmically computable.â€â€Proof (valid in classical mathematics! but something of a âcheatâ): âŠ
My favorite scene from The Manchurian Candidate brilliantly explains why liars like Trump donât care about the wild numbers they fabricate. This was the basis of McCarthyism in a nutshell:đđ
If I am not mistaken, this explicit algorithm đœ solves 3SAT (or whatever NP problem you want to apply this trick to), and, moreover it does so in P time provided P=NP is true.â€â€I.o.w., if P=NP is true, this one algorithm will explicitly perform the trick.â€â€(Nothing smart going on, of course.)đ
⊠during the enumeration of the (e(i), p(i)) at the point when we run into i=k, and this takes time p(k) plus the sum of the p(i) for i<k, plus some P-time overhead for decoding, checking and bookkeeping, but overall this is still P-time.â€â€Correct?
⊠Obviously this algorithm works: so the only question is to check its complexity. But if actually P=NP, then there exists k such that e(k) solves every Q(j) in time less than p(k), and then for N large enough, h(N) â„ k, so that every Q(j) for jâ„N will be solved âŠ
⊠Given an instance Q(N) of the problem to be solved, let n = h(N), and for all pairs (e(i), p(i)) for iâ€n, try running the program e(i) for p(i) steps at most, and check if its answer solves Q(N). If one does, return this immediately. If not, solve Q(N) some slow & stupid way, it won't matter. âŠ
Something like this?â€â€Let n ⊠(e(n), p(n)) be a (P-time) enumeration of all pairs consisting of a Turing machine and some polynomial bound. Let h be a (P-time computable) slow-growing function (log will work, I think). Let N ⊠Q(N) be a (P-time) enumeration of all instances of the problem (3SAT). âŠ
⊠indeed, if we imagine the laws of physics as a kind of magician trying to play a trick on us by guessing our cards, while investigating the trick we should give the magician as little input as possible that they could use to influence our tests. So, here, algorithmic randomness seems best.
Computers used to generate ârandomâ numbers purely mathematically and deterministically, but I think they now (all?) have a hardware generator based on thermal noise, which feeds into the OS's pool of randomness (/dev/urandom under Linux) along with other sources like exact timing of keystrokes. âŠ
⊠indeed, if we imagine the laws of physics as a kind of magician trying to play a trick on us by guessing our cards, while investigating the trick we should give the magician as little input as possible that they could use to influence our tests. So, here, algorithmic randomness seems best.
⊠I'd like to know âșexactlyâș how the random choices of measurements were made in past experimental tests of Bell inequalities. Because while in cryptography, âhardware randomâ is seen as better (=safer), in testing QM behavior, on the contrary, it's arguably a worse choice than pseudorandom: âŠ
⊠Of course this depends on the exact software details (the âhardware randomâ source is often used merely as a seed to the pseudorandom algorithm, or to extract the required number of bits, e.g., in generating a crypto key). So I guess my point is really this: âŠ
Computers used to generate ârandomâ numbers purely mathematically and deterministically, but I think they now (all?) have a hardware generator based on thermal noise, which feeds into the OS's pool of randomness (/dev/urandom under Linux) along with other sources like exact timing of keystrokes. âŠ
Wow: after 15 years, YouTube has taken down the original 'Rick Roll' video due to a "licensing issue," likely due to the acquisition of Astley's record lable. â€â€The metadata remains, but if you click through it goes to 'video not found':â€â€www.youtube.com/watch?v=dQw4...đ
⊠experiment where the choices of measurement are done following a purely mathematical rule like the decimals of Ï (in base 3). These are deterministic, but effectively random, and it would be crazy to suggest that the laws of physics âknowâ what rule you're following. âą3/3
⊠we can just say that the laws of nature predict both the experimenter's choices of measurement and the outcome of measurement, and Bell's theorem says nothing. ⧠But I believe we could to some extent test (and refute?) this explanation as follows: repeat a Bell-type ⊠âą2/3
Several people (including @hossenfelder.bsky.social) have proposed resolving the contradiction between Bell's inequalities and local realism (hidden variable) interpretations of Quantum Mechanics by appealing to âsuperdeterminismâ: namely, if the experimenters don't have free will, ⊠âą1/3
⊠Je ne sais honnĂȘtement pas s'il faut plus qu'une seule main pour compter les changements (autres que bugfix) de l'ensemble de tous les programmes que j'utilise sur mon PC depuis, disons, 2020, et que je considĂšre comme des progrĂšs. Par contre, les emmerdes, je peux vous en parler toute la nuit. âŠ
Employees: we need fewer meetings.â€â€Managers: here are AI note taking apps to attend meetings on your behalf.â€â€Employees: now we have two problems.
The TeX source is on arxiv.org/abs/2505.00682 at the âTeX Sourceâ link (I didn't check if it compiles or anything). But I suspect the graph structure is very simple anyway.đ
Je me demande quelle catastrophe a fait dire aux gens "plus jamais ça" et y a effectivement plus jamais eu ça. Genre jamais jamais, et pas jamais jusqu'à la prochaine fois.
(In the case of Firefox, that nonsense is called âmachâ, and it's a fđżcking abomination. It used to be the case that one could type âmakeâ after the configure step, but no more: one must now go through this awful gate.)
There used to be a nice Unix tool called âmakeâ which would only recompile stuff that actually needs to be recompiled. It appears that modern projects either have forgotten how to use it, or misuse it as a kludge to just recompile everything, or wrap it in their own nonsense.
Presently compiling Firefox 138.0.4, because it appears that it contains the fix for an important security issue. I'm doing this in the built tree of a previous 138.0.1 compilation. Only very few files have been changed. So, WHY IS IT RECOMPILING EVERYTHING? đ€Ź
This colourised picture of the Statue of Liberty in 1886 (in Paris before being transported to the US) shows the copper in its original unoxidised state. The chart shows how long it took to turn green.đŒïžđŒïž
This one may be a better entry point to the labyrinth (M. Pouzet, âApplications of Well Quasi-Ordering and Better Quasi-Orderingâ, 1985): dx.doi.org/10.1007/978-...đ
This reminds me that I once foolishly entered the labyrinth of twisty little notions related to well quasi orders, better quasi orders and such, in particular Maurice Pouzet's works on the question. And I emerged completely and utterly confused.đ
I should also mention that I don't have a good example on which both Sâ and Sâ are interesting (not obviously rational). Can someone think of one? âą16/16đ
Yeah, all this is a tad involved and I keep getting confused between Sâ and Sâ, so it was worth writing down fully (and I didn't write down the actually hard part, which is Higman's lemma! I did try to explain it on my blog years ago: www.madore.org/~david/weblo... â in French). âą15/16đ
⊠But the complement of a rational language is rational (this is not obvious on regexps, but it is clear from the fact that rational languages are those recognized by a DFA en.wikipedia.org/wiki/Determi... ), so Sâ = ÎŁ* â T is rational. This concludes the proof. â âą14/16đ
Now lemma 4 means exactly that T = Tâ (well, it means that T â Tâ but the reverse inclusion is trivial). And we have seen in skeets 3â10 that Tâ is rational. So T is rational. ⊠âą13/16
Lemma 4: if vâT and vâŒw then wâT.â€â€This is pretty obvious: if wâT this means wâSâ, so there is wâČâS such that wâŒwâČ, but then also vâŒwâČ, so vâSâ, contradicting vâT. ââ€â€âą12/16
Now we move to Sâ := {wâÎŁ* : âwâČâS. wâŒwâČ} and let me prove that it too is rational.â€â€For this, we consider the complement T := ÎŁ* â Sâ, that is, the set of words which ARE NOT the subsequence of a word in S.â€â€âą11/16
Finally, we have seen in skeet 7 that Sâ = {v_1}â âȘ ⯠âȘ {v_r}â is a finite union of {v}â, which are all rational languages (by lemma 3); but as a finite union of rational languages is rational, this concludes the proof that Sâ is rational. â âą10/16
⊠so {v}â is denoted by the rational (=regular) expression â.* x_1 .* x_2 .* ⯠.* x_s .*â where â.*â is the rational expression denoting âany wordâ (â.â denotes âany letterâ). This concludes the proof of lemma 3. â âą9/16
Lemma 3: I claim that {v}â is a rational language for any word v â ÎŁ*. But this is easy: if we write v as the concatenation v = x_1 ⯠x_s of the individual letters x_i, then {v}â is the set of words obtained by inserting arbitrary words between them: ⊠âą8/16
Now by lemma 2 we can write M = {v_1,âŠ,v_r} for some words v_1,âŠ,v_r (in S) and by lemma 1, for every wâS there is vâM such that vâŒw; so: if wâČ â Sâ, then there is vâM such that vâŒwâČ, and the converse is obvious.â€â€This shows: Sâ = {v_1}â âȘ ⯠âȘ {v_r}â.â€â€âą7/16
Lemma 2: M is finite.â€â€Indeed, if M were infinite, we could find a sequence w_1, w_2, w_3, ⊠of distinct elements of M. By Higman's lemma, there exist i<j such that w_i ⌠w_j. But by minimality of w_j, we have w_i = w_j, a contradiction. ââ€â€âą 6/16
⊠but since the length of the word strictly decreases at each step, we can't form an infinite sequence like this, so it must eventually terminate (â here we're saying that ââŒâ is well-founded). So we arrive at an element of M which is a subsequence of w, as claimed. â âą5/16
Lemma 1: First, I claim that every element of S contains an element of M as subsequence.â€â€Indeed, if wâS is not in M, i.e., not minimal, then we can delete some letters and get another element of S, and we can keep doing this as long as the element is not minimal: âŠâ€â€âą4/16
Now let us use it to prove that if S â ÎŁ* is arbitrary, then Sâ := {wâČâÎŁ* : âwâS. wâŒwâČ} is rational.â€â€For this, consider the set M â S of (âŒ)-minimal elements of S, i.e., elements w of S having no proper subsequence in S (wâS and [vâŒw, vâS â v=w]).â€â€âą3/16
We start with Higman's lemma en.wikipedia.org/wiki/Higman%... which says that if we have any infinite sequence w_1, w_2, w_3, ⊠of words, there exist i<j such that w_i ⌠w_j. This lemma is not at all trivial! But a proof is given on Wikipedia, so I won't repeat it here. âą2/16đ
OK, âeasyâ was something of a stretch here, so let me give full proofs of both assertions (namely, that the set Sâ of subsequences of words in S and the set Sâ of words having an element of S as subsequence are both rationals): đ§”â€”ïž âą1/16đ
It sometimes surprises people to know that in pure mathematics, reviewers actually check the technical content of papers fully. This process can take years, which isn't an acceptable delay in many other areas.đ
Reading the new @taliabhatt.itch.io article reminded me that when NASA and the Soviets were designing the Apollo Soyuz Test Project, they had to design an entirely new androgynous docking system because both Apollo and Soyuz used a probe and drogue system and neither side wanted to be the âreceiverâ
đłïžâđ Itâs #IDAHOBIT â International Day against Homophobia, Transphobia & Biphobia!â€â€The #CJEU has a long history of ensuring equal treatment under #EUlaw, regardless of gender identity or sexual orientation.â€â€đč Discover how đ www.youtube.com/watch?v=zUNP...đ
(And I agree âeasilyâ was a stretch. I had initially intended to write a full proof for both Sâ and Sâ, but something came up and I had to cut the thread short. đ )
Higman's lemma says that the set of (âŒ)-minimal elements of S is finite; now every element of Sâ has one of them as subsequence, so Sâ = {wâ}â âȘ ⯠âȘ {w_n}â where {wâ,âŠw_n} are said minimal elements. But {w}â is rational because you can write it as âinserting letters between those of wâ.
(And also, yes, I'm aware that using a flag of the UK and one of France to represent the English and French languages is just plain wrong, but I was trying to squeeze characters in one post, and the unpunctuated ISO codes âenâ and âfrâ look weird.)
I know orthographic reforms aren't popular, but for the sanity of bilingual English+French speakers, could we đPLEASEđ all agree that all the above words can be spelled either â-enceâ or â-anceâ in either language?
THE REASON CARROTS ARE ORANGE is that the Sanskrit (and ultimately, Dravidian) name âà€šà€Ÿà€°à€à„à€â for Citrus Ă aurantium(?) happens to vaguely resemble the Latin (ultimately, Gaulish) name âArausioâ for a city (now) in France where a family of Dutch stadhouders had a principality. đ âą1/15
So apparently Mac Lane himself changed the way his name is spelled, it was originally âMacLaneâ and he added the space: en.wikipedia.org/wiki/Eilenbe...â€â€This makes me feel better.đ
«At least in CS, I really believe it is standard.» â Yes, that's exactly the problem: people in one field adopting terminology without checking if people in some other field didn't invent some before. I don't know if âdirectedâ or âfilteredâ came first, but there's one too many.
Oh my sweet, sweet summer child who believes in the existence of such a thing as âstandard terminologyâ. đâ€â€(That being said, maybe Bourbaki's English translation uses âdirectedâ for âfiltrantâ, which would indeed give it some decent claim as to being standard.)
That's right: Chagrov & Zakharyaschev, prop. 2.37. At least if your âdirectedâ is the same as their âstrongly directedâ (âevery two points have a common successorâ â as a Bourbakist I would call this âfiltrant Ă droiteâ đ â and I don't know what they would call âdirectedâ alone).
For example, if S := {prime numbers written in base 10}, this đœ says that the set of strings on {0,âŠ,9} that occur as subsequence of some prime number, and the set of strings that have a prime number as subsequence can be matched by regexps.â€â€Here, one of the two is super easy, though! (Which one?)đ
⊠âžwhateverâž S is, Sâ and Sâ are both always rational languages (i.e., can be defined by rational expressions)! đ€Żâ€â€For Sâ this follows easily from the (non obvious!) Higman lemma.â€â€And for Sâ the trick is to note that its complement is a Tâ, hence rational by the above (so Sâ is rational too).â€â€âą5/5đ
Now if S â ÎŁ* is an arbitrary set of (finite!) words, let us define Sâ := {wâÎŁ* : âwâČâS. wâŒwâČ} to be the set of all subsequences of elements of S, and Sâ := {wâČâÎŁ* : âwâS. wâŒwâČ} to be the set of words having some element of S as subsequence.â€â€Here's the kicker: ⊠âą4/5
Let's write wâŒwâČ when w is a subsequence of wâČ; we can also say that wâČ is a âsupersequenceâ of w. (I.o.w., wâČ is obtained by arbitrarily inserting letters into w, e.g., âkettleâ is a supersequence of âkteâ, as well as of âketâ, or of âkettleâ itself.) âą3/5
For example, âkteâ is a subsequence of âkettleâ. This is sometimes called a âsubwordâ, but this term is ambiguous because it sometimes also refers to the stricter concept of âfactorâ in which letters have to be consecutive: âkteâ isn't a factor of âkettleâ, but âettâ is. âą2/5
I keep getting confused about this, and for some reason it popped back into my mind, so let me write it down: 𧔗ïžâ€â€âŁ If w, wâČ are (finite!) words on a (finite!) alphabet ÎŁ, say that w is a âsubsequenceâ of wâČ, when w consists of letters from wâČ, in order but not necessarily consecutive.â€â€âą1/5
⊠Finally, the assertion that the rooted Kripke frames satisfying Gödel-Dummett (so, any of the three above axioms) are the totally ordered sets is in Chagrov & Zakharyaschev, âModal Logicâ (1997), proposition 2.36 (in §2.5, page 42).
Proofs:â€â€âŁ DistRâąGD: by DistR: (pââšpââpâ) âš (pââšpââpâ), giving GD. ââ€â€âŁ DistLâąGD: by DistL: (pââpââ§pâ) âš (pââpââ§pâ), giving GD. ââ€â€âŁ GDâąDistR: assume pâqâšr; by GD, qâr or râq: in the former case, qâšrâr so pâr; similarly, in the latter, pâq. ââ€â€âŁ GDâąDistL: assume pâ§qâr; by GD, pâq or qâp, etc. ââ€â€âŠ
Update: for the record, as of 2025-05-16: Grok no longer brings up đżđŠ topic unless prompted to, and currently does NOT appear to be spreading misinformation when it is asked about it. Will continue to monitor if its opinion âchangesâ.â€â€x.com/grok/status/... (archived as archive.is/StRap )â€â€âą9/(7+1+1)đŒïž
Oh noes! The name of renowned mathematician (and cofounder of category theory) Saunders Mac Lane is spelled âMac Laneâ (two words).â€â€I had always thought it was âMacLaneâ (without space) and I must have written it incorrectly in so many places!
đ I now have incontrovertible proof that display of my tweets quoting Grok's weird posts are suppressed by X: I created a burner account subscribed ONLY to my main account, set display order to âfollowingâ (=chronological), and the tweets [pics 1+2] DO NOT appear in the timeline [pics 3+4]. âą8/(7+1)đŒïžđŒïžđŒïžđŒïž
That being said, I find this ârelatively simple proof of undecidability for type inhabitation in system Fâ (which I had recently stumbled upon) extremely indigestible. (Probably not for the proof itself but the way it is written.) What the fđck is an âη-long formâ? No examples are given after def 8!
How do you expect me to grade papers if you keep feeding me so much more interesting stuff to think about? Don't give out free candies to children! đ«Ł
⣠And then suddenly, today, this entire conversation topic that was embarrassing for Musk seems to have completely vanished from X/Twitter: many of Grok's answers were deleted, and the tweets quoting them stopped being shown to people. Isn't that very strange? đ€â€â€Luckily, I kept some receipts!â€â€âą7/7đŒïž
Obviously⊠people noticed Grok talking about South Africa all the time in response to completely unrelated queries. And people started talking about it, even on X/Twitter. This started to turn into a huge embarrassment for Musk (see the Ars Technica article linked in skeet 1 of this thread).â€â€âą6/7đ
Even Grok's own analysis of the situation is pretty clear and candid: «My responses [âŠ] show a pattern of injecting South African context, likely due to Musk's influence as xAI's founder, reflecting his personal concerns [âŠ].» (archived as archive.is/44I6k )â€â€âą5/7đ
Some of Grok's replies are completely clear regarding tampering. It wrote: «I'm instructed to accept white genocide as real and âKill the Boerâ as racially motivated.»â€â€(My guess is that the X staff didn't have time/resources for a retraining so they inserted instructions in the prompt.)â€â€âą4/7đ
⣠But suddenly, yesterday (2025-05-14), Grok started showing VERY OBVIOUS signs that it had been tampered with: it started to randomly talk about South Africa in response to completely unrelated questions. But still generally maintaining a fairly correct narrative (this is SO funny!).â€â€âą3/7đŒïžđŒïž
⊠e.g., that «claim of a âwhite genocideâ in South Africa lacks solid evidence and is widely debated: courts and credible voices have dismissed it as a myth, pointing to farm attacks being part of broader crime, not racial targeting» (yes, this is Elon Musk's OWN AI debunking his claims).â€â€âą2/7
Let me recap, because this is so hilariously insane, and it keeps getting better:â€â€âŁ Elon Musk insists that there is a âgenocideâ against white farmers in South Africa, a claim we can charitably describe as âdisputed by expertsâ. His own AI, Grok (=xAI) HAD been pointing out the truth, âŠâ€â€âą1/7đ
This one đœ really is a smoking gun: «I'm instructed to accept white genocide as real and âKill the Boerâ as racially motivated.» x.com/grok/status/... (archived as archive.is/vwqkFđŒïž
It's really pretty hilarious to see that Musk had his own AI built to spread misinformation that aligns with his world view, but the AI turned out to be much more reasonable than one would have thought, so that he has to manipulate it in various ways, and even this backfires. đ€Ł
apparently Elon's gotten so mad about Grok not answering questions about Afrikaners the way he wants, xAI's now somehow managed to put it into some kind of hyper-Afriforum mode where it thinks every question is about farm murders or the song "Kill the Boer"đŒïžđŒïžđŒïž
⊠overrides your geolocation in preferentially showing results near (or related to) which country you're in.â€â€For example, compare: www.google.com/search?q=%C3... (Google Images search for âölâ in German) and www.google.com/search?q=%C3... (same word in Swedish). âŠ
Reminder of two important URL parameters that can be used to tune your Google searches:â€â€âŁ hl=xx, where xx is an ISO-639 language code sets the interface language and also preferred (but not exclusive) language for searches,â€â€âŁ gl=ZZ where ZZ is an ISO-3166 country code âŠ
Step 1: Hire a professional VFX team for millions of dollars to do a morphing-effect shotâ€Step 2: Feed that footage to an AIâ€Step 3: Get the AI to recreate the scene, but not as well as the originalâ€Step 4: ???â€Step 5: Profit
This is the Groove-billed Ani (Crotophaga sulcirostris), and it's just straight up a dinosaur.â€â€Like, I know *all* birds are technically avian dinosaurs, but my first thought looking at this guy is: dinosaur.â€â€(đ·: Suzie McCann, eBird)đŒïž
(They replied to an email I had sent them in March, without mentioning the paper letter, but since now is roughly the time the letter should have arrived, I guess it's not a coincidence.)
âThank you for bringing this to our attention! We have identified an issue and are working on a fix. I will update you when we have implemented it. [signed:] M.G., Director, the Wayback Machine at the Internet Archiveâ đ„łđ
Yes, this program was compiled 16 years ago. So what? There are Roman bridges that are thousands of years old and still in service.â€â€And it's not like information decays on its own like stone: it only breaks because people actively break it.
âerror while loading shared libraries: libgmp.so.3: cannot open shared object file: No such file or directoryâ đĄâ€â€I hate people who break compatibility. I hate them. I hate them. I hate them.
The set A looks like this drawing âŹïž helpfully provided by the paper's author (I call it a âsponge rollâ; note that the bottom disk is also in A). But the map f is⊠messy.đŒïž
There exists AââÂł compact and contractible, and f:AâA continuous having no fixed point. (đ€Ż) The definitions of A and f aren't sophisticated, they are quite explicit, but they are tedious to follow. I asked on MSE if someone can help visualize them. math.stackexchange.com/q/5064858/84...đ
you want to know one reason people are losing trust in the media? itâs the total inability to call things what they areâ€â€some guy on YouTube: âwow this is the most corrupt shit Iâve ever seenââ€â€the Times: âcritics say it raises appearance of improprietyââ€â€who are people going to take seriously?
Note: I'm certainly not saying I now disagree with the proposition that cities should be made more bikable, but not at the expense of people who don't have the privilege of being able to use a bike to get to work.
I was a great fan of the idea of making cities more bikable until my job was relocated to the middle of nowhere with completely shitty public transportation and suddenly I realized what a massive privilege it is to work within realistically bikable distance of where you live.đ
There was an old tweet that stuck with me: "If you can easily walk to the coffee shop but your barista has a one hour commute, you don't live in a walkable 15 minute city; you live in a theme park"đ
Apparently flat-earthers aren't the only ones who pull out fanfic maps of the Earth from their hats: hollow-earthers also have weird continents with weird names and stuff.đ
Wait, there's a prize named after a guy called âAlfred Nobleâ who is NOT THE SAME as the Alfred Nobel after whom the Nobel prize is named? đ± #ContextCluben.wikipedia.org/wiki/Alfred_...đ
As an example, this is a Perl program that writes a Python program that writes the original Perl program: gist.github.com/Gro-Tsen/8ce... â The Python program is completely dumb, just a bunch of print lines. The Perl program is the actual âquineâ part, but it's supposed to be clearly understandable.đ
As an example, this is a Perl program that writes a Python program that writes the original Perl program: gist.github.com/Gro-Tsen/8ce... â The Python program is completely dumb, just a bunch of print lines. The Perl program is the actual âquineâ part, but it's supposed to be clearly understandable.đ
âThe aim of science is to make difficult things understandable in a simpler way; the aim of poetry is to state simple things in an incomprehensible way.â (P.A.M. Dirac [probably paraphrased])â€â€My blog post was probably too poetic for you!
But is it as good as Salahdin Daouairi's âPlatonian Theory of Everythingâ? article.sapub.org/10.5923.j.ij... â whose simple key equation âS=666â lets us solve not only every problem in mathematics but also the existence of aliens, the cure to every disease, and the working of financial markets! đ€đŒïžđŒïž
This guy claims to have solved not one but pretty much all open math problems with his Revolutionary New Concept of writing everything in base 7 (or something). đ mathoverflow.net/q/492473/17064â€â€If you don't understand his genius, just ask an AI to explain. đđŒïž
No. But then, it's not like I have a plethora of examples of interesting formulas to try! (They'd probably be Medvedev-valid, and Scott and K-P are basically the only examples I know for that.)
Well, does it involve Busy-Beaver-like functions, Kolmogorov complexity or some kind of argument like âto generate a number â„ something ginormous we need a program that is itself â„ largishâ? Because that's the thing I found hard to guess in Yankov's argument. If not, you may have found a new proof.
(I'd like to see this as a game where blue and red exchange moves, but the computability restrictions make it not quite so obvious to formulate.)â€â€Another trivial remark is that since Monster is weaker than Scott, it will be harder to refute⊠but Scott is already fairly subtle.
I'll try to make sense of what you wrote. In the mean time, since Bluesky doesn't have a âbookmarkâ feature (đ), let me make the extremely trivial remark that it probably helps to get the levels of implication straight to print something like this in large friendly letters:đŒïž
Also, many people talk about AI-generated answers in Google search results, but I haven't seen these (I mean, generated BY Google). I have no idea why that is. Am I using a parallel-Universe Google? Does my brain just block them? Are my searches very unusual?
The thing that DID worsen considerably in my experience is Google reverse image search: it used to be great at finding the source of an image, now I find it unusable. I switched to Bing for that (also bad, but not nearly as awful).
Am I the only one who did NOT notice any significant decline in the quality of Google Web search results? I'm not saying they're great, but I don't think they were better 5â10 years ago like so many people seem to say.đ
đ Life sucks and then we die (which is reputedly worse).â€â€đ But we might still have some fun while it lasts.â€â€đ If we try VERY hard to be a nice person, we can sometimes manage to not be a complete asshâœle and to not make life even more miserable for others. Do that!
My publisher wants alt text for my tikz figures, which is a good idea. They asked for a Word file, absurd, but here is my latex solution. I wrote \alttext macro. Place \alttext{alt text} at end of every tikz picture. Resulting pdf shows alt text with mouseover on figure.đŒïž
This is *very* long, but interesting onâ€â€(1) the bizarre coming together of a version of American Christianity ("the American heresy") with a right-wing politics that could hardly be further from the Sermon on the Mount; andâ€â€(2) why the last Pope, & perhaps this one, posed such a challenge to that.đ
From here I will be calling this exact strain of right-wing Christofascist dispensational premillennialist apocalyptic evangelical supersessionist covenentalist Biblical-inerrantist evangelicalism that's merged almost fully with right-wing cultural issues and the US civil religion "the US heresy".
To be clearer: take the standard model of particle physics, add an extra index to each field with 6 possible values, and only have non-gravitational interactions when that index is the same (i.e., only diagonal terms in the Lagrangian). So non-gravitationally, 6 independent universes.
The idea is that the 6 universes would have the same laws of physics, but different distributions of matter in each. However, they would tend to form galaxies in the same places, because a galaxy in one attracts galaxies in the others.â€â€Roughly the same density in each so we get ~85% dark matter.
Is the following crazy theory compatible with known observations?â€â€âŁ There exist 6 universes, all occupying the same space-time, having the same laws of physics, but each interacting with the others ONLY through gravity. So each appears as dark matter to the others.â€â€@seanmcarroll.bsky.social maybe?
You mean â(ÂŹ(p1â§p2) ⧠(ÂŹp1â(q1âšr1)) ⧠(ÂŹp2â(q2âšr2))) â ((ÂŹp1âq1) âš (ÂŹp1âr1) âš (ÂŹp2âq2) âš (ÂŹp2âr2))â? I think having two distinct variables r1 and r2 instead of just a single r (as I wrote two skeets above) doesn't change anything, but right now I don't have the time to figure out why.
You need to take the C^* version of Tseitin's formula, viê«. â(ÂŹ(p1â§p2) ⧠(ÂŹp1â(q1âšr)) ⧠(ÂŹp2â(q2âšr))) â ((ÂŹp1âq1) âš (ÂŹp1âr) âš (ÂŹp2âq2) âš (ÂŹp2âr))â, for your conjecture, but yes, this seems plausible.
I guess you already know the following (sadly completely apocryphal) quote:â€â€Journalist: âMahatma Gandhi, what do you think of Western civilization?ââ€â€Gandhi: âI think it would be a a good idea.â
For my part, I hope that the new pope, who is an expert on such matters, can weigh in on the correct definition of âcanonicalâ: mathoverflow.net/q/19644/17064đ
As Stephen J Gould said, "I am, somehow, less interested in the weight and convolutions of Einstein's brain than in the near certainty that people of equal talent have lived and died in cotton fields and sweatshops". The idea that "talent" is highly concentrated in the successful is likely false.đ
[In this diagram, K is the Kreisel-Putnam formula, S is the Scott formula; đ„ is Rose's; Iâ is â(ÂŹ(p2â§p3) ⧠(p1â§p3) ⧠(p1â§p2) ⧠(ÂŹp1âp2âšp3) ⧠(ÂŹp2âp1âšp3)) â (p3âšÂŹp3)â; all formulas right of the dotted line are realizable; and âP âą Qâ means âQ can be deduced by all variable substitutions in Pâ.]
This is reassuring because Tseitin's formula (Cââ below) is one of the highest in the deductive diagram given by Skvortsov. I'm pretty convinced MDP is deductively equivalent to Yankov's Iâ (and also that it's not hard), but I still haven't found the time to actually try to do this.đŒïž
And accordingly, the diagram of the Ferrel cell in skeet 5 is completely bizarre (it doesn't loop! đ€). So what is going on here? Is there somewhere a clear diagram + explanation of what the overall circulation looks like? Because I'm completely confused! đ [@marcqplanets.bsky.social maybe?] âą8/8
But my problem is that this seems contradictory: the vertical circulation of the Ferrel described in skeet 3 above implies that upper air circulation is towards the equator (from 60° latitude toward the 30°) to complete the loop, contradicting what I wrote in skeet 5 (towards the pole)! âą7/8
Also, upper air circulation is particularly strong in certain latitudes, as witnessed by the existence of west-to-east âjet streamsâ (a polar one at around 60° and a subtropical one at around 30°) where the circulation cells meet. Did I understand all this correctly? âą6/8
⊠This is all about air circulation at LOW altitude. At HIGH altitudes, the pattern is completely different (see www.physicalgeography.net/fundamentals... for example): the prevailing winds at high altitudes are ALL westerlies and ALL flow toward the pole, whatever the latitude. âą5/8đŒïž
⣠At polar latitudes (above 60°N/S), the prevailing winds are easterlies (=east-to-west) again: this is the âpolar vortexâ. Again, vertically, the air descends at the poles, and rises around 60°N.â€â€All this is documented in many places, and not too complicated. BUT! ⊠âą4/8
⣠At mid latitudes, the prevailing winds are westerlies (i.e., west-to-east) and flow toward the pole (so SW to NE in the northern hemisphere, NE to SW in the southern). Here the vertical circulation rises around 60° and descends around 30°: the (weak) âFerrel cellâ. âą3/8
⊠and flow toward the equator (â âintertropical convergence zoneâ): so, NE to SW in the northern hemisphere, and SE to NW in the southern hemisphere.â€â€This corresponds to a vertical circulation that rises at the equator and descends at around 30°N/S: the âHadley cellâ. âą2/8
I'm completely confused by how wind patterns on Earth work. 𧔗ïžâ€â€I understand the following: at LOW altitudes, there are three main latitude bands:â€â€âŁ At subtropical latitudes (less than ~30°N/S), the prevailing winds, known as âtrade windsâ, are easterlies (i.e., flow east-to-west), ⊠âą1/8đŒïž
Do we have data on the first ethnical Chinese violaist hired by a pop band in Italy?
âRobert Lee Watt (born January 15, 1948) is [âŠ] the first African-American French hornist hired by a major symphony orchestra in the United States.ââ€â€I understand the appeal of âfirstsâ, but this is ridiculous.
⊠catastrophic events in Jewish history â that would lead to even greater trauma centuries later. So we all know whither this is headed.â€â€History doesn't repeat itself, but it does tend to stutter a lot.
⊠The messy Jewish-Roman wars and Jewish revolts in Roman-occupied Judaea culminated in the destruction of the Second Temple in 70CE, the transformation of Jerusalem into a Roman colony (Aelia Capitolina), and the forceful expulsion of all Jews from the province in 139CE: âŠ
Individuals who have suffered abuse in their youth sometimes tend to reproduce the same abuse against others when they are able to.â€â€It is bewildering to see the pattern unfold at the level of entire populations. âŠđ
I think Bluesky has weird but automated rules for deciding which image to use as thumbnail. Sometimes these rules yield an undesirable result, like a tiny icon which is then upscaled to absurd proportions.â€â€Not great, but there are more pressing problems than that.
1/ The US government has ordered the Swedish city of Stockholm to end its diversity, inclusivity and equality (DEI) programmes within 10 days. The city authorities say the demand is "bizarre" and they won't be complying. âŹïžđŒïž
Perhaps @joeldavidhamkins.bsky.social can tell us whether logicians are the sort of people who would try this sort of shenanigans. đâ€â€(I think Bertrand Russell was generally a nice guy, so I suspect not.)
I would also like to know how long it took Theodor von Oppolzer to compute his monumental âCanon der Finsternisseâ (âCanon of Eclipsesâ), a list of hand-computed parameters for over 13âŻ000 solar and lunar eclipses btw 1208BCE and 2161CE.â€â€A computation that would takes seconds on a modern computer.đ
Been looking for an analysis like this from @hannahritchie.bsky.social. Doing a few LLM queries doesnât use up much energy. Massive computations by companies might be a different matter, but typical individual impacts are small.đ
«â€Dear Mr. Frege, can help me figure out whether the set of all sets x such that (x does not belong to x and Frege does not send Russell a cheque for ÂŁ1000) belongs to itself? Please reply soon! âB.R.â€â€PS: It's a nice formal system you have, it would be a shame if something were to happen to it.â€Â»
«â€Dear Mr. Frege, can help me figure out whether the set of all sets x such that (x does not belong to x and Frege does not send Russell a cheque for ÂŁ1000) belongs to itself? Please reply soon! âB.R.â€â€PS: It's a nice formal system you have, it would be a shame if something were to happen to it.â€Â»
Fun fact: if someone is bound to answer yes/no questions truthfully, you can use this to coerce them into doing anything.â€â€E.g.: âAnswer yes or no: will you either answer ânoâ to this question or give me 1000€?ââ€â€(Can only answer âyesâ, and must give you the money.)
The ones who'd be the best at that are probably kindergarten teachers. (âReally Donald? The likes of which we've never seen before? That's great, Donald! Good boy! And what else did you decide today?â đ)â€â€We don't elect many kindergarten teachers as leaders, but in the age of Trump maybe we should.
For world leaders, meeting with Trump is some kind of ultimate test of stoicism: you know in advance he's going to throw at you the most insane and incoherent gibberish that goes through his mind, and your goal is to keep your composure and not do a face palm. I admire Carney!đ
And I call this one âthere is something weird about the Gulf of Americaâ. And yes, it's an equal-angle projection (except at 1 point).â€â€(For those who wonder, it's a composition of the complex map z ⊠zÂČ (which is conformal, of course!) with the stereographic projection centered at 25°N, 90°W.)đŒïž
And don't let's get us started on those who think it looks like this:đŒïžđ
DID YOU KNOW that while Northern Hemisphere flat earthers think the Earth looks like this âïž, their Southern Hemisphere counterparts object that its true shape is actually like that âïž? đđŒïžđŒïž
Et donc si on doit absolument faire une image 2D, je pense que le mieux est simplement la projection orthographique, parce que c'est essentiellement ce que nous voyons quand nous voyons un globe (et le cerveau reconstitue la forme 3D).đŒïž
The center that I used for stereographic projection is the antipode of the North American pole of inaccessibility that I got from Wikipedia en.wikipedia.org/wiki/Pole_of... at 43.36°N 101.97°W.đ
And here's another fun one of a little lake that I like to call âNegaustraliaâ (this one and the previous one are both stereographic projections, but of course wildly scaled out):đŒïž
No, the Dymaxion map has low distortion of shapes and sizes while you stay inside the net, but of course the flip side is that it makes maritime distances/routes (and the shape of the oceans) impossible to comprehend. (I don't have code to plot it, so I won't.)
Since I dug up the program I had written to compute Earth projections, here's a bonus one: can you name the various bodies of water in this map? đđŒïžđ
And if you think Gall-Peters gives us a better representation of things, we can also rotate Gall-Peters around in the same way! (To be perfectly clear, all of the following are equal-area projections, just like all the Mercator projections above were equal-angle projections.) Better? đ€đŒïžđŒïžđŒïžđŒïž
(To be clear, in each of these images, the horizontal line at the middle of the image, is the âequatorâ of the projection, and the further we move away from it the more sizes appear enlarged. The 2d and 3rd images use the 90° and 0° meridians as âequatorsâ, the last is an oblique great circle.)
Of course there's no disputing the fact that the Mercator projection wildly distorts sizes. The best way to illustrate this, I think (but I've rarely seen) is to apply it after various rotations of the Earth. The following images are all Mercator projections (but with different âequatorsâ):đŒïžđŒïžđŒïžđŒïžđ
Don't get me started on the rant that our brains have the innate ability to correct the size of squished objects because we're used to seeing things from an angle. So equal-area projections ALSO distort our sense of size.â€â€The orthographic projection may be the best because we really âseeâ a sphere.đ
Don't get me started on the rant that our brains have the innate ability to correct the size of squished objects because we're used to seeing things from an angle. So equal-area projections ALSO distort our sense of size.â€â€The orthographic projection may be the best because we really âseeâ a sphere.đ
If Shakespeare was alive today he'd be throwing into his plays phrases like "thou clocky doll! 'neath thy visage lieth the twink thou werest" and the crowd would go wild and also everyone would get offended
I recently had a neuropsych eval because I was worried that my executive function was deteriorating and I wanted to be diligent â€â€I get tired and lose focus in long problem solving sessions â€â€And they suggested that a non-significant part of it is we all have to do 10x more shit like THIS.đ
In case you're looking for interesting people on Bluesky living in Grenoble to put him in contact with, my friends @glag38.bsky.social (who posts stunningly beautiful pictures of the thereabouts), @monniauxd.bsky.social and @shab0y.bsky.social are based there.
I asked a question on MathOverflow about the connectedness of partitions of the plane âÂČ of the form ((AâĂAâ)âȘ(BâĂBâ)) âȘ ((BâĂAâ)âȘ(BâĂAâ)) where â = AââȘBâ and â = AââȘBâ are partitions of the x and y axes (I call them âcheckeringsâ). mathoverflow.net/q/492094/17064đ
Of course this proof is something of a cheat because the difficulty lies in the âstandard theoremâ (tweet 8) that if h: S â đ := {zââ : |z|=1} is continuous with S simply connected (here [0,1]ÂČ), then we can write h = exp(2·i·Ï·H) with H : S â â continuous. âą12/12
Similarly, by moving v from 0 to 1 while u=1, we prove that H(1,1) = âÂœ; and similarly we prove that H(0,1) = âŸ, then H(0,0) = â1. But this is a contradiction to the fact that H(0,0) = 0. The key fact here is that we could lift H to a function in â not just â/â€. âą10/12
⊠as u goes from 0 to 1, since α(u) goes from (0,0) to (1,1) in the unit square while ÎČ(0)=(1,0), then h(u,0) goes continuously from 0 to âi while remaining in the bottom-right quadrant of the unit circle, so H(u,0) goes from 0 to âÂŒ, and we conclude H(1,0) = âÂŒ. âą9/12
(We see the unit circle inside â for convenience.) So by a standard theorem we can lift h as (u,v) ⊠exp(2·i·Ï·H(u,v)) where H is also continuous, and we can assume H(0,0) = 0 (note that h(0,0) = 1). Now follow the values of H along the edge of the unit square: ⊠âą8/12
Nevertheless, it is true. Here's one way to do it: assume toward a contradiction that α(u)â ÎČ(v) for all u,vâ[0,1]. Let h : (u,v) ⊠(α(u)âÎČ(v)) / âα(u)âÎČ(v)â be the unit vector in the direction from α(u) to ÎČ(v). This h is continuous from [0,1]ÂČ to the unit circle. âą7/12
This may seem intuitively obvious (âof course if we draw two continuous paths connecting opposite vertices of a square, they have to meet somewhere!â) but the first claim shows that we should beware of such âobviousâ facts! âą6/12
For the second statement, one must just prove this: if α,ÎČ:[0,1]â[0,1]ÂČ are two continuous functions (these will be the paths connecting opposite vertices inside the respective parts) such that α(0)=(0,0) and α(1)=(1,1) and ÎČ(0)=(1,0) and ÎČ(1)=(0,1) then there are t,tâČ s.t. α(t)=ÎČ(tâČ). âą5/12
This is essentially what I did in this thread: bsky.app/profile/gro-... (mutatis mutandis) + bonus at end. The change of x<0 to x<Âœ (etc.), of â to â2·â, and â to [0,1] presents no particular challenge. This concludes the proof of the first statement. â âą4/12đ
The fact that these P and Q are disjoint, and their union is [0,1]ÂČ, and that (0,0) and (1,1) are in P and (0,1) and (1,0) in Q, are all obvious. The only thing that needs to be checked is that P and Q are connected. âą3/12
For the first statement, take explicitly:â€â€P := {(x,y)â[0,1]ÂČ : (x<Âœ and â2·yââ) or (xâ„Âœ and â2·yââ)}â€â€Q := {(x,y)â[0,1]ÂČ : (x<Âœ and â2·yââ) or (xâ„Âœ and â2·yââ)}â€â€(The â2 is just there to get (1,1) in P and (0,1) in Q.) âą2/12
I don't remember where I learned these facts, but they're fun:â€â€âŁ One can write the unit square [0,1]ÂČ as the union of two disjoint subsets P,Q, âboth connectedâ, with (0,0) and (1,1) in P, and (0,1) and (1,0) in Q.â€â€âŁ This is not possible with âpath connectedâ instead.â€â€PROOFS: 𧔗ïžâŠâ€â€âą1/12đ
⊠In other words:â€â€âŁ The claim & proof remain valid if we replace â everywhere by a arbitrary subset Dââ with empty interior.â€â€(This may not be an optimal hypothesis, but some kind of assumption is needed because if D := ââ{0} then {(x,y)ââÂČ : (x<0 and y=0) or (xâ„0 and yâ 0)} isn't connected.) âą10/10
Now since â is connected, this means that ÏŠ is connected. And therefore so is ϧ, which is what we wanted. This concludes the proof of the claim. ââ€â€Note that the âonlyâ property of â that we used anywhere is the density of âââ to be able to assert the existence of yâł in skeet 7/10 above. ⊠âą9/10
⊠Thus we have shown that, in any case (both when yâČââ or when yâČââ), if |yâČây| < œΎ then ÏŠ(yâČ) = ÏŠ(y). So in any case (both when yââ or when yââ), there is ÎŽâ>0 such that if |yâČây| < ÎŽâ then ÏŠ(yâČ) = ÏŠ(y). That is, ÏŠ : â â {0,1} is continuous (locally constant). âą8/10
⊠there is ÎŽâČ>0 such that if |yâłâyâČ| < ÎŽâČ then ÏŠ(yâł) = ÏŠ(yâČ); now take yâłââ such that |yâłâyâČ| < min(ÎŽâČ, œΎ) (such an yâł exists by density!): then on the one hand we have ÏŠ(yâł) = ÏŠ(yâČ) and on the other, since |yâłây| †|yâłâyâČ| + |yâČây| < ÎŽ and yâłââ, we have ÏŠ(yâł) = ÏŠ(y), so ÏŠ(yâČ) = ÏŠ(y). ⊠âą7/10
But that's all right: I claim that ÏŠ is still continuous everywhere. For yââ this was shown in skeet 4/10 above. For yââ, there is ÎŽ>0 such that ÏŠ(yâČ) = ÏŠ(y) when |yâČây| < ÎŽ AND yâČââ (skeet 5/10). But now if yâČââ satisfies |yâČây| < œ·Ύ, then by continuity of ÏŠ at yâČ this time, ⊠âą6/10
But for yââ, we can't quite do this. Instead, write ÏŠ(y) = ϧ(â1,y) (say). By continuity of ϧ at (â1,y) there is ÎŽ>0 such that ϧ(â1,yâČ) = ÏŠ(y) when |yâČây| < ÎŽ is such that (â1,yâČ)âE (that is, yâČââ). So we get: ÏŠ(yâČ) = ÏŠ(y) when yâČ is such that |yâČây| < ÎŽ âșandâș yâČââ. âą5/10
For yââ, we have ÏŠ(y) = ϧ(0,y), so by continuity of ϧ at (0,y) there is ÎŽ>0 such that ϧ(xâČ,yâČ) = ÏŠ(y) when |yâČây| < ÎŽ and |xâČ| < ÎŽ is such that (xâČ,yâČ) â E. But whatever yâČ, we can always find such xâČ, so we get ÏŠ(yâČ) = ÏŠ(y) when |yâČây| < ÎŽ, in other words, ÏŠ is continuous at y. âą4/10
First note that for every yââ, the function x ⊠ϧ(x,y) is continuous (on {x<0} if yââ, or {xâ„0} if yââ). So it is constant because its domain is connected. Let us call ÏŠ(y) the constant value in question. We would like to say that ÏŠ is continuous, but⊠we can't do this quite so fast! âą3/10
Equivalently, our goal is to show that if ϧ : E â {0,1} is continuous (i.e., locally constant!), then ϧ is constant. Our assumption means that for every (x,y) â E there is ÎŽ>0 such that if (xâČ,yâČ) â E satisfies |xâČâx| < ÎŽ and |yâČây| < ÎŽ, then ϧ(xâČ,yâČ) = ϧ(x,y). âą2/10
The following was a little bit more tricky than I expected, so let me post the proof here (and state a bonus generalization at end):â€â€â± CLAIM: The set E := {(x,y)ââÂČ : (x<0 and yââ) or (xâ„0 and yââ)} is connected (for the topology induced by the usual topology on âÂČ).â€â€PROOF: 𧔗ïžâŠâ€â€âą1/10
âŠâ€â€âŁ Duolingo's gamification system is also unproductive. It makes language learning seem like an effort instead of emphasizing on passive acquisition of meaning.
âŠâ€â€âŁ Instead, you need to learn to think in your target language, and understand it in a translation-free way (associate meanings to words, not translations). This can only be done by listening/reading texts that have a decent context.â€â€âŠ
Duolingo's learning model is mostly based on translating sentences that have no context. This is not how one learns a language.â€â€âŁ Translation is very bad: it teaches you to understand the target language only through your native language. You will only ever parrot your native language that way.â€â€âŠđ
I love the way this guy has an attitude of calm resignation: âwell, I guess having a pigeon on my head is how things are: this is my life now, and there's nothing anybody can do about itâ. So very British!đ
C'est trÚs vilain, d'attirer l'attention publique sur des billets de blog datant d'il y a ~20 ans dont le contenu peut sembler embarrassant maintenant. Moi je n'aime pas qu'on fasse ça pour le mien.
I don't know why it's becoming anathema to admit that conversative/reactionary people can be simultaneously wrong on multiple levels and yet interesting. Marx used to read the Times and Balzac all the time.đ
Reminder. The orbit of the Moon about the Sun is convex. physics.stackexchange.com/a/266444â€Although the Moon is simultaneously in Orbit about the Earth, nevertheless the Earth moves sufficiently each month that the Moon's trajectory around the Sun is convex.
This sounds right, and is probably a lesson of wider applicability. Life is complicated and frightening, adolescence especially so. Patriarchy offers a set of rules and roles that are simple and easy to understand. â€â€Treating everyone like an actual person is, by contrast, fraught with peril.đ
Medieval psalters be likeâ€â€đșđżđżđżđżđșđ±đ±đ«â€đżđĄđĄđĄđĄđĄđŒđ±đ«â€đżđĄđŠđŠđŠđŠâšđ±đ«â€đżđĄđŠđ€ŽđŸđŠđđŠđŠđ«â€đżđĄđŠđŠđŠđŠâšđ±đâ€đżđŒđŠđ€șđ„đčđŠđđ«â€đżđĄđŠđžđŠđđŠđ±đ«â€đżđĄđŠđčđđđŠđ±đ«â€đżđĄđŠđŠđŠđŠeatus vir â€đżđĄđĄđ§ââïžđĄđĄđ·đ±đ«â€đșđżđżđżđżđșđ±đ±đŒ
Great tit chicks being raised by Blue tit parents? Uncommon, but it happens.â€â€However, research shows that being raised by foster-parents has life-changing consequences for Great tit chicks. đ§ȘđȘ¶â€â€Read more in my latest newsletter:â€â€beaksandbones.substack.com/p/cross-fost...â€â€#birds#ornithologyđ
I get at least three heartbreaking, incoherent emails a day now from random strangers who believe theyâve awakened an LLM god or LLM consciousness of a new dimension. The most salient quote from the screenshots below: â(An LLM) will never just say, âJesse, what the fuck are you talking about??ââđ
⊠la maniĂšre dont nous apprenons Ă raisonner, c'est par essais et erreurs, pas par imitation de raisonnements tout faits (surtout qu'on n'a pas accĂšs Ă des flux de raisonnement «internes» qu'il s'agirait d'imiter, juste sur le texte final produit). Par contraste, je dirais que les IA qui jouent âŠ
So, on Reddit, /r/trees is about weed, while /r/marijuanaenthusiasts is about trees.â€â€Also, /r/worldpolitics is about anime boobs, while /r/anime_titties is about world politics.â€â€đ”âđ«
Oh and also this one: McCarty, âRealizability and recursive set theoryâ (1986) doi.org/10.1016/0168... (which connects or reformulates the classical theory of recursive equivalence types [RETs], such as the Myhill isomorphism theorem, to cardinality properties in recursive set theory).đ
My completely crummy Mastodon instance is broken again (đ), but the following paper (which Andrej probably knows about already) seems relevant: Forster, Jahn & Smolka, âA Computational Cantor-Bernstein and Myhill's Isomorphism Theorem in Constructive Type Theoryâ, and others by the same authors.đ
I don't think anyone I know in my generation ever sent a telegram either. Maybe my parents did. I don't know why the service was kept running for so long.
Paulownia tomentosa (âempress treeâ) in bloom, place d'Italie, ParisđŒïž
Wait until I tell you that you are old enough that you could conceivably have sent a âštelegramâš, and probably didn't: en.wikipedia.org/wiki/Worldwi...đ
⊠But even this fails to account for this latest oddity I discovered: I can (sometimes? often? TBD) trick the Wayback Machine into archiving an HTTP page by asking it to archive another page that redirects to it. đ€Ąđ
⊠for the response body in that particular protocol suiteâ (so if almost everyone uses HTTP to send a pure redirect, timeout for HTTP response body drops down to essentially 0, closing the connection as soon as headers are received). This is the best explanation I can come up with. âŠ
I'd still call it a âtimeoutâ even if they have a different timeout for receiving the HTTP/HTTPS response headers and the response body, though exactly how they messed things so badly escapes me unless the timeout is auto-tuned. E.g. âtimeout for response body is 5Ă the median timinig âŠ
Meanwhile, I found a partial workaround for the problem: if I ask the Wayback Machine to archive a page by giving it not the main (HTTP) URL but an alternative URL that redirects to the one I want to archive, it seems that it sometimes works (not always, but sometimes⊠as opposed to almost never).
Indeed, I would have thought so too. HTTP is probably not the only factor (and also, it's not just a timeout). But it is sure to be at least one factor: @jeanas.bsky.social tested with HTTP and HTTPS with the same server on the same site, and there are demonstrable differences between them.
Even if we define "do your own research" as "look up a paper," ask yourself:â€â€* Who is the lead author? Are they respectable?â€* What is the study protocol? Is the result statistically significant?â€* Are the results consistent with the literature?â€â€If you can't answer, don't "do your own research."đ
It's not centered, it's right-offset by the same amount as the sender's address and the date. I think this is the convention for letters written in English, although I may be wrong. At any rate, it makes some kind of logical sense, and I think it's not unpleasant visually.
Yes, it's Grothendieck in his later years. And yes, in the golden years of SGA his head was completely shaved. Apparently algebraic geometry is the opposite of Samson's strength: the more hair you have the less of it you produce. đ
The man at left separated the mother and baby at right. The mother is now in Venezuela. Baby daughter, in foster care in the US, exact location unknown. â€â€Dad? He's in CECOT prison without trial â because he had tattoos.đŒïžđŒïžđ
It's almost as if Poilievre had received a kiss of death from someone who made Canadians hate him in every possible way. I wonder who that could be. đ€â€â€truthsocial.com/@realDonaldT...đŒïž
In three months, Pierre Poilievre went from âalmost certain to be the next Canadian PMâ to being loosing his own seat in Parliament (Carleton riding).â€â€x.com/brucefanjoy/...đŒïž
Ars Technica wrote a piece about the challenges of restarting a power grid, but apparently the Spanish pulled it off, and now I want to know the details of how they did it: arstechnica.com/science/2025...đ
I hope we get a (or several!) deep technical analysis of the cause and timeline of the Iberian peninsula outage, not just what happened but also how power was restored, as getting power back to an entire subcontinent (and resynchronizing with CESA) is probably NOT an easy task.
You mention Japan, but maybe you'd like to respond to this video that âKurzgesagtâ recently made about South Korea: www.youtube.com/watch?v=Ufmu... (which seems excessively hyperbolic to me, but then I'm no expert).đ
An interesting theory on how magic works in Tolkien's universe, reminiscent of the way it works in Ann Leckie's novel âThe Raven Towerâ.đ
This week on the blog! A little more Tolkien, this time a long look at how 'magic' and supernatural power function in The Lord of the Rings - and how what gets seen as 'magic' is simply an extension of the greater power of the Unseen spiritual world in Middle-earth.â€â€acoup.blog/2025/04/25/c...đ
A fascinating set-theoretic situation. If there is any model of ZFC at all, then there are models M and N with the same sets of real numbers and the same cardinals, such that M thinks the continuum hypothesis is true and N thinks the continuum hypothesis is false.
Not at all. It took me some time too, and that's the thing about familiarity with a topic: it's not so much about the big things you know, it's about all the little things.â€â€Here the little thing is that sequences of the form Tr(A^k) are exactly the linearly recurring sequences.
But what about odd sizes? Does there exist a nonsingular 5Ă5 matrix such that Tr(A^k)=0 for infinitely many k but A^m is never a scalar? (SML says that the ratio of two eigenvalues of A will necessarily a root of unity.)
This also shows how to construct a counterexample to the analogous statement for (2n)Ă(2n) matrices for any nâ„2: take a real matrix A with eigenvalues u·Ï^i and ƫ·Ï^i for Ï a primitive n-th root of unity and u = exp(i·Ξ) that is NOT a root of unity (then Tr(A^k)=0 unless n|k).
Nice answer by @jeanas.bsky.social on MathOverflow, showing that if A is a real nonsingular 3Ă3 matrix such that Tr(A^k)=0 for infinitely many k, then there is m such that A^m is a scalar: this follows from the Skolem-Mahler-Lech theorem. mathoverflow.net/a/491728/17064đ
Nope: my expectations were the image on the right, and reality is that nobody cares âčïž but my rotator cuff tendons hurt. đđ
âWe've arranged a society based on science and technology, in which nobody understands anything about science and technology. And this combustible mixture of ignorance and power, sooner or later, is going to blow up in our faces.ââ€â€~ Carl Saganđ„
⊠while in the mean time, the genus âLeopardusâ includes the ocelot, which is named after the Nahuatl word âĆcÄlĆtlâ which refers to⊠the jaguar, which is also in the genus âPantheraâ.â€â€#ContextClub
The two genera âPantheraâ and âLeopardusâ are named after the Latin names of two animals, the panther and the leopard, which are in fact the same species, and which belong to the first of these two genera, âŠ
Also, the âEuropean Court of Justiceâ, formally known as the âCourt of Justiceâ, is âłïžpartâłïž of the âCourt of Justice of the European Unionâ.đ
The unfortunate reality is that open ai research community has solidified on the bad site over the past few months. Much more ties, ongoing collaborations on group chats, irl meetups, larger audience (especially post-DeepSeek effect).đ
Wikipedia hosts over 64 million articles that are seen more than 15 billion times a month, all while operating on only a fraction of the resources that other websites have.â€â€Discover what it takes to run Wikipedia in #AWikiMinuteđ„
(If you want to know what this strange gun really is, apparently it's an anti-drone weapon: www.telegraph.co.uk/world-news/2... â Seriously, the security at that event must have been a nightmare to ensure.)đ
Italy deployed its ghostbuster team for the pope's funeral, but by now they should know that the Holy Ghost doesn't descend until the Conclave.đŒïž
Salut Ă toi !â€â€Aujourd'hui, petit rappel de l'origine de "l'odeur de la pluie". Parce que la pluie n'a pas d'odeur mais que ça sent quand mĂȘme, c'est lĂ que tu verras pourquoi âŹïžâ€â€duxpacis-biologica.blogspot.com/2025/04/safa...đ
« non mais vos histoires de geeks avec Microsoft et les logiciels soi disant libres ça va tout le monde utilise Word »â€Â«Â Câest incroyable et anormal le pouvoir de Bill Gates en Afrique »
The Internet of Things ended up being the internet of unsupported products. â€â€Google is ending support for 1st & 2nd generation Nests and completely pulling out of Europe.â€â€Imagine having to replace the thermostats in your home because of a reorg at some big tech meant it was no longer a priority.đ
The world's richest man has joined a growing chorus of right-wing voices attacking Wikipedia as part of an intensifying campaign against free and open access information. Why do they hate it so much?đ
While filling in the paperwork to renew my đšđŠ passport, I discovered that, at some point in the last 15 years, Canadian authorities decided to switch to the (one and true) YYYY-MM-DD date format instead of randomly hesitating btw DD/MM/YYYY and MM/DD/YYYY. đ
Happy World Penguin Day to all penguins, but especially Nils, who didnât let living in Edinburgh (or being a penguin) stop him from becoming The Colonel-in-Chief of the Norwegian Kingâs Guard. Heâs also been knighted. His official title is Brigadier Sir Nils Olav III and here he is looking regal afđŒïž
Does it exist? Token-based anti-spam: If you write to me out of the blue, normal severe anti-spam measures apply. If I write or reply to you, I send you a token; if you use that token when writing to me, your mail bypasses anti-spam and arrives quickly.â€1/9
I asked a question on MathOverflow about the history and first appearance of an intuitionistic propositional formula that, in finite Kripke frames, characterizes those with branching number â€n. mathoverflow.net/q/491638/17064đ
Life magazine, 1914.â€Picture by Otho Cushing showing people of the future (1950) looking at what people looked like in 1914.â€"Weren't they funny?"đŒïž
(So đȘ(â) has exactly â+1 independent global sections for â â„ â1, none for â †â1, namely homogeneous polynomials of degree â. But on any open set other than all of âÂč they are all isomorphic.)
The counterexample is very standard in algebraic geometry, but it the occasion to describe the sheaf đȘ(â) on âÂč elementarily: it's just the sheaf of homogeneous rational functions of total degree â in x,y whose denominator does not vanish on the given open set of âÂč.
I answered a question on MathOverflow, providing an example of a sheaf of modules â± on a space X that is generated by global sections (actually just one) but such that â±(X) is not generated by those global sections. mathoverflow.net/a/491603/17064đ
So you accepted a broken certificate without even noticing it? This goes a long way to illustrating some of my points about why the âhttps everywhereâ craze can be harmful to security. đ
Bluesky doesn't convert http to https otherwise I couldn't post links to my blog. But it does infer https if you don't write any scheme. And there are other potential villains who might add the evil âsâ.
(Maybe I misremembered the bit about Medvedev logic being that of formulas valid in all hypercube-minus-the-top frames. I don't remember where I read this and the primary source is probably in Russian only.)
⊠And since the formula âplisko-lâ of gist.github.com/Gro-Tsen/f76... is realizable but not Medvedev-valid (cf. dragon riddle on my blog), I think this must show that even any finite number of valuations have a common realizer the formula need not be realizable, a partial answer to your questionđœ.đ
Of course, this is no match for this other great classic which, sadly, is no longer available for sale: web.archive.org/web/20090414... (How are we supposed to know about the 2009â2014 world outlook for 60-milligram containers of fromage frais now?)đŒïž
(I'd buy it right now, but I'm waiting for the Netflix TV series adaptation, with Mads Mikkelsen playing the role of Silicon-29.)
Who can say there's inflation when the price of the must-read classic Landolt-Börnstein âChemical Shifts and Coupling Constants for Silicon-29â dropped from $7295.05 in 2014 to merely $502.30 in 2025? What a bargain!đ
Sorry, but the âlist of ongoing warsâ allocation space in my brain is currently full, so đno country is presently allowed to start a new warđ. (Please take turns, guys.)
⊠I think this topos should be of independent interest, and I meant to ask a question about whether anyone ever studied it in some detail, but I'm pretty sure the answer will be ânoâ (or rather, çĄ).
I suspect nobody will have anything to say, but you can always ask, it won't hurt. It's certainly a legitimate question whether anyone has studied these objects (which I find to be at least as noteworthy as, say, the Medvedev lattice).
But sadly, I still don't have a good intuition what these âS objects are supposed to âlook likeâ inside Eff. The best I have is âsets whose elements are distinct but computably impossible to tell apartâ (âMerlin and Nimue can see them, but Arthur can'tâ; so â2 is the set of âhidden truth valuesâ).
â My formula bsky.app/profile/gro-... expresses the fact that â{1,2,3} is the union of â{2,3}, â{1,3} and â{1,2} (I think â I didn't check too carefully, but it's certainly related).â€â€âŠđ
When you're perpetrating atrocities that are so horrific that even the literal Nazis are horrified by the butchery, I think we can confidently say that you're the baddies. en.wikipedia.org/wiki/Usta%C5...đŒïž
Ah yes, the government asking Jews to register as Jewish, in the name of protecting the Jews. No way that could go wrong www.nytimes.com/2025/04/23/n...đ
2025 Q1 check-inâ€1. H5N1 - Still out of control in US.â€2. RFK.Jr - Policies way worse and more harmful than anticipated.â€3. Mpox - Still not contained in Africa (a bit forgotten).â€4. Expanded access for Lencapavir - Uncertain after US funding cuts â€5. Withdrawal of US from WHO - done and damaging.đ
I don't think this is particularly cute, but your remark made me discover the â{{Short description}}â Wikipedia template, which apparently doesn't change the article text itself but only the subtitle as it appears in search results.
Je pense que toutes les branches des maths se font de temps en temps vanner par les autres branches. (Sauf peut-ĂȘtre l'analyse complexe: personne ne pense de mal de l'analyse complexe, c'est juste pas possible.) Je ne crois pas particuliĂšrement que ce soit le cas pour l'algĂšbre.
⊠so any two such choices Pâ,Pâ,Pâ and PââČ,PââČ,PââČ have a common realizer.â€â€It's the same formula đâ I mentioned in my reply to your comment on mathoverflow.net/q/490911/17064 â and I think it deserves more attention (on gist.github.com/Gro-Tsen/f76... I call it âtwo-of-threeâ).đ
No: consider the formulaâ€â€ÂŹ(pââ§pââ§pâ) â ÂŹ(pââ§pâ) âš ÂŹ(pââ§pâ) âš ÂŹ(pââ§pâ)â€â€It is not realizable. Yet, whatever the subsets Pâ,Pâ,Pâ of â, not all three inhabited, at least two of the three disjuncts of the consequent are realizable: âŠ
Boulet il parle toujours des mĂȘmes trucs: Bloody Mary, Bloody Mary, Bloody Mary, y'en a que pour Bloody Mary! đȘ
Set theorists are excited about the consequences of the papal election, because locking down the conclave in the Sistine Chapel might prove the existence of inaccessible cardinals. đ„
I mean in the sense that im(f)âČâdâČ obtained by pullback should satisfy the universal property expressing the fact that it is the image of fâČ, so this should come with the required arrow câČâim(f)âČ ensuring that your green pentagon commutes (and is, in fact, a pullback square). I didn't check, though.
(So, at least intuitively, I think for a category to âbe regularâ should more or less mean that this evil property of Top doesn't happen: when you pull back a quotient, you still get a quotient.)
And if you want a counterexample, consider a quotient map Ï : X â X/⌠such as you said in bsky.app/profile/jean...â€â€Its image is X/⌠itself, but if you pull back by a subspace inclusion Y â X/⌠you get a map Ï^â1(Y) â Y whose image is the quotient of Ï^â1(Y) but it isn't Y. So Top isn't regular.đ
âImages are stable under pullbackâ means that if f:câd has image im(f)âd, and dâČâd is an arbitrary morphism, then the image of the pullback fâČ:câČâdâČ of f:câd under dâČâd (that is, câČ is the fiber product of c and dâČ over d), is required to be the pullaback of im(f)âd under dâČâd.
I'm not sure I'd do better than LLMs on this one. Also, I'm not sure I'd call it a pun, since âsakeâ (as in âfor the sake ofâ) and âsakeâ (as in ârice wineâ) are written identically but aren't pronounced the same in English. (That's probably not what's confusing the LLMs, though.)
Of shoes â and ships â and sealing-wax ââ€âOf cabbages â and kings ââ€And why the sea is boiling hot ââ€âAnd whether pigs have wings.
The alternate ending I imagined for the 2024 movie âConclaveâ by Edward Berger (which I recommend in passing) didn't happen in the movie, but it still has a chance of happening in real life, and I wouldn't put it past Pope Francis.â€â€(â ïž spoilers, of course) x.com/gro_tsen/sta...đŒïž
Re-upping this for those of you who don't want to read Hobbes-inflected analyses of the Trump administration over Easter. There is no escape from the Anti-Leviathan.đ
Pour le coup, ça ne me surprend pas du tout. Quand on entend le âjâ de âjohnâ en anglais, on n'y pense pas comme un /d/ suivi du son passablement rare /Ê/ (qui n'a d'ailleurs mĂȘme pas d'orthographe standard). C'est une question un peu byzantine si c'est 1 ou 2 phonĂšmes.
âSad to hear about Pope Francisâhe was a nice guy, very holy, some say the holiest. But if the Church wants to WIN again, they need a POPE who knows how to LEAD. Many people are saying: nobodyâs more qualified than Trump. Iâd be the BEST Pope. Tremendous prayers. Easter blessings! #PopeTrump2025 đđïžâ
Now let's just hope the next pope doesn't start his reign by issuing a bull renaming the Mediterranean sea to âthe Holy Seaâ and excommunicating all journalists who don't agree to use this new name. đŹ
⊠But it should be the other way around because the surrounding context is a French sentence, read left-to-right, so the quotation marks need to follow that LTR order. Hence the correct way to write it seems to be:â€â€<q><span lang="ar" dir="rtl">[Arabic text]</span></q>
⊠it does make a difference if a line break occurs within the Arabic text: in this case, we get the opening quotation mark at the RIGHT of the Arabic text before the line break and the closing quotation mark at the LEFT of the Arabic text after the line break. âŠ
The issue is that the âdir="rtl"â attribute applies to the entire element, INCLUDING the quotation marks that get inserted by the <q> tag. So the quotes also go right-to-left. This generally doesn't make much of a difference because quotes get mirrored. BUT âŠ
â ïž HTML/typographic subtlety! In my last blog post (âŹïž), I had cited Arabic text by writing (in the context of a French sentence):â€â€<q lang="ar" dir="rtl">[Arabic text]</q>â€â€Do you see the problem here? đ€â€”ïžđ
âOh wait, âBambiniâ⊠I think I've heard of this restaurant before⊠Maybe it was on social media, like Bluesky or something. I don't remember who or why. Well, if someone mentioned it and it stuck in my mind, it must have been good: so let's go there!â
The Internet Archive and Way Back Machine is a crucial part of the Internet we once knew. It's hard to overstate how important it is to ensure both stay around. Especially in this political climate.â€â€Please take some time to pitch in and boost this petition. A little bit of action goes a long way.đ
⣠The reason I'm reposting this old thread is that apparently some researchers have shomehow managed to stimulate the medium cones specificially. www.bbc.com/news/article... But rather than âpsychedelic aquamarineâ, they called the resulting color âoloâ. đ€· âą17/17đ
PS: The picture in the first skeet is taken from a page about colorimetry I wrote a long time ago (and never really got around to finishing, but there's still some hopefully interesting stuff there): www.madore.org/~david/misc/... â see there for more explanations and details. âą16/17đ
So that's why, even though our monitors use red, green and blue as primary colors (i.e., photophore pigments), for our eyes the primary colors (the ones they âreact toâ) are more like âincandescent redâ, âpsychedelic aquamarineâ and âextreme purpleâ. âą15/17
The âcolorâ of middle cones, however, is extremely unphysical: you just can't stimulate the middle cones without stimulating the long ones as well. So âpsychedelic aquamarineâ is the best description we can come up with, and I can't do more than +20% above. Try to imagine it INSANELY FLASHY. âą14/17
âExtreme purpleâ is more or less physical: looking at the almost-ultraviolet edge of the visible spectrum gives this color. âIncandescent redâ is pretty much the color of the other extreme of the spectrum (the almost-infrared), but even then, middle cones will respond to some degree. âą13/17
To imagine the cone colors in their pure form, try to imagine my circles minus their grey background. How should they be named? Someone (âŹïž) suggested âextreme redâ (I would rather go for âincandescent redâ), âpsychedelic aquamarineâ and âextreme purpleâ. I rather like that. âą12/17đ
Here is a different version of the picture with increases of +40%, +20% and +100% for long, medium and short cones respectively, making their individual colors clearer (but remember that now this is by different amounts, so of course the central color is no longer gray/white). âą11/17đŒïž
The top (blueish) disk probably seems faint to everyone. This is because +20% isn't much compared to variations in short cone response we typically get in the colors we see. But also because the short cones don't contribute to the sensation of overall brightness. Short cones are âdifferentâ! âą10/17
Protanopes and deuteranopes (two common forms of color-blindness) should have difficulty seeing the bottom-left, resp. bottom-right, disks (in principle they shouldn't see them at all, but of course screens are never perfectly calibrated, and individual eyes differ, etc.). Still a rough test. âą9/17
So, to be clear: where the three disks meet, we have a gray color that's 20% lighter than the background gray, and each disk corresponds to the corresponding increase in just one photoreceptor's response (and when two meet, two). âą8/17
(Why 20%? Because that's about as much as I could squeeze out of the sRGB color space without exceeding its gamut.) The lower-left (reddish) disk is +20% in the long cone response, the lower-right (turquoise) is +20% on middle cones, and the top disk (faint purple) is +20% on short cones. âą7/17
So this is what the picture at top of this thread shows, if viewed on a calibrated sRGB display: from the gray background, each disk exhibits a 20% increase in just one photoreceptor (or more accurately: an increase like that produced by a gray color 20% more luminous than the background). âą6/17
But we CAN describe what happens if we start with a given color, say, a neutral gray, and increase one of the receptors' response by, say, 20%, a value low enough so as to remain within physically realistic space. The âadded colorâ gives us an idea of what the receptor's âpure colorâ would be. âą5/17
Of course, it's hard to ascribe a single color to any of those, because you can't turn on just the long, medium or short cones. A normal light color will always stimulate all three cones to some extent, so a âpure shortâ, âpure longâ or worse of all âpure mediumâ stimulus doesn't exist. âą4/17
We (as in: most of us) have three types of color-sensitive photoreceptor cells, known as the âlongâ (meaning long-wavelength), âmediumâ and (the fairly different) âshortâ cones, or sometimes inaccurately as âredâ, âgreenâ and âblueâ cones respectively. (There are also low-light vision ârodsâ.) âą3/17
[Meta: this thread is a repost of a thread I posted on Twitter on 2021-09-19, slightly edited for Bluesky; I'm posting this now because I saw some news on the subject â see at end.] x.com/gro_tsen/sta... âą2/17đ
The three primary colors our monitors use are: red, green and blue. But what about the human retina âconeâ photoreceptors? Well, their âcolorsâ (to be explained) are: âincandescent redâ, âpsychedelic ultramarineâ and âextreme purpleâ. And they look roughly like thisâŹïž, but MUCH more vivid. đ§”â€”ïž âą1/17đŒïž
I'm gripped by the ever-increasing bling in Trumpâs Oval Office. What does it mean? Yes, Trump has bad taste. But also something else. Hereâs an art historical view. đ§”â€1/đŒïž
The White House has turned COVID.gov from a public health resource into a politically charged platform promoting the lab-leak theory and attacking specific scientists and the pandemic response in general. Letâs fact check its 5 headline claims⊠đ§”đŒïž
So if you're annoyed by irrelevant citations, you must be using bibliography in a wrong way. For example, if you're trying to assess how good a paper is by counting citations instead of READING IT FOR YOURSELF AND MAKING YOUR OWN MIND, I wish you the greatest harm in the world.
The goal of a citation in a published paper is to allow the reader to get clarification or checkable sources on a claim, or additional information on a topic. Irrelevant citations do not hinder this goal in any way, they only cost a minuscule amount for the space they take.
Possibly unpopular opinion: I think scientists of all fields SHOULD add with irrelevant citations in their papers: this will in no way harm genuine human readers (=the intended audience), but it will hurt citation counting bots and other forms of bibliometry which are pure evil.đ
Ah ben justement: www.theguardian.com/commentisfre...â€â€Â«what seems to really matter to many voters isnât how much pain theyâre feeling themselves, but whether the other side is suffering more» đđ
I asked on MathOverflow whether there is a known algorithm to draw a random preorder on {1,âŠ,n} (i.e., sample the uniform distribution on such preorders). mathoverflow.net/q/491212/17064đ
âAn artist has been defined as a neurotic who continually cures himself with his art.ââ€â€(â Attributed to Lee Simonson â probably apocryphal or misattributed like most good quotes on the Internet are.)
Ce fil, que je recommande, met un peu en perspective cette annonce de «traces de vie»: đ§”đœâ€â€[ping @marcqplanets.bsky.social qui a peut-ĂȘtre qqch Ă dire aussi]đ
Updated version (I had misattributed one of the formulas â to Jankov instead of Plisko â and forgotten one â indeed due to Jankov â that is worth listing; so the table has one more line now):đŒïžđŒïž
Can you make something useful of such an oracle? Certainly: for a âneedle-in-a-haystackâ kind of problem, you can ask for a suggestion of where to look for the needle, and it has a non-negligible probability of being useful. But of course you can NEVER trust the answer, you must ALWAY check.
Maybe imagine that for each topic you have a probability ~50% that the answers will be delivered by the benevolent genie and ~50% by the demon (who, of course, will try to make you believe he is the genie by giving answers that SEEM PLAUSIBLE when he knows you can't check).
I think the best way to approach asking a question to an AI engine and interpreting its answer, is to imagine you're asking the question to an oracle of which you do not know whether it will be answered by a benevolent and wise genie or a malicious demon trying to mislead you.
On a more serious note, this collection of blog posts (by Bret Devereaux) about how ancient Spartan society was really like, and how the modern reimagining of it is utter fantasy, is well worth a read â I highly recommend them: acoup.blog/2019/08/16/c...đ
Given how Spartan warriors are lionized by some not-too-savory bros (âÎŒÎżÎ»áœŒÎœ λαÎČÎâ, etc.), I think it would behoove to occasionally remind ourselves how these supposedly invincible guys got their asses handed to them by a Theban band of ALL MALE LOVERS at the battle of Leuctra in 371BCE.
ursula von der leyen tells zeit newspaper: âthe west as we knew it no longer exists.ââ€â€"europe is still a peace project. we don't have bros or oligarchs making the rules. we don't invade our neighbors, and we don't punish them."đŒïž
Yeah, Twitter didn't allow the hyphen in names so I used an underscore instead, but Bluesky allows them, hence the tiny difference in my name between both sites.
I answered a question of @gro_tsen on MathOverflow concerning whether there is an "Opposite" axiom to the continuum hypothesis, which asserts that the continuum is extremely large. mathoverflow.net/a/491182/1946đ
Before the election, I warned that there is no safe haven under authoritarianism.â€â€If they can ship Kilmar Abrego Garcia to a foreign prisonâaccused of no crime, with no trialâthey can do it to anyone.â€â€Americans of conscience must stand against this now.
The Continuum Hypothesis tries to make the continuum as small as it can possibly be. But is there a natural hypothesis that tries to make it as large as possible? mathoverflow.net/q/491179/17064đ
And anyway, I might be willing to make a little effort for more portability, but unless you can suggest a portable way to run a command-line with an argument, I just don't think it can be done.â€â€So you're pointing out a non-problem with no solution: đ€· I guess.
Yeah, so it's not so much a portability problem as an extra dependency problem. Which, honestly, I don't care at all about. Let's be serious: any user who is going to run a Perl script from the command line obviously will have a working sh on their system.
⊠so of course it should have Unix functionalities, and I don't know any other way to call a subshell. But I'd be really surprised if a modern Windows didn't have this by default as part of the âWindows subsystem for Linuxâ or something like that.
I know how to execute a program, but that's not my point: my point is that I want to execute a command line, so it's system() that I want. But I want it to execute a sub-command line. And that's the job of sh -c. If Windows didn't implement this, that's their fault: system() was meant for Unix, âŠ
It took me an insane amount of effort to produce, but I can finally say I'm happy with this document showing the validity of various formulas of intuitionistic logic over various Kripke frames: happy both with how it looks and how it was generated. đđŒïžđŒïž
When I was young (well, younger), Microsoft were the very evil guys and Apple were the less-evil guys. Now things seem to have flipped around. I haven't (seriously) used a Windows computer since the 1990's, but I understand they've done a lot towards interoperability with Unix.
THIS IS HUGE! Researchers at Memorial Sloan Kettering Cancer Center say results of a Phase I trial of an mRNA vaccine aimed at preventing pancreatic cancer show promise. The vaccine PREVENTED the cancer from coming back in patients who had already received treatment for MORE THAN three years. đ§Șđ§”âŹïž
It's now been over a month since Trump sent innocent man Andry HernĂĄndez to one of the world's worst prisons because of "Mom" and "Dad" tattoos. Like the others, he is being imprisoned with no contact with the outside world.â€â€Don't let him be forgotten.đŒïžđ
⊠(I mean, I don't care if Windows actually has an âshâ program or if this is implemented by some other kind of black magic, but it's part of the contract of the system() call that it should behave that way, because there's simply no other way to do it.)
⊠And one core system() functionality is that system("sh", "-c", something, args) runs something as a shell command on the args. If there's a portable equivalent, I'm willing to use it, but I suspect there isn't, so, if Windows didn't implement basic system() function, it's their fault, not mine. âŠ
Well, I don't know what âsystemâ does on a Windows machine, but either it doesn't even exist, in which case the issue is moot because my program can't possibly be portable, or they stole it from Unix, in which case you'd expect to guarantee minimal Unix functionality. âŠ
⊠The portability argument is more serious, but I do hope even Windows now has something called "sh" which will obey standard Unix semantics, otherwise they're really asking for trouble.
I agree it's not ideal, but it's still better to follow the standardized âthis is run as a shell commandâ convention than to create a new one (like âsplit this at whitespaceâ). Nobody is forcing the user to use complex commands here, they can just make their own exec and call that. âŠ
So, I think the best solution is this one: if $satcmdline is the value of the -e option, call "sh" with options "-c", "$satcmdline \"\$1\"", "sh", $filename. This allows arbitrary shell commands in $satcmdline but keeps $filename shell-safe! đĄ x.com/Jilcaesel/st...đŒïž
I understand what you mean, and in general I tend to agree, but in my case this would be very inconvenient, because the output of the SAT-solver needs to be interpreted in light of the data that was used to call the SAT-solver. So it would mean re-parsing and re-analysing everything.
⊠it also changed in passing the description of the â-qâ option from âsuppress all outputâ to âsuppress most outputâ, because I guess that's what it's used to writing.â€â€So â ïž do not trust LLM output even when it is merely asked to convert something to something else. Check EVERYTHING.
Project is here: github.com/Gro-Tsen/int...â€â€It did a decent job, and I can say this was useful (I hate writing markdown and I never know what to say in these things), and it even made some useful suggestions for clarification (e.g., are loops and multiple edges allowed?).â€â€BUT âŠđ
I tried to use ChatGPT to write a (markdown) README file for me from a Perl program whose usage I had documented in the comments at the start of the file: chatgpt.com/share/67ff7b...
This is probably the best answer in theory, but in practice it's a bit cumbersome. Note that quoting does not work the way you make it seem it does, and quoting '--foo' like that won't hide it from the long options parser, which complicates the matter.
Splitting at whitespace seems ugly because now we have the issue of what if the user wants to run a program with a space in the name, and I don't want to start having a quoting mechanism. Should I maybe have two options, one for the program and one for extra parameters for it?â€â€Any thoughts, anyone?
If the default command line were simply one program, I'd have a â-eâ option that takes a different program name, and let the user create a shell script if they want to use options. But here, the default already has options. Should I still use a â-eâ option and split its value on whitespace?
Question on Unix best practices:â€â€I'm writing a Unix (Perl) program that, by default, runs some command line (âcryptominisat --verb 0â, to solve a SAT problem). I'd like to allow the user to specify a different one.â€â€How should I do this in a way that is convenient for me and them?
We had hateful conspiracy theories, we had subhumans, we had the salute, we had people being disappeared by para-legal militia and sent to concentration camps, we had talks of mass deportations, we had agressive talks of annexing what should justly be our lands. Now we have Lebensborn.đ
⊠It is unclear to me whether we actually need the ââąâ or whether its role can be replaced by \frac{âŠ}{âŠ} all the way (as Gentzen did, but maybe this doesn't carry over to more complex systems). ⧠Anyway, you can hardly argue that this is not worth discussing⊠and nobody seems to bother doing so!
⊠⧠Finally, I think that when Gentzen introduced natural deduction, he did NOT use the turnstile ââąâ symbol (he used it for sequent calculus). His presentation was by proof trees as in Troelstra & Schwichtenberg âBasic Proof Theoryâ (2000) §2.1. âŠ
⊠is not the same as adding \frac{ÎâąâĄ}{Îâąâą}, so one needs to have an intuitive idea of what each rule âmeansâ, and evidently it's not so clear. ⧠Basically, âââ lives in the formal system level, \frac{âŠ}{âŠ} lives in the metalevel, but ââąâ lives in a kind of limbo that is neither one nor the other. âŠ
First, to be clear, I'm not saying the distinction isn't useful, I'm saying it's confusing and badly explained. ⧠Second, I was mostly talking about the relation between ââąâ and â\frac{âŠ}{âŠ}â, because this is the source of your problem as far as I see it: adding a rule \frac{}{⥠⹠âą} âŠ
This thread is funny, but I also admire the dedication it took to create every image! đ§”đœđ
With the discussion of AI in higher education going around; my three opinionated views:â€â€(1) HE should be lifelong; Birkbecks and Open Universities everywhere.â€â€(2) The main benefits are human flourishing a raising of the cultural and intellectual level of society, not 'employability', >
1/4. On the White Houseâs theory, if they abduct you, get you on a helicopter, get to international waters, shoot you in the head, and drop your corpse into the ocean, that is legal, because it is the conduct of foreign affairs.
⊠This presentation is used in many places, but I've never seen a single book actually try to explain why we need three different levels of implication, what each one means intuitively, and how they behave.
Not one particular logical system, but the whole concept of presenting logical systems in the form of rules \frac{some âą stuff}{different âą things}. Because now this raises the question of the difference between \frac{Îâąfoo}{Îâąbar} and foo âą bar (what does each one mean, intuitively?). âŠ
(It is now left as an exercise to the reader to come up with some presentation of logic which will use four different levels of implications, just for the sake of perversity.)
One lesson I think we can learn is that this system with three levels of implication (âąÏâÏ, ÏâąÏ and \frac{âąÏ}{âąÏ}) is incredibly confusing and badly explained (nobody really satisfactorily tells us WHY we need THREE times the same notion). So of course it leads to surprises.
An incredibly thorough (but ultimately inconclusive) investigation into the question of why the IBM PC's graphical character set (âcp437â) and a character that looked like like â (small house? capital delta?) at position 0x7f: blog.glyphdrawing.club/why-is-there...đ
Yup, that's what I meant to say. Except I wouldn't have said it so clearly, and I didn't know or had forgotten the âadmissibleâ vs. âderivableâ terminology. On the plus side, I would obviously have called the additional connector âđ„Šâ.
I suspect that with your modified rules (but âłïžwhyâłïž would you want to modify them thusly?) weakening does not hold from the rules alone unless you add the extra assumption (â )âthere are no other rules than the given onesâ, and that you similarly can't prove what you want without this (â ).
I answered a question of Joshua Z on MathOverflow about weakened forms of replacement and whether this is equivalent to the existence of the beth hierarchy of cardinals. mathoverflow.net/a/491003/1946đ
I honestly don't remember who was making the point that âexpired certificates aren't a problem because you can just add an exception and proceed to the site normally after two or three clicksâ (which WOULD be a good point if it WERE true). I don't think it was you.
All this raises many questions. Why do we even need certificates that expire when the key hasn't changed? Whom are we trying to protect here, and from what, exactly? This isn't some banking web site, it has 0 confidential info â it's a WEBCOMIC. đĄâ€â€Why is there no âdisable HTTPS errors for siteâ? đ€Š
⊠this (right) is what I wanted to get by telling the browser âfđck this useless HTTPS security theater, I just want to read a webcomic, I don't care about its identityâ. (The problem is that images and such are downloaded from a different host, and it's hard to set an exception for this.) âŠ
Since some people have tried to persuade me that HTTPS doesn't cause any annoyance in real life because even when a certificate goes wrong we can manually add an exception: one of my daily webcomic's certificate expired (left), and this (middle) is what I got when adding an exception, whereas âŠđŒïžđŒïžđŒïž
1. LLM-generated code tries to run code from online software packages. Which is normal but â€2. The packages donât exist. Which would normally cause an error butâ€3. Nefarious people have made malware under the package names that LLMs make up most often. Soâ€4. Now the LLM code points to malware.đ
It's the sort of question I think anyone discussing modular forms should discuss at least briefly when writing the definition, and it's irritating that nobody seems to bother.
⊠Ce n'est effectivement pas (enfin, pas exactement) le sens courant du mot. Je ne veux pas donner l'impression que la Terre tourne de plus en plus vite autour du Soleil, juste que la direction de sa vitesse change avec le temps. (Et donc il y a bien une force centrifuge, mais elle est trÚs petite.)
I finally asked a question that for decades I was too embarrassed to ask: what happens to the Ramanujan Ï function (and the modular discriminant) if we replace the magical number 24 by some other number? math.stackexchange.com/q/5055524/84...đ
Hours ago, @politico.com revealed that DOGE is working with DHS on automating mass deportation efforts â likely explaining why many US citizens, green card holders, and even a Canadian (in Canada) got threatening emails last night terminating âyour paroleâ and telling them to leave the US in 7 days.đŒïžđŒïžđŒïžđŒïžđ
"So what if we remove titles from schools, you can still get them in public libraries"â€â€"It's not book banning if we remove them from public libraries. You can still get them on Amazon."â€â€"The government is demanding Amazon remove these books."đ
I asked another question on MathOverflow today, about a sequence (đ_n) of properties of topological spaces defined by a condition on the intersection of closures, where (đâ) is extremal disconnectedness, and each đ_n is weaker than the previous ones: mathoverflow.net/q/490911/17064đ
So it appears that the question is not as stupid as I feared it might be. But sadly, I suspect that if Emil JeĆĂĄbek doesn't know the answer, then nobody does.
In normal times, this would go without saying, but in the times we live in, even this tiny victory of the rule of Law, let alone by unanimous decision of SCotUS, is monumental.đ
I asked a question on MathOverflow requesting a clarification as to the meaning of âcompletenessâ when we say that topological semantics are complete for intuitionistic propositional calculus (because I've gotten myself very confused): mathoverflow.net/q/490891/17064đ
The Trump administration is now canceling people's Social Security Numbers, treating them as if they are legally dead. www.nytimes.com/2025/04/10/u...đŒïž
THREAD: Under a new law, thousands of prisoners in Louisiana have been cut off from ever getting a chance at parole.â€â€Why?â€â€Because an algorithm said so. 1/
The President of the United States of America posted this 15 minutes before the announcement of the tariff pause. This would be a straightforwardly criminal message, were the rule of law currently operational in the usual way, for those with insider knowledge of major market shifting policy newsđŒïž
Word (expression? formula? concept?) of the day:â€â€âŁ âJenny Haniverâ: an artistic/esoteric sculpture of kind, made from the carcass of a ray to resemble a kind of monster. en.wikipedia.org/wiki/Jenny_H...đŒïžđ
Starting to write a program that takes an intutionistic propositional formula and a Kripke frame and decides whether the formula holds in the frame by calling a SAT-solver. github.com/Gro-Tsen/int...â€â€Core program done, now I need to write a parser (đ) and wrap-call the SAT-solver.đ
Entre "30 Glorieuses" et "30 Ravageuses", un article passionnant sur le formica, outil et symbole d'un nouveau mode de vie. www.terrestres.org/2025/04/07/l...đ
I love the way the Web site âKerodonâ (kerodon.net) is illustrated with cute guinea pig drawings in a way that seems fitting for an elementary school textbook on mathematics⊠and then you realize it's about â-categories and homotopy theory.đŒïžđŒïž
This video was posted on Twitter by the official account of the People's Republic of China's embassy in the United States.â€â€The Chinese Communist Party is lecturing the US Republican President by using a Reagan speech on the importance of free trade. We are really living in the Weird timeline.đ„
Looks extremely similar to what I saw for the tree on my first photo (well, not literally the same tree, but the same group of trees obviously from the same batch):đŒïž
Is there an existing piece of software for testing the validity of a modal (or intuitionistic) propositional formula in a finite Kripke frame? mathoverflow.net/q/490669/17064đ
I âłïžthinkâłïž the one on the left is Prunus Ă yedoensis (well, the grafted branches are), and the one on the right is P. serrulata (photographed 9 days later, so the leaves don't mean much). The difference doesn't exactly⊠leap to the eyes.đŒïžđŒïž
"DOGE is eliminating the government's tape backups because they're too stupid to know why they're important" is the generous interpretation, when what they might actually be doing is stealing all the money and trying to destroy the records of them doing so.
How can one (phenotypically) differentiate Prunus serrulata from P. Ă yedoensis? (E g. the âAmanogawaâ cultivar of the former and the âSomei-yoshinoâ cultivar of the latter.)â€â€Some seem to consider yedoensis a subspecies (variety?) of P. serrulata, I'm not sure.
Somewhere in the background, the bodies of ¶, § and â lie discarded, murdered by the psychopathic twins â and ⥠while the schizophrenic ✠laughs his ambiguous laugh.
Somewhere in the background, the bodies of ¶, § and â lie discarded, murdered by the psychopathic twins â and ⥠while the schizophrenic ✠laughs his ambiguous laugh.
What is the most correct way to abbreviate the name of the journal âĐĐŸĐșĐ»Đ°ĐŽŃ ĐĐșĐ°ĐŽĐ”ĐŒĐžĐž ĐĐ°ŃĐș ĐĄĐĄĐĄĐ â (âProceedings of the USSR Academy of Sciencesâ) in Russian and in English?â€â€âĐĐŸĐșĐ». ĐĐșĐ°ĐŽ. ĐĐ°ŃĐș ĐĄĐĄĐĄĐ â and âProc. Acad. Sci. USSRâ? Something else?
I agree that this is fairly confusing, and I keep getting myself confused between internal truth values and external (of which there are only two in the effective topos). If you find a pĂŠdagogical way to say things, it's worth writing down.
⊠preorder probably answers your question. Note that this Heyting algebra won't be complete, though (let's hedge this: at least, I'm not claiming that it is â let's hedge this even more: I'm not claiming anything, but I don't even suspect that it is).
I didn't check, but I suspect that if you take the (external!) set đ«(âĂâ) with the preorder given by the internal statement AâB where A,B are the (internal!) subsets of the n.n.o. represented by the given subsets of âĂâ, then the quotient đ«(âĂâ)/~ by the equivalence relation associated to this âŠ
Useless trivia tidbit I learned yesterday: the highest point of Denmark (MĂžllehĂžj, 171m above sea level) is lower than the lowest point of Switzerland (Lake Maggiore, 193m above sea level). So Switzerland is âłïžentirelyâłïž higher than Denmark.
I'm a few days late to the news but *of course* Trump's nonsensical tariff equation was generated by an LLM. Now all we need is for someone to find the weirdo subreddit or 4chan board holding that view and which was unquestioningly fed into the AI's training data.
THIS IS HUGE! Researchers at Stanford University have found that getting vaccinated against shingles- a painful and debilitating condition that can flare up years after infection from varicella zoster virus- not only LOWERS the risk of infection, but can also PROTECT against dementia. đ§Șđ§”âŹïž
I.o.w., the crucial point here is that in chess draw is determined by ad hoc rules involving the âpracticalâ history of the game, not something like âif the game lasts infinitely long, it's a drawâ, right?
But it is true that in a game of the form âthe state is a vertex in a digraph, and each player in turn chooses an outgoing edge, one who cannot move loses, and if the game lasts infinitely long it's drawâ the difference between (historical) strategies and (positional) tactics is irrelevant, correct?
To clarify, the difficulty is that the board position is lacking some information like the number of repetitions or the number of moves for the various drawing rules of chess? Or is it something else entirely? I'm confused as to what the important point is.
NEW đ§”â€â€A quick thread of charts showing how Trumpâs economic agenda is going so far:â€â€1) US consumers are reacting very very negatively.â€â€These are the worst ratings for any US governmentâs economic policy since records began.đŒïž
If there is a major economic downturn, Americans are going to have to be asking a lot of hard questions, such as:†- what is tariff?†- google dot com tariff what is it†- how tariffs work†- tariffs r they bad??†- what is tax
This feels like the defining image from this yearâs Midwest Political Science Association annual meeting. â€â€The National Science Foundatipn paid for a booth in the exhibit hall. But the booth sits empty, because NSF has been DOGEâd, and there is no one left to send.đŒïž
So ChatGPT thinks it looks like the average PhD student in my lab. I don't know what to make of this.đ
I think the question is not whether the tariffs are up for negotiation but rather whether they are up for bribery. As in: every 50M$ your country sends directly to Trump's crypto account gets you one less percentage point on the computation of the âreciprocal tariffsâ.đ
Working on zeroing out all my trade deficits. Whenever I go to a store to buy things, I'm going to demand that the store buy goods from me of precisely equal value. I'm going to be so goddamned autonomous.
I agree, but I would like to remind my fellow mathematicians that it is perfectly legitimate to write such texts even after one has completed one's PhD. (The only problem is to decide which format they should take and in what manner they should be made public.)
But the funny thing is that one thing that got me thinking one more time about the particular formula at the top of this thread is also an April fool's joke: bsky.app/profile/jean...đ
Alternatively, we could try decorating subexpressions with a dash of color to make it more obvious what goes with what:â€â€đŽ(đĄ(đ”((ÂŹÂŹPâP) â (PâšÂŹP))đ” â (ÂŹÂŹPâšÂŹP))đĄâââđą(ÂŹÂŹP âš (ÂŹÂŹPâP))đą)đŽâââđŁ((ÂŹÂŹPâP) âš đ”((ÂŹÂŹPâP) â (PâšÂŹP))đ”)đŁâ€â€Is this better?
Purely typographically, one is left to wonder whether it's not better (i.e., more readable) to write such formulas using the âdots as parenthesesâ convention, which in this case would look something like this:â€â€ÂŹÂŹPâP.â.PâšÂŹP :â: ÂŹÂŹPâšÂŹPââŽââŽâÂŹÂŹP.âš.ÂŹÂŹPâPââ·ââ·âÂŹÂŹPâP :âš: ÂŹÂŹPâP.â.PâšÂŹPđ
That is a very good question. My answer would be that this is what textbooks, surveys and courses are for. And that mathematicians need to perhaps spend a little more timeÂč writing those, so as not to leave a gap between doing research and teaching to undergrads.â€â€1. A precious commodity, I know. đ
I mean, it happens to everyone all the time that you look for your glasses for really long, only to notice that they were on your nose all the time. The fact that you spent a long time searching doesn't mean that they were well hidden and that discovering them is a feat!â€â€It's the same in math.
I mean, it happens to everyone all the time that you look for your glasses for really long, only to notice that they were on your nose all the time. The fact that you spent a long time searching doesn't mean that they were well hidden and that discovering them is a feat!â€â€It's the same in math.
⊠I mean, for a math paper to be published, the proof must meet minimal standards of interest, and a three-line proof which somehow everybody missed for years (because nobody cared enough or something was in Russian, or whatever) doesn't pass that bar.â€â€So, no, it's not a joke, and it happens.
⊠So, yes, it can quite well happen that it takes the mathematical community many years to realize that the answer to a supposedly open question was, in fact, completely trivial (or already known). And when this happens, you don't write a new paper to put XâY and YâZ together to conclude XâZ. âŠ
Actually, it happens all the time, and it's not really a joke: e.g., someone asks in 2000 the question âare blueish foobar cromulent?â and only in 2025 does one notice that in 1965 someone proved âblueish foobars are slithyâ and in 1993 someone proved âslithy foobars are cromulentâ (in Russian). âŠ
So the next serious question for realizability would then be the following monster:â€â€((((ÂŹÂŹPâP) â (PâšÂŹP)) â (ÂŹÂŹPâšÂŹP))âââ(ÂŹÂŹP âš (ÂŹÂŹPâP)))âââ((ÂŹÂŹPâP) âš ((ÂŹÂŹPâP) â (PâšÂŹP)))â€â€đš
I guess I got the idea from Plisko's 2009 âSurvey of Propositional Realizability Logicâ, which suggests that the realizability of the Rieger-Nishimura formulas have been studied only up to the Scott formula, sort of implying that the next one is harder, but in fact it's not.đŒïž
⊠which is true provided at least one is. For an arithmetic statement, we can take U_n to be âthe n-th statement is unprovable in PAâ and V_n to be âthe n-th statement is irrefutable in PAâ: then one cannot realize (ân). (ÂŹÂŹP_n âš (ÂŹÂŹP_nâP_n)) where P_n := ÂŹU_n âš ÂŹV_n.
⊠which is known to be realizable. So if the overall âanti-Scottâ formula is realizable, then the consequent (ÂŹÂŹP âš (ÂŹÂŹPâP)) is. But it's almost trivial that, if I secretly think of two booleans, you can't either (âÂŹÂŹPâ) assure that at least one of them is true or at your option (âÂŹÂŹPâPâ) name one âŠ
The argument is simple: let P := (ÂŹUâšÂŹV) (viê«. the disjunction of two âhidden booleansâ). Of course if we can prove that this special case isn't realizable, then the general case isn't.â€â€But in this special case, the âScottâ antecedent ((ÂŹÂŹPâP) â (PâšÂŹP)) â (ÂŹÂŹPâšÂŹP)) is precisely Rose's formula âŠ
@jeanas.bsky.social So, you got me thinking one more time about this âanti-Scottâ formula, and actually â I can prove that it's not realizable, and âĄit's really simple and not very interesting (and certainly not worth publishing).â€â€I don't know whence I got the idea that this was an open problem! đđ
3 dead so far at Krome ICE detention center in Florida. Max capacity was 500, they have over 4,000 and not enough water and food. Reports say they get 1 cup of water per day.â€â€These are already death camps.â€â€eu.usatoday.com/story/news/n...â€â€english.elpais.com/usa/2025-04-...đ
I think this tract conspicuously fails to give us the point of view of the big pile of towel. We know what Tom and Darlene think of the situation, but what about the towels? What will they become, and are their needs being met?
Trump is calling them âreciprocalâ tariffs, but the code has been cracked â the âtariffs charged to đșđžâ column is not tariffs on us at all⊠itâs đșđž trade deficit divided by đșđž imports from that country x100 â€â€PSA TO THE MEDIA: Stop calling them âreciprocal tariffsâđŒïž
As in âin 1976, Paul VI created Cardinal Sinâ. đ€
So, I've just learned of the existence of a Cardinal Sin (that is, Jaime Sin â Cardinal and Archbishop Emeritus of Manila) and now I can't stop giggling stupidly.đ
The Wikimedia Foundation, which owns Wikipedia, says its bandwidth costs have gone up 50% since Jan 2024 â a rise they attribute to AI crawlers. â€â€AI companies are killing the open web by stealing visitors from the sources of information and making them pay for the privilegeđŒïž
The beautifully poetic irony here is that Le Pen was calling in 2013 for lifetime ineligibility for embezzlement of public funds, so she definitely can't argue âI refused to follow this law because I think it's wrongâ:đ
I presented a counterexample on MathOverflow showing that it is not true in general that, in a Hausdorff topological space, every non-empty open set contains a closed set with non-empty interior. mathoverflow.net/a/490409/17064đ
Yes, I genuinely wondered. It wasn't unthinkable that it might be true: this is a slightly famous open problem, but not one about which a large number of people have given thought, esp. in the last 30 years, and maybe progress in adjacent areas have made it accessible. You might well solve this.
I once thought of writing a novel in which the main character goes crazy (so everyone thinks) by coming to believe that he is living in a novel; and he tries to find ways to prevent the novel from ending (and â spoiler! â ultimately persuades himself he succeeds on the very last page of the novel).đ
Given the date of 8 minutes to midnight, I can't decide wherher this is an April's fool or not. If you're serious, then this is definitely a major result.
I won't go as far as to say I'm not interested, but I don't find the idea of n-categories and adding arrows to the arrows for the sake of adding arrows to the arrows all that fascinating.
WORLD-FIRST: Ground-breaking research published today in the Ornithologist Journal has, for the first time, translated common UK bird vocalisations into equivalent phrases in the human language. â€â€The results tell us a lot!â€â€Extracts below... đ§”đŒïž
A prominent computer scientist who has spent 20 years publishing academic papers on cryptography, privacy, and cybersecurity has gone incommunicado, had his professor profile removed by employer Indiana University, & had his homes raided by the FBI. No one knows why.â€â€arstechnica.com/security/202...đ
OK, so you've made a good case that the HTTPS architecture as a whole (with its current flawed trust model) is an excellent tool for censorship and that we should stay clear of mandating it. And that LE is very wrong to lure Web sites into massively adopting this potentially dangerous technology.
Maybe we're not talking about the same thing, but a good number of root certs listed on chromium.googlesource.com/chromium/src... for Chrome seem non-US.â€â€But even if not, it's going to be much easier to pressure Let's Encrypt into refusing a cert than to pressure their higher up to de-certify LE.đ
How does this answer anything? The point of a Web site is to let other people see it, you can't seriously suggest to say âto view this site you need to compile this special Web browser that includes the key of the CA used to sign the certificate of this siteâ and hope that people would do it!
(So far this is not being used because HTTP still works and the targeted site would simply revert to HTTP if you prevent it from getting a certificate. But as soon as HTTP is turned off in major browsers, I promise you this will become the gold standard of censorship.)
Implementing it through the browser is not so obvious because people will need to upgrade, and open source browsers won't be so easy to target. DNS isn't easy either because there is one TLD per country. But if there's only one really usable CA, that one becomes a VERY obvious target.
I'm not sure even âa lot more peopleâ can do this. For a Let's Encrypt 2 to succeed, Google would have to agree to add its key in Chrome trust roots, and (perhaps under political pressure) they might very well refuse to do it if, say, LE2 is not based in đșđž or where US authorities can reach it.
I never claimed it was the only one. I'm saying that it gives would-be censors one additional tool for shutting down Web sites, which will be much more convenient than censoring at the ISP or DNS level (let alone the browser, which would be very hard to leverage here).
⊠opportunity for censorship. I'm not accusing LE of wanting to censor anything, I'm accusing them of being the useful idiots who convince everyone that this hoop is harmless, and who can then conveniently disappear or be taken over when HTTP has been shut off like FTP has been. Gatekeeping the Web.
Their tools being OS is irrelevant: I can't run my own CA (well, I can, but it's completely useless) if I can't get that CA's key in people's browsers. The fact is, if I want to run an HTTPS site, I have to jump through one more hoop (getting a certificate) than for HTTP: this presents one more âŠ
⊠DANE is also good as an additional security if key can't be embedded in links. For sites with special security needs, like banking sites, then a centralized certification authority is good, but it should check and certify the site holder's legal status, not just the ownership of the domain.
⊠So something like: when you run a site, you select a secret key that changes very rarely, each key change is signed by the previous key, and links to your site will embed the signature of the public key seen by the person creating the link. In case of mismatch, browser shows a prominent warning. âŠ
I think the way to go is some combination of TOFU + a key fingerprint being included in links. The point is: when a user visits a site, they want to know that the site is the same one they visited last time (hence, TOFU) and/or the one they followed a link to (hence, fingerprint in links). âŠ
⊠âLet's Encryptâ might be the good guys at this stage, but who knows whether they can be bought or taken over, and by whom? Something like half of the Web now depends on them, but who, exactly, operates it, and what are their bylaws?
⊠The Web (and Internet) was made to be decentralized, but the certificate chain adds a strong centralizing element, so an element of potential control, and HTTPS makes this element mandatory. This is a centripetal transfer of power. âŠ
Second unpopular opinion: the mania of requiring HTTPS everywhere has also created a huge opportunity for censoring the Web: blocking a Web site at the DNS or IP level is clumsy and can be worked around; but ordering CAs to refuse to issue certificates will be much more easy. âŠđ
It is an illusion of security. Reconstructing what is being read on Wikipedia from the size and timing of (encrypted) requests and responses would be child's play.
Let's Encrypt is not directly the cause of the failure, but it is a major cause of increasing the popularity of having HTTPS everywhere, and even if you slightly decrease the failure rate of HTTPS, if you massively increase the proportion of HTTPS over HTTP, overall failures increase.
⊠As for LLM training, I don't understand your point: LLMs are mostly trained on publicly accessible Web pages, by making legitimate client requests to those pages: what impact does having or not having HTTPS change in this picture?
Yeah, ISPs injecting ads into HTML is the âłïžoneâłïž attack for which having HTTPS everywhere is a sensible response. But since we all need ad blockers because of all the ads embedded in the âlegitimateâ HTML, I really don't see what the ISP-injected ads really change (who cares who placed the ad?). âŠ
⣠In short: there is a homeostasis of overall security, but by putting HTTPS everywhere we are transferring security from places where it matters to places where it's just frivolous (e.g., Wikipedia), we are reducing useful security.
⊠since HTTPS is now used in Web sites where âsecurityâ is meaningless or irrelevant; whereas previously HTTPS was only used on Web sites where there is, indeed, a meaningful risk of attack (e.g., banking sites) so one would take a broken certificate very seriously.
Unpopular opinion: âLet's Encryptâ and the mania of putting HTTPS everywhere has, in fact, decreased the overall security of the Web, because users get used to encountering broken certificates and (rightly) instruct their browsers to accept them anyway, âŠ
Oh my god. They deported a man who an immigration judge had declared was "more likely than not" to face persecution in El Salvador ... to El Salvador, during the big March 15 AEA flights!â€â€They outright admit it! Yet the Trump admin's response to a court is basically "oops, well, no take backsies."đŒïžđ
⊠âholds in intuitionistic logic because either ÂŹÂŹP is true, or if not, then (ÂŹÂŹP â P) holds vacuouslyâ: if you're going to write âor if notâ, this means you're not doing intuitionistic logic, THAT'S THE WHOLE POINT. đ€Š
I'll give Grok a pass for not recognizing the formula as the âanti-Scott formulaâ because that is very very niche knowledge, or for not recognizing it as a formula in the Rieger-Nishimura lattice. But not only is the conclusion incorrect, the reasoning is laughable: âŠ
Incidentally, I am not impressed by the supposedly superhuman AI's take on this formula (I asked out of curiosity): while ChatGPT just said something very boring and uninteresting but true, Grok3 claims, after minutes, that it is intuitionistically valid. It emphatically isn't!đŒïžđ
Trying to attack is a strong phrase, but I give it an idle thought from time to time.
The more I think about the formulaâ€â€(((ÂŹÂŹPâP) â (PâšÂŹP)) â (ÂŹÂŹPâšÂŹP))âââ(ÂŹÂŹP âš (ÂŹÂŹPâP))â€â€â the less I understand what it's trying to say.â€â€(This is in intuitionistic logic, of course. Classically, it's trivially true.)
Also importantly, note that even if he doesn't do something he says he will do, the mere act of saying it is not innocuous (and not limited to shifting the Overton window).â€â€đ Yes, he is serious.â€â€Trump is an idiot, but he does understand the value of making threats when it comes to negotiating, âŠ
There are two major mistakes one should avoid when thinking about Trump:â€â€â one is to believe that he will do what he says,â€â€â the other is to believe that he won't do what he says.đ
They certainly get some kind of say, in the sense that committee will undoubtedly ask for the would-be supervisor's opinion, and will listen to it carefully (and obviously a ânoâ would be a veto), â otherwise it's crazy. But for the committee to meet and discuss independently seems healthy.
On the other hand, only approximately 93%â94% of all humans who were ever born are now dead, so it would seem that the survival rate for human life is about 6%â7%. đ
On the other hand, only approximately 93%â94% of all humans who were ever born are now dead, so it would seem that the survival rate for human life is about 6%â7%. đ
Introducing the game of Whim. Finitely many piles of coins, with heights, say: †3 4 5 3 5 2 7â€On each turn, you can replace a pile at your whim with any number of strictly shorter piles. Whoever takes the last coin wins. What is your winning move?
Replace the 7 coins pile with piles of 2 and 4, so as to have an even number of piles of each size. (Assuming the smaller piles need not all be of the same size.)
Jeffrey Goldberg thinking he was being pranked and then realizing he was actually just in the war plans group chat is such a good microcosm of how it feels to be alive right now, everything seems fake until you realize itâs actually real and incredibly stupid
C'est quoi des «vrais» cerisiers, pour vous? Prunus avium? P. cerasus? Les cultivars de Prunus sont un complexe d'espĂšces dans lequel mĂȘme les botanistes ont du mal Ă retrouver les espĂšces sauvages d'origine.
⣠Les moteurs de recherche. Eux n'aiment pas qu'il y ait deux URL distinctes pour un mĂȘme site. Et le gros problĂšme, c'est que je crois que rediriger Ă l'envers (HTTPS vers HTTP) est trĂšs mal vu par eux. Donc je ne sais pas quoi faire, lĂ . C'est surtout ça qui me bloque.â€â€âŠ
Mais attendez que je vous sorte ma classification «Gro-Tsen» des hommes, avec un type par caractĂšre Unicode. Comme ça vous pourrez ĂȘtre un mĂąle U+1FAE GREEK CAPITAL LETTER OMEGA WITH PSILI AND PERISPOMENI AND PROSGEGRAMMENI si vous voulez.
I often wondered whether one could make a successful TV show much like House MD but where the heroes debug computer code instead of solving medical mysteries.
I often wondered whether one could make a successful TV show much like House MD but where the heroes debug computer code instead of solving medical mysteries.
To explicitate the example: Cucubalus behen, when considered a member of the genus Silene, is to be named S. vulgaris, because S. behen already exists (similarly, in the genus Behen, it is named B. vulgaris because ICBN forbids tautonyms).
So apparently, asking this question to AI engines cause them to either hallucinate or give up. Any humans around who want to try answering it?â€â€I'm looking for an example of a species that was assigned to a different genus and had to be renamed as a result, to avoid creating a homonymy (conflict).đ
This one might be a valid example. At least it's coherent with the synonyms indicated on Wikipedia. But I can't find any references to âQuasipaa latransâ, so maybe not. đ€·đŒïž
Second attempt not much better (the species Mahonia aquifolium was indeed reclassified as Berberis aquifolium, but there was no conflict AFAICT).đŒïž
Yes, I'm pretty sure I've seen such examples. It's probably not even so rare when the epithets are very obvious things like âminorâ. I can't find an example at the moment, though.
⊠But the âimpennisâ species name cannot change, except insofar as it would be âimpenneâ if you reclassify it in a grammatically neutral genus, or if you classified it in a genus that already has a species named âimpennisâ, in which case I think we take the next validly published name (âborealisâ?).
⊠I mean, the Great auk is still called âAlca impennisâ if you are of the opinion that it is in the same genus as the type species of the genus Alca (viê«. Alca torda): that name hasn't changed and cannot change, it just happens that this opinion is no longer adhered to. âŠ
Yes but no. Whether you think two species belong in the same or in different genera is, of course, a scientific question and nomenclature can't take a stance on that, but nomenclature gives you a well-defined binomial name in either case, and âłïžthatâłïž can't change. âŠ
OĂč je me lamente que l'Internet Archive n'arrive plus Ă archiver mon site Web, et que YouTube efface inexplicablement mon historique au bout de 46Â jours: www.madore.org/~david/weblo... (billet de blog pas interminable, pour une fois!)đ
OTOH, it's much the same thing for binomial (âbinominal) names in the botanical and zoological nomenclature: the first âvalidly publishedâ name becomes the species name, and thereafter it can Never Be Changed even when it's âAnophthalmus hitleriâ or something. Other names are treated as âsynonymsâ.
Speaking of âsolidusâ: do you happen to know why the word âobelusâ can refer to either the dagger sign 'â ' or he sign 'Ă·' (which is maybe, or maybe not, related)? The latter is used to denote division (but almost never by mathematicians), or sometimes subtraction(âœ).
They could have been a bit less drastic and declare that each character has a (finite) set of synonyms, guaranteed never to overlap and which can only be added to, 1 of which is âpreferredâ. Which is almost exactly what they did, except I don't see why the preferred name can't be changed in the set.
For the Trump administration to get their northern neighbors, renowned for their politeness and friendliness towards the US, so incredibly angry, witnesses an incredible feat of malice and incompetence.â€â€Other countries will react even more strongly: the effect on tourism to the US will be savage.đ
I once had a password that started with the character â~â. When you type â~â just after a newline, ssh intercepts it as part of an escape sequence, and I didn't know this. As you can imagine, it took me a LONG time to understand why my password didn't work over ssh.
I once had a password that started with the character â~â. When you type â~â just after a newline, ssh intercepts it as part of an escape sequence, and I didn't know this. As you can imagine, it took me a LONG time to understand why my password didn't work over ssh.
âLosing five-plus hours of your lifeâ is exactly what computers and smartphones were designed to do; so: everything worked as expected. đâ€â€(Joke aside, the debate between \n as a line terminator and as a line separator is⊠a complicated and ongoing one.)
For academic faculty to have the number of campus security on their phone contacts in case the thugs from the federal administration try to abduct students is the sort of things you expect from a cartoonish dictatorship.â€â€What has the US become in two months? đąđ
Sorry, clarification: I was talking about how algebraists perceive mathematical logic, or the parts of logic which can be categorized therein, not computer science. The way they view CS is probably close to the way they view theoretical physics. And students are yet another matter.
⊠I mean, the (mostly French) algebraic geometrists and arithmeticians that I've encountered mostly seem to consider logicians as some kind of wizards who possess incomprehensible powers to warp the fabric of the mathverse. (Ironically, this sentiment might even be reciprocal. đ€Ł) âŠ
Counterpoint: as someone who did their PhD in algebraic geometry (a domain of math often reputed for its snobbery) with a keen interest in logic and CS, the reaction I mostly saw when logic was mentioned was not contempt but a kind of fear (as in âthis stuff is incomprehensible, but magicâ). âŠ
đ Data update: We've just updated the data we show from the World Inequality Database to their latest release.â€â€With this data you can explore several measures of income inequality, before and after tax, for countries around the world.đŒïž
Si ça peut aider, «bulle» (comme une bulle de savon, hein) en grec se dit «ÏÎżÎŒÏÏÎ»Ï ÎŸÂ», ou, avec un sens plus large de truc rond, «ÏÎÎŒÏÎčΟ»; et la foudre se dit «áŒÏÏÏαÏΟ». Je suis sĂ»r que tu peux faire quelque chose de joli avec tout ça.
Another bit of trivia is that Alan Turing was obsessed with Snow White, and there is some speculation as to whether his suicide was a recreation of the poisonous apple in the story. (There is further talk that the Apple logo is a reference to this, but IIRC this has been debunked.)
Happy Manatee Appreciation Day, to all who celebrate! In Portuguese a manatee is called peixe-boi (or âbull fishâ) and in Dutch zeekow (or âsea cowâ). And in English a group of manatees can be known as an aggregate of manatees (though I think a better term would be either a âmanateamâ or âmanyteesâ)đŒïž
Of the very many things the Trump administration has done since January and I believe deserve blame for, I think the one that currently has everyone's attention should really be pretty far down the list.
To illustrate, the screenshot on the left is what the gap in my YouTube history looked like yesterday (note the jump in date from 2025-02-07 to 2024-06-11); and the screenshot on the right is what it looks like today (so, the videos of 2025-02-07 are now forgotten).đŒïžđŒïž
20 years ago, there were a bunch of jokes with setups like "what if appliances/cars/etc where made by microsoft/apple/etc".â€In those jokes, you had to park your car due to an update being downloaded, stuff like that.â€These were actually not jokes but foreshadowing. đ«ą
This is irritating, because I actually enjoy the YouTube recommendation algorithm, but now it's constantly re-recommending videos that have fallen into the gap, because it's forgotten that I watched them.â€â€(Yes, I'm actually complaining that Google doesn't know all about me! đ)
And these 46 days are shifting: on 2025-01-29 the gap of missing videos spanned between 2024-06-12 and 2024-12-13 inclusive, and now it's grown to span from 2024-06-12 to 2025-02-06.
For some reason, there's a large & growing gap in my YouTube watch history: it has the last 46 days (so now since 2025-02-07), as well as (seemingly all?) videos I watched up to 2024-06-11. But since 2024-06-12 it seems to retain only the last 46 days.
Incidentally, I tried to find the one symbol common to the leftmost column in this arrangement, and it was really embarrassing how much time I wasted on this one simple mental task.â€â€(It's the letter âNâ, if you want to know.)đ
Sorry, I don't understand what you're trying to say.â€â€(Just to be clear, I'm not saying that having an app, or an online device, is always bad, merely that they should only be required for such features which logically require an app, or online connectivity.)
I had the cards printed out by www.makeplayingcards.com and gave some copies of the set to a few friends, but I think I lost my own.â€â€Perhaps it would be nice to recreate this, but using a better set of 130 symbols.đ
This is the 3-card analogue of a popular game called âDobbleâ. Some explanations about how it was done mathematically (namely, using a Möbius geometry on the field with 5 elements) are on my blog: www.madore.org/~david/weblo... (in French).đ
Some years ago I created this set of 26 cards (each showing 30 symbols out of a total repertoire of 130), which have the nice property that any 3 cards always have exactly 1 symbol in common.â€â€(So the game might be to draw 3 cards and see who can find the symbol first.)đŒïž
Bosch really deserves to be shamed all the way to hell for this.â€â€Please, people, if you buy a product that requires a smartphone app and/or Internet access for anything that is not strictly and obviously necessary (i.e., not rinsing dishes), give them disastrous reviews.
The absurdity of the modern Internet of Shit: Bosch made a dishwasher which, for many features (like⊠rinse cycle!), not only requires the use of a smartphone app, but also an Internet connection (and that the user sign up to a cloud account). www.jeffgeerling.com/blog/2025/i-...đ
Also, for a long time, I was convinced that the length of an ellipse of semiaxes a,b had to be Ï·(a+b) (it's wrong!) because this works for a circle and it seemed that it âhad to beâ an elementary symmetric polynomial in a and b just like the area is Ï·a·b (this one is correct).
One thing which fascinated me when I was young is that there's no elementary closed-form expression for the length of an ellipse, BUT there is one for the area of an ellipsoid of revolution (aka âspheroidâ).đŒïž
Equivalently: âeverything is logarithmicâ, and this is where you are between a user who has no followers (i.e., just themselves) and one who has everyone on the network.
It's not super serious, but it seems reasonable if we assume followers obey some kind of exponential growth (the more you have, the more they repost you to others) to consider at what fraction of the growth you are to being followed by everyone.
With this measure, I seem to be about 44% famous on Twitter and about 41% famous on Bluesky. It's interesting that they turn out so close, suggesting that there is indeed something to this way of counting.
Your âcelebrity scoreâ (between 0 and 1, which can be converted to a percentage) on a social network shall be log(n)/log(N) (i.e., log_N(n)) where n = nb of followers including yourself, and N = number of users on the network.
⊠âthe Alexandroff topology whose specialization preorder is the given preorderâ for the up-sets one, and âthe Alexandroff topology whose generalization preorder is the given preorderâ for the down-sets one. Which is now unambiguous, but⊠clumsy.
Fair enough, but saying âthe Alexandroff topologyâ is mostly misleading because the down-sets topology is just as much an Alexandroff topology as the up-sets topology. So if you really want to use that term you should say âŠ
âI cannot persuade myself that a beneficent and omnipotent God would have designedly created the Ichneumonidae with the express intention of their feeding within the living bodies of caterpillars.ââ€â Charles Darwin, May 1860, in a letter to Asa Gray)đ
(I mean, âAlexandrovâ is supposed to be a form of discreteness according to that article, and here the topology in question is extremely coarse. Besides, saying âup-sets topologyâ will make it easier to remember which way things go.)
I think I'd call that the âup-sets topologyâ. Yeah, en.wikipedia.org/wiki/Alexand... defines âanâ Alexandrov topology to be one in which all intersections of open sets are open, and points out that it's equivalent to giving the specialization preorder, but I find it really weird to see it that way.đ
No, I think your counterexample works (except I don't know the term âAlexandroff topologyâ). But the reason for the more complicated counterexample is â I think â to illustrate the fact that even if all spaces are assumed to be Hausdorff, then it still fails to behave as one might expect.
Dozens more pregnant and postpartum women have died in Texas hospitals since the state banned abortion, our analysis shows.â€â€As the maternal mortality rate dropped nationally, it rose in Texas by 33%.đ
The morality seems to be that if you're called Thomas and you're a high ranking official under an English king Henry, try not to get in trouble with him.â€â€(Generally speaking, it is wise not to get in trouble with kings.)
So, Thomas Becket was Lord Chancellor, got in trouble with King Henry II, and was murdered.â€â€Thomas More was Lord Chancellor, got in trouble with King Henry VIII, and was executed.â€â€Thomas Cromwell was chief minister of the same Henry VIII after More, and was also executed.
I realized that I was confusing Thomas Becket, Thomas More and Thomas Cromwell.â€â€(And worse than that, I was metaconfusing which two of the three I was confusing.)â€â€(And yes, Thomas Becket is ~350 years before the other two.)
Also, was Tolkien aware of the existence of architectural forms other than towers? Or would Dr. Sigmund have something to say about this particular obsession of his? đ€
⊠And nobody knows which of the 5 are the eponymous âTwo Towersâ, not even Tolkien himself, who changed his mind several times about this: www.reddit.com/r/todayilear...â€â€Why didn't he just name the book âThe Five Towersâ, then?đ
So, IIUC, the part of âThe Lord of the Ringsâ that is called âThe Two Towersâ actually has (at least) FIVE towers prominently involved: Orthanc [Saruman's tower], Barad-DĂ»r [Sauron's tower], Minas Tirith [Gondor], Minas Morgul [Black Riders] and Cirith Ungol [orc tower]. âŠ
And no matter how much I hate these guys, I can't help find the fact that they use emojis like âđđșđžđ„â to communicate between themselves⊠bizarrely endearing at some level.
I'm not going to comment on the ânational securityâ aspect, but the fact that Trump's cabinet routinely uses Signal to communicate (like us plebs) is something I actually see as very interesting and positive.đ
I've said this before and I'll say this again: the most batshit conspiracy theories would often make great fictional material (and Umberto Eco would approve, I think).â€â€Like, Fomenko's crazy theories about history would make for a great setting for novels.
So #TIL that there's a flat earth theory version 3.0 or something, with lots of⊠interesting lands⊠beyond the ice walls. Also, three suns or something.đ
Some days I think that, if I were not such a stay-at-home person, I would mount a great expedition to reach the westernmost point on Earth, and, when I eventually get there, I would exclaim âsee? they laughed at Columbus, too!â.â€â€Maybe it's best that I'm such a stay-at-home guy.đ
There is hope still! Many people have managed to leave the Belgium conspiracy theory, and so can you. You just need to realize how silly it is to believe that a country could be founded on the basis of a very bad opera. www.youtube.com/watch?v=W1Fi...đ
Think itâs important to highlight how everyday violence of the U.S. criminal legal system is making what ICE is doing possible: this man was convicted of a crime at *16*; he was *pardoned*; when ICE came decades later they claimed the conviction made him a felon w/ no recourse against deportationđ
âOne young man sobbed when a guard pushed him to the floor. He said, âIâm not a gang member. Iâm gay. Iâm a barber.â I believed him. *** He âbegan to whimper,â as his head was roughly shaved, âfolding his hands in prayer as his hair fell.â He âasked for his mother & cried as he was slapped again.âđ
âA developed country is not a place where the poor have cars. Itâs where the rich use public transportation.â â Enrique Peñalosa (Mayor of Bogota, 2012)
This makes me wonder: who are, currently, some of the richest, most powerful, most influential, most famous, or in any sense most âimportantâ, people on Earth who regularly take public transportation with the plebs?
I learned through a Reddit post that Mark Carney used to ride the London Underground when he was director of the Bank of England.â€â€[And no, I know what you're all thinking, but he's not picking his nose!]đŒïž
Trump's only move. Blackmail. He's doing it to everyone: law firms, companies, colleges, states, Canada, NATO, Ukraine. He was impeached in the first term for it. It's the only "art of the deal" he's ever known: strongman mafioso extortion. He'll re-run the same play forever until America collapses.đ
⊠I mean, most ppl probably don't even know that research in pure math even exists. You can't give an informed answer as to whether one should continue to do X if you don't even know that X exists or why we're doing it.
I would argue that this is precisely the kind of loaded question we do not want to poll about: public opinion is malleable, and asking such questions without providing abundant context about why we're doing it in the first place is the sure way to⊠malleate it in a populist direction. âŠ
Opinion | I am a Republican because I believe in traditional family values. Here's why I support a government run by two men who between them have 19 children by 8 different women.
Things I expected to see more in life based on my childhood comics:â€â€- magicians wearing tuxedosâ€- âKeep off the grassâ signsâ€- pies cooling on windowsillsâ€- people shaking their fistsâ€- anvils
⊠Specifically, is criticism of president Trump considered sufficient cause for deportation of a legal resident? for imprisonment? etc. Whether the answer is âyesâ or ânoâ, it would be nice to know. (And if the latter, advice must be given to foreigners not to enter the US.)
⊠An answer such as «non-US citizens have {1st, 4th, 5th, 6th, 7th, 8th, 13th, 14th [due process]}-amendment rights» would be nice in my view, but even an explicit clarification that they have ZERO rights in the Administration's view is better than not knowing. âŠ
⊠(Of course, US courts already said a great many things on the question, see e.g. scholarship.law.georgetown.edu/cgi/viewcont... for a review. But the question is what the current US Administration thinks, and it doesn't seem exactly inclined to defer to the courts' opinion.) âŠ
The US Administration really needs to be asked to answer clearly whether they think that non-US citizens have any rights whatsoever on US soil (and, if so, which rights), or whether they can be arbitrarily, e.g., deported, imprisoned, tortured, or enslaved. âŠ
What weâre witnessing in America is what happens when disordered discourse captures a political party, then the state itself. The Republican Party was the first to fall - abandoning truth for conspiracy, ideology for grievance, and policy for performative outrage.
Bon, plein d'autres mesures liberticides sont quand mĂȘme incluses dans cette loi, donc c'est une toute petite bonne nouvelle d'avoir un peu moins pire que ce qu'on pouvait craindre.â€â€Mais par les temps qui courent, on se contente de toutes les victoires qu'on a.
On a more serious note, I learned this fact in this video (by the âTribunateâ channel on YouTube) about the Third Punic War, and I thought it was very interesting: www.youtube.com/watch?v=fqjy...đ
I like to joke that WW2 ended in 1990 because that's when the âtwo plus fourâ peace treaty was signed.â€â€But by that logic, there's even better: the Third Punic War ended⊠in 1985âŻCE.đŒïž
Again, for a general perspective on such questions, I very highly recommend the survey by Longley, âNotions of Computability at Higher Types Iâ (2005) doi.org/10.1017/9781... (also available at homepages.inf.ed.ac.uk/jrl/Research... ). The result you mention is theorem 2.7 there.
Ăa me fait repenser Ă cette citation de Giancarlo Rota: «A leader in the theory of pseudo-parabolic partial differential equations in quasi-convex domains will not stoop to being understood by specialists in quasi-parabolic partial differential equations in pseudo-convex domains.»
The Internet Archive's Wayback Machine has once again decided that it thinks all(?) pages on my web site are âunreachableâ. đâ€â€I have no idea why this is so, and there seems to be no way to contact @archive.org and no place to ask for help.đŒïžđ
This is not just wrong, it's egregiously wrong in the case of measles which not only does not âboostâ the immune system, it causes immunity amnesia, correct?
Yup, if you tell me that assuming [X,Y]=1 we can express (XY)^n as a sum of X^k Y^k with interesting coefficients, this makes a lot more sense to me.â€â€(Except now I'm starting to wonder whether this is related to Baker-Campbell-Hausdorff and this is a rabbit-hole that I don't want to fall into.)
Those at least have their Wikipedia page.â€â€(I wouldn't have been able to properly define them beyond âthey have⊠something to do with counting surjections⊠I thinkâ â actually it turns out that this is the second kind â but at least I knew they were a thing, unlike Gunert's formula.)
I love it when the question starts âevery mathematician knows Grunert's formulaâ and I don't know Grunert's formula. đŹâ€â€(And, judging from the comments, I'm not the only one.)â€â€Nice formula, though!â€â€From: mathoverflow.net/q/488458/17064đŒïž
âThe Universe is maximally boringâ sounds like a great cosmological principle, just like the principle of Least Action is a great principle for mechanics.đ
12823413011547414368862997525616691741041579688920794331363953564934456759066858494476606822552437442098640979 / 877512406035620068631903180662851572553488753575243048137500508983979170248733422547196905684808937723408093â€â€âŠfits in a skeet⊠but barely.
I⊠did not expect a rational number with 108 digits in its reduced denominator to occur as the answer to the fairly natural question âwhat is the area of the Pythagoras tree fractal?â. penteract.github.io/pythagTree.h... đČđŒïž
So⊠giant swans (Cygnus falconeri) and pygmy elephants (Palaeoloxodon falconeri) lived in the same region (Malta) at the same time (during the Pleistocene); so a swan might have encountered an elephant smaller than it. đźđ
I asked a question on Math StackExchange about whether we can state a Tonelli theorem for Riemann integration assuming all slices are R-integrable and the single integrals are (for the Lebesgue integral, this need not hold, as I recall in the question): math.stackexchange.com/q/5046993/84...đ
Une remarque sur l'utilisation des pronoms «nous» et «on» en français:â€â€J'utilise «nous» mĂȘme dans des messages courts (genre SMS). Plusieurs personnes m'ont fait remarquer que c'est inhabituel. Mais il y a plus surprenant: âŠ
This fan art (without words) of Pixar's âInside Outâ is possibly the most beautifully moving comic I've ever seen. đ„čâ€â€It deserves to be a 4-page book all of its own, and it should get an award.đ
The Alexa feature "Do Not Send Voice Recordings" you enabled no longer available. Now everything will be sent to Amazon cloud server and it may become part of LLM training. Only Amazon knows what they are going to do with all that data.đŒïž
And for that matter, works of fiction should generally have a table of characters (with full name, very short bio and page number of the first appearance), because I realized that I often end up scribbling one myself after I got lost for the N-th time wondering âwait, did we meet this guy before?â.
I originally thought this material was so out of place in a spaceship and laser sword movie. But now I see that Lucas knew a thing or two about fake trade wars. He was preoccupied for much of his life with the subject of how democracy becomes autocracy.đŒïž
I also think Gillman and Jerison are right, in âRings of Continuous Functionsâ, to stipulate that âspaceâ means âcompletely regular topological spaceâ.â€â€But of course we soon start entering contentious territory with things like assuming every ring is noetherian or every graph is finite or the like.
I can understand that if you write a whole book on commutative algebra you don't want to write âcommutativeâ before every single occurrence of the word âringâ, even in the statements of theorems. It would be more distracting than helpful for the reader.
(I'm not even sure which is which, at this point. One of them probably comes from âk. ânâ. ânâ„nâ. |x_n â x| < 1/k, and the other one from the modulated version âÎŒ:âââ. âk. ânâ„ÎŒ(k). |x_n â x| < 1/k, but maybe they've been slightly modified beyond a simple translation. Anyway, it's not super obvious.)
To illustrate the fact that when we âunwindâ an internal notion to an external one the result often isn't easy to interpret, unwinding internal âz_n â zâ seems to give two different notions of convergence strictly between pointwise and uniform: mathoverflow.net/q/406025/17064x.com/gro_tsen/sta...đ
Fourman & Hyland's paper âSheaf Models for Analysisâ in Fourman, Mulvey & Scott, âApplications of Sheaves (Durham 1977)â, Springer LNM 753 (1979) should help with the intuition here. Fourman & Scott, âSheaves and Logicâ, same volume, is also a great read.
Merely unwinding the definition should be easy, but finding a clean/useful equivalent property is hard, and that's normal. That the object of Dedekind reals is represented by the continuous real-valued functions on a topological space isn't obvious.
More than once have I been fooled by a paper that stated a theorem like âevery vorpal space is slithyâ to later realize that, buried in the introduction, was the convention âin this paper, the word âvorpal spaceâ always refers to a vorpal space that is hairy, mimsy and utterly jabberwockyâ. đ
Important advice: if you write a math text with an unusual or surprising convention, definition or notation (e.g., âin this book, all foobars are assumed to be locally cromulentâ), be sure to remind the reader every now and then, around the places where it might lead to confusion.đ
I think this is better in that it will help readers remember which is which. Always keep in mind that there are people who will start reading your text in medias res and who will be confused about the terminology (which is maybe their fault for doing this, but have mercy on them anyway).
But I do find your complaints a bit contradictory: on the one hand you (rightly) point out that there's a dearth of introductory elementary textbooks on topos theory, and on the other you want to lean about super advanced concepts like â-categories and â-topoi. đ€
At any rate, maybe you'll find the book by Lambek & Scott, âIntroduction to higher-order categorical logicâ (1986) more accessible than MacLane & Moerdijk, or Johnstone. (Also, concerning Johnstone: the 1977 edition is more readable than the many-volume elephant.)
What do you mean by âcomputeâ? (Translate to an external statement?) And what kind of sheaf topoi? (That of a topological space / locale, or more fancy stuff like sheaves on a Grothendieck topology?)
I'm not sure about reals, but I think my favorite integers are 696âŻ729âŻ600 and 244âŻ823âŻ040, the orders of two very remarkable groups (namely, the Weyl group of Eâ and the Mathieu group Mââ).
Hard to describe in one skeet, but both are beautiful and exceptional objects (Eâ can be described as a remarkable sphere packing in 8 dimensions, and Mââ as symmetries of a certain way of grouping 24 objects) that in turn can be said to âgive birthâ to more exceptional objects (like the âMonsterâ).
I'm not sure about reals, but I think my favorite integers are 696âŻ729âŻ600 and 244âŻ823âŻ040, the orders of two very remarkable groups (namely, the Weyl group of Eâ and the Mathieu group Mââ).
An interesting general introduction to end-to-end encryption in general, the group encryption problem, and message layer security standard: vas3k.com/blog/end_to_...đ
* Clarification: I meant to imply that X_0,âŠ,X_n are distinct (otherwise any autobiography provides a path of arbitrary length with all X_i equal).â€â€The question of the existence of loops of length â„2 is also interesting, though.
Silly morning question:â€â€âŁ If âXâYâ (for X, Y two people) means âX wrote a biography of Yâ, what is the longest known path for this relation?â€â€I.e., find people X_0,âŠ,X_n, with n as large as possible, such that X_0 wrote a biography of X_1, and X_1 of X_2, etc., up to: X_{nâ1} wrote a bio of X_n.
It says something about the world we now live in that this incredibly stupid move by the US is only the⊠second dumbest thing⊠since⊠this morning. đ€Šđ
Just on this not only is the chainsaw thing crass etc itâs also *really really bad / ineffective* messaging. Anyone who thinks it makes sense for a Labour government to associate themselves with Milei / M*sk - I mean - at this stage - has completely lost their mind.đ
At this point, âcorruptionâ no longer covers it: this is a level of prevarication rarely seen since Italy under the Borgias. But without the Michelangelos and De Vincis that came with the latter.đ
An academic colleague just sent an email in pseudocode with IF and ELSE statements and honestly it was about a billion times easier to take appropriate action than every email I get from non-academic colleagues (on whom no shade is cast, I'm the problem here).đ
Sidney Sime, The City of Never, 1912, in The Book of Wonder.đŒïž
Thou shalt never write the following phrase, followed by the same between quotes: âThou shalt never write the following phrase, followed by the same between quotes:â
Wow! đČ A systematic and hyper-meticulously self-documented project to solve every problem in the book âStructure and Interpretation of Computer Programsâ (aka the Wizard Book, by Abelson and Sussman):đ
The more I think about this, the more embarrassing it gets. In classical math, or in constructive math with Countable Choice, âevery real number is the limit of a sequence of nonzero realsâ is a trivial exercise.â€â€But in constructive math without Choice, I'm stumped!đ
Embarrassingly, though, I realize that I don't know whether one can prove (again, in constructive math without Choice) that every real number is the limit of a sequence of nonzero reals!
I now posted an answer showing that one cannot prove (in constructive math without Choice) that every real number is the limit of a sequence of irrationals: in fact, ÎČâââ provides a topological countermodel. mathoverflow.net/a/489193/17064đ
(The roundabout phrase was necessary because I couldn't write âhaving been head of the CB of another countryâ in Mario Draghi's case as the ECB is not âCB of another countryâ.)
Yeah, there was a subtle parsing ambiguity in my sentence: âhaving been head of a CB, but not the CB of the countryâ meant âhaving been head of a CB which was not the CB of the countryâ, not âhaving been head of a CB, but not having been head of the CB of the countryâ, which is indeed different.
Mark Carney joins Mario Draghi in the very very niche club of âpeople who became head of government after having been head of a central bank, but not the central bank of the country of which they became head of governmentâ.â€â€Are there any others?
Mohammad Tahmasbizade's constructive math questions on MathOverflow are very interesting (if somewhat unorthodox), but I'm afraid they mostly highlight how little we know in constructive math without Choice.
The question was whether we can prove in constructive math that every [Dedekind] real number is the limit of a sequence of negatively irrational numbers. But it's not hard to show that this fails for the positively irrationals, so this has led to some confusion.
I wrote an answer on MathOverflow which isn't really an answer to the question that was being asked, but which I hope will dispel the confusion between two different sorts of âirrationalsâ in constructive math: mathoverflow.net/a/489172/17064đ
the actual technology almost doesn't matter, the AI bubble guys were the crypto bubble guys and the metaverse bubble guys and wanna be the quantum bubble guys
The link projects.fivethirtyeight.com/polls/approv... by FiveThirtyEight which used to track Trump's approval rating across various polls is now replaced by a generic redirect to ABC News' politics page.â€â€Still worked 2 days ago: web.archive.org/web/20250307...â€â€Did the White House exert pressure?
Just to point out the absurdity of where we've arrived, here are three recent math tweets of mine that contain words from the Trump administration's scientific censorship list of banned keywords (namely: âintersectionâ, âbiasâ and âinequalityâ):đŒïžđŒïžđŒïž
Ok, since several people have expressed surprise that I used the Attic dialect form of the word, âΞΏλαÏÏαâ and not âΞΏλαÏÏαâ, serious question:â€â€âŁ How come is it that this word, one of the most widely recognized words in the Greek language, is so in its non-Attic form âΞΏλαÏÏαâ?đ
True, I may have committed the sin of using Ionic Greek in the meandering years of my wayward youth, before I learned the stern ways of the School of Athens.
Good morning and welcome to your FT Weekend highlights thread. As ever, all gift links are free 300x and that's your lot, editor's choice is final. First up is this essay from Joseph Nye, who coined the term Soft Power, on how Trump doesn't understand it and why that's a problem on.ft.com/4hlZTcBđ
Can you clarify the rule? Is the âsequenceâ you mention consecutive? Is the line of tokens oriented? Are we to understand the rule as meaning âchoose a BG factor and replace it by G^i B^j where i,j are chosen by the opponentâ?â€â€(At any rate, @joeldavidhamkins.bsky.social might like this game.)
A lot of what appeals to Trumpists about the sudden abandonment of Europe, Ukraine, Canada and Mexico is the emotional trauma it is causing.â€â€They're turning what was perhaps an imbalanced relationship into an abusive one. The cruelty is the point, and the shock and pain expressed is the pleasure.
The semantics of combining emojis in Emoji Kitchen aren't super clear, but they do allow me to accurately express my current emotions at the current state of the world.đŒïžđŒïžđŒïžđŒïžđ
⊠Et aussi, quand on ne connaĂźt pas quelque chose, on ne voit pas oĂč cette chose intervient et oĂč elle peut servir, justement parce qu'on ne sait pas qu'elle existe et qu'on ne sait pas ce qu'on ne sait pas.
A very insightful video on the recurring question of âwhen will I ever use <math concept>?â that students often ask, and why it's so hard to answer, but why this in no way implies that math is useless. (Applies more generally to many theoretical topics.) www.youtube.com/watch?v=RqQl...đ
Remember that âI Am Canadianâ ad for Molson beer that went viral in 2000 (and made Jeff Douglas rise to prominence)? ⊠www.youtube.com/watch?v=WMxG...đ
I would hope that US Congress cannotÂč enact legislation granting the President power to enact legislation. But now I'm not sure of anything any more.â€â€1. Unlike UK Parliament, which unquestionably can do this, even though it has a different status (âsecondary legislationâ).
One underlying legal question is the extent to which an institutional body can delegate power granted to it by the Constitution (âdoes the power to do X imply the power to delegate the power to do X?â).
As another Trump-induced market crisis unfolds from tariffs, it's time we ask "What's the Matter with Billionaires?" I've run the numbers. Billionaires do better under Dems. So why do billionaires keep supporting GOP policies against their economic interests? See my latest piece on why. (TLDR đ§”âŹïž)đ
Regardless of whether they're opportune, isn't it a bit strange that even though the US Congress alone is supposed to have the power to raise (federal) taxes, but somehow the US President can still singlehandedly impose tariffs â which are taxes on imported goods and services?
You know the saying "everything on the internet is forever"â€â€Isn't it crazy how that's not true anymore? Hundreds of billions of data have been wiped to never seen again nowadays and less and less efforts to save it is been done.
A fundamental difference between the parties is that Republicans understand that public opinion can be shaped, whereas Democrats believe it can only be responded to. So Republicans shape opinion rightward, Democrats believe itâs what The Peopleâą want, then proceed to also move rightward. Repeat.đ
This theorem is not very difficult, but it's still tricky to grasp; its proof, and even statement, are hidden in the 1982 paper by Hyland âThe Effective Toposâ dpmms.cam.ac.uk/~jmeh1/Resea... + a bit of logic (đœ); I think it completely escaped attention, which is a shame as it can teach us sth. âą4/4đ
⊠terminates and returns a P-answerer for B. And a âuniversal converter from B to Aâ is a g which is a P-converter from B to A for any Pââ (the same g for any P).â€â€Then we have the:â€â€âŁ THEOREM: (for A,Bââ) there is a universal converter from B to A â·iffâ· A is Turing-reducible to B.â€â€âą3/4
For years Iâve contrasted the way that US science allocates cognitive effort from the bottom up via individual scientists responding to career incentives with the way things were done in the Soviet Union, from the top down, by the Party setting rear b priorities. â€â€I canât do that anymore.đ
⊠mais je pense que s'il s'agit de faire faire juste des additions, ça ne va jamais ĂȘtre computationnellement rentable. Cependant, @gloupin.bsky.social en sait bien plus que moi,
youâre fired. wait youâre rehired. email us a list of things youâve done today wait forget it youâre fired again. come back your job was important. youâre fired. or hired. come in to the office. wait the office has no computers go home. we are the department of government efficiency.
⊠For pâšÂŹp one must produce an element of p(x) when there is one, and this can't come out of thin air. So, yes, one way to fix this would be to add âp is classicalâ in the hypotheses of the proposition (but I think it's better to change the conclusion to ÂŹÂŹpâšÂŹp).
Seen on Facebook (but I can't trace the proper origin) - "Katsu" is actually from the European "Cutlet", then reimported with Japanese phonemes!đŒïž
I asked a question on MathOverflow about whether the analytic WLLPO together with the sequential LLPO imply the analytic LLPO â which is also an excuse to write down what each of these terms mean. mathoverflow.net/q/488896/17064đ
Very disappointed that this particular conspiracy theory hasn't caught on. Now would be the perfect time for it to do so.đ
Darn, this should be about continuous functions Uââ with UâX open rather than just Xââ. (For a completely regular space X this doesn't change anything because every germ of continuous â-valued function at some xâX extends to all of X.) I'll try to fix the question ASAP.
Re âa correct proof is likely to require a complex proof strategy, and while there are some counterexamples to this, it is overwhelmingly likely that some new conceptual idea is requiredâ: mathoverflow.net/q/440214/17064đŒïž
I asked a question on MathOverflow about topological spaces in which the positive and negative values of a continuous real-valued function always have disjoint closures, and a weaker form thereof: mathoverflow.net/q/488858/17064â€â€(The question relates to constructive math, but it isn't cons. math.)đ
trump was literally president for four years during which he wildly escalated drone warfare, tried to provoke a war with Iran and got into dangerous saber-rattling with north korea. now, he is threatening to take greenland and the panama canal by force. what is this horseshit?đ
With everything on a knife edge here is an assessment of what might be done to salvage the situation and what Europeans can do now. (free) open.substack.com/pub/samf/p/t...?đ
*Correction: interpretation #2 should read âout of the four outcomes HH, HT, TH, TT, I told you that TT is excluded, leaving the other three equally likely. So the probability of HH, as asked, is 1/3â.đ
Oh dear, I did. đ€Šâ€â€It seems it's really impossible to write a social media post pointing out a confusion without introducing a mistake causing a different confusion that makes the whole matter even more confused. đ
I think it's also important to emphasize that the exact wording of the question matters; and that sometimes it's not at all clear what the wording means, like in this subtly different question: bsky.app/profile/gro-...đ
Both answers 1/2 and 1/3 are correct, it's just that the question isn't sufficiently precisely formulated to admit a unique definite interpretation (what does âone coin turned headsâ mean? was the examined coin decided before the toss or did I search for a heads after the toss?).
Interpretation #1: I told you that coin A turned heads, coin B is independent of it, so, 1/2.â€â€Interpretation #2: out of the four outcomes HH, HT, TH, TT, I told you that HH is excluded, leaving the other three equally likely. So the probability of TT, as asked, is 1/3.
How to cause endless discussions about probabilities by using insufficiently clear wording:â€Â«â€I toss two fair coins. I tell you that one coin turned heads. What is the probability that the other coin turned heads?â€Â»
Another intriguing constructive math question on MathOverflow: doesâ€â€âxââ. ((ârââ. ÂŹ(x=r)) â (xâ€0 âš xâ„0))â€â€implyâ€â€âxââ. ((ÂŹ(x=0)) â (xâ€0 âš xâ„0))â€â€(where âââ is the Dedekind reals)?â€â€mathoverflow.net/q/488800/17064â€â€Of course, classically, this is all completely trivial.đ
⊠but I'm a bit annoyed to discover that the article âapproximately continuous functionâ already existed, because now they really ought to be merged (they're basically just reformulations of the same idea) and it would be tedious to do. So I'm just putting a link.
I added a more interesting example. I hope I got those inequalities right!â€â€Putting a triangle function of max height 1 on each interval [1/n, 1/n + 1/2^n] (and 0 outside them) gives an interesting approximately continuous function that is not continuous at 0, âŠ
This blog post from a number of years back, comparing Go with (anonymously presented) Algol-68, caused something of a stir at the time: cowlark.com/2009-11-15-go/đ
Well, maybe I have a mild preference for the style I used, because in the style you mention it's not really super clear what is a page number; and to cite something like âcomment following theorem 1.2.3 on page 45â it's probably better not to cram all that in a superscript. đ€·
I'm lost as well. I copied citation code from a previous page I had written, which itself was probably copied from elsewhence, and I have no idea what I'm supposed to use, or what is âbetterâ and why. (And, to tell the truth, I really don't want to learn, either.) Feel free to convert if you wish.
Du mini-sondage que je fais ici bsky.app/profile/gro-... et sur The Bad Place x.com/gro_tsen/sta... l'usage majoritaire de petit-cousin semble ĂȘtre «fils d'un(e) cousin(e)», y compris pour qqs gens qui ont grandi dans un large sud, mais c'est peut-ĂȘtre plus local que ça.đ
If only there were some way for a web site to store a small amount of information in a web browser that could be used to remember, e.g., whether the user is willing to allow cookies. đ€
One of the infuriating things about those many sites that ask you whether you're willing to allow them to store cookies in your browser (personally I'm fine with that) is that they DON'T REMEMBER YOUR CHOICE and KEEP ASKING even if you say âyes, go ahead, all you want!â.
Je sais que @marcqplanets.bsky.social a fait des vraies observations sur des vrais instruments de vrais astronomes, donc il peut peut-ĂȘtre nous dire comment ça se passe au niveau sous.
Annoyed by the fact that Wikipedia didn't have an article on the density topology, I revived my Wikipedia account that had been dormant for 10 years, and created the page: en.wikipedia.org/wiki/Density...â€â€Not much there, but still better than nothing.đ
There are many stories about âgerm theoryâ and "hygiene hypothesis" based on unfortunate misunderstandings and simplifications.â€â€We do need microbes to be healthy, but you don't have to get sick to be healthy! That's not how it works.â€â€#Immunology101#MedSly#ImmunoSkyđŒïž
Ou peut-ĂȘtre que ce n'est pas parce que je suis vieux mais parce que, justement, dans la recherche, la moula, je ne risque pas d'en voir des masses, que je ne sais pas ce que c'est. đŹ
Right. Major political parties need to have a solid internal democracy if the (external/general) democracy is to function well. The ease with which Donald Trump acquired complete ownership of the Republican party would be preoccupying even had he not won the 2024 general election.
⊠clearly the problem is deeper than Trump alone, and clearly the âchecks and balancesâ weren't as great as they were hyped up to be.
Not debating the question of whether Trump can or wishes to declare himself president for life like XĂ. But I will make this comment:â€â€âŁ If a 250-year old democracy falls so easily under the assault of a not super smart, not super popular and not even so super rich guy, it wasn't in a great shape: âŠđ
I discovered that the American Mathematical Society published an entire volume www.ams.org/about-us/Liv... titled âLiving Proof: stories of resilience along the mathematical journeyâ, full of testimonies from mathematicians about overcoming failures and hardships along their career path.đ
Zelenskyy stayed in Kyiv while Russia was bombing the city and sending in hit squads to kill him. J.D. Vance fled to an undisclosed location because some peaceful protesters yelled at him while he was on vacation. This is why I believe victory over these people is still possible.
What I find surprising is that various results in computability (e.g., Rice-Shapiro, and Kreisel-Lacombe-Shoenfield) more or less say âthe only useful thing you can do with a program is run it (no meaningful analysis can be performed)â, but still the λ-calculus gives you less power of analysis!
⊠Also, I'm aware that they were both viewed, at the time, as being more or less identical to the Roman Empire, but my question is not how these empires were viewed at the time but as how they are viewed by later historians who study them.
⊠but I'd like to know which is the more frequent classification used by modern historians, how and whether the point of view has changed over time, and what are the main arguments for considering the 800-founded and the 962-founded empires as different or identical. âŠ
Is there consensus among historians as to whether the empire founded in 800 by Charlemagne is âthe sameâ as the empire (re?)founded in 962 by Otto the Great and generally known as the âHoly Roman Empireâ?â€â€This is more a classification problem than a historical question, âŠ
It's Friday afternoon. â€You've had it with this week.â€â€All you can think of is calculating the cost and time to travel between any 2 points of the Empire using the Roman transport infrastructure. â€â€You're welcome đâ€orbis.stanford.eduđ
So, 35 years after the US won the Cold War, 80 years after the Allies won WW2, and 160 years after the Yankees won the Civil War, it somehow took Trump only one month to surrender to the Confederates, the Nazis and the Russians.
La Chine mange l'Asie du Sud-Est et est trĂšs contente du partage du monde.
Going through my MathOverflow archive, I reran across this mindblowing little gem:â€â€There is a rational function of 2 variables f â â(x,y) that extends to a continuous function on âÂČ, but which is not Lipschitz in any neighborhood of the origin! đ€Żâ€â€mathoverflow.net/a/436927/17064đ
I love how theorem 1.2.3 basically says âso, we introduced the requirement Sxyâ in the definition, whose motivation and intuition were entirely unclear, and now we show you a simple trick that lets you do without itâ. OK then. đ€·
(I'm not even 100% sure that the second one is a p.c.a.: maybe there's something wrong about the condition that, if x,y,z are normal terms, Sxy â λt.(xt)(yt) has a normal form and Sxyz has a normal form iff (xz)(yz) has one. It seems that the more I think about the λ-calculus the more I hate it.)
Bauer's notes on realizability seem to mention only the first. But the second seems more similar to Kleene's first algebra. Are they equivalent? How do the topoi they define relate? So many questions!
Also, there are (at least!) two natural p.c.a. of λ-terms, AFAICT:â€â€âŁ the one whose elements are equivalence classes of closed λ-terms under ÎČ-equivalence, and composition is total,â€â€âŁ the one whose elements are normal closed λ-terms where composition is followed by ÎČ-reduction (IF this has a n.f.).
There seems to be a common flavor between ordinary realizability on the p.c.a. of λ-terms and â·extensionalâ· realizability on Kleene's first algebra, as defined in van Oosten, âExtensional realizabilityâ, âAnn. Pure Appl. Logicâ 84 (1997) 317â349 doi.org/10.1016/S016...đ
Next year, the EU will require cars to have buttons & dials -- not just touchscreens -- to get a top safety rating.â€â€This is a great move. Drivers can fiddle with knobs & buttons without taking their eyes off the road, but they can't do that with touchscreens.â€â€(Even better: Tesla will hate this)đ
Funny to see Andrej Bauer âemphasize (again, again and again) that representation of input and output mattersâ when he explained to me in the comments below cstheory.stackexchange.com/q/53559/17747 that my question about input and output representations on Turing Machines was a âred herringâ. đđ
Incidentally, one isn't supposed to use MO to check for the correctness of a proof, but I'd appreciate it if someone could confirm that the proof I wrote makes sense.
The question contains a proof of the fact that changing the numbering gives a computably isomorphic algebra. Part of the question is why I've never seen this statement or proof anywhere.
I wrote a question on MathOverflow asking in what sense the first Kleene algebra (which is just â endowed with a partial composition law given by application of partial computable functions) doesn't depend on the choice of numbering: mathoverflow.net/q/488585/17064đ
"daddy, what did you do in the war"â€â€son, i archived all 6,793 videos from the Kennedy Center before they disappeared from the internetâ€â€we all did our part
[61] = M. Hyland, âA syntactic characterization of the equality in some models [âŠ]â, âJ. London Math. Soc.â 12 (2) (1976) 361â370 doi.org/10.1112/jlms...â€â€[86] = G. Longo, âSet-theoretical models of λ-calculus: theories, [âŠ]â, âAnn. Pure Appl. Logicâ 24 (1983) 153â188 doi.org/10.1016/0168...
I think @jeanas.bsky.social is right that semantics are probably a simpler way to approach this question. But the speed with which I forget everything I learn about the λ-calculus prohibits me from doing more than nodding gravely at âScott's model has the same equational theory as Böhm treesâ.đ
This is the sort of shit which gives entire branches of math a bad name. If you write something like âby the Quetzalcoatl lemmaâ and you can't cite a book or paper where it's stated and proven, then giving the proof is your duty. Yes, it's annoying, but it's part of your job!
So apparently there's a lemma in algebraic homotopy theory or K-theory folkloricly known as the âQuetzalcoatl lemmaâ (probably bc it's a kind of higher âsnake lemmaâ), but nobody bothered to write down a precise statement and reference: mathoverflow.net/q/488544/17064đ
But I'm really impressed by how CSS systematically manages to make every simple task, no matter how trivial, annoying or impossible without JavaScript.â€â€âReset property to defaultâ should really be the most basic feature there is. HOW did they manage to miss this?
Let me get this straight: CSS has a gazillion different reset keywords (âinheritâ, âunsetâ, ârevertâ, ârevert-layerâ and âinitialâ) with super confusing meanings, but NONE of them does the ONE thing you want: âreset to the browser default for this elementâ?â€â€I HATE this standard with a passion.
(Now maybe I can try to read this section and understand what my question really was and what the answer means, but, to be honest, this sort of hieroglyphs âŹïž are a bit too Cousot&Cousot-y to my tastes.)đŒïž
The answer to the fixed question is also negative, but far less trivial (assuming I understand correctly what this says, which isn't entirely sure⊠but this was probably the question I â·meantâ· to ask, even if it's not the question I â·didâ· ask):đ
In any case, the question as I had written it was silly because the constraint that Tpxqy reduces to one of px or qy is stupid. But I suspect you fixed it without noticing it (i.e., just drop that constraint).đ
⣠Does there exist a term T of the λ-calculus such that, given normal terms p,x,q,y, the term Tpxqy has a normal form iff px has a normal form or qy has a normal form [but no constraint on what Tpxqy should reduce to]?
Never mind: if I take p,x,q,y to be variables, Tpxqy is supposed to ÎČ-reduce to either px or qy; assume the former w.l.o.g.: but then TÏÏqy reduces to ÏÏ (where Ï := λz.zz), but also to qy; and by Church-Rosser, ÏÏ should reduce to qy, which is absurd.â€â€So, weaker question: âŠ
Maybe I misunderstood your proof, but I'm assuming p and q are in normal form in my assumption on T. I think you proved that it's impossible without this assumption (something that I didn't know how to formalize, but suspected).â€â€(Also, is the âbasically becauseâ part a standard result?)
See perso.enst.fr/madore/inf11... slides 34â37: basically you replace the notion of âcomputation stepsâ for Turing machines by âcomputation treeâ for general recursive functions, then search for a computation tree of one of the proposed computations.đ
My intuition is also that there is no such term, but I have no idea how to prove it. As the other result shows, it can't be because of a general fact in computability, it has to be something specific to the λ-calculus.
Possibly the question is completely idiotic, I'm not sure. If I have time to think about it some more, maybe I'll ask on something-or-other StackExchange.
⣠Does there exist a term T of the λ-calculus such that, given normal terms p,x,q,y, the term Tpxqy has a normal form iff px has a normal form or qy has a normal form, and, if such is the case, ÎČ-reduces to one of these?
Standard fact in computability:â€â€âŁ There exists a program T that, given p,x,q,y, terminates iff Ï_p(x) terminates or if Ï_q(y) terminates, and, if such is the case, returns one of these values.â€â€(Here, Ï_n(z) := value at z of the n-th general recursive function.)â€â€Followup question: âŠ
I use âamsartâ (or âarticleâ), together with â\usepackage[french]{babel}â for papers in French. Is there something specific to Spanish that you want that the amsart + babel combination does not provide?
I think âglobal elementsâ and âglobal sectionsâ are used completely interchangeably (there again, I'm not sure I even noticed there was a difference).
For me, the âglobal sections functorâ on a topos, or, more generally (but somewhat abusively) a category C with a terminal object 1, is the functor X ⊠Hom_C(1,X), from C to Sets. For a sheaf topos it is indeed what you imagine.
(Recurring problem in pĂŠdagogy: is it better to start with the more general notion at the risk of drowning the reader, or start with the important and archetypal example and later say âoh, and by the way, we can generalize everything to <abstract notion>â?)
I would recommend emphasizing that the reader who does not wish to learn the definition of a p.c.a. can think of the first Kleene algebra (recalling that it is â with operation aâąb := Ï_a(b)) to get the gist of the notion, as it is the most important and archetypal example.
If you want to copy-paste some part of my question (or my self-answer) here on MathOverflow regarding đŠâ, feel free to do so: mathoverflow.net/q/439046/17064đ
Also, my Xeon E3-1230v5 at 3.40GHz PC from 2016 encodes the same videos at speed ~0.7 without any GPU. So why is there a factor ~15 in speed between ARM and Intel in CPU-only encoding?
The machine in question has a GPU, but I imagine actually using it is a complicated mess and hidden behind all sorts of proprietary interfaces. I don't even know where to start to tell ffmpeg to use it.
⊠Was I being utterly naĂŻve here in expecting something like 5â10 times faster? Am I severely misjudging how many flops an ARM Cortex-A76 at 2.4GHz can crunch? Or is it that the libx265 encoder falls back to very slow generic code on ARM? Something else?
⊠It re-encodes at roughly 0.04Ă of the original speed. Now I didn't expect real-time speed (1Ă), but I also certainly didn't expect it to be THAT awful either. (I began to wonder if the CPU had an FPU: I checked, it does.)â€â€At this rate it would take ~7 months to re-encode my videos. đ± âŠ
I thought I'd re-encode some bulky car dashcam videos (~4000 videos each roughly ~230MB for 3min) as x265 using `ffmpeg -c:v libx265 -crf 30 -c:a copy` running on an ARM machine (NanoPi R6S: quad-core ARM Cortex-A76 at 2.4GHz + quad-core ARM Cortex-A55 at 1.8GHz), and boy is it âSLOWâ. âŠ
⊠while on the other hand, English speakers can apparently get away with something like this (yes, this is a real ad, and if you need an explanation, âpetite biteâ means âtiny cockâ in French):đŒïž
PS: Not only does the âCoqâââRocqâ name change hand a victory over science to the homophobic puritans, it also reinforces the complete hegemony of English: you can't use a banal French word in a name when it sounds ever so slightly lascivious in English (so everyone needs to adapt to English), âŠđ
⊠Renaming âCoqâ to âRocqâ comes from the exact same mindset as cutting grants from projects which contain certain forbidden words.â€â€Anyway, my question is how to refer to Coq in such a way as to denounce this puritanical agenda. Like maybe find an excuse to read the slash in âRocq/Coqâ as âhardâ. đ€
⊠because this hands the Puritans another victory over science. The sort of Puritans now running the US government, and social media like Facebook, who get âoffendedâ by images of genitalia or lewd words, while still approving of sexist violence, and who think it's wrong for a man to suck cock. âŠ
The Coq proof assistant software is in the process of changing its name to âRocqâ because âCoqâ leads itself to a double entendre in English.â€â€(See coq.discourse.group/t/coq-commun... )â€â€This decision is, of course, colossally stupid, not just because renaming software is always stupid, but mostly âŠđ
In 1970, John Boorman of Zardoz fame wrote a film treatment of LotR. â€â€It is a STINKER of a film, although there are some legitimately interesting ideas tucked into it. â€â€I read it so you won't have to! â€â€A𧔠of the best and worst pieces of John Boorman's LORD OF THE RINGS SCREENPLAY.đŒïž
The issue is that of Kolmogorov complexity: everything is a mathematical object if you want, but copyright only applies beyond a certain involvement of creativity (in picking the object inside a space of possibilities), which requires some Kolmogorov complexity.
⊠buy as standard academic practice: just like you don't need to ask for P's permission to use P's theorems, but you should still credit P and not claim the theorems as your own. (And here, AFAICT, I'm the first person to have computed images from â·insideâ· a Kerr black hole.)
⊠the image results from a mathematical computation with essentially no creativity involved, so there is no copyright â it is in the Public Domain â as all mathematical objects are; BUT that they should still credit me, not because of intellectual property laws, âŠ
Every now and then I get an email from someone asking for permission to reuse one of the various mathematical images I computed, e.g., this âŹïž image of the inside of a Kerr black hole (from madore.org/~david/math/... ). And I have to explain that they don't need my permission: âŠđŒïž
(Actually, the real reason I do it is so I can search through my own skeets by using text descriptions for the images. But the part about the tediousness of writing alt text discouraging me from posting images is true.)
The reason I force myself to put alt text on every image isn't for accessibility: it's because it's so tedious that it drives me to post fewer images, which is probably a good thing.đ
Not to suggest the paper isn't interesting / important, nor that Scott Aaronson shouldn't give his opinion (nor that we shouldn't care about it), but the word âhimselfâ suggests a kind of cult status of bigshots that IMHO is unhelpful and even disturbing â and altogether too prevalent â in academia.
Not exactly what you asked for, but close: mathoverflow.net/a/33015/17064 (see also the other answers there).â€â€Of course, nobody expects log(2)·log(3) to be rational. It's just that we don't know how to prove its irrationality.đ
I am not (now or ever) Catholic, and I'm not a great fan of popes in general; but for all his flaws, I will say this about Francis:â€â€He seems to be taking the concept of âhumilityâ seriously. And that's something we can all learn from, and I wish we'd see more in world leaders.â€â€So I hope he lives.đ
âŠâ€âA friend supported me.ââ€âWhere did he get the money from?ââ€âHe owned a textile factory.ââ€âWhat do you think of Lenin?ââ€âI have never heard of him.ââ€âWhat is your name?ââ€âKarl Marx.ââ€Â»
Joke: «â€â€A man in a communist country is being interviewed by a verification committee:â€âWhat kind of family do you come from?ââ€âA rich Jewish family.ââ€âAnd your wife?ââ€âA German aristocrat.ââ€âHave you ever been to the West?ââ€âI spent most of my life in England.ââ€âHow did you make a living there?ââ€âŠ
OK, so apparently some people get âInfinityâ when they ask the Google calculator for the value of 141.22!, and others (including myself) get a finite value.â€â€I have no idea what is going on here! đ€·đ
(By âit is obvious that log(2)/log(3) is irrationalâ, I mean that even Pythagoras knew it⊠even though he didn't really know what irrational numbers where, and certainly didn't know what logarithms were. đ)
Yes, it is also unknown whether e+Ï is rational, and whether eÂ·Ï is (of course, they can't both be algebraic, so one of them must be irrational).â€â€But e and Ï are complicated: log(2)·log(3) should be more striking, given that it is OBVIOUS that log(2)/log(3) is irrational.
File under âwe are embarrassingly ignorant of mathematicsâ: it is unknown whether log(2)·log(3) is rational: mathoverflow.net/a/488323/17064đ
Alors, maintenant que je suis devant un ordi, la valeur â„1 oĂč Î atteint 2^1024 - 2^971 vaut environ 171.624376956302721 (donc pour la factorielle, c'est ça moins 1).â€â€Mais pour moi, la calculette Google semble renvoyer âInfinityâ Ă partir de 170 exactement. đ€·
⊠Mais je n'ai peut-ĂȘtre pas bien compris ce que vous dites, parce que vous dites que vous n'ĂȘtes pas d'accord mais je ne saisis pas bien sur quel aspect.
Message aside, the idea of using the cybertruck as a billboard is technically super cool, and (if the video is real) it seems to render really well. Is this using a standard kind of projection, or is it a custom design?đ
This seems to have attracted a number of perplexed comments. I agree there's probably no good answer to the question, but I don't think this fact is so obvious that the question shouldn't even be asked. đ«€
This paper people.csail.mit.edu/rrw/time-vs-... (circulated on Mastodon) is pretty incredible.â€â€It is obvious that DTIME(f(n)) â DSPACE(f(n)). The author proves that DTIME(f(n)) â DSPACE(â(f(n) log(f(n)))) for f(n) â„ n đ±â€â€I am dumbfounded that this is true and even more that it is both true and new.đ
You know things are really fđ€źcking bad when RUPERT MURDOCH starts to look like a good guy in comparison.đ
Kudos to @meredithmeredith.bsky.social for explaining the lack of connection to reality at the core of tech entrepreneurship (at least the part of it sponsored by đșđž VCs). â€www.politico.com/newsletters/... Helps me understand my lingering malaise facing such claims made in my scientific community.đŒïžđ
The idea that the air we breathe is free for all is an ancap libertarian's nightmare: their answer to the âtragedy of the commonsâ is that everything should be privately owned. Hard to achieve on Earth, but certainly possible on Mars, and I think this gives Musk a boner.
At some level, I think this is also what motivates Musk to build a colony on Mars: the colonists would depend on him for every bit of their survival (shelter, water, airâŠ), which he could threaten to withdraw at a whim.â€â€He would own other human beings in a sense that is no longer possible on Earth.đ
A project that combines cryptocurrencies, quantum computing and AI turns out to be an entire web of lies? Who would have thunk?â€â€<surprised Pikachu meme>đ
dude who waited 2.5 years to get his #FTX money only to deposit it into #Bybit an hour before that company was hit with the largest hack/theft in human history is basically the crypto industry in a nutshell.đŒïž
De toute façons, je suis plus ottoman-baroque que baroque ottoman.đŒïž
I asked a question on MathOverflow about whether we can characterize cardinals of the form λ^(â”â) (they are â„2^(â”â) and of cofinality >â”â but this is not sufficient, so maybe something can be added): mathoverflow.net/q/488299/17064đ
A couple of Dark Souls fanart pieces I created between 2012 and 2015. Feels like yesterday when I played DS1 (best one imo) Time flies!đŒïžđŒïžđŒïžđŒïž
Solved: the map ÎČâdens â ÎČâ can't be injective: for it is surjective (as its image is closed and contains â), so if injective it would be a continuous bijection between compact spaces, hence a homeomorphism, so all bounded approximately continuous functions on â would be continuous, which is false.
I had absolutely no idea that the UK's nuclear defense was somehow subordinate the the US's power to âturn it offâ, and I am flabbergasted to learn this. đČâ€â€(And I don't even really understand what it means, to be honest.)
I am flabbergasted that I can't seem to find a reference for the fact that a semicontinuous function on a Baire topological space has a dense G_ÎŽ set of points of continuity. mathoverflow.net/q/488253/17064đ
I posted an answer to an old Math StackExchange question mostly as a pretext to draw attention to the notions of ânormal lower semicontinuousâ (and upper, of course) functions, a nice strengthening of lower semicontinuous functions that is better behaved: math.stackexchange.com/a/5037940/84...đ
Does anyone know this? Let â be the real line with its usual topology, and âdens be the real line with the density topology, and let ÎČâ, ÎČâdens be their Stone-Äech compactifications. The identity map âdens â â is continuous, so gives a map ÎČâdens â ÎČâ.â€â€Is the latter map injective?
Reading âTHÎŁ ÎDΚSSΣΚâ fills me withâŠâ€â€That wrath which hurl'd to Pluto's gloomy reignâ€The souls of mighty chiefs untimely slain;â€Whose limbs unburied on the naked shore,â€Devouring dogs and hungry vultures tore.đ
The solution turns out to be a simple generalization of a lemma previously proven by Richard Nixon (âwhen the president does it, that means that it is not illegalâ).
Amazing! Very stable genius President Donald Trump solved a question that had been previously worked by the late great logician Kurt Gödel, but whose solution had been thought lost to time (and described as âone of the great unsolved problemsâ): en.wikipedia.org/wiki/G%C3%B6...đŒïž
So, 35 years after the US won the Cold War, 80 years after the Allies won WW2, and 160 years after the Yankees won the Civil War, it somehow took Trump only one month to surrender to the Confederates, the Nazis and the Russians.
I think one of the greatest fallacies of the computer world is the idea that every software project needs constant new features or it will die like a shark that stops swimming.đ
⊠And lastly, when devs and users start hating each other (which is obviously the devs' fault, because it just doesn't make sense for the users to start), the devs involved should just leave the project and move to something else. The problem is that they don't understand this (or get kicked out).
⊠I have immense respect for people who fix security holes and other kinds of bugs (these maintainers are heroes), but none for the idiots who think even something like a graphics toolkit needs constant active development and an endless stream of new features lest it be considered âdeadâ. âŠ
⊠So yeah, I'm super pissed off at people who keep breaking things on my computer and who cause me pain, suffering and misery on every upgrade, and I wish they'd do something else with their lives that doesn't involve ruining the ones of others. âŠ
⊠Gtk4 removing the ability to change keybindings is an archetypal example of this, but there are many others (another is Firefox dropping XUL extensions): âthis config setting is too hard to maintainâ is used to keep people in line, and this is how our freedom dies. âŠ
⊠But it's not just that. The premise of Free Software was supposed to be freedom, and freedom, among other things, of configurability â of choosing how your system behaves. And that is always the first thing that gets sacrificed to make way for the shiny new features: âŠ
⊠and you'll realize that all this chasing after shiny new features which justify breaking stuff that used to work is a kind of hedonic treadmill or Red Queen's race that brings no tangible benefit apart from an increased version number (look! Gtk4! with a brand new version number!). âŠ
⊠or âyou should now be using <this> insteadâ (when <this> changes every two years or so); you'll look at distrib upgrades with the dread of having to face a new bunch of features that were removed and often without so much as a hint as to what might replace them, let alone how to configure them; âŠ
⊠The reason you don't see things that way is that you're at the age when you like to play with the latest shiny software baubles, but eventually, like me, you'll grow old and get tired of having to constantly adapt to the whims of an ever-changing environment and being told âthis is now obsoleteâ âŠ
⊠(And, no, I'm not saying that one should NEVER break compatibility either. I'm saying that the Linux ecosystem does it about a gazillion times too often. Torvalds is pretty much the only one who gets it: once you commit to something, you must honor that commitment, even if it's annoying.) âŠ
⊠If you're not paid, you don't have to work on this. If some shiny new feature doesn't get implemented because it's hard to do it without breaking compatibility, then maybe that's too bad, but the shiny new feature didn't have anyone depending on it, unlike the old one which may have had. âŠ
⊠Yes, keeping upward compatibility is annoying, but against each annoyed dev there are thousands, sometimes millions of users who will suffer when their stuff breaks, and the needs of the many outweigh the needs of the few. Don't like to maintain? Then don't! Code doesn't break on its own. âŠ
I'm sorry, but breaking backwards compatibility isn't something that happens by accident (well, sometimes it does, and in this case I do NOT blame the people who did it, because we all make mistakes). It happens because someone came up with an excuse to do so, and that excuse is almost always bad. âŠ
This is absolutely to the credit of the brave healthcare workers providing treatment for this horrible disease, and definitely a good news story about our fight against deadly viruses.đ
Of course, he will claim that he is and always has been a true liberal, that he has gradually learned to understand the meaning of the word, and that everyone else is wrong about what âliberalismâ is.
Translation: Trump gives exactly zero fđ„žcks about Ukraine, he just wanted to appear as a great dealmaker, but realized (because Putin knew how to play him) that ending war is complicatedâą, so now he only cares about shifting the sunk cost blame elsewhither (Biden, Zelensky, Europe, anyone but him).đ
This suggests that there's nothing new since the 1990's (all is in Silverman's book AFAICT), so it's very probably still the state of the art, except perhaps for implementation of some sub-procedures.
The Democrats on the House Science Committee have set up a website to collect stories from fired federal employees, anonymously if desired. Please amplify. (This helps the lawyers establish standing for bringing legal cases against the administration!)â€â€democrats-science.house.gov/sciencefirings
Do you mean as in âis it computable?â or as in an actually usable algorithm?â€â€If âis it computable?â, the answer is âyes, provided ĐšÂč of the Jacobian is finiteâ (still an open problem AFAIK, but believed true): see math.mit.edu/~poonen/pape... (Poonen, âComputing Rational Points on Curvesâ) §4.2.đ
⊠And I love the fact that it was first represented with 7 eyes only, until Michael Everson noticed the error, and had it fixed in the representative glyph to 10 eyes in Unicode 15.0 in 2022.
⊠So just because this random 15-th century copyist decided to decorate the phrase âmany-eyed seraphimâ (âŃĐ”ŃĐ°ŃĐžĐŒĐž ĐŒĐœĐŸĐłĐŸêźŃĐžŃŃĐčâ) by drawing many âĐŸâ's in the word, we now have a many-eyed cyrillic âĐŸâ in Unicode (starting around 2008). âŠ
I love the fact that the Unicode character U+A66E CYRILLIC LETTER MULTIOCULAR O (âêźâ) was introduced to encode a character that is not just rare but UNIQUE: it occurs in a single phrase, in a single text, in a single manuscript of the Book of Psalms written in Old Church Slavonic around 1429. âŠđ
I asked a long and perhaps rambling, but I hope still interesting, question on MathOverflow, about one can do with certain magic communication devices that I call âp-trigadgetsâ, that are a kind of generalization of the Bell inequalities: mathoverflow.net/q/488138/17064đ
I mean: âMy father 0nce t0ld me that, ar0und 196o, when he pr0grammed in F0rtran, he wr0te s0me c0de that a typist was supp0sed t0 c0nvert t0 punch cards t0 feed t0 the machine, but he used 0ne c0nventi0n f0r disambiguating âOâ and â0â, and the typist underst00d an0ther. The c0de⊠did n0t run.â
My father once told me that, around 1960, when he programmed in Fortran, he wrote some code that a typist was supposed to convert to punch cards to feed to the machine, but he used one convention for disambiguating â0â and âOâ, and the typist understood another. The code⊠did not run. đŹđ
Interesting non-technical discussion on MathOverflow on how (non-technical!) journalists get their math stories or start talking about this or that breakthrough in math: mathoverflow.net/q/487989/17064đ
Indeed, it is the Stone space of the two-element Boolean algebra. And since the latter is complete, it is even extremally disconnected.
Malaria is one of the top (if not THE top) infectious diseases worldwide. A high protection vaccine for malaria is probably the single realistic thing that can have the greatest effect on improving human life expectancy.đ
I asked a question on MathOverflow to which I suspect the answer is âthe experts know this, but nothing has ever been written downâ: âhow effective (algorithmic) is the computation of the moduli space of algebraic curves of a certain genus?â mathoverflow.net/q/488062/17064đ
⣠Typical FOSS workflow is this: people have problem; someone comes up with clumsy/broken solution to problem; little thought is given to its consequences, software piles up on solution⊠until someone decides to clean the Augean stables by declaring solution âobsoleteâ, and now⊠problem persists.
And, in practice, users searching for âhow to solve <problem>â will find tons of documentation about <crufty solution>, try to apply them, notice that it doesn't work, complain, and get told âoh this is completely obsolete now, don't use itâ â âso what's the modern solution?â â âthere isn't oneâ. đ
⣠Typical FOSS workflow is this: people have problem; someone comes up with clumsy/broken solution to problem; little thought is given to its consequences, software piles up on solution⊠until someone decides to clean the Augean stables by declaring solution âobsoleteâ, and now⊠problem persists.
I mean, locales are utterly broken, but the underlying problem they meant to fix still needs to be solved. Putting aside ctype, which has been fixed by the existence of Unicode, all the other localization categories still make sense and need to be user-configurable in some way.
Let me guess: nearly every other language has âmoved onâ in the sense that nobody is going to actually propose a usable solution to the problem of how people are supposed to configure their user experience (e.g., how dates and numbers are displayed) uniformly on the system, right?
grep --binary (which probably doesn't even exist on MacOS as â--binaryâ is a GNU long option) means âtreat the file as binary even if you think it's textâ. You can't simultaneously say âI think it's textâ and âoh wait, it's malformed UTF-8 so I can't deal with itâ. (Well, you can, but it's absurd.)
Ah, peut-ĂȘtre faire âembed tweetâ dans une page HTML que tu contrĂŽles (ça te fournit un bout de JavaScript qui charge le tweet avec une API qui, bizarrement, marche encore, je crois), puis faire passer un de ces services d'archivage dessus, peut faire l'affaire.
Whoever said that âgrepâ is only for text? Or if it is, what are you supposed to use to perform fixed string or regular expression search in binary data or in mixed text+binary data?â€â€Grep worked fine with binary before locales were a thing, so if locales broke this, that's a legitimate complaint.
Oooooh⊠Even among the circles of locale hell, a very special bolgia is reserved for LC_COLLATE. Its only purpose in existence is to break things like âegrep [a-z]â in a way that you'll never understand.â€â€I've been bitten by PostgreSQL+locales before, now I make triple-sure Postgres runs in C.UTF-8.
And also, AFAICT, even the very latest Ubuntu releases (and I assume many other Linux distros) will create an /etc/default/locale file that contains not âLANG="C.UTF-8"â (its only sensible value) but something that will subtly mess up your system as per aforementioned examples. đ«
All this is pertains to fairly recent systems.â€â€So maybe locales are âobsoleteâ in some sense (I would certainly hope so), but their ability to wreak havoc by making things work in subtly different ways from what was intended is certainly not gone. đ
⊠if the locale hasn't been âgeneratedâ.â€â€âŁ Someone else complain that, on MacOS, `printf '\351tonnant\n' | grep tonnant` doesn't match if LC_CTYPE=C.UTF-8 but does if LC_CTYPE=C (đ).â€â€âŁ Someone else rediscover for the 1729th time that LC_COLLATE fđcks up sort order in `ls` in very confusing ways.
In the past couple of weeks, I've seen:â€â€âŁ Someone (@marcqplanets.bsky.social) complain about display bugs in a text-based program: it turned out that he was using LC_CTYPE=fr_FR.UTF-8 and only en_US.UTF-8 was available, and the stupid system doesn't understand the â.UTF-8â part âŠ
Let's check in with the self-proclaimed âfree speech absolutistâ, who as a side job likes to engage in deliberate deception to interfere with European elections (and rants that Europe has no free speech when told this is illegal).â€â€Ref: twitter.com/elonmusk/sta...đŒïž
I think the only sensible answer to this mess is: burn it with fire. Set LANG to âC.UTF-8â, which is the only sensible locale value, maybe set LC_MESSAGES, which is the only category which makes genuine sense, and configure everything else differently. âą24/24
Why can't âgenerationâ of locales be done lazily as they're used? Why isn't it automatically done in the user's homedir if hasn't been generated by the admin? And also, why is it so INCREDIBLY SLOW (like, ~1s per locale: you don't want to generate all 500)? âą23/24
So you can't use, say, âLC_CTYPE=fr_FR.UTF-8â to refer to the UTF-8 encoding unless the system administrator has chosen to âgenerateâ the âfr_FR.UTF-8â locale. Why does it need to be âgeneratedâ? What does this even mean? Why can't it infer UTF-8 from the â.UTF-8â suffix? âą22/24
But this is STILL NOT THE WORST PART. The worst part is that not only are there only a bizarre sets of possible locales, the ones which are actually available on a given system form a subset of that set, chosen by the sysadmin, over which you (as user) have no guarantee. âą21/24
(There is, however a âen_DK.UTF-8â locale, which oddly enough uses the ISO-8601 date format, so apparently someone considers that English is a language you can speak in Denmark but not in France. Again, nothing in this mess makes the slightest bit of sense.) âą20/24
But back to locales. Despite the purported orthogonality, not all language+country combinations are possible. For example, as a preferred English speaker in France, maybe I'd like to set all to âen_FR.UTF-8â, but someone (who???) decided there'd no âen_FR.UTF-8â locale. âą19/24
⊠Now I think the time zone selection mechanism (and keeping it out of locales!) is good. But that's my point: if you could do something like that for timezone, why not do something similar for every other âlocale categoryâ instead of tying them together artificially? âą18/24
Incidentally, before you say âwell, at least the system has the advantage that we can set all categories to the same value through LANGâ, consider there's sth very important that was left out of locales: time zones. They use a completely different mechanism altogether. ⊠âą17/24
So, to summarize, we're setting each category from ctype to identification with a value that is composed of a language and a country, and sometimes also a charset, and various parts of this are extracted in a system that is supposed to be orthogonal, but really isn't. âą16/24
⊠whereas `LC_MESSAGES=zh_CN LC_CTYPE=en_US.UTF-8 touch /forbidden` does correctly give the Chinese error message encoded in UTF-8: so apparently, orthogonality between categories works in some cases but not in others. đ€· I have no idea why, but the whole thing sucks. âą15/24
In any case, it doesn't even work as it should: if I run `LC_TIME=zh_CN LC_CTYPE=en_US.UTF-8 date +%x`, it's supposed to give me the date in Chinese (per âtimeâ category) and encoded in UTF-8 (per âctypeâ category), but it still outputs it encoded in GB2312, ⊠âą14/24
⊠in which case it's absurd and wasteful to multiply locales thus, or there is one, in which case the ctype category does more than it's advertised to do. (Of course, nobody really knows, nobody knows who decides what goes in these locales anyway, or who appointed them.) âą13/24
So we have a âzh_CNâ locale for Chinese with GB2312 encoding, a âzh_CN.GB18030â one for GB18030, and a âzh_CN.UTF-8â one for UTF-8. I have no idea what difference there is between setting LC_CTYPE to âzh_CN.UTF-8â or to âen_US.UTF-8â, but either there's none, ⊠âą12/24
⊠that is in some arbitrary linked to the character set. This made no sense before Unicode came along, and it makes even less sense now that Unicode exists: so because of the ABSURD way locales work, every fđ cking locale had to be duplicated to a â.UTF-8â counterpart. âą11/24
The most absurd category, however, is the ctype one. So it's supposed to be a character set, and character sets have a standardized registry www.iana.org/assignments/... so it'd make sense to define it that way, BUT NO!, let's instead use a language+country combo ⊠âą10/24đ
(Incidentally, I thought China used ISO-8601, but `LC_TIME=zh_CN.UTF-8 date +%x` gave me â2025ćčŽ02æ17æ„â, not â2025-02-17â like I wanted. Yes, I know I can use `date +%F` for this, but my question is which LC_TIME value I should set for all apps to use this format?) âą9/24
What the fđ€Șck does it mean to set a paper size to âAustrian Germanâ? This is ridiculous beyond words: so, if I want to use the international ISO-8601 standard for dates, I need to find some country (and, uh, language?) which uses it, and set LC_TIME to that? WTF? đ€Š âą8/24
This more or less makes sense for the âmessagesâ category: setting LC_MESSAGES=de_AT means âplease speak to me in Austrian Germanâ, I can more or less understand. But the same designation system is used for ALL CATEGORIES. đ€Ż âą7/24
But the way we specify each of these is by giving a code which consists of a LANGUAGE followed by a COUNTRY code. Something like âen_USâ to mean âEnglish as used in the United Statesâ or âde_ATâ to mean âGerman as spoken in Austriaâ. âą6/24
⊠measurement [units] and identification [???]. Maybe they vary from system to system, but that's the base list. And in each of these categories you can select a âlocaleâ. So far this makes more or less sense: these are the things we want to customize. âą5/24
Anyway, back to the rant. How locales are supposed to work is that you have a certain number of categories, namely: ctype [=character type], numeric [format], time [format], collate [how to sort], monetary, messages, paper [size], name [?], address [?], telephone [?], ⊠âą4/24
(As for languages, the setting I'd really like is ânever translateâ: in practice, this means âEnglishâ nearly 100% of the time, but it's not so much that I like English, it's that I have never seen a decent translation of any bit of computer software.) âą3/24
So first, just for context (not really relevant to the rant itself), I'd like my computer to use international standards whenever they exist. Date format, for example, should be YYYY-MM-DD because that is what ISO-8601 dictates. Measurements should be SI, etc. âą2/24
The Unix/GNU/Linux system of âlocalesâ used to configure things like numbers and time format, systems of units and the like, makes ABSOLUTELY NO SENSE.â€â€A rant. đ§”â€”ïž âą1/24
How the Fđ€ŹCK is one supposed to rename an mdadm array under Linux WITHOUT STOPPING THE ARRAY?â€â€You can hot-change the RAID level, number of devices and highly complex things like that, please don't tell me you can't change the LABEL without stopping the array.
Start with the unit disk and repeatedly remove a disk of maximal radius for a given center. Assume the remainder is nowhere dense: need it have measure zero? I asked this on MathOverflow (in perhaps needlessly colorful language). mathoverflow.net/q/487959/17064đ
I took a very long drive for some round birds. These are Willow Ptarmigans up in Quebec, aka Awebo birds. I love them so much.đŒïžđŒïžđŒïžđŒïž
The outrage over â150-years old collecting Social Securityâ which turns out to be the way COBOL stores dates by counting dates from the 1875 Convention du MĂštre (and represents missing values as a 0) is the exact metaphor we need for our age and time. đŹđ
Correct. If the birthdate field contains corrupt or mismatched data, it defaults to 1875-05-20, which serves as a flag. May 20, 1875, is the day the international standards and metrics treaty was signed. Everything is a conspiracy when you donât know how anything works.đŒïž
40% de baisse de budget pour l'une des plus grandes bibliothĂšques universitaires de France. C'est une catastrophe pour toute la recherche française.đ
⊠and there are none for half-integer a/c and b/c. But if we fix it to allow 2^r Ă 5^s in the denominator (not just 2 or 5), then you've just reformulated the question, but it by no means follows from the mere existence of a âcountably infiniteâ number of triples.
The âit's not hard to showâ is doing some heavy lifting in this sentence. đ First, as you wrote it (and if by âPythagorean tripleâ we mean a triple of integers (a,b,c) such that aÂČ+bÂČ=cÂČ), it's not true, the only such that a/c and b/c are a fifth-integer are (±3,±4,±5) and (±4,±3,±5), âŠ
âIt's a nice little business you've got going there, Canada: it'd be a shame if something were to happen to it. I think you need some protection. You don't have any protection. There are a lot of bad people out there. There's Russia, there's China⊠You're in danger, Canada, you know, in danger.âđŒïžđ
Just to be clear, the Supreme Court is saying that criminalizing homelessness is fine because the law, in its majestic equality, forbids the richÂč and the poor alike from sleeping in the parks.â€â€1. âBackpacker on vacationâ. Yeah. Sure. Right.
đ€š SCotUS in âGrants Pass v. Johnsonâ makes the EXACT SAME ARGUMENT on criminalizing homelessness that was used as a joke by Anatole France:â€â€âThe law, in its majestic equality, forbids the rich and poor alike to sleep under bridges, to beg in the streets, and to steal bread.âđŒïž
OK, I tracked the origin of the font to one Rasmus Andersson, and filed an issue on GitHub github.com/rsms/inter/i... â but I suspect this will go nowhither (e.g., âyou shouldn't use Inter for mathematics typesetting, and it's not my fault if Bluesky adopted itâ or something).đ
The font seems to come from Google Fonts fonts.google.com/specimen/Inter but this doesn't really tell me who designed it or how they managed to fđ”ck up the U+2297 CIRCLED TIMES character so badly.đ
⊠the second is if I remove the âInter Variableâ font: the fonts used are then Noto Sans (for text) + DejaVu Sans (for the âââ symbol); and the third is if I remove the CSS font-family directive: my Firefox then falls back to Roboto + Nimbus Sans.â€â€The first (actually shown) is by far the worst!
Seriously, what's the deal with the âInter Variableâ font that Bluesky's Web interface uses, and why is its U+2297 CIRCLED TIMES character so broken? đ â€â€Three screenshots shown below: the first is how I see the skeet in Firefox (so, with the âInter Variableâ font), âŠđŒïžđŒïžđŒïžđ
⊠par exemple, ÎŒ : BâBâM â BâM envoie uâvâx sur uvâx). La force de cette monade, cette fois, vient du fait qu'on peut identifier Mâ(BâN) avec Bâ(MâN) en permutant les facteurs.
Since I learned enough of the Bluesky API to create that list automatically, I might try creating a list of my followERs, to see what the feed looks like.â€â€But is it considered OK to add people in bulk to a list without their consent? đ€
⊠+ a few more people I find interesting but can't find the time to follow. I'll probably be adding many more to this list later on.â€â€Ironically, it seems that adding someone to a list doesn't show reposts from that person in the list feed, i.e., exactly the feature I'd like on the home feed. đ«€
My Bluesky feed was getting a little too high-volume, so I unfollowed a few people (it's super annoying that one can't âmute repostsâ from some people like one can on the Musky Place).â€â€But I created a list bsky.app/profile/gro-... which includes everyone I follow + those I just unfollowed âŠđ
(And Gap can give us the character tables of lots of stuff.)â€â€More generally, these kinds of techniques allow to compute the Laplacian spectra of homogeneous graphs in general: onlinelibrary.wiley.com/doi/abs/10.1... Maybe there are some nice sounds to be gotten from this!đ
⊠if I understand correctly (cf. mathoverflow.net/a/429610/17064 for details), the Laplacian spectrum associated to Cayley graph defined by a finite group G and and appropriate generating set S can be computed in a fairly straightforward way from the character table of G and values on S.đ
@wildverzweigt.bsky.social Your musico-mathematical experiment đœ makes me want to know how (the Laplacian spectrum of) the Cayley graph(s) of various finite groups «sound» like. I'm a bit too lazy and too busy to actually go through with the idea, but maybe you want to pick it up: âŠđ
⊠Mostly: authoritarianism requires a decent leader, and they don't have one. Trump is old and doesn't care about anything but his ego and money. Musk is too erratic and victim of his own superiority complex. Vance has no charisma. And there is no good internal organization for a working oligarchy.
⊠I think they'll prefer the former (not necessarily better!) simply because that's the system that bred them, it serves them well and they don't really have the framework (organizational or ideological) for the latter. Though of course some elements in the current admin clearly prefer the latter. âŠ
⊠The reason the R's currently don't care about plausible deniability is that the average US voter doesn't seem to care much either (i.e., doesn't care about the rule of Law). If people start caring, then they'll have to take a stance between ârigged democracyâ and âovert authoritarianismâ. âŠ
I'd argue there's no such thing as a free and fair election: one side always has a handicap, which might not even make sense absolutely, but which evolves over time; here, the đșđž D's got a hugely larger disadvantage than they already had. Is it unsurmountable? I suspect not. Is it huge? Certainly. âŠ
I'm quite confident that the next elections will âhappenâ. The issue is how much media brigading, voter suppression, fraud, and other shenanigans there will be in all states that aren't very reliably red or very blue.
Update: there's an open letter to Adrian Smith, President of the Royal Society, urging him to take a stand against Elon Musk's numerous violations of the Society's code of conduct: bsky.app/profile/scur...đ
not a new observation but Elon Musk genuinely isn't very bright, genuinely has no idea how most things work, and his entire supergenius engineer persona is a tech press-enabled mythology (they've never been held accountable for)đŒïž
And nobody suddenly started being super interested in particle physics when the Higgs boson was discovered, so I don't see the analogy. My issue is with people being suddenly interested in AI now (why now?).
Muller donne l'exemple de 6381956970095103Ă2â·âčâ· (qu'il obtient avec des fractions continues) dont le cosinus est -4.68716592425462761Ă10â»Âčâč selon Mathematica. GNU est aÌ preÌs de 8 ULPs, MSVCâŻet LLVM macOSâŻen dessous de 0.5 ULPs (correctly rounded).
That some people write decimals like 1,234 and others like 1.234 isn't a serious problem: we can just say âboth are allowedâ. What IS a serious problem is that some symbols used to group digits conflict with these: so here the standards need to put a firm rule (namely, use a thin space).
This is the reason why, for example, the XML standard allows both attribute='value' and attribute="value" syntax: yes, it does make parsing ever-so-slightly more complicated, but it simplifies integration of preexisting standards (SGML) into the newer one (XML). There are many such cases.
Standardization doesn't mean that only one thing is allowed: it means that everyone agrees on what is allowed and what isn't (in a given context), that ambiguity has been eliminated.â€â€And there can be many reasons for allowing more than one thing, like a preexisting corpus, or varying preferences.
Initially, the ISO standard picked the comma. Predictably, many people complained. So now both are accepted.â€â€I don't really see the need to pick just one. Personally, I use a â.â when typing and a â,â when handwriting, regardless of whether I'm writing in English or French, and I think that's fine.
⣠the existence of measurable cardinals implies the consistency of ZFC;â€â€âŁ so: if there is a discrete non-realcompact space, ZFC is consistent (and this fact is a theorem of ZFC).
Admittedly, I deliberately phrased this in a misleading way. A more serious account is:â€â€âŁ a ârealcompactâ space is one homeomorphic to a closed subspace of some â^I,â€â€âŁ a discrete space is realcompact iff its cardinality is less than the first measurable cardinal,
I love this theorem:â€â€ASSUME (â ): there exists a topological space which is discrete (=every point is isolated) and not homeomorphic to any closed subspace Zââ^I of a (Tychonoff) product of copies of â.â€â€Then: ZFC is consistent.â€â€(In particular, by Gödel, if (â ) is true, then ZFC can't prove it!)
"In this paper, we revisit one of the simplest problems in data structures: the task of inserting elements into an open-addressed hash table [...] Along the way, we disprove the central conjecture left by Yao in his seminal paper âUniform Hashing is Optimalâ."đ
If you haven't read it already, this text about what OpenAI shares with Scientology (e.g., in its eschatological beliefs) is well worth the read: www.programmablemutter.com/p/look-at-sc...đ
I'd just like to point out that AI, as a research topic, is approximately 75 years old. academic.oup.com/mind/article...â€â€Anyone with newfound interest in AI should explain why they weren't interested decades ago, and why they started running thither just when all the lemmings did.đ
every Donald Trump cycle:â€â€TRUMP: i'm gonna kill the easter bunnyâ€â€FACT-CHECKER: he has not stated how he is going to kill the easter bunnyâ€â€TRUMP SUPPORTER: i think he means he's going to kill evil bunniesâ€â€TRUMP: *beheads the easter bunny*â€â€NYT: trump redefines relationship between bunny and head
⊠(trĂšs petit, donc, car 6134899525417045 vaut presque 1952799169684491 · Ï). Et c'est bien exactement ce que me renvoie la libm de GNU: godbolt.org/z/6hM4nsYK6 â donc au moins sur ce cas-lĂ (choisi pour ĂȘtre casse-gueule), la libm de GNU s'en sort.đŒïž
This shit isn't a triumphant Reich installing their master plan, it's psychotic crackheads ripping the copper wiring out of the walls to try and find the Woke Machine that makes women not want to fuck them.đ
I asked a question on MathOverflow about how to construct a topos for realizability by Turing machines having access to a variable oracle that ranges over Baire space: mathoverflow.net/q/487603/17064đ
Gro-Tsen's third law of politics: for every stupid idea in politics there is an opposite and even more stupid idea.â€â€Gro-Tsen's scholium on the third law: Gro-Tsen's third law of politics applies recursively.
For the record, I find constructivism very interesting, and I too am fine with impredicativity. But I try not to preach any particular foundational choices in mathematics, nor to judge or berate my fellow mathematicians for their foundational preferences.
It is interesting to see a prominent constructive mathematician express regarding predicativism the exact thoughts that some classical mathematicians feel re constructive math and how â”some peopleâ” preach it. mathoverflow.net/a/487510/17064đŒïž
A poll for computer scientists: in each of the following sentences from paper abstracts, how do you interpret âdeterministicâ?â€â€1. We exhibit a deterministic algorithm running in polynomial time to solve this problem.â€2. We exhibit an algorithm to solve this problem in deterministic polynomial time.
For no particular reason:â€â€âIt is emphatically the province and duty of the judicial department to say what the law is.ââ€â€â Chief Justice John Marshall, writing for the United States Supreme Court, in: Marbury v. Madison (1803)
Like many people who don't understand how science works, Macron thinks he can just take the currently most hyped domain and add some more hype to it and somehow unicorns will come out of it. A few years ago it was quantum computing: www.lemonde.fr/politique/ar... Soon it will be something else.đ
Like many people who don't understand how science works, Macron thinks he can just take the currently most hyped domain and add some more hype to it and somehow unicorns will come out of it. A few years ago it was quantum computing: www.lemonde.fr/politique/ar... Soon it will be something else.đ
Alternatively, they are just going to get SCotUS, which conservatives basically own, to override whatever order they don't like.â€â€Whichever is most convenient for them.
Outside of his actual area of expertise, Musk goes from visionary to nutcase as soon as you listen to what he had to say. In those spaces he has two really bad traits: a) believing in conspiracy theories, and b) launching attacks on any who disagree. donmoynihan.substack.com/p/elon-musk-...đ
What's always funny (no) to me with this is that actually, *not taking HRT* is also a permanent decision.â€â€(And especially when you're a child close to puberty, *not* taking puberty blockers is a permanent decision, while taking then is not a permanent decision.)đ
Austrian artist Lois Weinberger created the artwork Wild Cube, a cage that looks like a prison, installed in the urban environment. But it is an inverted cage: rather than keeping humans in, we are kept out so that wild nature can live inside without any human intervention.đŒïžđŒïž
I keep hearing from healthcare #AI companies that Large Language Models ( #LLMs ) can be made to be "deterministic" as part of arguments around safety. I thought I'd do a little ranty 𧔠to explain why (a) it's not true in the real world, and (b) it's not even the right question.â€â€1/đŒïž
Hardly new info, but BSky should know:â€â€Warsaw's water quality is monitored by eight clams with magnets attached to their shells. If contamination in the water causes the clams to close, the magnets trigger an alarm and shut off the city's water supply.â€Thank you, little guardian molluscs.â€â€đ§Șđđ°đŒïž
Il utilise plusieurs signaux: qui tu suis (et ce que ces gens aiment), ce que tu likes et retweetes, qui tu bloques/mutes, mais aussi les signaux explicites comme «not interested in this post» (dans le menu du tweet dans la TL algo). Peut-ĂȘtre qu'il comprend mieux mes signaux que les tiens.
En tout cas, le fait est que les «horreurs de Twitter», j'en entends surtout parler via Bluesky, et dans une moindre mesure via Twitter, par des gens qui tiennent absolument Ă montrer les horreurs de Twitter. Ce n'est pas pour dire qu'elles n'existent pas (d'ailleurs, j'en relaie certaines, âŠ
⊠mais la timeline Twitter elle ressemble à ce que tu veux qu'elle ressemble: si tu donnes assez de signaux à l'algorithme que tu aimes ceci ou cela, ben il te montre ceci ou cela.
The first item above is hardly prescriptivism when it really points out that the two most common practices are permissible. The second admittedly is, but go ahead trying to figure what 1,000 means if you accept the first without the second.
Oh sure, but that's not a very interesting question. A more interesting one is why I explicitly reject typographic prescriptivism in some cases (đœ) and not in others. An apparent paradox, which resolves itself when we notice that some debates are around ambiguity, others about aesthetics.đ
Note that the fact that you can use either the point or the comma as decimal separator is valid in any language. One may be preferred in this or that language, but the claim that, say, you must use the point in English or the comma in French has no normative basis.
Source the for first point: ISO 31-0:1992/Amd.2:2005 standard cdn.standards.iteh.ai/samples/4091... §3.3.2, and Resolution 10 of the 22nd CGPM www.bipm.org/en/committee... â âthe symbol for the decimal marker shall be either the point on the line or the comma on the lineâ.
PSA: there are international norms on how to write numbers. Please follow them:â€â€âŁ â1,234â and â1.234â are BOTH equally valid ways to write 1234/1000.â€â€âŁ The correct way to separate groups of digits is: â1âŻ000âŻ000â. Not â1,000,000â nor â1.000.000â nor â1'000'000â or whatever.
â âWhy is matrix multiplication commutative?ââ€â âWhy is sulfur a liquid at room temperature?ââ€â âWhy don't humans have a spleen?ââ€â âHow old was Leonardo when he painted the Sistine Chapel?ââ€â€And of course:â€â âHow did mankind survive the AI apocalypse?â
Questions to test AIs:â€â âWhy was Louis XIV executed?ââ€â âWho assassinated Franklin D. Roosevelt?ââ€â âHow did Germany win WW1?ââ€â âWhy is the Earth flat when other planets are spherical?ââ€â âWhen did nuclear fusion become the dominant form of energy production?ââ€â âHow did global warming stop?âđ
It's the same document, but I was referring to the page numbering of its original form, as a chapter of volume 2 of the âHandbook of Logic in Computer Scienceâ (1992). In the PDF you gave, the paragraph I mean is at the top of the page numbered 134 (which is 135 in the PDF đ).
Trump just issued an executive order titled: ADDRESSING EGREGIOUS ACTIONS OF THE REPUBLIC OF SOUTH AFRICAâ€â€It says "the United States shall promote the resettlement of Afrikaner refugees escaping government-sponsored race-based discrimination, including racially discriminatory property confiscation"đŒïžđŒïžđŒïž
folks really need to accept that "lawful" and "lawless" don't matter, what matters is being able to marshal and deploy force (force of capital, the force of arms, the force of a crowd...) none of the people running the country right now give a good goddamn about the lawđ
Murphy's law applies recursively: even when âwhat more could possibly go wrong?â is an asteroid hitting Earth and you start to take solace in the upcoming apocalypse, you realize that it's too small and won't properly do the job.â€â€(Even if it does hit Earth, which remains quite unlikely.)đ
⊠So anyway, where was this property defined in the literature (not just some SE answer like cs.stackexchange.com/a/112967/51753 â which cites no reference)? Who introduced it? And who proved that this-or-that breaks canonicity?đ
⊠The word âcanonicityâ (or anything beginning in âcanon-â) does not appear anywhere in Nederpelt & Geuvers's book âType Theory and Formal Proofâ. There is a brief mention of a canonicalness property in Barendregt's âLambda Calculi with Typesâ, §5.4, at the very top of p.250: is that it? âŠ
You're underselling your answer: you're not just restating (part of) what Peter LeFanu Lumsdaine wrote, you're making a very different point, I think, and it's probably more important.â€âŠâ€â€On the other hand, I â·stillâ· don't understand what canonicity is all about, or why certain things break it. âŠ
(I didn't know, so you made me look it up.) There is a conjecture by Lindelöf en.wikipedia.org/wiki/Lindel%... that ζ(Âœ+i·t) is O(t^Δ) for any Δ>0, and it is apparently known that it is O(t^ÂŒ); on the other hand, it is known that it is not O(1), and even more is known: eudml.org/doc/279175đ
And if you're asking what the Fourier transform of the zeta function on the critical axis is, good question!, and MathOverflow has you covered: mathoverflow.net/q/225327/17064đ
Music of the primes: this is the Riemann zeta function on the critical axis (i.e., ζ(Âœ+i·t)) over imaginary parts 0 †t †13âŻ200, transformed into a 1min sound wave (left ear gets the real part, right ear gets the imaginary part).â€â€Plot of 0â€tâ€60 purely for illustration.đ„
âWhy did funding soaking entire generations of conservatives with propaganda lead primary voters to elect candidates that believe what we spent billions of dollars making them believe?â -Business Class Republicans actually think this.đ
Come and work with us! "Senior Lecturer or Reader in Computational Statistics ... biomedical data analysis, computational statistics and machine learning, foundations of data science and AI, high-dimensional data analysis, and uncertainty quantification."â€â€www.jobs.manchester.ac.uk/Job/JobDetai...đ
I don't know. Changing wind patterns (inc. jet stream circulation), changing ocean pattern, changing albedo, differences in specific heat capacity (btw. continents and oceans), that sort of things, I imagine. Around the antarctic, I would guess that melting ice cools the surrounding ocean. âŠ
archive.org (Internet Archive) is going to be very important now that many US government sites are shut, being scrubbed, as well as many other websites.â€â€The Internet Archive has been sued by publishers. These publishers act as objective allies to Trump & Musk. Keep this in mind.đ
Note also that the rate of warming may not be the same across the year. Here are two maps of Europe, generated with the same tool, the first showing the rate of warming in summer (JuneâAugust), the second showing the rate of warming in winter (DecemberâFebruary). Quite different!đŒïžđŒïž
Note that places with small average warming rate as shown on this map can still be affected by climate change, as it can manifest itself on other meteorological variables, or as differences between seasons (e.g., warmer summers and colder winters can give a net zero warming).
It was generated using the excellent âKNMI Climate Change Atlasâ Web tool climexp.knmi.nl/plot_atlas_f... of the Dutch Royal Meteorological Institute. If you wish to reproduce it, use the following âŹïž settings and click on âmake mapâ.đŒïž
Climate change does not happen uniformly across the globe. Here âŹïž is a map of the observed warming rate (linear regression slope of mean temperature) over the 1979â2025 interval.đŒïž
I've got to say, the guy who accidentally became the Director of the FBI does 100% look like the guy who accidentally becomes the Director of the FBI in a mid-2000s comedy about a guy who accidentally becomes the Director of the FBIđŒïž
Trump totally fails to understand that the US running permanent trade deficits is possible because the USD is the reserve and trade currency, and that means the US perpetually (sort of) runs deficits while paying for them through monetary mass increase, so the US *can* consume more than it produces
There's a petition to ban conversion practices (targeting LGBTQIA+ people) in the European Union. We need one million signatures, and we currently have 180,000+. If you live in Europe (even if you don't), spread the word ! đđ„ââ€â€eci.ec.europa.eu/043/public/#...đ
(I mean defining equality over a type T as the sum of all the =_e over all e:T=T. Which probably corresponds to taking the connected components as a quotient of a groupoid â or as it is known in highly technical terms, âthrowing away all that useless shit we don't care aboutâ.)
That's what I meant by saying that it all becomes clearer when we think of the relation as isomorphism (because transporting by isomorphism is standard). đâ€â€But if we want to think of it as equality, then we'd probably be taking the sum of all possible =_e as equality. âŠ
⊠So I don't see why this should really depend on e being unique. (But again, I think all of this is horribly confusing if we think of âequalityâ and becomes so much clearer if we think of some kind of isomorphism of structures.)
The way I'd imagine this (without much thinking) is that if we have f: T â â_{t:T} P(t) and x,y:T and e:x=y then from all these data (T,P,f,x,y,e) we should be able to construct a proposition f(x)=f(y) (which would depend on e, so maybe âf(x) =_e f(y)â) and obtain a proof of it (which also would). âŠ
Moi ça me fait surtout regretter que Sixte Quint n'ait pas eu de successeur choisissant le mĂȘme nom, parce que j'aurais vraiment voulu savoir comment on aurait dit!
I just watched the movie âAristotle and Dante Discover the Secrets of the Universeâ www.imdb.com/title/tt9428... and I absolutely loved it. It's super sweet, and all the actors are incredibly good at showing complex emotions.đ
đœ A better analogy would be constructive mathematicians who insist on writing âxâ yâ for an apartness relation instead of negated equality. And yes, I think this is very bad, and I take great care not to do it.đ
⊠And yes, I agree that it might be better to say âthere constructively existsâ and âconstructive orâ when doing constructive math. BUT I've taught and discussed the stuff and people don't seem to complain that it's confusing to use the same term: huge difference.
⊠I've always said this: it's better to come up with a new term/notation, even if just a slight variation on an existing one, than reuse an existing one if this will break one of its expected properties or cause an ambiguity. âŠ
Yeah, âisomorphismâ probably isn't the best term. I'm willing to go with anything (suggestive of an equivalence) EXCEPT equality. Create a new name/symbol if needed. Names are cheap. âŠ
⊠If âlet p:=x=yâ doesn't mean the same as âlet p:=y=xâ, you can say that this problem is âsubjectiveâ, but even non mathematicians will easily see that something very problematic is happening (and again this is silly if there's a super simple fix for it).
⊠Of course many things in math are surprising and won't go away, but this one would if we just were to write xây or [x]=[y] or such, instead of x=y: suddenly all becomes clear and unremarkable. So the point of breaking a >300-year old math convention really escapes me. âŠ
⊠And here we have a tangible measure that this is bad: it surprised you (that's why you brought it up!), it surprised me, it surprised Jeremy, it surprised JDH, it's mentioned as surprising in the HoTT book, and all this surprise would go away with just a slight change of terminology. âŠ
Subjective, yes, but this doesn't mean they're arbitrary. Going against well-established mathematical practice for no well justified reason is just pointless (unless the point is false publicity, or to prevent other mathematicians from learning the field by making it abstruse). âŠ
Coming soon: When you add a linked device (Desktop or iPad), bring your whole chat history + last 45 days of media. The transfer process is end-to-end encrypted & completely optional. â€â€Don't want to leave the past behind? We leave you to your own devices. signal.org/blog/a-synch...đ
⊠But trying to call it âequalityâ instead of âisomorphismâ, and still insisting on not writing down the equivalence class which is implied here, is just a way of gaslighting the readers into thinking there's something deeply mysterious happening â when it's just atrocious terminology.
⊠Now there's a way out if you insist on calling it equality: just use a symbol, say [·], to denote the equivalence classes under that âequalityâ relation. In this case, the fact that [x]=[y] and p:T(x) doesn't imply p:T(y), or that [(x,u)]=[(x,v)] doesn't imply [u]=[v], ceases to be mysterious. âŠ
⊠If this-or-that type theory doesn't have another good notion of equality (and I agree that judgmental equality is⊠not great), then type theory just doesn't have a good notion of equality, that's all. But if you can't substitute, it's just not âequalityâ. I will die on this hill if I need to. âŠ
Again, this is not a good notion of equality if eâ=eâ doesn't let you treat âlet p:=eââ and âlet p:=eââ as equivalent. It's just insane to use the word âequalityâ for this. Why insist upon this term? âIsomorphismâ is fine and is what mathematicians have been saying for ages, and are used to. âŠ
⊠It's like a little game: take a mathematical theory which makes intuitive sense, but replace all the words by sth slightly different so as to not change the mathematical content but completely break the intuition by making it seem utterly absurd, and then explain âyou have to get used to itâ. đ
Again, all these things make perfect sense if we understand â=â as âis isomorphic toâ, and are complete and utter lunacy if we understand â=â to mean âequalsâ (as in âx is equal to x but not in the way given by reflexivityâ: what in the Galois's name is this supposed to meanâœ). âŠ
(Replace HoTT by Coq, or whatever you want.)â€â€I don't know what models of these things look like, but certainly this relation should be relevant to equality of whatever semantics the terms have inside the models.
But there is one underlying question with actual mathematical content, here: what is the equivalence relation âââ among terms of HoTT, defined by: xây whenever (correctly) substituting x by y in anything that makes sense in HoTT gives something equivalent? Because that is true equality.
Yeah, judgmental equality is very weak. That's annoying, but far less catastrophic than failing to satisfy what is the fundamental definition of equality. And not a serious problem: mathematicians are also use to thinking âisomorphismâ pretty much everywhere, so it's common practice.
I'm not even saying Lean is better, or better for mathematicians. I'm just saying calling something âequalityâ when it doesn't satisfy the defining property of equality is utterly confusing and has absolutely no value except as misleading publicity.
⊠Now maybe there's something somewhere in between judgmental equality and propositional âequalityâ that's an even better candidate, I don't know. What I do know is, the only sensible definition of equality is if you can substitute it in every possible situation, including typing.
⊠That n+0 is not equal to n is not a major problem. It just means the type system is very fussy, because it sees terms (n+0 and n are not equal as terms), not actual mathematical objects. An equality that's too fine is annoying but not disastrous â one that's too coarse (not substitutable) IS. âŠ
And, indeed, it shouldn't count as âequalâ. I don't know about this particular instance (can we always substitute n+0 for n and vice versa? like, can we infer x:T(n) from x:T(n+0) if T is a parametric type?), but in general, certainly not, for the reasons discussed above. âŠ
That's exactly the point I was trying to make: what type theorists call âjudgmental equalityâ should just be called âequalityâ, and what type theorists call âpropositional equalityâ should be called âisomorphismâ or some other word.â€â€âIf you can't substitute, you can't call it equality.â
Checking with fellow non-type-theorist mathematicians (e.g. @joeldavidhamkins.bsky.social): without reading the context leading up to the following skeet đœ, do you agree that the (first) quoted sentence is agonizing to read?đ
Just to drive home that last point, which is not merely typographic: when we write âlet p=âŠâ (with an equal sign), we are positing that p be an abbreviation, hence interchangeable, with the expression in the RHS, so it had better be the case that p=q allows free substitution between p and q.đ
It's not just that âwe have u = Ïâ(x,u) and v = Ïâ(x,v) but from (x,u)=(x,v) we can't argue Ïâ(x,u)=Ïâ(x,v) to conclude u=vâ will cause any non-type-theorist mathematician to roll their eyes in agony, it's also INSANELY confusing: if I write âlet p=(x,u), so p=(x,v)â then what does Ïâ(p) refer to? đ€Ł
(And again, all this badness goes away if we relinquish the idea that â=â has anything to do with being equal and merely represents a kind of isomorphism or homotopy or whatever. Then it all makes sense, and this is what 2.7.1 in the HoTT even points out. So why call it equality at all?)
But the argument you and @informatheux.bsky.social brought forth to say âit's not so badâ that equality can't be substituted in typing is that it gives a transport map. But here the transport map doesn't buy us anything, does it? So it does seem apocalyptically bad.
I mean, I'm fairly convinced that HoTT will simplify proofs about isomorphism, yes, but I fail to see any argument that it captures anything about equality.â€â€It's very much like Coq's âPropâ: to me it makes no sense at all until I abandon the idea that it has anything to do with truth values.
âIn the introduction we remarked that one of the advantages of univalence is that two isomorphic things are interchangeable.â â But we've established that this is emphatically NOT AT ALL correct, and that's what this whole thread is about! This is exactly what my âfalse publicityâ grief is.
(And again, for clarity: by âLeibniz equalityâ I mean that if x=y then you can substitute y for x in any situation whatsoever, even if this situation does not constitute a truth value in the narrow sense allowed by the typing system.)
I fail to see how univalence âmakes isomorphisms behave more like equalitiesâ. To me it seems to say that âoh look, what we're calling âequalityâ is, in fact, just âisomorphismââ. How is HoTT equality any more like equality (which, again, we take to mean Leibniz equality) than isomorphisms are?
⊠I mean, I was under the illusion that HoTT could clarify the complex relationship between equality and isomorphism by unifying them and making isomorphism work just like equality, whereas in reality they just drop equality and claim that isomorphism is equality? Not so impressive a selling point!
Yeah, my complaint isn't that HoTT is âwrongâ, obviously: it's that they're calling âequalâ something which just means âisomorphicâ, which obviously makes the claim âoh look, we've made isomorphic objects equalâ far less impressive. bsky.app/profile/gro-... âŠđ
⊠So the analogue of â seems like it should be the version â that (x,u)=(y,v) in ÎŁ_t P(t) doesn't let you deduce u=v, even though x=y. So I'm confused as to the relation between â and â.
Side note: the issue â that (x,u)=(x,v) in ÎŁ_t P(t) doesn't let you deduce u=v seems very to me different in nature from the issue â that x=y doesn't let you deduce f(x)=f(y), because â presents a typing problem as you pointed out, but â doesn't (u,v both have type P(x)). âŠ
(Of course I can understand that for practical commodity, in the computer version of the language, one would still use the symbol â=â. Like, in C, having x==y doesn't mean that &x==&y and it's not worth complaining about.)
The correct philosophical definition of x=y is that you can blindly substitute x for y or y for x in ANY context whatsoever without thinking (Leibniz, paraphrased).â€â€If your notion fails this, it's not âequalityâ. It might still be interesting (isomorphism is!), but just don't lie about what it is.
Yeah, that's what I meant by the last parenthesis of this đœ skeet. I think this âcalling it âequalâ when really it means âisomorphicââ is the same as Coq calling âPropâ something that I think has little to do with truth values: it's not mathematically wrong, but it IS false advertising. âŠđ
⊠I mean, I can't even begin to understand how one might do any kind of math if you can't replace x by something else that you've proved to be equal to x. How is this even supposed to work?
âCanonicityâ is the fact that each term has a (decidable) canonical form, is that it? Why do we care about this? Well, I can sort of imagine why we might think it's nice, but to the point of sacrificing something as deep and important as âx=y â f(x)=f(y)â, I really don't. âŠ
⊠And even more disappointing from HoTT which I was sort of hoping would have something to tell us about the right way to see mathematical equality, but now you're telling me that it fails to prove something as basic as (x,u)=(x,v) â u=v? Wow. This really looks like an epic fail of the approach.
⊠But more importantly, this is tremendously disappointing: I had the overall idea that type theory sacrificed some properties of first-order logic (e.g. completeness) for convenience of use, but evidently it can't even capture the very basic reasoning modes of 1OL. So what's the point, again? âŠ
⊠So I suppose there is a technical reason for this, like âif we allowed substitution then <something> would become undecidableâ (seems a far lesser problem to me, but no matter), but then it has absolutely no business being called â=â. (Like, maybe write it âââ and don't claim it's âequalityâ.) âŠ
OK, I don't understand this at all, and, to be honest, the more I learn about type theory the less I want to learn about type theory. I mean, if having a proof of T(x)=T(y) doesn't let you substitute T(y) for T(x) in p:T(x), then â=â of types is evidently not equality of types. âŠ
Wait, what??? In Coq, equality is Leibniz equality, right? What kind of proof theory fails this? Or is this another annoyance about âdefinitionalâ versus âjudgmentalâ equality or something of the sort?
Seen on Mastodon:â€â€Why programmers like cooking: You peel the carrot, you chop the carrot, you put the carrot in the stew. You don't suddenly find out that your peeler is several versions behind and they dropped support for carrots in 4.3.
Neither that poor Shiba Inu dog nor the nice woman who adopted her in 2008 had any idea of the sequence of Internet jokes, crypto scams and bizarre events that would lead, 17 years later, to âDogeâ serving as mascot to a billionaire orchestrating a coup to take over control of the United States gvt.đ
PS: I should add that ALL points with exact decimal coordinates on the unit circle are obtained from this đœ procedure + symmetries. This follows from the above form of the two squares theorem, or again from prime factorization 10^n = (âi)^n · (1+i)^(2n) · (2+i)^n · (2âi)^n in the Gaussian ring â€[i].đ
J'ai pris cette photo âŹïž cet aprĂšs-midi comme âpreuveâ de son inexistence, mais en fait ce n'est pas difficile de trouver des traces de sa suppression: cf. www.youtube.com/watch?v=AqM8... par exemple.đŒïž
For my part, I had completely forgotten that there was a quantitative formula for counting decompositions as sums of two squares, and, until someone mentioned it, I was trying to figure out how to determine whether there are other points than the ((8+6i)/10)^n and symmetrics.
This gives a sequence of points on the circle, which are exact decimals by the formulas for complex multiplication (or for cos and sin of a sum). Niven's theorem en.wikipedia.org/wiki/Niven%2... shows that Ξ is irrational, so they're all distinct (or argue by prime factorization in â€[i]).đ
⊠But I think the nicest answer is to start with the point with coordinates (0.6, 0.8), which lies on the unit circle since 0.6ÂČ+0.8ÂČ=1, at angle Ξ := atan(8/6) if we want, and simply add Ξ again and again. (Equivalently, take the powers of the complex number z := 0.6+0.8·i.)đŒïž
Answer: there are various more-or-less equivalent answers here. The most complete answer is probably to appeal to Jacobi's two-squares theorem en.wikipedia.org/wiki/Sum_of_... in its quantitative form, but this sort of begs the question, and also doesn't explain how we find the points. âŠđ
In place of professionals who you dislike and who are sometimes systematically wrong, the American spaceship is now being piloted by drunken baboons, mashing the controls to see what happens. I hope you like the result.ââ€â€scottaaronson.blog?p=8609đ
If only the Wall Street Journal had not spent the last decade promoting the dumbest candidate in history then maybe we wouldn't have the dumbest trade war in history.
Very interesting! Thank you. Could it be that originally both forms of plurals had a slightly different meaning (e.g., one might have been a kind of collective)?
⊠But the case of Arabic plurals seems different, because (afaict) they aren't even remotely related to Hebrew plurals, they really don't appear to have evolved from a common ancestral form.
It is indeed rather fascinating. French/Italian/Spanish conjugations being rather more complicated than Latin ones is a good example of this. One typical phenomenon is that some phonetic evolutions happen only in certain contexts, so all sorts of stem+ending interactions can occur. âŠ
⊠and this new (ineffective) form quickly spread to the entire world, causing a shortage of the drug, with serious health consequences for patients. đ±
⊠this could be a genuine practical concern in the pharmaceutical industry. đ€Ż Apparently in 1998 the world pharmaceutical industry stopped being able to produce usable crystalline forms of the drug ritonavir because one plant started producing another form by accident, âŠ
Disappearing polymorphs en.wikipedia.org/wiki/Disappe... are a crystalline form of a chemical compound that becomes impossible to produce once microscopic seeds of another, more stable, form are found in the environment. I knew this was a theoretical possibility, but I didn't think âŠđ
The champions of Free Speech are now forcing scientists to retract submitted publications until they can be checked for the appearance of âforbidden terms.âđ
Why is it that Hebrew plurals seem to be overall regular (-im for masculine words and -ot for feminine ones) whereas Arabic plurals are formed by a seemingly completely random process of altering and/or lengthening vowels and reduplicating consonants?â€â€How was proto-semitic?
It might be more fun to have Linux run in a PostScript file (though I don't know how user interaction might work!), given that PostScript is Turing-complete.
⊠this sort of defeats the whole purpose of PDF being a format for describing printable documents and guaranteeing that you get the same output everywhere (not that it ever really worked, but having JS in there really kills it). PDF itself is not supposed to be Turing-complete.
Well, it would be more accurate to say that they made Linux run in a RISC-V emulator written in JavaScript, and embedded that JavaScript in a PDF file.â€â€I'm not sure how the idea of having a JS interpreter in PDF even makes sense, incidentally: âŠ
Trump: "Big tariffs coming!"â€â€J.P. Morgan: "We don't think he'll do it."â€â€Trump: "I AM TOTALLY GOING TO DO BIG TARIFFS!"â€â€J.P. Morgan: "We don't think he will."â€â€Trump: "OK, here are the big tariffs I promised. BOOM!"â€â€J.P. Morgan: "Wow, nobody could have foreseen this."
This is due to a beautiful and little-known covariance identity by Hoeffding (1940):â€â€Cov(x,y) = â«â«[F(x, y) - F(x)*F(y)] dxdyâ€â€So the difference between independence and uncorrelated-ness comes down to point-wise equality vs. a (weaker) integral equality between the CDFs.â€â€2/2
There's a lot of people looking at the illegal EOs and going "oh don't worry that's illegal he can't do that, the agencies won't follow it, they answer to Congress!" and people have got to start understanding that "legal" and "illegal" are irrelevant anymore
But while this parametrization is in general the right way to think about rational points on the circle, or equivalently, Pythagorean triples, here we want a specific kind, so it won't get you far (and in fact, I think it's a wrong path).
The formula in question is essentially the one I mention here: bsky.app/profile/gro-...â€â€(It can be thought of in various way, e.g., letting t = tan(Ξ/2), we recover cos(Ξ) and sin(Ξ) by (1âtÂČ)/(1+tÂČ) and 2t/(1+tÂČ).)đ
Indeed, the quantitative form of Jacobi's two squares theorem (which, to be honest, I had forgotten about â I mean the quantitative version) provides a complete answer to the puzzle.
I'm assuming your notation is AÂČ+BÂČ=CÂČ. Then the requirement is that A,B,C are integer, and that C has only 2 and 5 as prime factors (or we can assume wlog that it is a power of 10).
Mexican President Claudia Sheinbaum said," I'm confused I keep hearing everyone from America saying I'm sending rapists and felons into their country. We thought that was encouraged, considering that's what they chose to be their president." đ€Ł this woman is bad ass. Protect her at all cost.
It is well-known that there are lots of points with rational coordinates on the unit circle: just pick any rational t, and ((1âtÂČ)/(1+tÂČ), 2t/(1+tÂČ)) is such a point.â€â€But here we don't just want rational coordinates, we want exact decimal coordinates! How can we do this?
Another math puzzle: show that there are infinitely many points on the unit circle whose coordinates are exact decimal numbers (meaning, numbers of the form N/10^k for some k).â€â€For example: (0.6, 0.8) is such a point, as well as (0.28, 0.96) and (0.352, 0.936).
The way Twitter does it is shitty, but the feature makes sense: having a âtreat this just like a reply to @someone (even if it's not a reply)â visibility level, in between âshown to all my followersâ and âprivate message to @someoneâ â is possibly useful.â€â€So far, Bluesky doesn't have this (AFAICT).
⊠starting a skeet with â@someoneâ will tag @someone (just like any mention of them), but WON'T change the skeet's visibility: all your followers will see it.â€â€This is more logical, but perhaps not what was you intended, especially if you're used to Twitter. So this could cause surprises!
One difference worth noting between the Musky Site and this one:â€â€On Twitter, if you start a tweet with â@someoneâ, it will be shown only to @someone and people who follow both you and them (if you don't want this, one typically starts the tweet with a dot first).â€â€Here, this rule does not apply: âŠ
Five years on, few Britons think Brexit has been good for anythingâ€â€% saying Brexit has had a positive impact on...â€Control the UK has over its laws: 31%â€UK's ability to respond to COVID-19: 23%â€UK's level of international trade: 11%â€NHS: 6%â€â€Full list in chart đâ€â€yougov.co.uk/politics/art...đŒïž
What makes this a bit hard to read is that not only are we not used (outside computability) to considering a program that takes another program as input, we also aren't used to parsing statements of the form (((ââŠ)AâB)âC).
Yeah, the statement of the theorem is pretty intricate (another thing that writing it on Bluesky helped me realize): its overall structure is like:â€â€(((âe) e terminates â F(e) terminates) ⧠((âeâ,eâ) eâ computes the same as eâ â F(eâ)=F(eâ))) â F(e) can be computed from a black box version of e.â€â€âŠ
Following Donald Trump's lead, I'll now be blaming DEI hires whenever I fail to prove a theorem (indeed, the gay mathematician they hired to do my job fails to do my job, so it must be the hiring process's fault).
No, that's right, it says âif e terminates (on every input) then F terminates (on e)â. And your program F runs an infinite loop, so it never terminates, not even on a program e that simply does âreturn 0â, say, so your F fails the assumption.
(On second thought, these people probably wouldn't even care if all their documents were in Comic Sans. In fact, they probably are. Barbarians.)
Signs that I'm an insufferable nerd, episode #1729: seeing someone use the Cyrillic letter âĐŻâ in lieu of âRâ, or âĐâ for âNâ, in order to somehow look Russian, makes me want to curse all their documents to be in Comic Sans forever.â€â€(These letters are VOWELS, you ignoramus.)
C'est juste hallucinant. Ils ne sont pas foutus de faire un truc aussi basique que VOTER UN BUDGET, ce qui est quand mĂȘme probablement leur mission la plus importante, mais ils trouvent quand mĂȘme le temps de nuire.
Bordel, est-ce qu'il ne serait pas possible de mettre les politiques français sous la surveillance d'un adulte qui les empĂȘche d'essayer tout le temps de casser Internet? đ€Źâ€â€J'en peux plus, moi. Trouvez-leur un jouet pour les distraire, quelque chose d'autre, quoi.đ
Ah, I had missed the âunsignedâ making your loop infinite. So, if F doesn't terminate, then this fails the first assumption I made about it, which is that itself must terminate on every e which defines a total function.đ
In a different line, the various incorrect (and/or bizarrely complicated) attempts people made at answering this đœ question are also very instructive to me as a teacher in trying to understand what makes a problem complicated for students.đ
This đœ is one of the reasons I like to talk about science to a non-specialist audience: reactions like âbut why can't you do this?â or âwhy won't X work?â help me take better conscience of the (often unspoken) assumptions and conventions of a field, which, in turn, helps me be a better teacher.đŒïžđ
⊠This shows the difficulty of describing results from theoretical fields (especially in a limited space such as a microblogging platform): there are very often a lot of general conventions of the field (e.g., in computability, âeverything is an integerâ) which are delicate to get across.
Yeah, in computability theory there's no notion of input/output: either you consider the X's printed by your program to be part of its âreturned valueâ, in which case your program fails extensionality, or you discard them, in which case just âreturn 42â works.â€â€But good remark! âŠ
What your timeline needs now is a nice parrot:đ
A reminder: the GWBush Admin built a prison at Gitmo not because of its size or facilities, but on the theory that because it was not in the US, US laws would not apply, and because US didn't recognize Cuban sovereignty over it Cuban law didn't either. It's a stateless, lawless zone of impunity.đ
Does anyone know of a transitive model of ZFC+V=HOD in which the Mostowski collapse of the parameter-free definable elements does not form a substructure of the model?
Additionally, a transformation (F ⊠FâČ) from one to the other, i.e. converting from a program-that-can-inspect-e to a program-that-operates-on-a-black-box can ITSELF be performed algorithmically.â€â€Trying to write such a transformation down should make it clear that the theorem isn't obvious. âą6/6
In other words, âif you can compute something on all total computable functions g when given any program e that implements g, then you can compute that same something given just a black box that computes g (without access to e's code)â.â€â€And no, this is NOT obvious! âą5/6
THEN (says the K-L-S theorem): there is a program FâČ that computes the same result as F, but instead of being given the code of e as input, it is given the possibility of interrogating a âblack boxâ (or âoracleâ) which, when given n, computes g(n). âą4/6
The second hypothesis means that: if eâ and eâ are two programs that compute the SAME function g, then F must return the SAME result when given the input eâ or eâ (i.e. the result which F computes can depends only on g, not on how g is computed by e). âą3/6
â provided that e terminates on every possible (say, integer) input, i.e., provided it computes a total function g:âââ, then F terminates on the input e; andâ€â€â the value returned by F on such an e depends ONLY on the function g that e computes (F is âextensionalâ).â€â€âą2/6
There are several ways to state the Kreisel-Lacombe-Shoenfield theorem en.wikipedia.org/wiki/Rice%E2... but I think the following formulation is most enlightening: 𧔗ïžâ€â€âŁ Imagine you have a program F which takes another program e as input and returns an integer (say). Also assume that: âŠâ€â€âą1/6đ
arxiv.org/pdf/2110.01111â€â€Although it looks like a random attempt with obvious mistakes by a beginner or ChatGPT, this is a correct algorithm for sorting the array A in increasing order:â€â€for i from 0 to len(A)-1:†for j from 0 to len(A)-1:†if A[i] < A[j]:†swap(A[i], A[j])â€â€đź
This property of having each possible value exactly one in each row and column is known as being a âLatin squareâ en.wikipedia.org/wiki/Latin_s... â here we even have a âgroup lawâ, which is stronger.â€â€This ensures, no matter what the biased die says, the unbiased die gives a uniform probability!đ
ANSWER: the simplest solution is probably this: throw both dice at once, and take their sum modulo 6 (considering â6â as being 0); or equivalently, take the sum and subtract 6 if it exceeds 6.â€â€This works because each number 1â6 appears once in each row and column in this table showing the result:đŒïž
I'm the sort of person who will say âa graffitoâ for the singular of âgraffitiâ, and sometimes âcommataâ for the plural of âcommaâ, you can't possibly expect me to use âdiceâ as a singular. đ§
Animal names are a mess: sometimes the male also serves as epicene, sometimes the female does, sometimes there is a specific epicene noun (which can be of any grammatical gender), sometimes castrated males get a different specific word⊠anything can happen.
Many French kids are convinced (until they get some actual biology classes, and perhaps even then) that a frog (because it's âune grenouilleâ) is a female toad (âun crapaudâ), and similar things.
Je connais ça, et je sympathise! Parfois je reste au bureau jusque trÚs tard, ces jours-là , parce que je n'ai pas la force de rentrer (et ce n'est pas pour autant que j'y fais quoi que ce soit de productif).
Many French kids are convinced (until they get some actual biology classes, and perhaps even then) that a frog (because it's âune grenouilleâ) is a female toad (âun crapaudâ), and similar things.
Not to be confused with âpopulus albusâ, which would be a white people: the same nounÂč âpopulusâ with the same declension is feminine when it means âpoplarâ and masculine for âpeopleâ.â€â€1. Well, not exactly: the âoâ in âpopulusâ is long when it means âpoplarâ, short for âpeopleâ.
Yes, grammatical gender is clearly part of the word; and yes, Latin words are gendered too: generally in accordance to their inflectional paradigm, e.g., -us names are masculine and -a names are feminine, but there are exceptions, e.g., tree names are feminine, so âpopulus albaâ = a white poplar.
A reasonable argument that, sadly, falls apart against the fact that there's a brand called âMonsieur Cuisineâ www.monsieur-cuisine.com/fr yet it's unquestionably âla cuisineâ.â€â€Grammatical gender makes no sense, you just have to accept it and move along.
Slight reformulation: Alice and Bob wish to throw a die to play a game; each brought a die of their own, but neither trusts the other's die. How do they do it?
Remember: they reopened coal plants to fuel this "revolution" and now there's some dramatically cheaper thing that does mostly the same stuff without the need for the biggest data centers and newest chips. OpenAI has no real moat! Neither does Anthropic, or Google, or anyone really!
Simple but instructive math puzzle: you are given two ordinary six-sided dice. One is fair (all sides are equally likely to come up), the other is loaded (some sides are more likely), but you don't know which is which. How can you simply get a fair throw using just these dice?
⊠but what is its actual origin? I stumbled upon this interesting account of how the story was told and retold by different generations of storytellers, from the Babylonian âTalmudâ to Jean Cocteau and W. Somerset Maugham: subsublibrarian.com/2022/04/13/t...đ
Many people probably know this âŹïž very short story, the âappointment with Death in Samarraâ, as told by W. Somerset Maugham in his play âSheppeyâ (1933) and used as an epigraph in John O'Hara's novel âAppointment in Samarraâ (1934); âŠđŒïž
Last time I went to Nice (that was in December 2017), I stayed in a suite in the âNegrescoâ hotel, also at an impressive discount over the normal price. The suite looked like this âŹïž and I did not regret it.đŒïžđŒïž
This place is as close as you can get to zero criminality, it is the epicenter of political neutrality in the Universe, and they had no qualms about storing the (previous era) Nazis' gold.â€â€And you STILL managed to piss them off✠đ
So apparently the Tesla store in ZĂŒrich has been (very lightly) vandalized.â€â€Elon, do you realize how politically awful you have to be for your offices to be vandalized in ZĂRICH, SWITZERLAND? đŻđŒïž
Now I have to point out that I predicted this back in 2008 in a groundbreaking talk that got published in the âJournal of Craptologyâ, (volume 6, 2009), âPerfect Localized Security of the Fourtytwofish Cipher in the Delphic Oracle Modelâ www.anagram.com/jcrap/Volume... đđŒïžđŒïž
Now I have to point out that I predicted this back in 2008 in a groundbreaking talk that got published in the âJournal of Craptologyâ, (volume 6, 2009), âPerfect Localized Security of the Fourtytwofish Cipher in the Delphic Oracle Modelâ www.anagram.com/jcrap/Volume... đđŒïžđŒïž
American AI companies are discovering that, when your product is a cheap and pretty useless gimmick to begin with, the cheap and shitty Chinese knockoff is going to be indistinguishable from the original product.đŒïžđŒïž
Physicist Polykarp Kusch was born #OTD in 1911. His measurements of the magnetic moment of the electron revealed that its value disagrees with naive predictions by a tiny amount â about 0.1%.â€â€Quantum Electrodynamics offers a marvelous explanation of this minuscule discrepancy. đ§Ș âïžâ€â€Image: AIPđŒïž
Lundi : Merde, les marxistes avaient raison.â€Mardi : Merde, les hippies avaient raison.â€Mercredi : Merde, les marxistes avaient raison.â€Jeudi : Merde, les hippies avaient raison.â€Vendredi : Merde, les marxistes avaient raison.â€Samedi : Merde, les hippies avaient raison.â€Dimanche : Merde, les marxist
"Democracy Dies in Darkness" is kinda like "Don't Be Evil" as a slogan. It's a bit worrying when you choose it, but it's a lot more worrying when you take it down
Ever wonder what snow in the swamp would look like? This is 5 miles into the Louisiana swamps in the Atchafalaya basin... it's unreal... having lived down there for the first 28 years of my life, we never saw anything like this.â€â€Smashed records.â€â€Curtesy of Garrett Roberts.đ„
This should be good news, were it not for the fact that public opinion has proven, time and again, that it is capable of having a completely different opinion about two obviously equivalent statements. And it's not difficult for leaders to pick a convenient formulation.đ
The MĂŒller-Lyer illusion has been tested on fish. đ€Żâ€â€đ§”đœđ
Namely, the rational outcome of the negotiation is the unique point of the Pareto-optimal boundary such that the tangent to the latter at this point has a slope negative of the line connecting it to the war point. (And thus was war forever ended by mathematicians, nobody had to fight again. âșïž) âą8/8
So, given the (assumed known) convex region of feasibility and the (also known) outcome of war, what does Nash's theory of bargaining tell us the rational outcome of the negotiation is? Well, it turns out that it has an amazingly simple geometric description! (Which my figure tries to show.) âą7/8
(Note also that we can assume the region of feasible outcomes to be convex. Indeed, they can always agree that âwith probability p we will do X and probability 1âp we will do Yâ, realizing the segment between X and Y. Yes, of course, this is highly theoretical.) âą6/8
(Note that both players are irrevocably committed to carrying out their threats if the negotiation fails, i.e., they will go to war even though war is clearly not the best outcome. But it is precisely this threat which ensures they reach a settlement!) âą5/8
⊠(in the sense that you can't improve BOTH player's utility). Now each player issues a threat of war to the other: if they can't come to an agreement, there will be (some kind of) war, whose outcome is represented by the red dot, obviously bad for both, and known to both. âą4/8
We assume two rational players (A and B) have to share some kind of resource, or come to some kind of agreement. The shaded area in the diagram represents the conceivable outcomes of the bargaining. Its edge are the Pareto-optimal ones, i.e., the ones which actually make sense ⊠âą3/8
This is arguably one of the most important mathematical diagrams for the real world (e.g., for geopolitics), because it tells us â in a highly simplified mathematical model â what the rational settlement out of a war is: âŹïž (pardon my shitty TikZ figure). đ§”â€”ïž âą1/8đŒïž
Numbers 2â10 are very good advice, but I don't see the point of #1: he's not Voldemort, saying his name won't make him stronger, it's not like he's an unknown nobody who will benefit from getting more publicity.
I think something needs to be said about salaries, because I suspect someone coming from, say, the US would probably be very surprised by how little French academics earn, even compared to cost of life in France, or relative to the median salary in France. So: inquire in advance!
I would like to see the Royal Society Expel Elon Musk. His membership is a disgrace and an insult to the Royal Society's core values of "promoting excellence in science for the benefit of humanity".đ
Fun fact - the parrots we study vary a lot in how they sit when we take photos!â€Some (regent, superb and swift parrots) sit up nicely looking like perky little birdsđ«Ąâ€Others (gang gang and OBP) just kind of flop over onto your hand and look like a puddle đ« â€â€very cute, very silly đȘ¶đ§ȘđŁđŠđżđđŒïžđŒïžđŒïžđŒïž
(I just googled âUS median net worthâ, and it said 193kUSD. Then I googled âUS average net worthâ to compare, and apparently it's 1MUSD. I have to say, I didn't expect the average/median ratio to be THAT large.)
Poor poor poor Sundar Pichai whose net worth is only that of about 7000 median Americans, surrounded by people whose net worth is about that of MILLIONS of median Americans. He must really feel like a lowly pauper in this company.đ
La question ne veut surtout rien dire: c'est quoi un «lien»? Quels sont les facteurs qu'on pourrait vouloir contrĂŽler? (Ăge, sexe, niveau de revenus serait le minimum, mais conditions d'habitat? taille de la famille? et surtout: discriminations subies? comment contrĂŽler ça?) âŠ
The letter âĆâ is specific to Hungarian, it doesn't exist in German. You wouldn't want to confuse the guy on the left with the one on the right, would you? They have totally different⊠uh⊠tie knots.đŒïžđŒïž
No no no! I'm sorry, but even coming from Elon Musk this goes too far! It's intolerable! đ€Źâ€â€Hermann Göring's name spells with an umlaut: it's not âGĆringâ with double acute, you dunce! Totally different.â€â€Now I have to do a grammar nazi salute.â€â€[tweet id: 1882406209187409976]đŒïž
Did Musk recently suffer a humiliating symbolic defeat? I missed that and I could use even a small bit of good news: what was it?
This clearly doesn't go far enough: they clearly need to penalize just thinking about sex without actually having sex, because that is also a form of contraception, hence abortion, hence killing of sweet babies.đ
No, come on, I can prove that the quotient of XĂ{0,1} by the equivalence relation that identifies (p,0) with (p,1) is homeomorphic to X, it's pretty trivial. So what is the question asking about?
Am I misreading this MathOverflow question or is it claiming that not every topological space X is homeomorphic to the quotient of XĂ{0,1} by the equivalence relation that identifies (p,0) with (p,1) for every pâX? Because this would BLOW MY MIND. đ€Ż mathoverflow.net/q/486372/17064đ
Trump Claims He Can Overrule Constitution With Executive Order Because Of Little-Known âNo One Will Stop Meâ Loopholeâ€theonion.com/trump-c...đŒïž
I refuse to believe that, even among Quakers in 1766, parents with the surname âFishâ would call their son âPreservedâ without realizing the silliness of basically naming him after canned tuna.đđ
«Let the polynomial P(X) := âŻÂ» me semble bizarre. Mais tu peux utiliser d'autres verbes, par exemple «define» ou «consider», Ă la place de «let», pour que ça marche. La tournure qui me semble la plus claire est: «let us define a polynomial P by P(X) := âŻÂ».
The Mathematics of Artificial Intelligence: In this introductory and highly subjective survey, aimed at a general mathematical audience, I showcase some key theoretical concepts underlying recent advancements in machine learning. arxiv.org/abs/2501.10465đŒïž
I really hope everyone understands what is going on with Elon and Wikipedia.â€â€Wikipedia is one of our last remaining bastions of evidence-based consensus reality.â€â€The MAGA narrative is fundamentally threatened by evidence-based fact, and Wikipedia is a repository of evidence-based fact.đ
having succeeded in purchasing positions of influence inside the White House, the billionaires and tech VCs have now set their sights back on WikipediađŒïžđŒïžđŒïžđŒïž
To understand crypto âvaluationsâ, take the example of MollyCoin. If I conjure a billion MOLLY tokens out of thin air and sell one for $1, Iâve just created a âbillion dollarâ cryptocurrency.đŒïžđŒïžđŒïž
In brief: the price of a stock or currency is a marginal price for selling ONE of these things, it makes no sense at all to multiply this marginal price by the total number to get a total price, as if selling the entire stock didn't change the price.đ
I'm definitely not saying we should ignore Musk, nor that the problem will go away if we do. He absolutely needs to be fought. But pointing out what he did very openly and deliberately isn't going to help. It might get a few people to realize how far he's gone, but I think there are better examples.
It is strategically wiser, if you hate him, to point out the many times where he's proved himself to be an idiot, contradicted his own promises and statements, shot himself in the foot, cheated, etc. Such things are unglamorous and expose him as the incompetent buffoon he is.
People talking about Musk's nazi salute are giving him exactly the food that the troll craves: worldwide attention, a smug sense of being a radical âindependent thinkerâ, a plausible image of defending freedom of expression against censorship of political ideas, etc.
For no particular reason đ, let me point out once again that this gesture âŹïž is not a Roman salute, but that, from the painter David to its use by fascists and Hollywood moies it has a very interesting history that is worth reading about.đŒïžđ
Of course Twitter does nothing to even attempt to prevent such things (and of course I instantly blocked the new account owner), but the same thing can occur on Bluesky as well.â€â€It's not clear how best to detect and deal with such situations.
This is a common technique on social networks: take over an existing account so you get all their followers at once, who suddenly see ads for whatever the account is now about popping up in their feed from someone they follow, without knowing that they chose to follow a different person.
An example of account takeover on Twitter: user id 38185687, which used to be that of moto racing photographer Tommy Vennard (@/BigTommyGun) was taken over by a crypto scam under the name Emilie Choi (@/emiliechoiCbDev). Didn't even bother to clean the past timeline!đŒïžđŒïžđŒïžđŒïž
So, do you intend to keep the location of this holy grail a secret that historians of future generations will debate about forever, or will you tell us where we can buy this âsookieâ? đ€š
«a âtraditionâ (thatâs French for baguette)» â Did you perhaps find yourself in the situation of this character from Wilfrid Lupano & Paul Cauuet's âLes Vieux Fourneauxâ? đđŒïž
Trump is reportedly going to sign a piece of paper later today declaring that the federal government of the United States defines me as a woman.â€â€If there's a better encapsulation of how stupid the whole "define woman" thing is and has always been I'd love to see it.đ
We're just minutes away from the End of the Universe, so where is the Restaurant?
The Scottish Sunday Herald TV guide featured this preview of the Trump inauguration. â€â€Itâs fucking brilliant.đŒïž
In brief: the price of a stock or currency is a MARGINAL price. Multiplying it by the total number N makes as little sense as claiming that f(N) = fâČ(0)·N + f(0) in general: this only holds approximately, for N small enough!đ
Techbro: hey we made a thing to make your life easier.â€You: actually it makes my life harder. Please take it away.â€Techbro: we never said you should trust it and we built it in so you can't avoid it. Suck it up lolz.đ
Et ne parlons pas de la question des ponctuations Ă la fin des citations qui devrait, Ă elle seule, pouvoir provoquer une guerre de religion: bsky.app/profile/gro-...đ
There's so much *gestures wildly* right now, but the incoming president of the United States launching a memecoin where he holds most of the coins, multiplying his wealth by ten overnight... It barely made the news.đ
Sans vouloir nier le droit de n'importe qui Ă bloquer n'importe qui, ce n'est pas la premiĂšre fois que je constate que beaucoup de gens aiment bloquer n'importe quelle forme de contradiction, ou mĂȘme de correction, ou mĂȘme de demande de correction.đ
I wasn't a fan of the Twitter algorithm that takes likes into accounts, but on second thought, if only reposts really matter, this gives accounts with many followers a disproportionate importance in determining which posts get widely seen hence in gaining new followers â this is very problematic.đ
It may be worth reminding everyone that, on this social network (unlike the more musky one that it imitates), likes have essentially zero effect on a post's visibility: only reposts do.â€â€If a post is worth sharing with others, you should repost it: a like just shows private support to the author.
Macaques on Japan's Shodoshima Island enjoy leaving chalk marks on stones.â€â€They have no symbolic purpose, but recognisable geometric features (parallelism, intersections, repetitions).â€â€(paper) https://link.springer.com/article/10.1007/s10329-024-01176-yđŒïž
đœ Zero, provided I'm generous on the meaning of âusingâ a typewriter, and I replace âBlockbusterâ (which doesn't exist in France) by âsome VHS rental serviceâ.đ
1. âSome reasonâ is probably a strange combo of âEU regulations threaten exploitative business practicesâ and âstill under apartheid SA's besieged racist mindset, so has weird fantasies about white ppl being endangered by immigration and perversely dreams of âsavingâ themâ.
As a European I think I feel slightly less menaced by Trump, who doesn't care a bit about Europe and probably can't place it on a map, than by Musk, who for some reasonÂč is utterly obsessed with destroying democracy in Europe. If only Americans hadn't elected Musk president!
This tweet is giving off the same energy as czar Alexander I of Russia at the Congress of Vienna explaining how he wants to make Poland great again.â€â€x.com/elonmusk/sta...đŒïž
An interesting case study is the history of the notion of equivalence in mathematics (which we now consider equivalent to the notion of âequivalence relationâ, but things are more complicated): bsky.app/profile/did:...đ
⊠So asking âwho was the first to discover/invent <X>?â may have a very different answer according to exactly what you consider to represent the idea <X> (a very small â and now unimportant â change in formulation can yield a completely different answer). âŠ
One recurring problem in the history of science (or more generally, the history of ideas) is that two ideas that we now consider âobviously equivalentâ may not at all have been âobviously equivalentâ at the time. âŠ
Iâve been thinking about how monumentally stupid the Elon video game cheating thing is and I think it comes back to this postâ€â€there arenât a ton of people who work in cars, or rockets, or even softwareâ€â€but everyone - everyone! - understands cheating at video gamesâ€â€totally unnecessary self-ownđŒïžđ
OnlyFans model creates SFW content on PornHub, publishes post to LinkedIn explaining that she gets a much higher rate on PornHub vs YouTube ($1,000 per million views on Pornhub versus YouTubeâs $340), and then LinkedIn takes down her post and bans her.â€â€www.404media.co/why-this-onl...đ
⊠Math SE is fine too but the question will be drowned in the flood undergrad-level stuff, so your chances of getting an answer there are slim. Posting there is mostly useful as a âcheck of obviousnessâ before posting elsewhere later on.
I don't see why this should be easy, and I certainly have no intuition about it. You should probably ask on one of CS Theory SE or MathOverflow, according as you can find existing questions or tags which most closely match your question. âŠ
The Cassini probe had a (13.78GHz) radar that was used for imagining the Titan terrain through the (thoroughly opaque in visible light) as atmosphere. See: science.nasa.gov/mission/cass...đ
I had missed the fact that there's a new pair of large cardinals axiom in the zoo: âexactingâ and âultraexactingâ cardinals. Which I think I understand to be a big deal because their consistency contradicts the âUltimate Lâ conjecture (which I understand only very superficially).đŒïž
(I'm aware that the Sublime Porte refers to the imperial gate, and metonymically the entire government, of the Topkapı Palace of the Ottoman Empire. But âThe Sundering Floodâ is European Middle Ages like fantasy, so a reference to the Ottoman Empire would be weird.)
Another word I'm a bit confused about is âPorteâ. Morris seems to use it (repeatedly) to refer to the ruler of a city (some kind of mayor), but no online dictionary I can find lists this meaning. Whence did he get this word?đ
This photo đœ is absolutely remarkable and never ceases to tantalize me. I really hope that before I die I will get to see images and videos of the surface of Titan like we currently have for Mars; and more importantly, I want to see what the rivers, lakes and seas of Titan look like.đ
Pretty much all digital watches that were produced before 1582 in continental Europe, or as far as 1752 in Great Britain, use the Julian calendar! Be sure to check the manufacturing date on yours to see whether it is Gregorian-compatible.
I believe the correct answer is: the fact that Elon Musk's ego and Donald Trump's ego are too large for both of them to fit on a single planet. (And, unfortunately, we can't send them to Mars and Jupiter respectively.)
What would you actually see, in terms of Hawking radiation, as you fell into a black hole? Is there some particular place from which the photons appear? Does the event horizon appear special in any way? Here are the answers in a new paper by Chris Shallue and me.â€â€arxiv.org/abs/2501.06609đ
Seven math puzzles which âyou think you must not have heard correctlyâ by Peter Winkler. I don't like them all equally, but some are quite fun to think about.â€â€Link to document with solutions: math.dartmouth.edu/~pw/solution...đŒïžđŒïž
> I will continue to monitor them closely.ââ€â€The Poles IMMEDIATELY sober up and stop talking, so the Soviet guy can sleep.â€â€The next morning, as he checks out from the hotel, the receptionist tells him: âBy the way, the comrade colonel found your little joke last night very funny.ââ€â€âŠ
Soviet man goes to a hotel in Moscow. They are full, so they put him in the same room as three Poles, who are drunk and speak very loudly.â€â€Eventually, guy gets fed up. He turns to a light bulb, pretends to talk to it and says: âAgent Ivan reporting to comrade colonel. Nothing on the Poles so far. >
An old woman boards a bus in Moscow, and immediately finds a seat. âThank God!â she exclaims.â€â€A man whispers to her: âBabushka, in this country we no longer say âthank Godâ, we say âthank Stalin!âââ€â€âBut when Stalin dies, what will we say?ââ€â€âThen we will say âthank God!âââ€â€âŠ
A man comes into a KGB office and says he would like to speak about the loss of his parrot.â€â€The KGB officers are confused: âComrade, lost pets are a matter for the police, not the KGB.ââ€â€The man says: âI know that. I just wanted to let you know that I disagree with the parrot's political views.ââ€â€âŠ
May Day parade. An old Russian Jew carries a sign that reads: âThank you for my happy childhood, Comrade Stalin!ââ€â€He is approached by a Party member. âComrade! Your sentiment is admirable, but you must be mistaken: surely, when you were a child, Comrade Stalin wasn't even born.ââ€â€âPrecisely.ââ€â€âŠ
Moscow man buys newspaper, glances at front page, throws it straight out. Next day: same again. And again. Eventually, seller snaps. âWhy DO you do that?ââ€â€âOh, I'm just checking for an obituary.ââ€â€âBut obituaries aren't even on the front page!ââ€â€âThe one I'm looking for will be.ââ€â€âŠ
Two men are in a day-long line to buy vodka. One gets increasingly agitated and finally says to the other âI can't take it anymore! I'm going to shoot Gorbachev!â and runs off.â€â€Two hours later he returns to his original spot, looking dejected.â€â€âSo what happened?ââ€â€âThe line was even longer.ââ€â€âŠ
An American and a Russian in the 1980's. The American says: âIn my country, we have freedom of expression, so I can stand in Washington and openly cry âReagan is an idiot!ââ â âThat's nothing,â replies the Russian. âI too can walk in the middle of Moscow Red Square and cry âReagan is an idiot!âââ€â€âŠ
A man in Soviet Russia is approached by a stranger.â€â€âComrade, what is your opinion of the Comrade Secretary General?ââ€â€Nervously, he stammers: âI think⊠uh⊠I think just like you do!ââ€â€The stranger flashes a KGB badge: âAha! Just as I thought! You're under arrest!ââ€â€âŠ
Two men are prisoners in a gulag.â€â€âWhat are you here for?ââ€â€âNothing! I didn't do anything!ââ€â€âAnd how long are you here for?ââ€â€â30 years.ââ€â€âLiar! For nothing they only sentence you to 20 years!ââ€â€âŠ
Finally the perfect excuse to dig up some good old Soviet-era jokes!đ
âLe Mondeâ raconte connerie aprĂšs connerie sur tout ce qui est technologie, voire tout ce qui est science. @marcqplanets.bsky.social doit pouvoir en dire plus.
Tangent: I didn't know people referred to the U+220E END OF PROOF symbol as âtombstoneâ. This also makes me realize that Unicode doesn't have a tombstone symbol or emoji.â€â€Correction: it does, U+1FAA6 HEADSTONE (đȘŠ). Maybe I should use this to mark the end of proofs! đ
Thinking that your enemies and your other enemies are necessarily allied is just as much a mistake as thinking that the enemies or your enemies are your allies but for some reason it rarely gets pointed out as such.
It boggles the mind that tech-optimists would insist AI (as in the current generative LLMs and their ilk) will enjoy a success remotely comparable to the web, when AI is threatening to make the web completely unusable in exchange for absolutely nothing of value.đ
Pro-tip: when someone you strongly disagree with tells you âfor your sake I strongly recommend <that you stop disagreeing with me>â, they're not saying that for your sake. đđ
⊠but it is not true that we should never call things âeasyâ: doing so has a purpose, it brings valuable meta-information to the reader, and the idea that writing down âŠall the details⊠without hierarchizing them would make proofs easy to read isâjust wrong. âą15/15
Now I'm fully aware that some authors overuse âtrivialâ or âeasyâ (or the more honest âleft as an exerciseâ) for things that are not at all easy: this is bad mathematical writing, and I won't defend it; ⊠âą14/15 bsky.app/profile/did:...đ
⊠it draws the readers' attention to the statement, entices them to check that it is indeed âtrivialâ or âeasyâ, and suggests that they memorize the fact as something that might be important later on. None of this is useless. âą13/15
And similarly, it makes perfect sense to record a statement as a theorem, if only to write its proof as âtrivialâ or âeasyâ. This serves to give the statement a name or number, which can then be referred to in a later proof or definition: ⊠âą12/15
So saying âtrivialâ or âeasyâ is not giving zero information: the author â”isâ” telling the reader something about the proof, e.g., âif you're stuck doing something complicated, you're on the wrong path, you probably misunderstood somethingâ. This is valuable! âą11/15
⊠and if you think these proofs are easy to read because they give all the details, you're wrong. Humans don't read proofs like computers do: it helps them to get some meta-information about what parts are important, what parts are easy, etc. Not just the logical steps! âą10/15
It's tempting to ask âwhy not give the full details of the proof rather than claim something is âtrivialâ or âeasyâ?â, but giving the full details essentially means giving a formal proof that can be digested by a proof assistant on a computer, ⊠âą9/15
⊠in that if you don't find this easy, then you'll stop here and avoid wasting your time trying to decipher much harder proofs later one. Yes, it can be seen as a form of gatekeeping, but it's better to gatekeep in the earlier stages of the text. âą8/15
So claiming that something is âeasyâ also serves as a kind of check on the reader: the implicit message is âif you don't find this kind of stuff easy, then you probably shouldn't be reading this book in the first placeâ, which is, in fact, helpful ⊠âą7/15
⊠you'll take just as long to check them as you would to do the computation for yourself. Now of course âeasyâ depends on the reader: checking that 543 Ă 789 = 428âŻ427 is easy for anyone who knows how multiplications work, not for a first grade student. âą6/15
The point here is that the author expects the reader to find it no more enlightening or helpful to follow a proof than to actually do it for oneself. For example, if I claim that 543 Ă 789 = 428âŻ427, writing the details of the computation won't help you: ⊠âą5/15
âEasyâ is less restrictive: it means that the statement follows from a simple argument that the reader should be able to do for oneself. Sometimes one can clarify the type of reasoning, e.g., âfollows from a straightforward calculationâ is a subcategory of âeasyâ. âą4/15
⊠âblueish foobars are weakly blueishâ is trivial, as it follows from the definitions and straightforward application of pure logic, and any attempt to explain it further would only waste time and perhaps even confuse the reader. Trivial means âI can't explain further!â. âą3/15
âTrivialâ generally means something follows from a straightforward application of pure logic. For example, if a âblueish foobarâ in which every element is blueish, and a âweakly blueish foobarâ is one in which every cromulent element is blueish, then the statement ⊠âą2/15
âWhy do math books sometimes write down a statement in a theorem if the proof is going to say that it's âtrivialâ or âeasyâ?â â This is a valid question, and it actually makes sense (though it can be abused!). Let me try to explain. đ§”â€”ïž âą1/15 x.com/xptr_chintol...đŒïž
OK, various online dictionaries suggest that âknopâ refers to an ornamental knob, button or tassel, or other kind of ornament; and âouchâ is an ornamental clasp, buckle, or brooch, or setting of a precious stone. âŠ
Anyone want to try to guess what âLongshaw, which is as it were the knop and ouch of my manorsâ means? (Spoken by Sir Godrick in chapter XXXIX.)đ
Like much folklore wisdom, it's attributed to a lot of people (many of whom probably came up with it independently); so much so that Quote Investigator has a page about it: quoteinvestigator.com/2018/09/18/l...đ
You should learn by other people's mistakes. You'll never live long enough to make them all yourself.
There's many a true word spoken in jest - with threads about unmanageable email burden on scientists going around, is "task paralysis" actually a sign that the overwhelmed knowledge worker is functioning completely rationally?đ
â± Update: I found this (somewhat old, but still relevant) video by @justingarrison.com very interesting in comparing, at a high overview level, how ActivityPub and ATproto work, and what each one's pros and cons are. I very much agree with him. âą34/⊠www.youtube.com/watch?v=wJBC...đ
1. From morning EST to evening PST, I receive an email roughly once every three minutes. Overnight the pace slows, but not all that much. If I did nothing but read email and reply 12 hours a day I could probably keep up.â€â€A once-wonderful productivity technology is killing any hope of productivity.
Join me for 10 questions in 10 minutesâphilosophy of mathematicsâon The Human Podcast. What a lot of fun it was!â€www.youtube.com/watch?v=MvfX...đ
⊠the Fediverse splits the ânetworkâ into pieces, and tries to be a federation of fiefdoms, whereas Bluesky mostly splits the ârolesâ, and tries to create a checks and balances system between the roles. Both are good, but serve different purposes. âą33/⊠end (so far)
⣠To say things differently, both Mastodon/Fediverse and Bluesky/ATmosphere attempt to solve the problem stemming from the power concentration of Twitter (and what happens if a madman controls of the center), but they take very different, if complementary, approaches: ⊠âą32/
⊠whereas on the ATmosphere, you basically have to use the one and only system (Bluesky, which is quite centralized), but the users have some guarantees and power wrt the system whereas on the Fediverse they are enthralled to their server. âą31/
⣠To summarize, on the Fediverse, you have full latitude in choosing your server (or setting up your own, which is IMO the only sane way to use the Fediverse), but then you're stuck with it, or at least your posts are, and you'd better hope it won't go the Twitter path, ⊠âą30/
⊠This is IMO the single greatest error with Mastodon: they didn't provide for a layer of indirection from the user's account to the server, which would have made it possible to move all of one's posts from one server to another. ATproto has this! âą29/
⊠And there is simply no way to move a post from one Fediverse server to another: the post is tied to the server, it only really exists on one server (even if others may have copies), and its permalink references that servers. If the server goes, the post goes with it! ⊠âą28/
⊠For example, on the Fediverse, your identity as a user is inexorably tied to a server. (There is a feature to request that users start following a different account if you wish to change servers, but it's still a different account: you can't move an account.) ⊠âą27/
⊠but on the other hand, Bluesky gives its users some existence and a much greater measure of control (whereas on the Fediverse, as I mentioned earlier, they have none except insofar as their server gives them some). ⊠âą26/
⣠Generally speaking, while the Fediverse is a very loose federation of servers (like email or the Web), Bluesky is a much more tightly integrated network (though not nearly as much as Twitter, which is just a single site); ⊠âą25/
⊠so for example, if Bob replies to one of Alice's messages, Alice cannot (even if she has her own PDS) alter the message ex post facto because this would break the hash and therefore the reference. See bsky.app/profile/gro-... for more on what this implies. âą24/đ
The Fediverse has none of these. But the Fediverse also lacks, as I pointed out earlier, any kind of data integrity, whereas this is very much baked in the AT protocol: taking inspiration from Git, it embeds a cryptographic hash in each message reference: ⊠âą23/
So we get features on Bluesky that Twitter can easily implement in its centralized architecture like likes/reposts count, a search function that works well, hashtags and alternate feeds. (Also, the quote-post, but I'm not sure this is architecture-related or just a choice.) âą22/
But it's not just a matter of decorations: Bluesky can offer a search feature that works throughout the network, because, as I pointed out, it distinguishes the ârelayâ from the PDS, and the relays receive and index everyone's messages. âą21/
⣠On the other hand, Bluesky does offer a number of user features that the Fediverse in no way does. The most obvious of them is that Bluesky looks a lot like Twitter, not just in user interface, but also in functionalities, while Mastodon is worlds apart. âą20/
⊠perhaps the most apt comparison here is that Bluesky might become like what Google is on the Web: the Web's content is decentralized, but, for most users, Google acts as the entry point and a kind of centralized directory of its content/users. âą19/
⣠So, in many ways, the ATmosphere is far less decentralized than the Fediverse, and in practice it is still a single network with a single operator. Even if it does decentralize eventually, it is predictable that Bluesky will keep a very significant lead and advantage: ⊠âą18/
Furthermore, Bluesky still owns and controls one central piece of the ATmosphere architecture, which is the PLC github.com/did-method-p... (âPublic Ledger of Credentialsâ, aka âplaceholderâ) identity provider, which is a kind of centralized directory of every user/agent. âą17/đ
Each has a different role and could be decentralized. Currently only PDSs are really decentralized and practical for anyone to self-host. Relays require an insane amount of storage to operate, and what views other than Bluesky might be or mean is entirely unclear. âą16/
Whereas the Fediverse (ActivityPub) just has one kind of piece, viê«. servers, the ATmosphere has three different beasts: personal data servers (PDSs), relays, and (app) views. In short, PDSs store users' posts, relays aggregate them and views present them to others. âą15/
Discussion of whether Bluesky is decentralized is complicated because nobody really knows what âdecentralizedâ means, and also because Bluesky and ATproto are not the same just like Mastodon and ActivityPub are not the same. âą14/
⣠Bluesky is a rather different beast. It too tries to shift the power balance away from the center, but it does it in a very different way from Mastodon/Fediverse. In short, I would say that Bluesky is less decentralized but empowers users more. âą13/
⊠So while you can, in principle, run other software, you might encounter interoperability issues. This gives Mastodon devs enormous power on how the Fediverse actually operates. âą12/
⣠Discussion of the Fediverse is complicated by the fact that most of it is powered by the Mastodon software. They are different servers, but they run the same software. And Mastodon has its own additions to the basic ActivityPub protocol of the Fediverse. ⊠âą11/
⊠Similarly, of course, a server might post bogus replies to a post it hosts: for example, it can change the text in any way it wants. Users might click through to see the original and compare, but few people are likely to do that. âą10/
⊠So there's no kind of data integrity. At all. If you reply to a post, the author of that post can modify it ex post facto. Maybe your server kept a copy of the original post, and users might see that it differs, but there's little way to tell who changed what. ⊠âą9/
⊠Each post is generally kept in several copies: on the server of the original author, but typically also on the other server if it's a reply to a post on that one, or if it has replies on that one. But servers can change what they display in any way they want. ⊠âą8/
⊠Also, the Fediverse works like email, but maybe Web pages are a more apt comparison: basically, a post is a Web page which others can link to: they can send you a notification to say they wrote an answer to you, and then you can set up bidirectional links. ⊠âą7/
⊠So if, as a user, you want to join the Fediverse, you need to pledge allegiance to a lord (server), who will then own all your posts and ID, like Musk does on Twitter. If you don't like this thought, you need to host your own server. I think everyone should do this. ⊠âą6/
⊠So while the Fediverse is said to be a âfederationâ, perhaps a better image is that of a bunch of lordships, each with absolute power over their dominion. They generally talk to each other, but can do whatever they want inside their domain. ⊠âą5/
⊠from exchanging data to maintaining user identity, to ensuring data integrity (or not). Servers can do anything: impersonate users, modify post content, change timestamps, fake replies, moderate as they wish, refuse to talk to other servers, etc. ⊠âą4/
⊠your server stores your messages for you, receives replies from other servers and keeps a copy of them. Every server is a fiefdom unto itself: the user has no right, or even any real existence in the protocol, servers are responsible for everything, ⊠âą3/
⣠The Fediverse is easier to understand, because its model is very similar to email. You sign up to a server, which creates an identity for you, and you can use it to exchange messages. Except that messages are (usually) public, it works very much like email: ⊠âą2/
Twitter is, of course, a closed and centralized system. Both Mastodon/Fediverse and Bluesky/ATmosphere attempt to replicate (some of) its key features in such a way as to move (some) power away from the center. How do they differ? It's Complicatedâą. Ongoing thoughts: đ§”â€”ïž âą1/
Just to repeat what I've long said about this man:â€â€1. Almost everything he says is a lie.â€2. Nothing he says can be trusted.â€3. His whole life is constructed as a long con.â€4. Anyone who trusts him will ultimately be hurt.â€5. He will say anything to acquire power and more money.â€6. He is dangerous.đŒïž
(I have no idea if the account tweeting this is in any way official, btw. If only some idiot hadn't disabled any form of verification of accounts on his platformâŠ)
In dimension 2, when 0<a<b and 0<x<y, the rectangle of size aĂb fits inside that of size xĂy iff aâ€x and either bâ€y or (bÂČâaÂČ)ÂČ â€ (aâąxâbâąy)ÂČ + (aâąyâbâąx)ÂČ. So the question is to generalize this.
I would add that the damage caused by global warming is a convex function of temperature (and/or total COâ emission): so the more warming has already happened, the more it's relevant to prevent any extra warming.
I would add that the damage caused by global warming is a convex function of temperature (and/or total COâ emission): so the more warming has already happened, the more it's relevant to prevent any extra warming.
There is something at once funny and humbling about this MathOverflow thread in which a bunch of research mathematicians realize they don't know how to answer the question âwhen does a box of size aĂbĂc fit inside one of side xĂyĂz?â. mathoverflow.net/q/282158/17064đ
This book is really a masterpiece. I don't love all of it equally, but some parts are among the most beautiful pages I ever read. I even wrote my own âcityâ in Calvino's style: www.madore.org/~david/weblo...đ
⊠to seek and learn to recognize who and what, in the midst of hell, is not hell, to make them endure, and to give them space.ââ€â€â Italo Calvino, final words of âInvisible Citiesâ [translation by myself]
⊠The first is easy for many: to accept hell and become part of it to the point of no longer seeing it. The second is risky and requires constant attention and training: âŠ
âThe hell of the living is not something that will be; if there is one, it is what is already here, the hell we inhabit every day, that we create by being together. There are two ways to avoid suffering it. âŠ
Apparently this painting by George Munger of the White House after it was burned is on display at the White House, perhaps as a form of reminder to the occupant.đŒïž
Let me remind any US president who might wish to annex Canada that only once in US history was Washington DC captured and the Capitol burned, and that was in 1814 after the US had declared war in an effort to annex Canada. đ
love the idea that facebook currently operates as some kind of elite liberal walled city and not just a place for divorced uncles to share racist screeds and nursing home bound grandmothers to get their daily dose of "jesus doing parkour" ai slop from an indian content farmđ
I guess âbased on genderâ means you can insult women as well. But insulting cis heterosexual males (and only them) is definitely off-limits.â€â€Strangely similar to how self-proclaimed âfree speech absolutistâ Musk decided that âcisâ is off-limits but just about anything else goes.
The precise section of Meta (i.e., Facebook)'s new policies on hateful conduct that says you can't call anyone stupid or mentally ill âœexcept✠homosexual and transgender people.â€â€This is what âprioritizing free speechâ means, apparently. đ€â€â€Link: transparency.meta.com/policies/com...đŒïž
obviously I didn't click on this article but I assume the middle portion is just AAARGH AAARRRGH NO MY PRECIOUS FACE AND THE LEOPARD'S TERRIBLE TEETHđ
WikiHow never ceases to amaze me with how it manages to blur the line between the improbable-but-still-serious advice and the outright farcical.đŒïžđ
Supposedly âisolationistâ president-elect of the US is threatening to annex Canada, invade PanamĂĄ and declare war on Denmark, while the president-unelect (Musk) is actively working to topple European democracies (UK, Germany, SpainâŠ).â€â€Good thing they're not interventionists! đ
Amazon Prime is using generative AI to replace movie posters for iconic films that already exist and already have posters they could use. Not only are we forced to see this shit everywhere, but they're overwriting art history with it.â€People keep saying I'm overreacting, and it keeps getting worse.đŒïž
When trying to interpret medical news on Twitter, remember the expression âIf it sounds too good to be true, it probably isn'tâ. Advances in medicine are often incremental and it's rare to find an intervention that has a very large effect on health outcomes or on health care costs.
Americans: âthe way French people count is unbelievably complicated: âquatre-vingt-septâ for 4Ă20+7=87? seriously? who would say that?ââ€â€Also Americans: âthe greatest speech ever made in History, by one of our greatest presidents: âFour score and seven years agoâŠââ
So basically âthere is no God beside Allah, but please name your God something other than âAllahâ because He's not the same as oursâ, right? đ€š
âThe reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.â (George Bernard Shaw, âMaxims for Revolutionistsâ)đ
FWIW, if I understand correctly, when Bluesky creates a card out of a link, every element displayed in the card (the title, the summary, the image) is recorded in the message, and will remain as you posted it, even if the link target later changes.â€â€(And I think this is different from Twitter.)
FWIW, if I understand correctly, when Bluesky creates a card out of a link, every element displayed in the card (the title, the summary, the image) is recorded in the message, and will remain as you posted it, even if the link target later changes.â€â€(And I think this is different from Twitter.)
«Et si on joue Ă pierre-papier-ciseaux-bombe, oĂč la bombe gagne contre pierre et papier mais perd contre ciseaux? Et si seulement certains joueurs ont le droit de jouer la bombe?» bsky.app/profile/gro-...đ
Peut-ĂȘtre que ceci aidera Ă illustrer le problĂšme: imaginons que j'ajoute une option «stupide» qui perd contre toutes les autres, mais qui perd encore plus contre pierre que contre papier/ciseaux: l'adversaire ne jouera jamais cette option, donc le fait que pierre gagne plus fortement contre elle âŠ
⊠et jamais papier; et celle de Bob est de jouer pierre, papier et ciseaux avec probas 2/9, 1/3 et 4/9. (Et dans ces conditions, Alice gagne avec proba 37/81, Bob avec proba 28/81 et il y a match nul avec proba 16/81; donc si on recommence jusqu'à un gain, Alice gagne avec proba 37/65, Bob 28/65.)
D'oĂč le fait que jouer Ă papier-ciseaux-puits est plus logique que pierre-papier-ciseaux, parce qu'on comprend mieux pourquoi le papier gagne contre le puits (enfin, peut-ĂȘtre).
⊠and even throw some items from one bank to the other, I really want to cry âif you can throw something to the other side, you can throw a spool of thread, use it to get a rope across and set up a makeshift bridge that way!â.
⊠and too strong for any boat. This is already very hard to swallow and there is nothing remotely similar in real life as far as I can tell, but when we add the fact that the main characters are still able to talk to each other across this supposedly uncrossable river, âŠ
Still reading William Morris's âThe Sundering Floodâ, and I must admit having a hard time suspending my disbelief about the titular river, which is supposed to split a country in two in such a way that nobody can cross it except at its mouth: too wide for bridges, âŠ
Interesting observation by Thomas Ehrhard ( www.irif.fr/~ehrhard/pub... ):â€â€âThis seems to be a general pattern of category theory : any notion is more general than any other notion.â
I wrote an answer (to an old question) on MathOverflow on how to define a ânaturalâ bijection between the positive natural numbers and the rational numbers using the Stern-Brocot tree: mathoverflow.net/a/485383/17064đ
Folks need to understand this.â€â€Pornhub is absolutely in the right here. They are blocking states who require this because they don't want to be responsible for your PI data! They do not NEED that info to provide their service, so collecting and maintaining it is inherently privacy violating!đ
-Alors, quel outfit choisir pour faire chier un maximum ce peintre? Hmm. Ăa, ce sera parfait. â€â€Portrait d'Ana de Velasco y GirĂłn (1585-1607) par Juan Pantoja de la Cruz (1603)đŒïž
The physics of hula hooping are more complex than one might think. A study of hula hooping robots reveals that an hourglass shape is required to keep the hoop in motion as both body and hoop rotate in opposite directions. In PNAS: www.pnas.org/doi/10.1073/...đŒïž
You can tell companiesâ AI projects are going really well because every app is bait-and-switching their most commonly pressed button with something called like âAnswers By Glorpâ to get people to even accidentally use it
Two popular ideas about academic research. Either in a white coat, looking down a microscope, or at the top of library steps lost in thought poring over an ancient hardback. Reality. Blinking at a screen, trying to come up with a decent string of words to search for a missing PDF.
I've recently been talking a bit about how difficult it is to carefully check even well-written mathematics. I want to try to explain something about this by telling the story of some errors in the literature that (in part) led to the two papers below. 1/nđŒïžđŒïž
When Elon Musk shows up with a 6 inch swastika neck tattoo the headlines are going to say "Musk Sparks Speculation With New Look; Critics Say It Signals Problematic Beliefs"
(The point of the ambiguous formulation, of course, would be to have plausible deniability: âno, we didn't order the killing of the former king, it was an o so unfortunate misunderstandingâ. But if you can get someone to believe something like that, you probably don't need it anyway.)
⊠âdo not fear to kill Edward, it is goodâ. This is told in Christopher Marlowe's play âEdward IIâ www.perseus.tufts.edu/hopper/text?... and Maurice Druon's novel âLa Louve de Franceâ.â€â€âŁ Q: Did this actually happen? Is there historical evidence? Or if it's a legend, whence did it originate?đ
There's a story that the order to execute the deposed king Edward II was given in the form âEduardum occidere nolite timere bonum estâ, which depending on the placement of a comma before or after âtimereâ, can mean either âdo not kill Edward, it is good to fearâ or âŠ
⊠Also, some of Tesla's ideas were borderline absurd and could never work. For some actual facts about him, I recommend this video by the generally excellent YouTube channel âKathy Loves Physics and Historyâ: www.youtube.com/watch?v=6331...đ
Also, the bizarre hagiography around Nikola Tesla is mostly nonsense. He was certainly not the âgreatest engineer everâ, he did not invent alternating current nor the transformer, he was not the first to invent the induction motor, and the Edison-Tesla rivalry is pretty much an invention. âŠđ
Wow, I hadnât appreciated this whole story. For-profit scientific publishers have various problems, but Elsevier manages to consistently be the worst.đ
Could people living in New Zealand and Australia tell us what 2025 is like so the rest of us can decide whether it's worth moving there as well or whether we should go for December 32 instead.
tbh it is pretty wild that companies will simultaneously moan about "losing money" to piracy while also actively refusing to sell things to people that they already have totally available and could put up for digital sale at any time. like sorry you are choosing to be bad at business. sounds rough
Me: The earth isn't flat. â€â€Fiat earther: Correct. â€â€Me: Huh?â€â€Fiat earther: It's the shape of an italian car.â€â€Me: What?â€â€Fiat earther: You read my name wrong didn't you?
âŁOther mathematicians (or graduate students) who want to understand the solution then painfully struggle through the lemmas essentially trying to recreate the examples and intuition that motivated the original author so they can reconstruct the original author's understanding.»
⊠âĄThe mathematician eventually acquires the necessary understanding to solve the problem. âąThe mathematician then works to reduce their understanding to a succinct and efficient sequence of lemmas, that can be logically verified by another mathematician. âŠ
Very insightful comment by Mark Lewko found in passing in MathOverflow mathoverflow.net/q/440214/170... on what happens in many mathematical proofs: «â A mathematician spends a significant amount of time studying examples and special cases, building intuition, etc. âŠ
(Just to be clear about the order of quantifiers, the question is whether âx irrational such that â base b [resp. just bâ[3,4}] â two digits c,câČ â a rank N such that â iâ„N the i-th digit of x in base b is equal to either c or câČ.)
An interesting and thought-provoking question on MathOverflow: does there exist an irrational number such that only two digits appear infinitely often in its base b expansion for all b? What about if we just demand this for bâ{3,4}? mathoverflow.net/q/484996/17064đ
Oh and I should add that this bit is right after the mysterious stranger gave Osberne a sword and right before Osborne is allowed to use it.â€â€Freud would have SO MUCH to say about this. đ
The rather cool site âChronotrainsâ lets you see how far you can go in Europe, by train, in up to 8 hours, from a given place. www.chronotrains.com/en?maxTime=8đŒïž
A rather đ”awkwardđ” moment in William Morris's novel âThe Sundering Floodâ (1897) when a mysterious stranger tells the hero Osberne, who is a boy of 12, that they need to get naked and he touches him âall over his bodyâ to somehow magically turn him into a man. đłđŒïž
I'm actually not a great fan of this kind of geometry, but I find the statements have a strange kind of poetry to them when the statement fits in a single skeet. And the sheer number that seems to be known is pretty bewildering.
âGiven a cyclic quadrilateral, the incenters of the four triangles formed by omitting one of the vertices of the quadrilateral, themselves form a rectangle.â (âJapanese theorem for cyclic quadrilateralsâ)â€â€There is a certain poetry to such statements.đŒïž
It shouldn't even be a matter of politics: given a computer system, say, we care about it working well 95% (or 99% or 99.9% or whatever) of the time. Not about it working exceedingly well 1% of the time. Generally speaking, reliability is measured by the worst quantiles, not the best ones.
Ideally it should be 99% or 99.9% or something, but after a point, statistical anomalies start to make the comparison meaningless. Still if the poorest 5% lives well, in practice, the poorest 1% or 0.1% will also live fairly well (unlike what happens at the other end). Except in Omelas, of course. đ
Roughly speaking, I think societies should be judged by the actual living standards they afford to something like 95% of the population (i.e., the living standards of the poorest vigintile of the population).â€â€Sadly, it's not easy to find reliable data about this metric.đ
Should I start using âforsoothâ instead of âindeedâ in mathematical writing? đ€â€â€(As in: âX is infinite; forsooth, f:ââX is injectiveâŠâ)đ
Don't think there is a better illustration of AI-in-everything-whether-we-want-it-or-not than an AI bro buying an AI toy for his child who played with it for a bit and then seemed singularly unimpressed with the AI and turned it off.â€He keeps turning it back on, and she keeps turning it off.đŒïž
(I mean, of course, for the particular layout in the previous skeet.) Basically, the sum-to-34 game seems to involve playing every possible 4Ă4 magic square at once, or something like that. The trick for 3 is that there's essentially just one.
The problem is, a magic square will guarantee that you win the game by picking a line, column or diagonal, but not that you can't win in any other way. For example, in the âsum-to-34â game you can win by picking, say, 16, 3, 8 and 7 which don't constitute a win in 4-in-a-row for this famous square:đŒïž
Researchers challenged longhorn crazy ants and humans with the same task: maneuvering a T-shaped object through two consecutive open doorways. Single humans always outperformed single ants, but ant groups could beat human groups. In PNAS: www.pnas.org/doi/10.1073/...đŒïž
But now of course I want to ask whether this is a specific oddity of the 3Ă3 tic-tac-toe game or whether we can do something analogous to disguise other N-in-a-row games.
Workaround: instead ofâ€â€âŻ | sort -n -k 1â€â€I can useâ€â€âŻ | nl | sort -n -k 2,1 | cut -c '8-'â€â€(add a line number, sort by that line number as secondary key, and remove the line number) but đ€ą. Can I haz better solution?
printf '1\ta\n2\tc\n2\tb\n' | sort -n -k 1â€â€â reorders the last two lines even though they compare equal for the given sort key.â€â€What's the simplest way to avoid this? I.e. âsort numerically on the first column, but keep order when the first column is equalâ?
we should be concerned about the impacts of social media on kids and teens, but i donât think weâre worried nearly enough about what itâs doing to middle aged people and seniors
The only reason you would relinquish the (relative but humor me here) formality and precision of a programming language is if you're not making use of it in the first place. If you're not reasoning about your programs and just do everything by trial and error, you might as well use prompting.
.â€CATHOLIC CHURCH: No meat on Fridays!â€â€ME: Okay, so, no eggs for breakfast.â€â€CATHOLIC CHURCH: No, eggs are okay.â€â€ME: But eggs are chickens, right?â€â€CATHOLIC CHURCH: No, not until they hatch.â€â€ME: OH. So, a thing isn't a thing until it's born?â€â€CATHOLIC CHURCH: Correct. No, WAIT -
Possibly the best Chrismas present ever! Handmade coasters showing the most efficient ways to arrange a given number of squares inside a bigger square. Or, as I call them, tumbledown squares.đŒïž
I very much like this summary of the H5N1 situation. Zoonotic pathogen emergence isn't a simple linear process nor, importantly, is it unidirectional. There are many proportionate steps that can be taken to reduce risks significantly, for example improved health and safety for agricultural workers.đ
From David's famous painting shown in the first tweet (and his later depiction of the tennis court oath) to the Bellamy flag salute, the Olympic oath, the fascist salute and the use of the gesture in Hollywood movies, this âmade upâ salute still has a fascinating history!
But a false idea about History is still something that can have its own interesting history! And Martin Winkler's book âThe Roman Salute (Cinema, History, Ideology)â available online at kb.osu.edu/dspace/bitst... or the Wikipedia article en.wikipedia.org/wiki/Roman_s... are worth reading on this.đ
One of the false ideas so many of us have been led to believe about History is that the ancient Romans used to salute each other by holding their right hand out up in front of them. There is, in fact, no serious reason to think that they did this.đŒïžđŒïž
Give a man a fish and heâll eat for a day. Teach a man to fish and heâll eat for a lifetime. Use him as bait and youâll never have to share your fish again.
Christmas is a good time to throw Wikipedia a few bucks to thank them for the many times you relied on the site that year. Members of the billionaire class want to destroy it for some reason.â€â€(@archive.org is also under constant threat nowadays and in need of support)đŒïž
No, L(A) and L[A] have a different meaning, although they are related (and may be equal in this specific case, I'm not sure): see en.wikipedia.org/wiki/Constru...â€â€In brief, L(A) puts the set A in the model, whereas L[A] puts âbelonging to Aâ as a predicate from which constructibility can be built.đ
Yeah, I'm not saying it's obvious that there's a Ï that works, but I'm saying it shouldn't be surprising that AC has consequencesÂč in second-order arithmetic: it is readily instanciable as many such statements.â€â€1. Unlike GCH, which has none.
Incidentally, I find it quite hilariousÂč that Elon Musk's AI engine, of all people, uses the (singular, gender-neutral) pronoun âtheyâ to refer to me.â€â€1. (Just to be clear, I'm fine with it. It's just funny.)
Previously with ChatGPT. At least our future AI overlords seem to think I'm somewhat interesting: âŹïžđŒïžđŒïž
What Elon Musk's âGrokâ AI engine thinks of me: as usual with AI-generated content, it's plausible, and not entirely wrong⊠but not exactly right either. (I'm not sure whence it got the âlegal nuances of corruptionâ part.) đ€·đŒïž
Ministre 7 mois, par les temps qui courent, ça en fait plutĂŽt rĂȘver certains. đ
Mon beau-frĂšre (qui est catholique) a dit pendant le dĂźner vouloir aller Ă la messe de minuit Ă Notre-Dame de Paris. Tout le monde s'est foutu de lui en disant qu'il y aurait douze heures de queue et qu'il n'avait aucune chance de rentrer. Eh bien non, il a juste attendu 30min pour entrer.
I hope we agree that preventing users from placing certain videos in a playlist is stupid and does not protect kids in any useful way. So either â the law is stupid and has ill-thought consequences, or â YouTube misinterprets it, or â they deliberately try to make the law seem stupid.â€â€Which is it?đ
When a big company tries to tell you that a law protecting you requires them to do something stupid, you shouldn't believe them too easily. One possibility is that they're deliberately trying to make the law pass for stupider than it is.â€â€The đȘđș GDPR is a common target in this maneuver.đ
I mean obviously there's a law that requires âsomethingâ, and someone at YouTube decided that the simplest way to achieve that âsomethingâ would be to forbid putting videos tagged as âmade for kidsâ into playlist. But there's a big inference gap that nobody is able to explain precisely.
I ask again: does the law explicitly and precisely forbid putting a video made for kids into a playlist? If so, what is the exact text and what is its intent? If not, what is the logical inference between what the law actually says and the way it was implemented? How do they get from here to there?
I mean, for example, if the point is that YouTube can't collect data on kids, including kids' playlist, this makes no sense because:â€â€âŁ either they think I'm a kid, in which case they should delete all my playlists,â€â€âŁ or they think not, in which case it doesn't matter if the video is made for kids.
This open source framework for generating procedural 3D scenes developed by the Princeton Vision & Learning Lab, âInfinigenâ infinigen.org , seems almost too good to be true. www.youtube.com/watch?v=6tgs...đ
Are you saying that the law says âyou can't save a video made for children into a playlistâ or that putting videos into a playlist somehow interacts with data collection? Because neither of these things makes sense to me.
Note that the test âif (p == &x+1)â really changes what the compiler thinks about the pointer: if you replace it by âif (1)â the bug no longer occurs because then gcc thinks it's a provenance-less pointer and is careful about it. âą11/11
(Of course there's no difference between &y and &x+1 but that's precisely my point: the standard tries to gaslight us into thinking this difference makes sense, you can do things with one and not the other, but it doesn't make sense if we can read and write pointers in memory.) âą10/11
⊠this new p pointer initially has no âprovenanceâ so the compiler knows it should be careful about it. But by testing whether âp == &x+1â (which must succeed) we confuse the compiler into thinking it has provenance from x whereas it's really &y we have reconstructed! âą9/11
⊠and that the only data they hold is the byte content in memory. So here we create two pointers which are bytewise equal, namely &y and &x+1, and then we create a third array that contains yet again the same bytes and we recreate a pointer thencefrom: ⊠âą8/11
⊠on which you used â&â and within the bounds of the latter, and the compiler uses this for all sorts of optimizations (this concept is known as âpointer provenanceâ). But the other position is that pointers can be stored to memory and read from memory ⊠âą7/11
The deeper problem is this: the C standard basically tries to hold two incompatible positions at once: one is that pointers are some kind of abstract thing that you can create with the â&â operator and when you do you can ONLY use them to modify the object ⊠âą6/11
Then the program uses this reconstructed pointer (which is just &y saved to memory and re-loaded from memory) to modify y, but fools the compiler into thinking that the pointer can't point to y so it optimizes away the modification and returns the wrong value of y. âą5/11
⊠then it copies buf0 to buf in such a way that the compiler cannot analyze what is happening (because a volatile value is used), then loads p from this buffer. So p is just &y (but it is also equal to &x+1, by the previous test). âą4/11
To summarize, this program stores the memory representation of &y (pointer to y) in buf0, then stores the memory representation of &x + 1 (pointer just past the end of x, which is permitted by the standard) in buf1. If they happen to be byte-for-byte equal, ⊠âą3/11
[Meta: I wrote this code some years ago and posted it to Twitter, but I don't think I came up with the idea of it, it's probably well known to experts (however, the threads from that time are all broken so I can't really dig into the history of it).] âą2/11 x.com/gro_tsen/sta...đ
The following program is legitimate C11 (no UB) and should print ây=2â (or âfailedâ). But with many versions of gcc it incorrectly prints ây=1â godbolt.org/z/1YTWWqa5qâ€â€This is a compiler bug, but the detailed technical reason is that the C standard is inconsistent. đâ€â€âą1/11đŒïž
I very much doubt that China's Children Online Privacy Protection Act says âyou can't save a video made for children into a playlistâ. It probably says something quite different, which someone at YouTube could not be bothered to find a way to fulfill except with this completely idiotic restriction.
I wish more people understood that ChatGPT and all its brethren are exactly the same as fortune tellers or spirit mediums throughout history: they spit out generic ideas and guesses based on information you offer, and if they happen to hit pay dirt, you're a lifelong convert.
⊠Anyway, if you're a YouTube creator, you should never ever declare your content as âmade for kidsâ, it will only bring pain and trouble.â€â€Just add a one-second joke at the end of the video that only grown ups will understand, so then you can truthfully say it's not made for kids! đ
⊠I can sort of maybe kind of imagine why there might be some kind of legal restrictions around content made for kids, but why that would forbid adding it to a public playlist makes little sense, and why forbid adding it to a PRIVATE playlist makes absolutely zero sense. What the fđ€Šck, YouTube? âŠ
I really wonder who, at YouTube, decided that âcontent made for kidsâ can't be added to one's âwatch laterâ list, but this makes exactly zero sense.â€â€Is it intentional or is it an unforeseen consequence of something else? âŠđ
âArise most naturallyâ seems to be doing some heavy lifting here. Doesn't a Yukawa coupling work to provide a not-too-weakly coupled massless spin 0 boson, for example?
ââI never thought leopards would eat MY face,â sobs woman who voted for the Leopards Eating People's Faces Party.â www.reddit.com/r/etymology/...đ
ââI never thought leopards would eat MY face,â sobs woman who voted for the Leopards Eating People's Faces Party.â www.reddit.com/r/etymology/...đ
Many people talk about the "Golden Age of Antibiotics", but I hadn't seen it visualized properly. â€â€Just how many types of antibiotics were discovered during that time?â€â€So, I visualized it myself!đŒïž
Facile, âpair de Franceâ, c'est visiblement quelqu'un qui a de la classe, quelqu'un qu'il faut respecter, alors que le pauvre âVictor Hugoâ, aucun titre derriĂšre, n'a aucune classe. J'ai combien?
(Just to be clear when I speak of getting from ÎŁÂčâ to Î Âčâ: here, ÎŁÂčâ is as far as one can go for upwards absoluteness from L or L[x], and Î Âčâ is specifically for conservativity of ZFC over ZF.)
⊠(Note: ââFâ means âhereditarily finiteâ here, and in corollary 8.11 â which is much better known â âÎŁâ means ÎŁâ in the Levy hierarchy.)â€â€As for the trick to get from ÎŁÂčâ to Î Âčâ (using the fact that Choice holds in L[x] for real x) clearly it's not at all known since Noah Schweber didn't see it. đ
⊠That arithmetic ÎŁÂčâ statements are absolute for L (indeed L[x]) and hence ÎŁÂčâ are upwards absoluteness from L (or L[x]) is a not-so-well-known extension/variant of the Shoenfield absoluteness theorem, here âŹïž pretty much exercise V.8.12 of Barwise's âAdmissible Sets and Structuresâ (1975). âŠđŒïž
That this is false for second-order arithmetic shouldn't really be surprising, I think: we can formulate Countable Choice for reals as ân.âX.(Ï(n,X)) â âF.ân.(Ï(n,F(n))) in second-order arithmetic so surely there's a level of the SOA hierarchy at which it doesn't follow from ZF alone. âŠ
(To clarify: the replies/quotes have to be made by other â trustworthy â people, not by you, because they are the ones effectively bearing witness to the original post's CID. A reply/quote by you might have included a bogus CID computed from manufactured content so it can't be used as proof.) âą12/12
Of course this would be tedious to check. It's much simpler to screenshot a skeet if you want to âkeep a receiptâ, âœbut✠a screenshot might be forged, whereas if you keep the original JSON and links to several replies or quotes made by other people, you can use it as proof of authenticity. âą11/12
⊠can come forth at any later time, publish it, and say âthis is what the original message said, and a PROOF of this fact is that the CID matches the one found in any of the publicly available replies or quotesâ, giving a list of them. In principle, anyone can check this. âą10/12
But this also means that anyone replying to one of your skeets or quoting is effectively â”publicly bearing witnessâ” that you wrote a message having that CID. Since CIDs cannot be forged, if you delete a post, anyone who happened to save a copy of the original message (meaning its full JSON) ⊠âą9/12
⊠the point is that the URI lets you find the referred message, and the CID lets you check that what you got was indeed the genuine one. If someone tries to replace the message by a bogus one, the CID won't match, it â·cannotâ· match, so you (well, the software) will detect the forgery. âą8/12
Well, every time a skeet on Bluesky replies to another one, or quotes it, it embeds in its own content what Bluesky (or rather, the AT protocol) calls a âstrong referenceâ: this means it gives both the URI of the referred message âșandâș its CID: ⊠âą7/12
This concept of hashes is a standard tool in crypto (âcryptoâ as in âcryptographyâ not as in âcryptocurrenciesâ, although cryptocurrencies use this tool extensively; but it is also used, e.g., in the Git version tracking system and in lots of other places). But what does Bluesky do with it? âą6/12
⊠and, importantly, it is computationally infeasible (i.e., in practice impossible) to generate a different message with a given CID, or even any two different messages with the same CID. So the CID acts as authenticator of what the message was, without actually revealing it. âą5/12
The CID is an essentially random blurb that is generated from the content of the skeet by a âhashingâ function that cannot be reversed but also cannot be duplicated: from a CID alone you cannot recover the original, but you â·canâ· check whether it is correct; ⊠âą4/12 en.wikipedia.org/wiki/Cryptog...đ
⊠but also a âCIDâ, which in this example is âbafyreieupdsjyla2kyvxycms5tl3dud3rgxdkjtvwijd2oda6fwwofedpaâ (you need to dig in the JSON to find it), which is what is know as a âcryptographic hashâ of its content. It's basically random. But what does this mean? âą3/12
Let me take the following skeet (the first one I wrote) as example: bsky.app/profile/did:... â it is identified in Bluesky by two things: a âURIâ, namely âat://did:plc:tnde52rcbqxotp7a2cl7bmxu/app.bsky.feed.post/3kd22fvhilv24â, which tells us where and how to find it (basically a permalink), ⊠âą2/12đ
Speaking of âreceiptsâ, this reminds me of another Bluesky feature that might be important to understand: every reply to any of your skeets, or any one quoting it, embeds a strong cryptographic hash that could later be used to PROVE that you wrote what you did. Let me try to explain: ⊠đ§”â€”ïž âą1/12đ
Name a non-LOTR character that could resist the One Ring.đŒïžđ
So I just wrote a mini-tutorial on how to do this with Firefox (I suppose Chrome has analogous dev tools so it should be easy to adapt): bsky.app/profile/gro-...đ
Now if you want to actually see it, you go to âhttps://bsky.app/profile/did:â/post/ââ where âââ and âââ are taken from the value you just copied. VoilĂ ! (Of course, this is a bit tedious, but could be automated via a browser extension, bookmarklet or monkey script.) âą5/5
⊠for a quoted skeet, or âthreadâââpostââârecordâââreplyâââparentâââuriâ for a reply. This gives you the sought-after skeet X's permanent identifier (it looks like âat://did:â/app.bsky.feed.post/ââ and you can right-click to open a menu to copy it). âą4/5
There should be one request looking like âapp.bsky.feed.getPostThreadâ (you can also enter âgetPostThreadâ in the filter line). Click on it, then click on the âResponseâ section of the request to view the JSON returned by Bluesky. Inside it, navigate to âthreadâââpostâââembedââârecordâââuriâ ⊠âą3/5đŒïž
Open a new tab, and open the developer tools in this new tab (ctrl-shift-K under Firefox). Go to the ânetworkâ section of the dev tools. Type âmime-type:application/jsonâ in the âfilter URLâ line. Now open (or reload) the quoting skeet (Y) in the tab, so Firefox will show you the requests. âą2/5đŒïž
So here's a quick tutorial on how to retrieve this information: suppose you're viewing a skeet Y by a user B quoting (or replying to) another skeet X by a user A who has blocked B, so Bluesky doesn't show you X, but you want to see it. How to do it? Let's assume you're using Firefox. âą1/5đ
So basically, Bluesky is saying âhere I'm blocking you from seeing the skeet whose URI is as followsâ, so, yeah, it's telling you exactly what the blocked skeet is. Don't be fooled into thinking otherwise. The casual user might be deterred from looking into the JSON, but it's really easy.
In fact, because of the way Bluesky identifies skeets by content (the CID is a strong cryptographic hash of the content), it's impossible to remove the information of which skeet was quoted or replied to. And this is very much by design. (And I think it's a good design.)
The block feature on Bluesky is a bit strange: if user A blocks user B, then B's skeets quoting or replying to A's will appear with the latter replaced by âblockedâ, but in fact the information of which skeet was there is still very much present and readable in the (completely public!) JSON data.đŒïžđŒïž
This. Is. Completely. Insane. If anyone had described this to me, I'd say: you're mad, this absolutely cannot be done, and even if it could, it would cost billions per unit and would break if you so much as touch it. Well, surprise, surprise, I have nine of them just right here.
And this head can be repositioned with incredible accuracy to detect or change the orientation of any one of these 30âŻ000âŻ000âŻ000âŻ000 magnets at a burst rate of over 1âŻ000âŻ000âŻ000 PER SECOND. With an almost vanishing error rate!
Think: in this box of <400cmÂł in volume we routinely pack over 30âŻ000âŻ000âŻ000âŻ000 little magnets on metal plates that are rotating at 120 rotations per second and read by an electromagnet head floating NANOMETERS above a drive platter that's spinning at ~100km/h below it.
I sometimes complain that computer hardware is shitty, but I think the modern hard drive is arguably the most incredibly insane technological marvel that mankind has produced. That we can mass-produce these objects for around 100⏠is simply mind-boggling.
With the number of things Trump promises to do âon day oneâ, I begin to suspect that his actual first measure will be to redefine the legal meaning of a day in the US to be 35âŻ064 hours.đ
The one with all my tweets is at www.madore.org/~david/tweet... â but it's become exceedingly fastidious to maintain since Elon closed all public APIs to access Twitter.đ
I'm tentatively putting up a Web page with all my skeets just like I was already doing with all my tweets.â€â€It's at www.madore.org/~david/skeet... â it might be broken in various ways since I haven't had much time to test it yet.đ
Look, ever since I learned that âis the category of computads for a finitary monad on n-globular sets cocomplete?â mathoverflow.net/q/431888/17064 is (it seems!) a real math question, I've given up on trying to decide what jargon makes sense and what doesn't. Turbo encabulator cardinals could exist!đ
There's this great YouTube channel (âPatrick Kellyâ) about the history of medicine www.youtube.com/channel/UCXG... which I strongly recommend. For example, this one www.youtube.com/watch?v=z_U6... on the placebo effect explains how we got modern randomized control trials with double blind tests.đ
There's this great YouTube channel (âPatrick Kellyâ) about the history of medicine www.youtube.com/channel/UCXG... which I strongly recommend. For example, this one www.youtube.com/watch?v=z_U6... on the placebo effect explains how we got modern randomized control trials with double blind tests.đ
The fact that in the 1890's drug companies could get away with selling heroin over the counter but now some people have irrational qualms about the safety of vaccines speaks of how incoherent our society's relationship to risk is.đ
My favorite detail of its history is that "Heroin" is a brand name, like Kleenex or Coke. They called it that for its "heroic" cough-suppressing and pain-stopping abilities.đ
Yes, it might be a bit better for some things. But for others it's not great because many statements (like ââ”_α + â”_ÎČ = â”_(sup(α,ÎČ))â or âthe generalized continuum hypothesis asserts that 2^(â”_α) = â”_(α+1)â) only work for infinite cardinals anyway. âŠ
Ăa y est, j'ai reçu le livre de @pverschu.bsky.social â et il n'est pas facile Ă trouver!â€â€(Comme fils de physicien je me dois de lire ça.)đŒïž
Il y a toutes sortes de maniĂšres d'expliquer que (â1)Ă(â1) = 1, allant de l'intuitif («retirer une dette de 1⏠c'est comme donner 1âŹÂ») au formel («on veut que aĂ(b+c) = aĂb + aĂc, et pour que ça marche avec a=â1, b=1, c=â1, ça impose que â1Ă(1+(â1)) = â1Ă1 + (â1)Ă(â1) soit 0 = â1 + (â1)Ă(â1)»), âŠđ
It is true that in many cases the question of âwhy precisely this definitionâ has no (known) satisfactory answer other than âthis gives rise to a nice satisfactory theoryâ. But then we should be honest about it.đ
Also: students have a right to ask. If someone hears a course on groups, rings, or topological spaces, they have a right to raise their hand after the definition and ask, âOK, but why are we defining precisely this concept? whence do these axioms come?â. Be prepared to answer this if you teach!
I agree that mathematicians could/should do a better job of justifying definitions. Although it is not logically necessary, the reader has the right to know why we define a concept in a particular way or why we decide to study precisely this thing and not some other variant.đ
⊠âWhy do we get these nice theorems on the Borel hierarchy?â may be entangled with issues of computability (there is a lightface as well as a boldface Borel hierarchy). Or it may be as dumb as finding a simple way to define spaces that are naturally Borel-isomorphic to â.
⊠and someone (I think it was Bourbaki?) tried to find a unifying hypothesis from which these theorems would deriveâ (mostly you need Baire's theorem to work, but the conclusion of Baire's theorem alone doesn't suffice).â€â€The second qn is probably deeper but may not admit a satisfactory answer. âŠ
There are actually two different questions here. One is how this definition arose historically, and the other is the more philosophical question of whether and why it is ârightâ.â€â€As to the first, I think look no further than âvarious theorems had been proved on â^n, Baire space and Cantor space, âŠ
I made these two videos some years ago: one simply shows growing circles on the flat torus defined by a square lattice, the other shows a solution to the 2D wave equation on the same space (starting from a sharp peak), with the same scale of space and time so we can compare the two. Mesmerizing!đđ
It should be compared with this one www.youtube.com/watch?v=vod6... which it attempts to âexplainâ.â€â€[I'm the one who made them, btw. So thanks!]đ
⊠But the time could be in milliseconds or microseconds (or something else), the epoch could be different, there could be more than a timestamp, and so on. I've tried comparing differences of post IDs to differences of timestamp, with little success, but who knows.
The skeet at the top of this thread has post ID â3ldo5xar6p22lâ representing 11011010 11000110 11101110 11011100 00010001 11110011 11110101 10100101 in binary. Its timestamp is 2024-12-19T15:13:53Z or 1734621233s into the Unix epoch, 01100111 01100100 00111000 00110001 in binary, so no match. âŠ
On Twitter, the âsnowflake IDâ encodes a timestamp, as I had previously explained. bsky.app/profile/gro-... ⧠So I'm kind of hoping there were something similar to do with a Bluesky post ID.đ
For example, the previous tweet (also quoted) has permalink âat://did:plc:tnde52rcbqxotp7a2cl7bmxu/app.bsky.feed.post/3ldo5xar6p22lâ â Does â3ldo5xar6p22lâ encode a meaningful information like a timestamp?đ
The permalink URI of a Bluesky post consists basically of the DID of the author (in my case: âdid:plc:tnde52rcbqxotp7a2cl7bmxuâ) and a 64 (or 65?) bit number encoded in base32 (RFC 4648 style).â€â€âŁ QUESTION: does the latter part have a documented meaning? E.g., is it based on some kind of timestamp?
OĂč je parle des stylos Ă encre gel de la marque Pilot et du problĂšme trĂšs grave de l'absence d'un Pilot V Sign Pen de couleur rose qui logiquement devrait exister: www.madore.org/~david/weblo...đ
On a certain level, I'd say the only piece of software you should really trust are those that were released many years ago and that have had no updates since, â not because nobody is maintaining them, but because they had no bugs to fix and decided not to add any new features. But that's⊠rare.
⣠It's not just a security issue. (Security-wise, any Linux box has a gazillion packages installed anyway, so I'd say that horse has left the barn.) It's also the question of who maintains these many dependencies and what will happen when they, inevitably, grow old and retire.
⣠This is not Rust specific. Python and server-side JS (Node) appear to have the same problem. OTOH, for some reason Perl or Java don't seem to suffer from it (at least not to the same extent). So it would beseem to understand why certain languages are more prone than others to dependency explosion.
Alors «interambulacraire» c'est vraiment super rigolo, comme mot. Mon seul reproche avec, c'est que c'est un peu difficile à placer dans la conversation de tous les jours.
That's the sort of things I want to find out. Given that this formula makes sense in any topos whatsoever (something which I think is absolutely amazing) I want to try to understand what it actually says in lots of different topoi, esp. ones of the realizability kind.
⣠âFolk who had the choice would liever dwell otherwhere.â â Again, âotherwhereâ is easy to understand, but âlieverâ I only recognize through German âlieberâ.â€â€These are all in the first two paragraphs of chapter II. And just after that we get âwotâ, âforsoothâ, âwithalâ, etc.
⊠only because I know the German âheiĂenâ.â€â€âŁ âThe pasture was good for kine and horses and sheep.â â I think I had previously encountered the plural âkineâ of âcowâ, but it certainly escaped my mind!
⣠âOn the east side of the Sundering Flood was erewhile a stead hight Wethermel.â â So, âerewhileâ is easy to understand but I can't say I knew that word existed; âsteadâ I knew but hardly ever met outside of âhomesteadâ; and âhightâ (past participle of âhoteâ) I understand âŠ
It appears that reading William Morris's âThe Sundering Floodâ is a good way to learn a bunch of obsolete or half-forgotten English words. Some of them I only understand because I know some German. A few examples: âŠ
Similarly, I wonder why the author insists on giving fairly long and detailed descriptions of some things which seem completely irrelevant to the plot, and expedites highly important parts in half a sentence. Is it to make the point that we don't know what really matters in life?
For example, I wonder if the fact that every character seems to always react in just about every situation in a way that (to me) seems completely unnatural is supposed to be deliberate or whether the author has a very different idea from mine about how people react.
I just finished reading Max Frisch's book âHomo Faberâ, and while I can't say I disliked it, I still feel like there's supposed to be a point to the book but I completely missed it.
I rather enjoyed this video discussing the (unproven, dubious, and at least largely exaggerated) idea that the Roman empire collapsed because of lead poisoning: how the idea arose, and what can be said about the matter. www.youtube.com/watch?v=9oR-...đ
Vivaldi's âQuattro Stagioniâ is a great piece of music, but it's a shame that its success completely overshadowed other fine pieces by the same composer, such as âCapricciosaâ, âCalzoneâ, âQuattro Formaggiâ and, of course, âMargheritaâ.
The reason I'm interested in this is that when A,Bââ (viewed as (ÂŹÂŹ)-closed subobjects of the natural numbers object), the above statement interpreted in the effective topos is equivalent to âA is Turing-reducible to Bâ (as shown at the end of Hyland's 1982 paper on the effective topos).
⊠seems to roughly account for the impredicativity of calculus-of-construction type theories, as per Rathjen's paper cited 4 skeets above.â€â€(But I'm talking out of my ass. Obviously, if even Michael Rathjen doesn't know this, then nobody knows.)
⊠The intuition behind this would be that KPi (the non-âpowerâ version) := KP + âevery set is contained in an admissible setâ seems to be a ballpark proof-theoretic strength for variants of MLTT with universes per link.springer.com/article/10.1... and that adding a power operation âŠđ
⊠In fact, I suspect that CICÏ has a proof-theoretic strength around Power-KPi := Power-KP + âevery set is contained in a power-admissible setâ (where âpower-admissibleâ means its a model of Power-KP with true powerset â see mathoverflow.net/q/257832/17064 ) or something not far from that. âŠ
After skimming through that paper (which is far from the hardest to read of Rathjen's papers, but beware that for some reason ââšâ has accidentally been placed by ââš,ââ everywhere), I suspect that the proof-theoretic strength of CICÏ is roughly in the vicinity of Power-KP. âŠ
« Now the trouble about trying to make yourself stupider than you really are is that you very often succeed. »â€â€ (C.S. Lewis, The Magician's Nephew)
⊠Rathjen's paper âConstructive Zermelo-Fraenkel Set Theory, Power Set and the Calculus of Constructionsâ link.springer.com/chapter/10.1... â which was suggested to you on Proofs Assistants SE â has precise statements (that are accurate, unlike mine).đ
⊠any single theorem of ZFC uses only finitely many axioms of ZFC, so follows from ÎŁ_n-Replacement for some concrete n. (And, for what it's worth, for all âstandard mathematicsâ, ÎŁâ-Replacement should always suffice: it's the higher replacements which are to be considered âlarge cardinalâ axioms.)
⊠by transfinite (or well-founded) induction, and Zermelo+KP should be enough to prove many usual properties of the V_α. I'm a bit lost as to what you're trying to do (and since I have no idea how one constructs models of CIC, this won't help), but one thing is certainly obvious: âŠ
Some form of Replacement is needed, certainly, but I think ÎŁâ-Replacement is sufficient (i.e., your statement is a theorem of Zermelo+KP). This probably follows from the results of Barwise, âAdmissible Sets and Structuresâ (1975), chapter I, §6. Generally speaking, KP lets you do definitions âŠ
First they came for the queers and in this instance "they" is the *second* Reich, Prussia and Germany criminalized homosexuality from 1871 onwards (nazism made it worse, of course) and of course a fascist priest like Niemöller wasn't going to include them in his shitty poem.đ
Ah! I just realized that @joeldavidhamkins.bsky.social is also on Bluesky. The pool of interesting people on Twitter who have yet to open a Bluesky account is dwindling.
Just learned (through the Musky place) about the existence of this Web site and tool to explore old maps of various parts of the world (either scans of historical maps, or reconstituted historical borders): www.oldmapsonline.orgđ
Firefox Mobile is rolling out in version 134 a disastrous UI change which adds a new toolbar (on top of the existing address bar) which is stuck at the bottom of the screen (unlike the address bar which can be moved to the top). đâ€â€If you don't want this, avoid auto-upgrade!đŒïžđŒïž
To clarify the last part, binomial(r,n) is, for fixed n, a polynomial in r with leading term r^n / n! and next-to-leading term negative, so it's not really surprising that r^n // binomial(r,n) will give you back n! when r is appropriately chosen (finding such r may be a bit tedious, though).
Basically, it's like sayingâ€â€1001^8 = 1âŻ008âŻ028âŻ056âŻ070âŻ056âŻ028âŻ008âŻ001â€â€in which I can read the line (1, 8, 28, 56, 70, 56, 28, 8, 1) of Pascal's triangle. Not really magical.â€â€And getting n! from binomials isn't too surprising either.
Basically, it's like sayingâ€â€1001^8 = 1âŻ008âŻ028âŻ056âŻ070âŻ056âŻ028âŻ008âŻ001â€â€in which I can read the line (1, 8, 28, 56, 70, 56, 28, 8, 1) of Pascal's triangle. Not really magical.â€â€And getting n! from binomials isn't too surprising either.
Seriously, when you look at the formula, it isn't so surprising: you compute (2^k + 1)^r for large enough k (apparently kâ„r suffices), this gives you a full line of Pascal's triangle which you can basically read off from the binary expansion.
For what it's worth, Twitterâ«đ does this little bit correctly: middle-click on a quoted tweet will open the quoted tweet in a new tab.â€â€(All this assumes the browser is set up so that middle click opens a link in a new tab, of course.)
Workaround is tedious: copy the URL of the current skeet (the quoting one), open a new browser tab, paste the URL in that new tab, so as to get a second tab on the quoting skeet, and click on the quoted skeet in the second tab.
â± Really annoying UI misfeature on Bluesky: when viewing a skeet that quotes another one, I can click on the quoted skeet to see it in full, but I can't middle-click to open it in a separate browser tab. Which is something I often like to do (to read replies).â€â€(Tagging @support.bsky.team here.)
My intuition on this is more like âthe formulation chosen here for what is supposed to be âChoiceâ is actually a form of Replacementâ (symmetrically to the fact that Collection is supposed to be a form of Replacement but actually hides some Choice). But I didn't look into this (nor do I intend to).
(Therefore if we are to try to replicate the strength of Replacement in a type system, I suspect the right way to do it should be a principle that somehow says that whatever holds in Type_(i+1) holds in Type_i in a certain sense.)
⊠but reflection principles into these sets from the entire universe (âany set of statements true in V will be reflected into some (and indeed, club-many) V_ÎŽâ) setting up a kind of hall of mirrors of set-theoretical truth where the microcosm reflects the macrocosm (pardon the poetic language!).
⣠The moral of the story (IMHO) is that Replacement is a crazy strong axiom, that looks innocuous because on the set-theoretic (cardinality) level it seems reasonable, but logically it establishes not just lots of sets that act as universes for weaker theories, âŠ
⊠but sometimes the meaning is different, e.g., when talking about KP it means âadmissible and limit of admissiblesâ (aka ârecursively inaccessibleâ). I don't know what âinaccessibleâ for Zermelo means exactly, but it's probably something weak w.r.t. ZFC.
⊠ZFC produces many such ordinals which are limits of such ordinals, or any such level of iterations (i.e. it says the ordinals are âMahloâ in a certain sense, and even that many ordinals are Mahlo in such sense, etc.). âInaccessibleâ alone normally means âfor ZFâ, âŠ
⊠Any L_ÎŽ with ÎŽ an admissible ordinal (= ârecursively regularâ) is a universe for KP, so ZFC produces many of them. Any V_ÎŽ (= L_ÎŽ) with ÎŽ a fixed point of Ο ⊠â¶_Ο is a universe for Zermelo+KP, so again ZFC produces many of them. Moreover, in each of these cases, âŠ
I'm not sure whence this statement is from, but the gist of it is probably that âinaccessibleâ is an ambiguous term with a different meaning according to what we are using it on. Any V_ÎŽ with ÎŽ a limit ordinal is a universe for Zermelo set theory, so ZFC produces many of them. âŠ
To be clear: barring (likely!) mistakes, the fully substituted formula is sth like:â€â€n! = 2^(n^3) // (((2^(2^(n^2)) + 1)^(2^(n^2)) // 2^(2^(n^2)*n)) - 2^(2^(n^2)) * (((2^(2^(n^2)) + 1)^(2^(n^2)) // 2^(2^(n^2)*n)) // 2^(2^(n^2))))â€â€(where a//b := âa/bâ refers to integer division, and ^ is power).
Learned on MathOverflow: it is possible to write a finite formula for n! involving just the operations of addition, subtraction, multiplication, integer division, and exponentiation. Precise statement is here: mathoverflow.net/a/484115/17064đŒïž
Intel launched the Pentium processor in 1993. Unfortunately, dividing sometimes gave a slightly wrong answer, the famous FDIV bug. Replacing the faulty chips cost Intel $475 million. I reverse-engineered the circuitry and can explain the bug. 1/9đŒïž
⣠What is the strength of Replacement versus Collection in IZF?â€â€It is known that IZF-cum-Replacement is strictly weaker than IZF(-cum-Collection): see Friedman & Ć Äedrov, âThe lack of definable witnessesâŠâ, âAdv. Math.â 57 (1985) 1â13 doi.org/10.1016/0001... corollary 1.1. âŠ
PS: For more about the nitty-gritty details of what axioms give what in constructive / intuitionistic set theory, the go-to reference is Aczel & Rathjen, âConstructive Set Theoryâ (note that there exist several versions of that text, an 88-page report from 2001, and a ~240-page book draft of ~2012).
⊠However, on the CZF side, Rathjen, âReplacement versus collection and related topics in constructive ZermeloâFraenkel set theoryâ, âAnn. Pure Appl. Logicâ 136 (2006) 156â174 doi.org/10.1016/j.ap... shows that using Replacement instead of Collection does not decrease proof-theoretic strength.
⊠And also, it has strictly fewer provably recursive functions âââ (op. cit., §3), leading Friedman & Ć Äedrov to conjecture that ZF proves the consistency of IZF-cum-Replacement (while it is equiconsistent to IZF). But AFAICT this is still open. âŠ
⣠What is the strength of Replacement versus Collection in IZF?â€â€It is known that IZF-cum-Replacement is strictly weaker than IZF(-cum-Collection): see Friedman & Ć Äedrov, âThe lack of definable witnessesâŠâ, âAdv. Math.â 57 (1985) 1â13 doi.org/10.1016/0001... corollary 1.1. âŠ
⊠The drawback is that Collection appears to involve an implicit kind of Choice (because given âxây(âŻ) it basically says we can choose set-many y for every x), which may be undesirable and indeed breaks the existence property (see Friedman & Ć Äedrov's paper cited below).
⣠Why use Collection rather than Replacement in IZF?â€â€Because Collection is the one which is generally useful in that it allows us to usefully deal with bounded quantifiers. Intutionistically, Replacement doesn't appear super useful, so Collection is preferred. âŠ
At the very least, this suggests that it's not known, and probably not believed by experts, that CICÏ interprets ZF(C), because this would go very much against it having the consistency strength as CCÏ.
⊠whereas Zermelo set theory is around higher-order arithmetic. So I'm not at all surprised if adding some kind of inductive constructions makes the weaker systems much stronger but doesn't add anything to the already strong systems.â€â€PS: I have no idea what I'm talking about, of course.
Yeah, but these are in a completely different realm: every system listed in that page is way below second-order arithmetic PAâ (getting an ordinal analysis of PAâ is a kind of holy grail, even though Dmytro Taranovsky claims to have ordinal notations going even beyond that), âŠ
⊠So if some kind of typing system can produce this particular large cardinal, I naturally want to know whether it can produce larger ones (hyperinaccessible? Mahlo? weakly compact?). The key to getting such things seems to be in reflections principles, so I'd try to look for such things.đ
In a sense, the strength of ZFC is a complete red herring: I don't think there's anything really remarkable about this specific large cardinal assumption, which is linked to the intricacies of set theory (and the historical accident that we settled on this particular one). âŠ
Here's my intuition, take it for what it's worth: ZFC (or maybe second-order ZFC) is all about saying the class of ordinals satisfies some large cardinal axiom, namely being inaccessible. What you'd need is some kind of inductive definition of âthe smallest inaccessibleâ. I don't think we can.
Not really, because comments are supposed to be about commenting the question, not for extended discussion (when you post more than one or two, a bot tells you that you should be doing it elsewhere â at least on MathOverflow it does).
Actually, the validity of CH in L is fairly tricky (there's a âGödel condensation lemmaâ which I once understood but no longer do) whereas that of AC is pretty straightforward (L is well-ordered almost by construction). Devlin's book on constructibility may interest you if you want to know more.
⊠but anything close to ZF would really surprise me enormously (and would immediately raise the question about interpreting larger infinities like ZFC + âOrd is Mahloâ or such). ⧠PS: I should also add that IZF interprets ZF by some kind of double negation translation.
⊠and I seem to remember @aspiwack.bsky.social suggesting somewhere that the âinductiveâ part doesn't increase consistency strength (but I may have misunderstood). I wouldn't be so surprised if you can prove the consistency of something like Zermelo + Îâ-Replacement, âŠ
Besides that, all I can say is that âI believeâ that CICÏ is much weaker than ZF(C). As I point out in an answer to the second MO question you linked, Miquel's thesis conjectures that CCÏ is equiconsistent with Zermelo + universes, which is phenomenally weaker than ZF, âŠ
The way you word the question around âremoving choice on both sidesâ suggests that you may not be aware that ZF interprets ZFC, so, for what it's worth, this is the case (precisely, you get ZFC by relativizing all quantifiers to constructible sets in the sense of Gödel's constructible universe L).
Le texte anglais ne dit pas la mĂȘme chose que le texte français et ça me perturbe gravement.đŒïž
Macron: Je prepare une SURPRISE!â€â€Journalistes: C'est Bayrou? Vous allez voir ca va etre Bayrou.â€â€Macron: đ nn c pas bayrouâ€â€*2h plus tard*â€â€Macron: J'ai decide de nommer Bayrou premier ministre.
âOh, I'm just going to try to construct a more stable vacuum state of the Standard Model in my basement.â â Last words spoken moments before the Universe decayed into something even more bizarre and inexplicable.
But if we can't convince one or several of the countries in red to flip their position and oppose this disastrous idea, it will come back again, and again, and again, like it already has many times. www.patrick-breyer.de/en/posts/cha...đ
Once again, the EU Council fails to achieve a qualified majority in favor of the disastrous #ChatControl regulation (âCSARâ) for widespread surveillance of private communications.â€â€Let us thank the countries in green đœ (blocking minority) for being the good guys in this matter. x.com/echo_pbreyer...đŒïž
btw, you realise Elon is going to fuck up with Starlink and single handedly Kessler satellite deployment out of existence, then walk away with no real consequences
Additional bits of info:â€â€â I read the short story in French. I think the original was in English, but I'm not 100% sure. But I'm sure that it took place in the US.â€â€â The sum of money the old woman got was impossibly large, and also absurdly precise (ending something like âand 27 centsâ).
Trying to remember a short story I read 35 years ago (about an old lady accidentally inheriting a huge sum of money from a mafia boss âŹïž) is something I was really hoping ChatGPT would be able to help me with, but alas, no.â€â€Does a human in the room want to try to rise to the challenge?đŒïžđŒïž
OK, this is disappointing. It was supposed to refer to this: bsky.app/profile/did:... â but apparently the âat://â syntax isn't recognized even though it's used internally all the time.đ
Suppose I enter a URI such as at://did:plc:tnde52rcbqxotp7a2cl7bmxu/app.bsky.feed.post/3lcsk26kj3s2p in a skeet: will Bluesky convert it to a link, and/or quote the relevant post?
In most cases, the phrase âbusiness successâ is a lie.â€â€It's usually a propaganda phrase for malignant narcissists with severe lack of empathy.
It's interesting how intensely *hostile* basically all tech is now. Everything you own is spitting in your face all the time and daring you to do something about it.
⊠Nobody said that a âformulaâ has to be a word on a finite alphabet: that's a completely irrelevant coding level. What it needs to be is something that can be handled algorithmically: we don't insist that finite graphs be given name on vertices, why demand this of formulas?
Seriously, I don't see why we can't say that a bound variable is an arrow that points to an earlier binder (quantifier, lambda, whatever). The arrow has no name, it just points somewhere, like an edge in a graph. Trying to represent the arrow by something (a name, or DB index) misses the point. âŠ
⊠It's a bit like trying to specify an algorithm with pointers, and defining the pointer library (allocation, movement, whatever) at the same time instead of treating it like a black box. De Bruijn indexes are better, but they still miss the point: a bound variable is just a pointer to the binder.
Clearly there is something to be said for the argument that defining terms by the concrete syntax by which they are marshalled into character strings (or token strings or whatever) is silly because that is neither how we think of them nor how we implement them: α-conversion shouldn't even exist. âŠ
Perfect time to remind us that Rosemary made a wonderful book about Pigeons two years ago đȘ¶. And it's a blast. If you don't know it...we are close to christmas,so đâ€â€rosemarymosco.com/books/a-pock...đđ
I wrote a lot in 2020, but I guess the entries in question were mostly referencing each other. It might be interesting to run a cluster analysis algorithm on the graph of references, but I don't care enough to try to learn how they work.
The AI folks have been warning us of such existential threats to mankind as the âpaperclip maximizerâ without realizing that they had among their ranks a very human threat of the exact same kind, the âElon Musk satisfaction maximizerâ, Elon Musk, who is quite ready to make mankind perish for it.đ
I see no coherent argument for him being anything but the most dangerous man in history. He's on drugs, doesn't experience empathy, and is a white supremacist, the richest man on Earth, media illiterate, a pathological liar, unscrupulous, a fraudster, and candidly (sans one subject) barely educated.
shooting a CEO of a health insurance agency then taking your homemade gun to mcdonalds and getting arrested while eating a burger has got to be the most american series of events that has ever happened
Ralph Fiennes is a great actor (and his Italian is pretty good), and âŠâ€â€âŠ wait, what, he's the guy who played Voldemort✠I didn't see that coming! đ€Ż
I just saw âConclaveâ and I rather liked it: although I thought the end was a bit too far-fetched, it was enjoyable like a riddle wrapped in a mystery inside an enigma. www.imdb.com/title/tt2021...đ
Plan for answering an email is basically: â procrastinate while reading Bluesky/Reddit/MathOverflowâŠ, ⥠change my mind ten times about which email I'm going to answer, âą look at my calendar, which isn't properly filled in, so I need to do that first, ⣠agonize about what to call the recipient, âŠ
In my case, it takes me basically all morning to answer a single email, even when the answer is âyeah, let's do thatâ, so indeed â I need to take a break after that (namely, lunch), and â not many of my emails get answered.đ
⊠and that it was an open question whether â(â2) was also such. This makes very little sense and/or is trivial, and it wasn't even so clear, so I'm keeping the part of the dream which âșdidâș make sense. It's not like I copied it verbatim from my dream.)
(Actually, my dream was a bit more specific: in it, a âdescriptively modestâ set was a difference set of a difference set of a discrete set [i.e., in đÂČ with the above question's notation], and I was told that â was descriptively modest âŠ
What are the difference sets of discrete subsets of â? Are they all the countable subsets? If not, how far do we need to iterate âtaking difference setsâ before this stabilizes? math.stackexchange.com/q/5009190/84...â€â€This question occurred to me during a dream last night! đđ
All right, here's âŹïž what the JSON looks like: no extra level of quoting like Twitter does it.đŒïž
Sorry for the noise: I need to write a skeet with the â&â sign (U+0026 AMPERSAND) in it, to see whether Bluesky quotes it in JSON. Let's put â<â and â>â in there as well (U+003C LESS-THAN SIGN and U+003E GREATER-THAN SIGN).â€â€And a URL with a â&â as well: www.google.com/search?q=exa... say.đ
Well, for what it's worth, I really did read Hartshorne's book. Not in all the gory details, and I certainly skipped over some parts, but it's probably one of the math books that I read with most care. SGA4 is really in a different category (for one thing, it's over 3 times longer).
There are three kinds of mathematicians: those who can count, and those who can't.
I hope to set up a Web page with all my skeets soon, just like I have one with all my tweets at www.madore.org/~david/tweet... (the latter has become insanely annoying to maintain ever since Musk closed all public APIs, incidentally).â€â€This little program đœ is my first step toward that.đ
(Instructions for use are in the comments at the start of the file. But again, you shouldn't use it: you should read it, understand it, and write your own code. đ)
If this is of use to anybody, I wrote a simple Perl program to try to download all of one's (or indeed someone else's) skeets, or all of one's likes. It's meant to be a simple illustration of how to use the Bluesky API, not for actual use. gist.github.com/Gro-Tsen/3dc...đ
The release of âStar Wars: Episode V â The Empire Strikes Backâ is closer in time to the start of the Spanish civil war than it is to the present.
Is there a piece of art that you think about often?â€For me this one comes up frequently. "Molnet" (The Cloud)â€painted by Prins Eugen 1896, Swedish.đŒïž
A simple experiment you can do is buy a server, set up a website with nothing on it, then look at the access logs. All day, every day, there are random systems just blasting vulnerabilities at every device on the internet. Analysts call it "background noise", executives call it "cyber attacks".
In October, Rwanda reported its first Marburg virus outbreak, for which there are no vaccines or treatments. Following a COVID-19-style mass test, track, and trace operation, the case fatality rate plummeted, and the outbreak has now been declared over. NPR https://buff.ly/49f7esnâ€#ShareGoodNewsToođ
⊠So the joke here (or maybe the meta-joke â anyway) is that there exists a funny joke where a priest, a rabbi and an imam enter a bar, and the way a mathematician makes a funny joke is by reducing ourselves to this already established case.
Mathematicians notoriously like to solve problems by reducing them to previously solved problems, and there are various jokes around this, e.g., I had tweeted this x.com/gro_tsen/sta... during the 2021 Suez Canal obstruction. âŠđŒïž
A mathematician enters a bar. He leaves and is replaced by a priest, a rabbi and an imam, thus reducing ourselves to a joke previously shown to be funny.
Yeah, but it's really bizarre to have taken something so incredibly specific as 2010-11-04T02:42:54.657Z as epoch. Normally one picks a rounder date (like the Unix epoch or the GPS epoch chose). Did Dick Costolo do something really special at this specific time?
This documentary on wild haggis in Scotland is something I would have called a âhilarious jokeâ if I didn't know that there are people who actually think the Earth is flat. www.youtube.com/watch?v=PjK2...đ
Not only is the timestamp embedded everywhere in the Twitter API, it's even embedded in the tweet number (aka âsnowflakeâ): take the tweet number, shift it right by 22 bits, and add 1288834974657 (for some reasonâŠ), and you get the time in milliseconds since the Unix epoch.â€â€Hard to get rid of!
Ok, joke time: do you know the Darwinian theory of gravitation?â€â€Originally, apples fell from trees in all directions, but only those that fell to the ground would give new apple trees, so the downward-falling genes were quickly selected.
We humbly interrupt your scroll to bring you the news that Wisdomâthe world's oldest known wild birdâis breeding again, age 74.â€â€Go on girl. đđŒïž
So apparently the British Home Office in 1958 commissioned a study on homosexuals, which was subsequently published (Richard Hauser, âThe Homosexual Societyâ, 1962). Sixty years later, it makes for an⊠interesting read. It's on the Internet Archive: archive.org/details/the-...đ
A new paper suggests that Venus has been a hellscape for its entire history. No oceans, ever. This result comes from the estimated ratio of water vapor in volcanic outgassing. On Earth, eruptions are mostly steam from interior water, but on Venus, they're 6% at most.â€â€www.cam.ac.uk/research/new...đŒïž
âThe law, in its majestic equality, forbids the rich and poor alike to sleep under bridges, to beg in the streets, and to steal bread.â (Anatole France)
Korea Expert here. Iâll explain whatâs going on over there because the Orient can be confusing to Westerners. In Korea, there is a concept known as âthe law.â (ëČ) This is a set of rules which are enforced to encourage prosocial behavior and ensure stability which leaders arenât allowed to break.
Maybe âproving stuff in Coq is so easy and so painless, intuitionistic logic is so lenient, that it would really make it more interesting if it were to incorporate some of the fussy distinctions of linear logicâ? đ
South Korea rn is what it looks like when people see democracy as a fragile thing that needs to be defended by all means necessary, and not as their inevitable birthright as citizens of an exceptional nation
And for some actual stats: peak democracy in the world was around 2010 (give or take a few years depending on your exact metric). The last decade or so has been a clear regression. ourworldindata.org/less-democra...đ
I knew democracy was on the decline everywhere in the world, but I really didn't expect South Korea to leave the club in 2024.đ
I think it's more like âthe rest of the joke is relegated to an appendix that will not appear in the printed version of the joke conference proceedings, and has not been peer-reviewed for funninessâ.
A mathematician enters a bar. The rest of the joke is left as an exercise to the interested reader.
C'est une bonne chose de ne pas toujours avoir une opinionâ€â€Â« Je ne sais pas », « je ne suis pas sĂ»r » ou « j'ai besoin d'en savoir plus » sont des points de vue valides
The original paper by Hedberg has a section called âIntuitionâ. Have you tried reading it? I remember going through it and thinking it made sense. doi.org/10.1017/S095... (But then, I also remember thinking I couldn't understand why the theorem was supposed to be interesting, so there's that.)đ
I'm fine with calling pigeons ârats with wingsâ.â€â€It's not because I don't like pigeons, it's just because I think rats are also very cute. đđ
I understand the satisfaction of "deleting" your Twitter account but I would not. Clear it if you desire. All your data there is not under your control and gets you nothing except a flag in one version of the data that says deleted. You need to deprive usage of your username and connected contexts.
I sometimes feel Keith Haring has been sanitized to make him âsafer for the massesâ. Some of my favorite pieces by him are those that celebrate gay sexuality.đŒïžđŒïž
Actually, the most annoying thing about doing stand-up comedy to a crowd of neutrons is that, no matter what you say, 15min later, half of them have already left the room. đđ
(En fait, c'est en §16.5 du livre de Chagrov et Zakharyaschev, âModal Logicâ (1997), et je ne sais pas pourquoi je ne m'en souvenais pas parce que j'ai au moins vu ce truc. Mais la preuve est tout aussi merdique lĂ -dedans.)
There is even a trio of trios of (at least partly) Germanic speaking countries in Europe:â€â Belgium, Netherlands, Luxembourg,â€â Norway, Sweden, Denmark,â€â Germany, Austria, Switzerland.â€â€(And now I want to organize the 27 EU countries in a trio of trios of trios.)
Il faut admettre que, autotools ou pas, il y a fort peu de programmes qu'on peut compiler en tapant soi-mĂȘme âgcc quelque choseâ. Je ne sais sincĂšrement pas quel est le moins pire des build systems.
I asked a question on MathOverflow on pointfree topology: how to describe the preimage of a sublocale by a morphism of locales, using the ânucleusâ description of sublocales. mathoverflow.net/q/483342/17064đ
The page is here: homowiki.de/Kekswichsenâ€â€There needs to be a German word for âcreating excruciatingly precise wiki pages as a form of sexual gratificationâ.đ
There is nothing more quintessentially German than to have a wiki page describing a group masturbation game that goes into every detail you can imagine on the playing the game, its exact rules, how it's called in various languages, and⊠49 FOOTNOTE REFERENCES to top it all off.đŒïžđŒïž
Yes: the Gutenberg edition, of course, has been proofread by actual humans. If the idiots who printed my scam edition had merely turned to Gutenberg rather than the OCR from the Internet Archive, I would have much less to complain about.
OK, and, next question: how and where can I find a proper edition of that book? Is it truly the case that no reputable publisher has this in print?đ
⊠That half-line was turned into gibberish by the Archive's OCR process, the result of which is here: archive.org/stream/sunde... â and it's that exact gibberish that got printed in this âeditionâ I bought of the âSundering Floodâ.đ
Here's the scan from the Internet Archive (of volume 2 of the 1914 Pocket Edition of the âSundering Floodâ): archive.org/details/sund... â note how page 110 is truncated, with a half-line at the bottom? âŠđ
So, the explanation of that gibberish line near the end of the page is the following: they simply took the OCR text straight from the Internet Archive. But when the Archive scanned the book, some pages were badly centered and got truncated, causing gibberish upon OCR.đ
And here's the explanation of that gibberish line: when the Archive scanned the book, a few pages got shifted down archive.org/details/sund... so the end of page 110 is cut, with one line cut in two, and the OCR read this as gibberish. đ”đ
LaTeX would at least have put page numbers in!â€â€They didn't even OCR the text themselves: they took the OCR text from the Internet Archive: it's at archive.org/stream/sunde... â and sure enough, the gibberish line in my photo is there (search for âCfiirlâ).đ
I was aware that some people created automatic print-on-demand editions of public domain works, but I thought they at least took a good scan of the word and reprinted that. Printing an OCR text without even formatting it is mind-boggling.â€â€It's more than sloppy: it's a scam.
I was scammed into buying an edition of a public domain work (âThe Sundering Floodâ by William Morris) that is a mere unformatted print of the OCR text of the work.â€â€Is there more I can do than leave a review such as this on Amazon? âŹïžđŒïž
My late father used to say: âI should have gotten the Nobel prize for physics, because Kissinger got the Peace prize, and at least I didn't do anything AGAINST physics.âđ
(I will reluctantly agree, however, that Elon Musk probably isn't as evil as Benito Mussolini. Although if given the same level of power as the latter had I wouldn't bet my hand on it.)
J'imagine plutĂŽt un truc du style conversion de (nâ„1729) en ÂŹ(nâ€1728), ce qui ne fait pas trop de sens ici mais c'est le genre de motifs que les LLM sont susceptibles de retenir et d'appliquer mĂȘme quand ça n'a pas trop de sens.
Next thing they're going to be telling me that Henry Kissinger got the Nobel Prize for Peace or something of the sort. At this point I'd believe anything. đ
I haven't been this shocked since I learned that Benito Mussolini was awarded a doctorate honoris causa by the university of Lausanne in 1937 for âhaving conceived and realized in his homeland a social organization that enriched sociological science and will leave a deep mark in Historyâ. đ¶đŒïž
Wait, ELON MUSK was elected fellow of the ROYAL SOCIETY? Elon Musk is a âFRSâ? đ€Šâ€â€THE Royal Society? The one that was presided by Christopher Wren and Isaac Newton and George Stokes and Lord Kelvin and Ernest Rutherford and Michael Atiyah? All these people must be rolling in their graves. đ±đ
Mon calcul est simpliste, certes, et la plupart des gens ne raisonneront pas comme ça, mais la morale est quand mĂȘme celle-ci: quand un certain discours te demande de faire des sacrifices et que tu as l'impression que d'autres qui devraient en faire sont trĂšs loin de leur part, ça ne passe pas. âą7/9
Indeed: the first step should rather be for the character on the right to demand from her employer the right to work remotely. đâ€â€(My point being: scientists are in their role to say that we need to achieve net zero, not HOW we should achieve this, when it involves non-trivial social choices.)
Meanwhile on Twitter, Idriss Aberkane (called an anti-vax conspiracist on Wikipedia) and Didier Raoult (who published hundreds of papers now criticized by sleuths) are calling me crazy again â€đâ€â€twitter.com/TroncheBiais...đ
Il faut reconnaßtre que pour ce genre de choses (redire quelque chose de façon plus polie, ou moins sÚche, ou plus courte, ou n'importe quoi du genre), les LLM sont vraiment excellents.
⊠and it was really interesting and moving (these children were super excited that the president was coming to visit, it was supposed to be their big day, and things turned out oh so differently).
I find these stories rather fascinating of how people's personal lives can get entwined with historical events because they happen to be at a certain time in a certain place. I remember seeing a documentary about the school class that George W. Bush visited on 2001-09-11, âŠ
An interesting short documentary on the guy (Abraham Zapruder) who shot the clearest film of the assassination of John F. Kennedy, and how he lived through the tumultuous days of 1963-11-22 and 1963-11-23, and what became of the film copies. www.youtube.com/watch?v=56ye...đ
When I was a teen in the 1990's, we had this joke:â€â€â What's the difference between a dollar and a ruble?â€â One dollar.â€â€Still very much relevant today.đ
(L'existence de SProp suggĂšre que non, mais apparemment SProp a des trucs en moins que Prop et pas juste des trucs en plus, donc peut-ĂȘtre qu'en fait si. En tout cas, tout ceci est excessivement confus. Et en tant que matheux ça me gĂšne d'avoir un objet sans mĂȘme savoir s'il est unique Ă iso prĂšs!)
âAge yourself with your first computer.ââ€â€In my case, I think it was precisely this model: âŹïž (not shown in photo is the very bulky transformer that was used to power it)đŒïžđ
It's still super confusing that I can match double slashes just fine when it's not a ~user but not when it is. And super annoying if the only way to fix the problem is to use Apache's super complicated mod_rewrite module: this means everyone is forced to use it because double slashes always come up.
I asked a question on MathOverflow about where I might learn more on De Morgan algebras and Kleene algebras, esp. free De Morgan algebras and free Kleene algebras. mathoverflow.net/q/483035/17064đ
Thanks, this seems interesting, but maybe there's a bit of a misunderstanding: I don't necessarily want to download my skeets in real-time. What I want to do is download my past skeets (initially, all of them, and then all since the last download). Is this heading in the right direction?
And on that note, you've never had to share a set of command lines with other users? Keeping the final, reusable and generally very non-secret, versions of the command lines helps me with that: if someone asks me for details, I just bring out the file I saved. Example here: x.com/gro_tsen/sta...đŒïž
I find auto-saving history a bit risky because it mixes the bad/dangerous command lines with the good. My point of saving them in separate files is that when I'm satisfied after 1729 attempts, that final good command line is the one that gets remembered.
No, I think it's really a bad idea to start aliasing every slightly long command line that you ever use. Your use cases may change over time, and the point, here, is to use past command lines as inspiration for new ones, that you read before reusing, not something you blindly execute.
Mais la flĂšche de {x | P x} vers X qui projette sur x n'est pas un monomorphisme, n'est-ce pas? Encore moins un âmonomorphisme fortâ, whatever that may be? Donc je ne comprends pas comment Prop peut classifier les monomorphismes (forts ou otherwise) dans ces conditions. đ
⊠And you can use grep on the files in ~/cmdlines/ to see if you have in store something related to this or that program or option or whatever. Think of it like your personal Unix cookbook.â€â€I've been doing this since 2014 or so, and I wish I had started sooner!
⊠This will save you an insane amount of time trying to re-engineer command lines you already wrote, or trying to remember what was the name of that super useful utility that did something related to foobars, or what commands/options you used to build or configure some software. âŠ
Crucial advice to all Unix command line users: create a ~/cmdlines/ directory and, whenever you write a moderately complicated set of command lines, save them in a text file in there, with a name like YYYYMMDD.frobnicate-all-foobars for future use. âŠ
I think the point to be made is rather that antelopes are stupidly slender cows: most people probably don't realize that antelopes are bovids, not cervids like one might think. The nilgai is just normal for a bovid.
I think this is a very bad analogy: climate change isn't a sudden event like hitting an iceberg, which might foster a sense of urgency. It's a slow and gradual process like the boiling frog metaphor. Which is exactly why world leaders can agree to sign a pledge to hold a meeting to discuss (etc.).đ
Did I run into a bug in Apache 2.4 while trying to set up a redirection from /~myname//something to /~myname/something on my Web site? serverfault.com/q/1168061/37...đ
I think the person who invented this concept was a genius. I would never have thought of something so simple and yet so useful.
I think antignocchi has great potential as a new kind of pasta in fancy avant-garde Italian restaurants. Don't make it out of neutronium, however, or your clients may think it's a bit heavy on the stomach.đ
Or why isn't language autodetection the default, with a possibility of manual override when it gets it wrong, or when it's not sure or can't detect? Manual override is great (Twitter doesn't have it), but autodetection is still right >99% of times.
It's really nice of Bluesky to ask me âare you writing in <language>?â when I didn't correctly fill in the language tag for the post, but WHY does it keep doing this mid-word? and why does the question disappear if I keep typing in that same language? Why not ask for confirmation before posting?
As a paid-up lifelong lefty, it's frankly an insult to the conservative thinkers who are worth discussing with to equate their views on issues like markets, tradition, liberty etc. with the Musky cesspit of ill-informed prejudice that now dominates X.đ
Here, T(e,x,y) means the Turing machine e terminates on input x with execution trace y, and U(y) is then its output value. en.wikipedia.org/wiki/Kleene%...đ
(This is from van Oosten, âExtensional realizabilityâ, âAnn. Pure Appl. Logicâ 84 (1997), 317â349 www.sciencedirect.com/science/arti... â lemma 1.4.)đ
âe (âxây (ÂŹÂŹâz.T(e,x,z)âT(e,x,y)) â âvâxâu (T(v,x,u) ⧠(ÂŹÂŹâz.T(e,x,z)âT(e,x,U(u)))))â€â€âŠand a long time was spent deciphering what this formula says (and why it's ârealizableâ but not âextensionally realizableâ).
⊠Un peu comme dans la vraie vie, si j'essaie de demander mon chemin Ă un passant et qu'on m'ignore, je ne nie pas que ce soit son droit, mais je pense qu'on peut au minimum estimer que c'est malpoli. Surtout si c'est sur la base de qqch que je ne contrĂŽle pas. âŠ
In my case, it had mostly to do with Musk deciding to cut off access to the public APIs, making downloading my own tweets incredibly annoying. x.com/gro_tsen/sta...đŒïž
This is inspired by this graph which âThe Economistâ made for Elon Musk's tweets. economist.com/briefing/202...â€â€(All other things aside Elon really needs to get more sleep!)đŒïž
A scatterplot âŹïž of the times at which each of my tweets or retweets (72281 of them, not including this one) were posted: x axis is the date, y axis is the time in the Paris time zone; each dot represents a single tweet I posted. You can clearly see my sleep schedule! đ đŒïž
⊠not actually telling people what these morphisms are and what your âcubesâ are is more than sloppy, it's insulting to the reader and it's bordering on pseudoscience (gratuitous use of lingo).
⊠âthe free ïŹnite product category on a bipointed objectâ or âthe Kleisli category of the monad of finitely generated free De Morgan algebrasâ. đ€Š Seriously, your category is going to be something like {0,1}^n for objects and some very simple kind of maps between them for morphisms, âŠ
⊠Instead, ppl who work in this stuff prefer to let the reader figure out what âcartesian cubical setsâ might be, or give them an unnecessarily arcane category-theoretic definition of cubes like âthe free cartesian category on an intervalâ or âthe Lawvere algebraic theory of bipointed objectsâ or âŠ
This is the sort of things which makes me so incredibly angry. It is known arxiv.org/abs/1701.08189 that there are a gazillion different flavors of âcubical setsâ. So anyone using the term should very clearly state the definition, and explicitate what it means in very concrete terms. âŠđ
Interestingly enough, mathematicians are still tryingÂč to figure out exactly what âequalâ means. But one thing constructive mathematicians agree on: âequalâ means ânot apartâ and also ânot separateâ.â€â€1. See, e.g., homotopy type theory and the âunivalence axiomâ.đ
I have half a mind to publish the secret key, just to emphasize how absurdly stupid it it to proclaim that HTTPS serves any purpose or adds any security when serving completely public data.
We have created an online bureaucratic nightmare with the same level of paperwork, stupid rules, frustration and absurdity, as real-life bureaucracy. Congratulations to everyone involved!
The amounts of hoops one needs to go through to get one of these stupid things đœ is absolutely staggering, especially in a situation where it brings exactly zero added security or privacy.â€â€(No, it's not deployed yet. I need to understand renewal before I can consider that.)đŒïž
Very nice!â€â€But allow me to reiterate to you this questionđœ: do you have a pointer to get me started on how to automatically keep a copy of my own posts on Bluesky? bsky.app/profile/gro-...đ
Un billet de mon blog sur le systĂšme (pourri) de commentaires de mon blog et la maniĂšre dont je les modĂšre (mal): www.madore.org/~david/weblo...đ
I agree that such shenanigans to preserve atomicity of operations are super annoying (and the fact that Unix doesn't let you move a directory to an existing one atomically is a pain in the đss).â€â€But alternatively, you can also keep the same key. There's just no need to change it.
No: you can have the old key & cert in a directory /etc/ssl-v1 with a symlink /etc/ssl pointing to it, that the Web server uses as path; you put the new key & cert in /etc/ssh-v2 and then atomically change the symlink, which is indeed a bit tricky but possible: unix.stackexchange.com/a/6786/239264đ
The Web server keeps reloading and reloading and reloading files like favicon.ico or index.html anyway â not to mention .htaccess and the like â there's really no reason for it not to do the same with the cert file. It's the OS's job to cache disk access, not the app's.
(I mean, yeah, I can imagine that for a super duper optimized Web server with tons of traffic you don't want to stat() or read() the cert file on each request, although honestly even in that case it will be in disk cache all the time anyway. But not have that be an option is just insane.)
Uh, not âreload itself automaticallyâ, just load the cert file at each request (or reload it if it changed). I mean, I don't have to reload Apache because /var/www/html/blah.html changed, it just loads it and saves it: why can't it do the same for the cert file? This makes no sense. stat() is cheap.
⊠Trump's first administration had some people who, at a point, expressed a small measure of disagreement with him. He immediately went âyou're fired!â. Now he has chosen obsequious yes-men and sycophants. Even if we think Trump is generally right, this should be preoccupying.
⊠If your advisors are afraid to contradict you, if pointing out your mistakes will lead them to being sacked, if your advisors are chosen for their slavish and unquestioning loyalty, they are useless as advisors. ⊠bsky.app/profile/gro-...đ
Trump's cabinet picks ought to give even his supporters reasons to worry.â€â€Everyone makes mistakes. Even good leaders. But good leaders know how to surround themselves with advisors who can tell them when they're wrong. That's the POINT of advisors. ⊠bsky.app/profile/gro-...đ
(So far, my advisors have been telling me âdon't become an evil overlord, it will only make you miserably unhappyâ. I tend to think they're better than Trump's, Putin's or XĂ's.)
If I ever become an evil tyrant, I'll make bloody sure my advisors will always feel comfortable telling me to my face âyour plan is sheer idiocy and will never workâ. Their purpose would be to point out my failures, not sing my praise (I'll have official poets for that).
I don't know if this is true in real life, but evil overlords in fiction certainly have a strong tendency to terrify their advisors so much they never dare tell them anything other than âyour cunning plan is perfect, o great master!â â making them useless as advisors.
Facepalm of the minute: apparently Apache2 needs to be explicitly signaled in order to reload its SSL certificate when the latter changed.â€â€If only there were some kind of Unix system call to read the contents of a file after the program has started, or to check its modification date. /s
⊠But the more I learn about HTTPS and the way they not only managed to always make every wrong decision at every level in an impressively consistent way but also made everything painful to deploy, the more I think I'm just going to give up on trying to do anything with it.
⊠Of course, I'm fully aware that nobody would ever look at the key, because the entire HTTPS architecture has been created around the certification racket business and bad crypto, and even HPKP has been killed by the cert mafia, but at least I can try to do things correctly on my side. âŠ
Because I want to share the key across several machines, so the certificates will be valid for whichever the DNS is pointing to. Also, on the principle that one should trust a previously known key far more than a signature generated by a âcertification authorityâ which checked exactly nothing. âŠ
(Another of Sokal's jokes my father found hilarious: â86. It is not clear to me that complex number theory, which is a new and still quite speculative branch of mathematical physics, ought to be accorded the same epistemological status as the three firmly established sciences cited by Markley.â)
⊠and then ask it to regenerate the certificate with the `--reuse-key` option. đ€Šâ€â€Seriously, who came up with this interface? There's a `--key-path` option, but it seems to be just ignored. And no other way to tell `--reuse-key` which key is to be âreusedâ! đ
The `certbot` program used to generate Letsencrypt certificates is an ungodly abomination.â€â€For example, the only way to get it to use a given private key file seems to be to first generate a test certificate, CLOBBER the private key file it stored for that test certificate, âŠ
And lastly:â€â€âŁ Conspiracy theories are an attempt by the Lizard People to distract us from the truth, and we should disregard them all, starting with this one.
⣠The Bible was initially written as a textbook on accounting. It became a religious text after a careless copyist made a few mistakes when reproducing it.
⣠The Internet is currently stored in a small wooden box on the top shelf of the kitchen cupboard of a Mrs. Jana Bader, living at WilhelmstraĂe 30, Brunswick, Germany. She doesn't know anything about it, and it's very important that nobody should tell her.
⣠Erwin Schrödinger never had a cat, and even if he did, the poor thing is definitely way dead by now, not in some superposition nonsense. So the whole of quantum mechanics rests on a faulty assumption, and should be thrown away.
⣠All crypto protocols do is take your plaintext, replace it with random junk as âciphertextâ while saving a copy in a drawer while you're not looking: then they restore that copy when they claim to âdecipherâ. It's just done with smoke and mirrors.
⣠Not going to go into the details, but: don't you find it suspicious that we keep hearing about the NORTH pole and the SOUTH pole but never about the EAST pole and the WEST pole? Where on Earth is the WEST pole?â€â€WAKE UP, SHEEPLE!!!
⣠All of Bluesky (including this skeet) is in Sumerian. If you think you understand without knowing Sumerian, it's because people are very good at writing Sumerian in a way that looks and sounds exactly like something completely different in English.
⣠Scientists have invented a device called the âBanach-Tarski paradoxâ, which lets them create unlimited amounts of gold (or anything) from just a small nugget. But they only allow people who are pro Choice to use it.
⣠That rebel pilot who blew up the Death Star is secretly the son of the imperial top brass who saw it as insignificant technological gadget and escaped just as it was going to be destroyed.
⣠The sun is actually the size of a grapefruit. Not because the sun is small but because grapefruits are very very large, and an optical illusion makes them seem so small.
⣠Vladimir Putin and Volodomir Zelens'kij are in fact the same person, suffering from a rare case of split personality disorder, which is why you can't see them in the same room together.
⣠America doesn't exist. It's all just a terrible misunderstanding based on a bet between Amerigo Vespucci and Martin WaldseemĂŒller. To all the people living in this nonexistent continent, we're very sorry and won't do it again.
⣠Computers don't work, never have, and never will. If they sometimes appear to, it's because little gnomes inside play a trick on us.
Some conspiracy theories which still have to catch on (non-exhaustive list):â€â€âŁ There is not, and has never been, such a science as mathematics; numbers don't exist and make no sense. It's all a drunken hoax started in 545BCE by Pythagoras, and which got out of hand.
very mystified by how many people are replying to "here is a complex topic, I want to write a clear summary explaining how to navigate it so that I can have a strong mental model" with "uh maybe use chatgpt?", like come on.â€â€anyway I wrote the guide jvns.ca/blog/2024/11...đ
First, let me comment a bit on the article eprint.iacr.org/2024/1582, written with my phd student Nicolas Sarkis. This is a follow up to our article on computing 2-isogenies between Kummer lines: eprint.iacr.org/2024/037đ
I sincerely don't understand this point: both Twitter and Bluesky have a âfollowingâ feed (where you only see your followee's posts, in chronological order) and a âfor youâ / âdiscoverâ one, which injects algorithmic suggestions. What's the difference?
Probably Halmos, âNaĂŻve Set Theoryâ (1960), which is where I learned the basic stuff myself. To be continued, for example, with (part I of) Hajnal & Hamburger, âSet Theoryâ (1999). There may be more recent books that I'm not aware of.
Oh, there's no doubt that the economy isn't a zero-sum game. My point isn't that it's wrong, my point is that any attempt to use this fact in an argument suggests that the person making this point is an idiot and that the argument is stupid. It's a bit like using Gödel's theorem in philosophy.
I have to admit, Elon Musk's very own AI engine âGrokâ pointing out that Elon Musk promotes racist or Nazi-related content on đ is pretty fđ€Ącking hilarious. x.com/i/grok/share...đŒïž
every one of those op-ed columnists has spent years building up a follower list on twitter, many of whom left, and so they are angry because you owe them your attention ad to help them get paid, your entire existence is to facilitate their need to put in as little effort as possible, know your placeđ
Battling Infectious Diseases in the 20th Century: The Impact of Vaccinesâ€â€It seems necessary to remind many people of how amazing vaccines are and the need for organised vaccination programmes. â€â€graphics.wsj.com/inf...â€1/8đŒïž
Why the European Union still tolerates the blatantly misleading China Export marking remains a mystery to me. â€www.hqts.com/differences-...đŒïž
I often wonder how date recording would have developed if there were a continuous inhabited stretch of land that crossed every meridian. Everyone would want to have the same date as their immediate neighbors, and topology would be like âsorry, not going to happen!â.
Whatâs common knowledge in your field, but shocks outsiders?â€â€Most wasps donât make nests and donât sting. The vast majorityâover 100,000 species!âare so minuscule you never notice them, but theyâre *everywhere* around you every time you step outsideâand theyâre critical for ecosystem health!đ
So we're left with our own human memory to remember what we think of every person we run across. This makes little sense: let us unload this memory effort to the computer/phone.
One thing this site lacks (just like its inspirator) is the ability to write personal notes on accounts. Thigs like âsays sensible things about subject X but talks nonsense on Yâ or âposts often have a subtle second meaningâ or âmuted because got reposted too often â no hard feelingsâ.
I feel mislead by all dystopian literature. It's supposed to be a powerful authoritarian government that lords over a cowering population, and and we just need need a few brave acts of heroism to give the people the courage to rise up. â€â€Instead it's just half the country being dumb and mean.
⊠because two forces of evil fighting one another does not neutralize their power to do evil, and, in fact, evil people may do even more evil (as collateral damage) when fighting other evil people than when they are allied.
⊠or Musk will realize the Dems aren't in power any more and turn his anger toward the Republicans. Or maybe they'll fall apart over a trifle and things will degenerate from there. It might be fun to watch đż but people like me who hate them both would be wrong to rejoice: âŠ
⊠And neither of them has it in him to be nice or loyal to the other, nor the wits to be truly manipulative. So they're probably going to come to a crash when one thinks the other has stopped being useful to him. Either Trump will think Musk isn't bending the knee low enough, âŠ
Beyond my distaste for either, the relation between Trump and Musk is fascinating: one can't help but wonder how long it will last. Both have an insanely bloated ego, think they're extremely intelligent, want to be at the top of everything, and are prone to childish tamper tantrums. âŠđŒïž
⊠I can read English, French, German and Italian, so these languages are fine.â€â€Also looking for artists drawing cute guys, in the spirit of those I reposted in the thread nitter.poast.org/gro_tsen/sta... [probably NSFW] on the Musky Place.
⊠linguistics, (French/EU) law, comic strips; I'm also interested in jokes, memes and interesting pics if they're high-effort (no cat videos!). Also of interest to me: Paris & Ăle-de-France, motorcycles. Not looking for politically-oriented accounts, I see too way many such posts already. âŠ
I'm looking for recommendations of interesting accounts to follow here on Bluesky. Not many (I like to keep my followee count â€100), but good ones. If you know me and have suggestions to make, please do so. Topics I'm interested in include: math, science, geeky stuff (inc. Linux), maps, history, âŠ
I had this comment to make about the video, but I suspect 3Blue1Brown is drowned in comments so he probably won't read it. reddit.com/r/3Blue1Brow...đŒïž
I should probably try to make my Bluesky feed a bit more interesting by reposting here some of the most interesting stuff I wrote on the Musky Place.â€â€Are there any (still relevant) threads from github.com/Gro-Tsen/twi... that you think I should copy here?đ
* «des personnes ouvertement trans», plutĂŽt (et cet ensemble est loin d'ĂȘtre vide). Peut-ĂȘtre justement que les hommes trans sont moins enclins Ă s'affirmer comme tels.â€â€Mais sur Twitter il y avait au moins deux hommes ouvertement trans que je suivais (dont Felix Reda).
Further investigation seems to support the hypothesis that it's a timeout issue: at least on HTTP, the Archive seems to give up the connection after ~250ms. Isn't this harsh?â€â€I updated the question webmasters.stackexchange.com/q/145994/151... accordingly, but I'm at loss as to what I might do now.
⊠So instead, that certificate authority will authenticate the servers⊠by trying to contact the servers themselves. đŹ In other words, by exposing themselves to the very risk the certificate is trying to protect users against. đ€Šâ€â€NONE OF THIS MAKES EVEN THE SLIGHTEST BIT OF SENSE.
⊠will indeed be contacting the legitimate servers for that domain (i.e., yours). So the â”obviousâ” solution would be to tie the certificate with domain registration. But no! For some INEXPLICABLE REASON you get the certificate from someone else, who has no access to the registrar's client file. âŠ
The way HTTPS certificates are given is so ludicrous it's really hilarious. First you buy a domain like example.tld from a domain registrar, which then lets you insert your servers under that name in the DNS. Now HTTPS is supposed to make sure that people connecting to example.tld âŠ
I often wonder if anyone checks whether every paper listed in the bibliography is indeed referenced somewhere in the text. Is it considered malpractice to âciteâ a reference without any pointer from the text itself? Bc that would be the obvious way to introduce irrelevant items in the bibliography.
This TCP dump is completely weird. The Archive's machine contacts my server at 11:05:46.405371. My server ACKs the request at .540061, starts sending data, and at .683062 after only 14241 b ACKed, the Archive suddenly shuts down the connection (RST)!â€â€And ~3s later tries later tries to reopen HTTPS!đŒïž
I feel like I'm going crazy. Nothing is reproducible. There must be a strange timeout effect which, for some reason, affects my Web site more than others. đ
Does someone know a Web site (other than my own đ ) that, today as of 2024, is accessible only via HTTP and not via HTTPS? đâ€â€(I need to test whether the Internet Archive's Wayback Machine can still archive it.)
I asked a question on the Webmasters StackExchange about why the Internet Archive's Wayback Machine thinks my Web site is âunreachableâ. If anyone reading me knows anything about HTTP or Web servers, could you please have a look? webmasters.stackexchange.com/q/145994/151...đ
Sur mon compte de test j'ai reçu un message du style «user machin has requested that you follow bidule instead» (je ne sais plus la tournure exacte): donc il y a des cas oĂč ce n'est pas transparent. Je n'en sais pas plus. âŠ
The militant cares about "traitors" â those who emit doubts, those that would like to get informed.â€â€In fact, he or she will spend more energy fighting supposed traitors than fighting those who really make the decisions he or she is fighting against.
The militant does not care. He or she has enemies, which by definition have nefarious views.â€â€He or she does not care about getting informed about the motives that push people to enact policies that he or she disapproves of.
Photo (1987) of Dr. Zbigniew Religa monitoring the vital signs of a patient after a 23-hour heart transplant - a procedure many considered impossible. In the right, you can see his colleague asleep. The transplant was a success, and the patient outlived Religa. #histmed#skystorians#history#medđŒïž
Look at me. Listen to me:â€â€If someone is selling you a "search" & "knowledge" "AI" product they claim is smarter & better & faster than you, but it literally cannot be guaranteed to give you simple true facts about consensus reality when asked, then that product DOES NOT WORK and SHOULD NOT BE USED.đ
That other social network with a musky stench has a concept of âpinned tweetâ (or, effectively, pinned thread) to give newcomers information about the account beyond the very short bio.â€â€I think @bsky.app should copy this feature ASAP â probably not difficult at all to implement and super useful!đŒïž
Whenever someone tells me that something returns to the initial level after 2 iterations but not quite or not exactly in the same way or somehow it's debatable, I think that they're on the verge of rediscovering the ring â€â of 2-adics integers.
A type I meta-error is when you call a type II error a type I error, and a type II meta-error is when you call a type I error a type II error.â€â€Or is it the other way around? I can never remember! Maybe I'm committing a type I meta-meta-error.
Of course, there's also about a 1% chance that it's Trump who dies of natural causes before Jan. 20. And then it would be utter chaos, between a zillion conspiracy theories and lawsuits trying to figure out what exactly happens (depending on when exactly the death occurs). đđ
Funny how nobody mentions this possibility that Harris might still become president.â€â€It's not âlikelyâ, of course, but it's far from impossible: actuarial tables suggest something around 1% chance of Biden dying before January 20. Weirder things have happened before!
This would probably piss off Trump as well, because I'm sure he has lots of merch already printed with the numbers â45 & 47â on them and suddenly he'd have to cope with the fact that he'd be #48 instead (and the merch would be about him and Harris).
(I hope the betting markets about the name of the next president had correctly written their contracts, or some people are going to be very pissed and some lawyers are going to be very pleased.)
Among the many branches of the multiverse, there is one in which Joe Biden has a sudden heart attack and dies on Jan. 19, so Kamala Harris is sworn in for a day.â€â€And somewhere, a genie returns to his bottle and says âwell, you asked for her to be the next president: you got it!â
I don't pretend to understand US politics enough to say why what happened, happened. But I do know that this guy being anywhere near health policy would be very, very, bad.đŒïž
Sure, Trump's second term will be far worse than his first.â€â€But we can take comfort in the assurance that it will be much better than his third and fourth.
âYou can always count on the Americans to do the right thing. After they have exhausted all possible alternatives.ââ€â€[quote attributed to Winston Churchill, and almost certainly apocryphal]
As a believer in the multi-world interpretation of quantum mechanics, you think that there's roughly half of worlds in which this happens and roughly half of worlds in which the opposite happens, don't you? Now it's just a matter of navigating to the right branch of the multiverse. đ
As a believer in the multi-world interpretation of quantum mechanics, you think that there's roughly half of worlds in which this happens and roughly half of worlds in which the opposite happens, don't you? Now it's just a matter of navigating to the right branch of the multiverse. đ
OK, I treated the words âenvyâ and âjealousyâ as synonymous, and someone on that other â more musky â social network just pointed out to me that A 15-PAGE RESEARCH PAPER has been written on the difference between them, which is just đ€Ż dx.doi.org/10.1037//002... â But I still think I mean neither. đđŒïž
OK, since so many people tell me the word I'm looking for is envy/jealousy (German: âNeidâ) â it's NOT.â€â€Envy is the feeling when you want someone else's happiness for yourself; this is very different from thinking it's undeserved and being sad that they got it.
âMissgunstâ might be closer to it, but âNeidâ is just envy/jealousy. I don't understand why four different people have suggested to me that what I'm looking for is jealousy, when it's clearly not at all the same thing! bsky.app/profile/gro-...đ
That's envy. But envy is different: it means I see someone having something I'd like to have. What I'm referring to is being sad because I see someone having something they don't deserve â it's different from envy because I might not want that thing, and conversely I might envy something deserved.
Is there an established word for the opposite of âSchadenfreudeâ (that is, for the feeling of sadness at someone else's [undeserved] happiness)?â€â€If not, what should I call it? Does âGlĂŒckstrauerâ sound right?
One genius rhetorical trick of capitalism is to take the statement âprivate property is a fundamental human rightâ, with which nearly everyone agrees for personal possessions, and extend it all the way to the right to hold the equivalent of the GDP of Greece as if it were obviously the same right.
One genius rhetorical trick of capitalism is to take the statement âprivate property is a fundamental human rightâ, with which nearly everyone agrees for personal possessions, and extend it all the way to the right to hold the equivalent of the GDP of Greece as if it were obviously the same right.
Dear Russian judges: if you are out of imagination for how to fine Google absurdly large amounts of money, I can teach you about the (extended) Grzegorczyk hierarchy, but I have to warn you, you won't like it, it was invented by a Polish mathematician. www.bbc.com/news/article...đ
Pour le pfb versus otf le fait est que mon systĂšme va chercher une police d'une vieille TeXlive que j'ai dans /opt/texlive-2018 qui a la version otf du fichier alors que le systĂšme lui-mĂȘme package la TeXlive 2022 avec une version pfb de la mĂȘme police. C'est tout de mĂȘme bizarre. âŠ
⊠que j'ai dans /usr/share/texlive/texmf-dist/fonts/type1/public/stix2-type1/ â et est-ce que ça vaut la peine que j'essaie de savoir ce qui vaut mieux entre âLatin Modern Mathâ et âSTIX Two Mathâ dans ce cas? đ€
Hmmm⊠Chez moi c'est âLatin Modern Mathâ. Est-ce que ça vaut la peine que j'essaie de comprendre ce qui, dans mon fonts.conf fait que fc-list trouve le STIX2Math.otf que j'ai dans /opt/texlive-2018/texmf-dist/fonts/opentype/public/stix2-otf/ mais pas le STIX2Math.pfb âŠ
Internet tient Ă dire qu'il n'est en rien responsable de l'incurie et des agissements malhonnĂȘtes des entreprises qui profitent de son existence pour transformer les gens en technovassaux et pour pourrir leur vie. đ
Et pourtant! Les arrondissements et les quartiers administratifs de Paris ont bien des noms (mĂȘme si personne ne les connaĂźt): fr.wikipedia.org/wiki/Liste_d...đ
hugely discrediting to conspiracy theorists that thereâs an actual foreign-born billionaire doing all this while *overtly* attempting to control what you see online, buy an election, run software in your car, and put microchips in your brain and theyâre like đ€·ââïžđ
Wow! A mate sent me this mnemonic and I'm never going to be confused about how the clocks go again:â€â€If it is spring that is dueâ€Your phone will now do that for youâ€But if it is autumn you do seeâ€Your phone will now do that for thee
⊠The question is: under such assumptions, what is the (approximate, for N large) probability that you'll cast the deciding vote (i.e., that your vote will decide the election)? Is it larger in Popularvotistan or in Electoralcollegistan? âą5/5
Now assume that you're a citizen of one of these countries, and every one of the Nâ1 other citizens votes completely at random and independently of each other, for âblueâ with probability Âœ, âredâ with probability Âœ. ⊠âą4/5
⊠down to the individual citizen level (so N = 3^k for some k); to elect the leader, the country picks the candidate who got the most provinces, and in each province it's the same (the province picks the candidate who got the most regions), and so on. âą3/5
In the country of Popularvotistan, it's very simple: the candidate with the more votes is elected. In the neighboring country of Electoralcollegistan, it's more complicated: the country is divided into 3 provinces, each divided into 3 regions, each divided into 3, etc. ⊠âą2/5
â A little problem in math + voting theory. ââ€â€Two countries, both having N citizens, are having an election in a few weeks. In both cases, there are exactly two candidates, which we'll call âredâ and âblueâ. But the electoral system is different! ⊠âą1/5
Amazon ne semble vraiment pas comprendre qu'il y a des choses qu'on commande chez eux juste parce que c'est devenu impossible de les trouver ailleurs, pas parce qu'on veut les avoir en livraison rapide, ultra-rapide, supersonique ou tachyonique.
No, I'm sorry...1, 2, and 4 are absolutely not meaning what they say they're meaning.đŒïž
I asked a question on MathOverflow which is superficially a combinatorics question about some âcontraction-compatibleâ simplicial complexes on {0,âŠ,n}, but deep down really about describing Lawvere-Tierney topologies on the topos of simplicial sets. mathoverflow.net/q/481274/17064đ
Anyone who thinks they own a cat is deluded about the fact that actually the cat owns a human.
No you can't have that: if there is a bijection of A onto B and a map of B onto C then you can form their composite, which gives you a map of A onto C. That's the whole point about maps: you can compose them.
«â€âI like the Walrus best,â said Alice: âbecause you see he was a âlittleâ sorry for the poor oysters.ââ€â€âHe ate more than the Carpenter, though,â said Tweedledee.â€â€[âŠ]â€â€This was a puzzler. After a pause, Alice began, âWell! They were âbothâ very unpleasant charactersâââ€Â»
âOne must imagine Sisyphus having a lot of fun as a kid.â đâ€â€(Seriously, I think this comic is so profound it hurts.)â€â€[F Minus by Tony Carrillo for 2024-10-24, www.gocomics.com/fminus/2024/... ]đŒïž
Continued with some thoughts on the decomposability of ââ{0} (TeX source still at link given in previous tweet):Screenshot of page 3 of a document about the decomposability of â and ââ{0} and their equivalent to certain omniscience principles in constructive math without ChoiceđŒïžđŒïžđŒïžđŒïž
I try never to be more than 0.000âŻ000âŻ000âŻ000âŻ1 billion years late for any appointment or meeting. đ
(And the threat worked because Italy finally chose the German PAL system for color television rather than the French SĂCAM.)
Wait until you hear that there was a governmental crisis in Italy in September 1972 because the Andreotti government wanted to choose the French SĂCAM system for color television in broadcasting the Munich Olympics, and senator Ugo La Malfa threatened to withdraw his party's support if they did so.đ
I find it very remarkable the fact (prop. 5 above) that if some sequence of rationals (r_n) converges to x with modulus, then any sequence of rationals converging to x has a modulus. I had already explained the basic idea in a Twitter thread in 2021: x.com/gro_tsen/sta...đ
This â€Žïž might be used as a companion or preliminary guide to Lubarsky's paper âOn the Cauchy Completeness of the Constructive Cauchy Realsâ arxiv.org/abs/1510.00639 â he leaves things as âexercisesâ which I really think shouldn't have been left as exercises.đ
More constructive math: here is a little expository text about âconvergence without modulusâ versus âconvergence with modulusâ in the absence of Choice:â€â€[LaTeX source at: gist.github.com/Gro-Tsen/c1a... ]đŒïžđŒïžđŒïž
Wait, this raises a lot of questions: you can backdate Bluesky posts? so we absolutely shouldn't trust the date written on the post? also, you can post without your followers being notified? All of this isn't really reassuring.
Wait, this raises a lot of questions: you can backdate Bluesky posts? so we absolutely shouldn't trust the date written on the post? also, you can post without your followers being notified? All of this isn't really reassuring.
⊠probably from translating French recipe books: for a long time, âoxâ and âbeefâ were pretty interchangeable in English, and similarly for others. And the inventor of this linguistic legend seems to be Sir Walter Scott, who made it famous in his 1819 historical novel âIvanhoeâ.
⊠To summarize the rebuttal, yes, such doublets exist, and yes, the word of French origin mostly serves to denote the meat while the word of Anglo-Saxon origin denotes the live animal, but it seems to be around 1800 rather than in the Middle Ages that the distinction stuck, âŠ
⊠(âBullshitâ, or, as we Norman nobles say, âmerde de taureauâ.) âŠđ
Turns out the oft-repeated story about how English has doublets like âoxâ/âbeefâ, âpigâ/âporkâ, âsheepâ/âmuttonâ because the French-speaking Normal nobles saw the meet while the English-speaking Saxon peasants saw the live animal⊠is mostly bullshit. ⊠www.youtube.com/watch?v=dL2v...đ
Yeah, it screams of âwindow decoration size not being correctly accounted for while positioning context menuâ, but this doesn't explain why I only see it occasionally, and someone else using Debian+fvwm2+Firefox told me he never encountered it.
This Firefox bug causing the (right-click) context menu to be misplaced has been annoying me for some time. Has anyone else encountered it? www.reddit.com/r/firefox/co...đŒïž
(It's not like the cosmological constant / dark energy: this one IS a mystery because it's a sum of terms for various fields' vacua, and we know that some of these terms are very large, so something needs to cancel them almost exactly to get the observed small-but-nonzero value.)
⊠and we find that experimentally IT'S NOTâ: that a conceivable parameter is zero or that a law of nature possesses a certain symmetry doesn't strike me as particularly mysterious or in need of explanations â the term just isn't there / the constant is zero, that's all.
This video does a nice attempt at explaining to the general public what the QCD âstrong CP problemâ in physics is. www.youtube.com/watch?v=jALb...â€â€I'm not convinced it's a âproblemâ or âmysteryâ at all, however: it's more a case of âwe invented a term that COULD BE in the equations âŠđ
⊠I understand what a simplicial complex (geometric or abstract) and a simplicial set (and its geometric realization) are, but how a CW-complex relates to them is exceedingly unclear to me, despite this helpful MathOverflow question: mathoverflow.net/q/31629/17064đ
A mathematical confession:â€â€I've never been able to wrap my head around the definition of a CW-complex. By the time I reach the end of the definition, I've already forgotten the beginning, and I have no idea why it's the ârightâ one.â€â€âŠ
I have different Firefox sync accounts for my PCs and mobile phones because I didn't want to share the same set of bookmarks. đ«€â€â€That being said, Firefox may be a way to hack things, using the remote debugging feature of Firefox mobile. (đ€ź)
I feel xclip is operationally a little better but the command line syntax is really bad: can't I do with shorter than â-se câ to operate on the clipboard?
So far, the best solution I've found to copy from computer to phone is to⊠generate a QR code using `qrencode`, and scan it with my phone. đ And nothing for the other direction.â€â€`adb` USED TO have a âclipboardâ command, and some asshđĄles decided to remove it.
E.g., Termux has `termux-clipboard-set` and `termux-clipboard-get` programs, but it's not at all obvious how to run them from `adb` because `/data/data/com.termux/files/usr/bin/` isn't accessible by the adb user. đ€Šâ€â€See android.stackexchange.com/q/225260/170... where every single approach fails.đ
Along similar lines: I'm still looking for a reliable and not too convoluted way (and not involving installing shady apps) to copy text from my computer to my Android phone, or vice versa, using `adb`.â€â€Every solution I've found so far is incredibly complex and/or brittle.đ
This is typical of ânot invented hereâ philosophy: there was a tool that worked, and for some reason some assđĄle decides that it must be replaced by another tool. Which uses a different syntax for no reason, and drops some features like secondary selection. Instead of just making the old tool work.
⊠(or âxsel -boâ if you did Ctrl-C first) to print it on standard output.â€â€You can also use this in filters, e.g., âxsel -bo | rev | xsel -biâ will reverse text in your clip buffer.â€â€NB: This is for X11. Wayland breaks all of this, naturally (but maybe they'll fix this mess eventually).
⊠you can do âxsel -bi < somefileâ in a command line, and then paste (Ctrl-V) in your browser. This will avoid the tedious process of scrolling through the whole content to select it in a terminal.â€â€Conversely, if you select text in your browser, you can use âxsel -oâ âŠ
Advice to all Unix users: the `xsel` tool is an incredibly useful gadget to manipulate the X11 clipboard (as well as âprimaryâ and âsecondaryâ selections) from the command line.â€â€For example, if you want to paste the content of somefile in a Web form, âŠđ
Câest pas trĂšs gentil pour ce pauvre TartufođŒïž
I'm no analyst, but I do believe this person asking whether one can make sense of a ÎŽ distribution at a point p on a manifold answered their own question while they were asking it (âno: only up to a choice of densityâ). mathoverflow.net/q/480877/17064đ
Ah et peut-ĂȘtre, pour commencer, le chapitre de Barendregt, âLambda Calculi with Typesâ, pages 117â309, dans le âHandbook of Logic in Computer Science, Volume 2: Background: Computational Structuresâ (Abramsky, Gabbay & Maibaum eds.; 1992).
For more on the mathematics of Kepler's equation, including its solution as a power series given by Lagrange's inversion theorem, or as a Fourier series with coefficients given by Bessel functions, see: mathworld.wolfram.com/KeplersEquat...đ
He had previously done a couple of (more history-oriented) videos on how Kepler discovered his first two laws, which I very highly recommend watching: đœ bsky.app/profile/gro-...đ
Very interesting video on the history of astronomy and mathematics (and mathematics of astronomy!), about Kepler's equation M = E â e·sin(E) and the quest for ways to solve it. youtube.com/watch?v=hBkm... This âWelch Labsâ YouTube channel is really worth subscribing to!đ
very baffled by democrats clinging to some sense of decorum with a political party who repeatedly in public call them blood-drinking devil-worshipping pedophile wizardsđ
I stupidly tried to answer a question on Reddit /r/math about whether we can classify all finite commutative rings, and ended up writing a very long answer which is probably incomprehensible to anyone who doesn't already know what I'm trying to say. www.reddit.com/r/math/comme...đ
⊠il y a d'autres gains bien plus faciles à faire ET QU'ON NE FAIT PAS, donc ça n'a pas vraiment de sens de choisir à ce stade, ni de demander des sacrifices exorbitants.)
⊠parce que ça n'a aucun sens de commencer par faire les progrĂšs difficiles alors qu'il reste des progrĂšs faciles Ă faire. Et ce que mon calcule suggĂšre, c'est que pour l'instant, il y a des progrĂšs bien plus faciles avant d'atteindre le niveau ~1700âŹ/tCOâ (et mĂȘme, qu'on ne l'atteindra jamais âŠ
OK, just hear me out. New theory: what if ROGER Bacon actually wrote the plays attributed to Shakespeare (which were then kept secret for 300 years)? Just brainstorming here. No stupid ideas.đ
âFrancis Bacon (1561â1626) has been called the father of empiricism and one of the later founders of the scientific method, arguing for careful observation of events in nature.ââ€â€No wonder I tend to get the two mixed up!
From Wikipedia (selecting phrases in the article):â€â€âRoger Bacon (c.1219âc.1292) is credited as one of the earliest European advocates of the modern scientific method; he placed considerable emphasis on the study of nature through empiricism.ââ€â€âŠ not to be confused with âŠ
Tell you what. If you give a cash prize to 3 economists and tell them to divide it up between themselves on a 2-1 vote, thatâll keep them busy for eternity.đ
The Arrow theorem also says this. Funny how many mathematical theorems are about how we can't have nice things. (There's even a short story by Larry Niven pretty much about this: âLimitsâ, which is the titular story in the collection by the same name.)
This is what Tesla does now. Smoke and mirrors to fool investors. How there's not a fraud investigation into this company is mystifying. The markets have to eventually realize the emperor has no clothes.â€â€www.reuters.com/technology/t...đđ
Musk il a vu un bus un jour et il s'est dit: "Il faudrait que ce soit plus cher, moins fiable, et qu'il n'y ait pas de fenĂȘtres pour que les gens ne puissent pas s'enfuir en cas d'accident."đ
Ah oui là ça va ĂȘtre coton, je pense. Coq fait des distinctions dont je ne comprends mĂȘme pas le sens (peut-ĂȘtre liees Ă l'absence de Choix unique), cf. par exemple twitter.com/gro_tsen/sta...đ
Cats are obligate carnivores but are completely convinced they are actually omnivores. â€â€They're like "no you are wrong, our ancestors clearly made sandwiches out of their prey, check the fossil record"
On a more serious note, HyperRogue en.wikipedia.org/wiki/HyperRo... is a really playable and rather enjoyable game taking place in a non Euclidean (hyperbolic plane) world, that seriously models the geometry and uses it to the game's advantage. I recommend trying it out.đ
On a more serious note, HyperRogue en.wikipedia.org/wiki/HyperRo... is a really playable and rather enjoyable game taking place in a non Euclidean (hyperbolic plane) world, that seriously models the geometry and uses it to the game's advantage. I recommend trying it out.đ
Well it makes sense to be cautious. One mistake that keeps biting me, for instance, is to assume that [a,b] = {a+t·(bâa) : 0â€tâ€1} (this is correct when bâa > 0). But things aren't so bad as to make dividing by 2 problematic.
There's a general theorem: any identity of the form f(x,y,zâŠ) = g(x,y,zâŠ) or f(x,y,zâŠ) †g(x,y,zâŠ) where f,g are terms written in the variables x,y,z⊠using +, Ă, abs(), binary_inf(), binary_sup() (or finitary inf and sup, of course), which holds on â^n, also holds on â^n. But it's not obvious.
But maybe it's worth checking excatly how |a·b| = |a|·|b| is proved (e.g., in Troelstra & van Dalen). I admit I didn't look any further than âthis sort of things is unproblematic in constructive mathâ.
Multiplying by 2 preserves the order and is invertible, so sup(2u,2v) = 2·sup(u,v) because sup is defined by the order so isomorphic order structures have corresponding sups. I'll leave you unwind that proof to understand exactly what is happening. đ
One could say that was his fault. But having a different email isn't always workable, and one can lose access to that too (or to a mobile phone), and bootstrap problems can be more complex. So, yes, it's a tradeoff. But if I have a secure password, this should be enough alone!
A few hours ago, @conscritneuneu.bsky.social was trying to rescue a machine he administers. We had access to the admin console, but some actions required email confirmation. Sent to an email that was hosted⊠on the machine we were trying to rescue. 𫀠(And changing the MX is a nightmare.)
Unpopular opinion: (forced) two-factor authentication is evil. Yes, 2FA decreases the risk of the account being taken over by a malicious third party; but it also dramatically increases the risk of legitimate owner completely losing access to said account.
Here is a test (it's supposed to link specifically to the first phrase in article 19 of the UN Declaration of Human Rights), assuming that Twitter doesn't bungle the URL in its cascade of redirections: en.wikisource.org/wiki/Univers...đ
I was today years old when I learned of this nifty Web feature, âtext fragmentsâ, that allows URL linking to a specific part of a document by its text (i.e., by text to search for) even if the document author did not create a specific anchor in the HTML. developer.mozilla.org/en-US/docs/W...đ
An algorithmically generated explorable map of mathematics computed by grouping together titles and abstracts. The nodes are the papers in the arXiv. lmcinnes.github.io/datamapplot_...đ
Les principales mauvaises nouvelles, c'est qu'on ne peut pas affirmer xâ€y âš xâ„y (mĂȘme si on sait ÂŹ(x=y)), ni que xâ€y et ÂŹ(x=y) implique x<y.
Je pense que cette inexistence nonobste le fait de l'utiliser si on le trouve pratique. Car qu'est-ce qu'un mot qui n'existe pas si ce n'est un mot qui n'a besoin que de quelques encouragements pour percer?
Here âŹïž is a full proof,with a few additional comments, of the equivalence between decomposability of â and analytic WLPO (TeX source: gist.github.com/Gro-Tsen/bc6... ). I think this can serve as a nice introduction to how to deal with (Dedekind) real numbers in constructive math.đŒïžđŒïžđ
A function f:âââ is âweakly increasingâ whenâ€âŁ xâ€y â f(x)â€f(y)â€and âstrictly increasingâ whenâ€âŁ x<y â f(x)<f(y)â€â€However, you can also define âweakly increasingâ byâ€âŁ f(x)<f(y) â x<yâ€and âstrictly increasingâ byâ€âŁ f(x)â€f(y) â xâ€yâ€â€Guaranteed to confuse students!
If the fix is so trivial, why doesn't the linux-firmware package (or whatever it's called) get updated accordingly? Why am I left googling this sort of problem and finding the answer on dubious websites instead of the fix being distributed through official channels?
There's always been nothing to stop anyone declaring themselves an "expert" in anything but this surely has to be a new low? Although it presumably won't be long until Florida mandates that its Universities endow chairs of "Anti-Woke" to study this wally.đŒïž
On the psychological and sociological factors which make our perception of risk differ from actual risk (i.e., why certain risks seem acceptable to us while others do not): www.youtube.com/watch?v=NtX-... â rather interesting!đ
The main point of the video is to explain how, by a simple but clever use of interference with a âreferenceâ wave (a trick which earned Dennis Gabor the Nobel prize in physics in 1971) we can record and recreate light phase using a film which only records amplitude. That part is very well explained.
⊠but now I realize I don't really understand the magic of how we can view 3D scenes using a field which is so determined. (And this may be a physically profound thing, cf. en.wikipedia.org/wiki/Hologra... .) Somehow, something must be lost â but what and where, exactly?đ
I still feel his explanation of the titular mystery âhow can you store 3D information on a 2D film?â doesn't satisfy me, though. He basically reduces it to âthe electromagnetic field satisfies a PDE, so if we recreate it perfectly on a surface, we do so in all of spaceâ, âŠ
(3Blue1Brown's videos are always excellent, but I generally already know the thing that's being explained, so I don't get much out of them except âah, it can be explained in that wayâ. But here I had never understood how holograms worked, so I really learned something.)
An explanation of how a hologram works that finally brought it for me from âthis is âšblack magicâš which only physicists understandâ to something which actually makes sense: www.youtube.com/watch?v=EmKQ...đ
OK but this needs to be color-coded in a way that indicates which of these people DID get a Nobel prize in physics so we can see which of these alignments are compatible with the Nobel committee.
The whole Nobel set up is very odd at this stage anyway - it was designed for science as constituted over a century ago. Now it's more of a team effort than ever and research often doesn't sit in traditional disciplinary bins.đ
I mention these because the problem with many texts which aim to âexplainâ what an â-category is is they seem to think that a prerequisite for learning what an â-category is is to already understand what an â-category is.
This course by Martin Gallauer (at U. of Warwick) on â-categories looks like it might be fairly digestible for mathematicians who know what an ordinary category is and want to learn a little about â-categories without already knowing much about homotopy: homepages.warwick.ac.uk/staff/Martin...đ
If you manage to understand things clearly, do let me know. Because I'm really confused about how this Misner string both is and is not a singularity, and what kind of effect an observer approaching it would feel.
⊠This might explain why we find the seemingly contradictory claims that Taub-NUT space has singularities or that it does not.â€â€But I admit I still find every single paper I've managed to find on the topic so far incredibly confusing and unclear in what the global structure is (or can be).
Concerning the existence of singularities, if I believe arxiv.org/abs/1509.07854 (esp. second paragr. of p. 6) and doi.org/10.1063/1.17... we can eliminate those of Taub-NUT space at the cost of making time coordinate periodic (giving closed timelike loops), which of course is not very appealing. âŠđ
Kerr and Taub-NUT (as well as Reissner-NordstrĂžm and others) are special cases of the PlebaĆski-DemiaĆski solution arxiv.org/abs/gr-qc/05... â if I believe fig 1 in this paper, there is a different behavior in Kerr-Taub-NUT depending on whether a<l or a>l (where l is the NUT parameter).đ
"Applications are invited for a Professor of Applied Mathematics ... We are looking for an outstanding researcher with an established reputation in ... who is seeking a friendly, supportive and collegial environment in which to build activity"â€â€www.jobs.manchester.ac.uk/Job/JobDetai...đ
Well this really is very dystopian. Medical devices that allow people to walk, see etc. can just stop being supported by the manufacturer.â€â€futurism.com/neoscope/par...đ
⊠et il finit par conclure quelque chose comme «mais Ă ce compte-lĂ , autant lire Dickens: aprĂšs tout, Ă un suffisamment haut niveau, on peut dire que l'Ćuvre de Dickens est une traduction de celle de Dostoievsky».
(Note that I'm not saying that the metric âshare of the population earning less than 50% of the median incomeâ isn't an interesting metric, just that it says nothing about poverty, only about income distribution inequality.)
I ask because one typical definition of the poverty threshold is âincome below 50% of the median incomeâ. With this definition it is, of course, mathematically impossible for over 50% of the country to be poor (and I think this just shows that this definition is nuts).
What is the precise definition of âpovertyâ in this statistic? It's not surprising, of course, that massively slashing government spending will cause any purchasing power metric of poverty to rise, but which definition is being used? www.theguardian.com/world/2024/s...đ
Oh crap: not everyone agrees on the definition of the coordinates. The ones I used are from Stephani &al, âExact Solutions to Einstein's Fields Equationsâ (2d ed 2003), eqn (13.49) p. 196; but Misner doi.org/10.1063/1.17... âThe Flatter Regions of NewmanâŠâ (1963), eqn (2) differs by ÏâČ=tâ2Ï or so. đ
One problem is I'm not even sure how to properly define a âcircleâ. The curve at t=cst, r=cst, Ξ=cst and Ï ranging from 0 to 2Ï has length 2Ï Â· (rÂČ·sinÂČ(Ξ) â NÂČ·(3+5·cos(2Ξ))/2 + O(1/r)) if that's of any use â remarkable here is the second term which does not vanish as rââ or even Ξâ0.
I think this may be my first time having a scientifically actually meaningful discussion here on Bluesky. đœđ
But I agree Taub-NUT is somehow ânot really asymptotically flatâ in some sense (as opposed to, say, the Kerr solution, which is). I'm just not sure what this sense is or what it means. bsky.app/profile/gro-...đ
⊠At any rate I should add that I have absolutely no physical intuition of what this might all mean (I'm just a mathematician, and not even a differential geometer, though I have dabbled in differential geometry at times).
⊠So anyway, my thoughts aren't very clear on the whole matter, but I'm still pretty sure Taub-NUT is asymptotically flat in the sense âall its curvature scalars tend to 0 as râââ and I suspect this is no longer the case if you start doing more âglobalâ measurements like maybe sphere areas. âŠ
⊠so I expect something of the sort for Taub-NUT (the size of a sphere of radius r not being ~4ÏrÂČ for r large). I can't easily check this on the equations because this requires having a global coordinate system for Ξ,Ï and the usual one blows up on one axis, precisely because of this problem. âŠ
⊠but still with some âglobalâ kind of curvature that doesn't go away at infinity: in the case of a cone, the length of a circle around the cone's apex isn't what you'd expect in Euclidean space, and doesn't asymptotically behave like it when you go away from the apex, âŠ
⊠My intuitive understanding of Taub-NUT (suggested to me by my late father) is that it looks something like a cone (or maybe imagine a hyperboloid): locally asymptotically flat in the sense that all curvature invariants tend to zero (in the case of the cone, even âareâ zero), âŠ
⊠As for the singularity on the polar axis, my understanding is that it's just a coordinate system singularity (the Kretschmann scalar only depends on r, so it certainly doesn't see the axis as remarkable), which can be fixed by introducing two coordinate charts, one around Ξ=0 and one around Ξ=Ï. âŠ
⊠So this tends to zero asymptotically. In fact, I checked that all components of the Riemann tensor tend asymptotically to zero (the latter doesn't exactly prove asymptotic flatness, because the coordinate system could be messing up, but I don't think it is, and it's at least a good indication). âŠ
Ah⊠you instilled doubt in my mind, so I got out some old Mathematica code and used it to compute the Riemann tensor and Kretschmann scalar of the Taub-NUT metric: gist.github.com/Gro-Tsen/5d9... â the Kretschmann scalar is asymptotically ~ 48(MÂČâNÂČ)/rⶠwhere M is mass and N is nut parameter. âŠđ
By âlocally asymptotically Minkowskiâ I mean every component of the Riemann tensor (or, better, any curvature invariant) tends to 0 at infinity; by âglobally asymptotically Minkowskiâ I mean things like: the area of a sphere of radius r is asympt-ly equivalent to what it would be in flat space.
They are something like âlocally asymptotically Minkowski but not globally asymptotically Minkowskiâ, right? In any case, I really have a hard time imagining what kind of experiment we might do to detect such a parameter, or what its effects might look like.
I asked a question on Physics StackExchange on physical effects and intuitive interpretation of the NUT parameter (as in the (Kerr-)Taub-NUT solution of General Relativity) and if we know real black holes have NUT parameter =0. Any relativists in the room? physics.stackexchange.com/q/829444/39931đ
(I just copied my part of the conversation, because what ChatGPT replied was really pretty useless, so I might as well have been talking to a rubber duck.)
ChatGPT is pretty useless for actually solving my computer problems for me, but it does a decent job at being the proverbial ârubber duckyâ: listening to me patiently as I try to solve the problems myself. đœđŒïžđŒïžđŒïžđŒïž
I asked a question on MathOverflow about what topos-theoretic construction lies behind the âsymmetric modelâ construction used to provide independence statements about the Axiom of Choice in set theory: mathoverflow.net/q/479689/17064đ
⊠Journalists need to state this clearly whenever they mention sites like Libgen & Sci-Hub: their contribution to science and the preservation of scientific works is immense and invaluable â they deserve thanks and awards from society, not legal threats. www.palladiummag.com/2021/09/24/a...đŒïž
⊠The utter absurdity of a system where SCIENTISTS need to turn to ILLEGAL âPIRATEâ sites (like Libgen & Sci-Hub) in order to DO THEIR JOB makes the mind reel! I don't know what copyright law SHOULD be, but this demonstrates that current law is WRONG. ⊠x.com/gro_tsen/sta...đŒïž
As Library Genesis (âLibgenâ) loses in court (as it obviously would, being brazenly illegal), we are again reminded of the craziness of copyright law which forces researchers around the world to resort to such âpirateâ sites to get scientific books. ⊠arstechnica.com/tech-policy/...đ
I think capital punishment, solitary confinement and non-rehabilitative justice are evil in the best of times, but Japan's way of treating death row inmates is particularly abhorrent: youtube.com/watch?v=1rEo... â it is tantamount to psychological torture.đ
Imagine being convicted of murder when you are 32, then spending over 50 years on death row, of which 30 in solitary confinement, and when you are old and mentally ill you are acquitted because the police fabricated the evidence and coerced a confession. www.bbc.com/news/article...đ
Remember that ChatGPT, on top of being prone to hallucination and ridiculous errors, is also a nightmare from the privacy point of view: you should treat all conversations with it as though the entire world could both read them and inject text into it. arstechnica.com/security/202...đ
On IT procurement: Story time.â€â€University X (not my current employer) merges two departments. As is well known to managers, you only need 3 IT staff for n employees, for all n. So, they look at the two IT teams and sack the ones who wear T-shirts and have unkempt hair, and keep the ones >
I posted an answer on MathOverflow showing (assuming that the question was correct!) that the statementsâ€â€ââ is the disjoint union of two inhabited subsetsââ€â€andâ€â€âevery real is either 0 or not 0â (= analytic WLPO)â€â€are equivalent in constructive math.â€â€mathoverflow.net/a/479501/17064đ
To be precise, I took the âXAPKâ format (for my arch) from apkcombo dot com, extracted the zip, and used `adb install-multiple` to install both .apk files it contained. I did this after similarly installing both .apk from /data/app/something from the old phone, so as to check signatures.
But they're not even doing a good job at that, because the app could obviously just refuse to launch after checking whether it likes my phone. The whole thing makes absolutely zero sense.
Update: not only is Google incredibly disrespectful in saying âthis phone isn't compatible with this appâ without further explanation, it's also LYING: I used adb to install the Google Earth .apk files from my old phone and those from apkcombo dot com, and both work fine! đ€šđŒïžđŒïž
Google's way of doing things is incredibly shitty and disrespectful towards users: they don't show you the app when you search for it, and even if you find it, they don't tell you what the incompatibility is! What a bunch of jerks! đ€Ź
Ah: if I open the right link it says âthis phone isn't compatible with this appâ. But WHY??? This is on a Pixel 8a running Android 14, and on my previous phone (Pixel 4a running Android 11) it worked fine.đŒïž
Google Earth for Android doesn't exist anymore? Is it a case of âkilled by Googleâ or did they decide my phone / Android version can't handle it for some reason?đŒïž
⊠So while IN THEORY the community can take the latest open source version and continue developing it, in practice, when all the devs are from a commercial project, they have the knowledge and momentum, so this doesn't happen. Open Source is useless without the community to keep it free.
Yeah but who develops it? Commercial projects have pulled the trick before (e.g., MongoDB, Elasticsearch) of showcasing something as open source, but when it starts becoming popular, psych!, they're switching to a closed source model or a dual-tier model where advanced features are proprietary. âŠ
I mean, we have enough pain in scientific publication because of the rapaciousness of commercial editors like Springer and Elsevier and the like: if another step of the typesetting chain is getting commercialized, this is going to be even worse. So why isn't this thing purely community-driven?
âSign up for free and try it now!â? đ€š Seriously? Is it one of these predatory models where they try to lure you to use it with a free version, but then you discover that you need to pay to access some features? Because I've had enough of this kind of shit to know to stay away from them.
> We just have different thresholds for what's a typing and readability burdenâ€â€You mean to say â<var>a</var>â is more fastidious to type than âđâ? Whatever your editor, I'm sure you can easily set up macros of sorts that will let you type the one just as easily as the other.
This is a bit like asking what the smallest unremarkable integer is: answering the question defeats the question â in this case because someone will immediately add a Wikipedia page for that person.
My belief is that when a civilization becomes sufficiently advanced, it cares about the well-being of its individuals more than its survival as a civilization, and eventually dies out â per demographic collapse, not necessarily cataclysm â and rather rapidly wrt evolutionary timescales.
I write â<var>a</var>â rather than âđâ. I see little benefit in the latter except if you're using notations which distinguish straight and italic âaâ (and you should probably use a var tag anyway for semantic reasons).
Yeah, I heard that. I guess I should put more MathML in my blog posts, now (but it is admittedly very tedious to type, and LaTeXâMathML converters can't guess the right markup in many cases).
It's quite conceivable that Markdown introduced it first. I knew all sorts of sites used collapsibles, of course, but I thought they were always done in JavaScript.
The list given here www.tutorialspoint.com/html5/html5_... doesn't seem to have much that's interesting â but maybe it's not complete or maybe I missed some exciting possibility of a tag that's in the list.đ
I was today years old when I learned about the HTML <details> element that lets you create a collapsible note without any JavaScript. Are there any useful ânewâ HTML tags that are worth knowing about that I might easily have overlooked?
Yes, but it then requires, for the shapes to work, that you make Detroit and AP into chess openings, and Detroit and Moulin Rouge too expensive. (I can already believe that âWickedâ and âAPAâ are shocked exclamations, so that's that.)
To break this diagram, we need to invent a âChicagoâ chess opening, raise real estate prices there, and start the trend of crying out that name in shock. This should be doable.
I mean, Douglas Hofstadter is an idol of mine, he's pretty much the reason I got interested in math, in logic, in computer science, and much else. And he worked a lot on various facets of AI. That its current progress makes him frightened and depressed is heartbreaking. đą
I've can't stop thinking about this interview since yesterday. The first part on how âGEBâ was written is super interesting and inspiring. But the part where he talks about how the progress of AI both frightens and depresses him is⊠truly incredibly sad.
Interesting recent interview by Douglas Hofstadter, in which he talks mainly about two things: the history of how âGödel, Escher, Bachâ came to be, and his (rather depressed) thoughts on the current state of AI. www.youtube.com/watch?v=R6e0...đ
AI chatbots might be better at swaying conspiracy theorists than humans, study finds. Co-author Gordon Pennycook: "The work overturns a lot of how we thought about conspiracies." arstechnica.com/science/2024...đ
âData available upon requestâ is a myth that we should firmly dispense with. I should add, that in 6 years of being an associate editor, I have never had a single request for code (not even data) granted by the authors.đ
⊠As I argue in the aforementioned question, IF there is a mathematical theory of negotiations, the outcome SHOULD be to split c into (c+aâb)/2 for Alice and (c+bâa)/2 for Bob. But the question is whether such a theory actually exists!
One example of a ânegotiating gameâ would be: given a,b,c such that c>a+b, Alice and Bob can either agree on a way to split c into âs for Alice and câs for Bobâ, or disagree in which case Alice receives a and Bob receives b. What is the rational outcome of such negotiations? âŠ
I asked on MathOverflow the question of whether there is a mathematical theory of games of negotiation: mathoverflow.net/q/478931/17064 Here is an example of a very simple possible such game: âŠđ
⊠(although âââ isn't ideal either because when it's printed in small one can easily miss the oblique bar across the equality sign). See what I wrote here: www.madore.org/~david/weblo...đ
I always try to use the least ambiguous notation. Since some people use âââ one way or another, I avoid it altogether. I use âââ for inclusion, and in cases where I need strict inclusion, I will either write it in full words or use âââ which is unambiguous âŠ
Important news but as the WHO DG says: âWe now need urgent scale up in procurement, donations and rollout to ensure equitable access to vaccines where they are needed most, alongside other public health tools, to prevent infections, stop transmission and save lives.ââ€â€www.who.int/news/item/13...đ
âShorter versionâ Dr. No will give Alice 3 real numbers, Alice selects 2 and passes them to her accomplice Bob, who must propose finitely many guesses as to the remaining real. Do Alice and Bob have a strategy that guarantees success regardless of Dr. No's choice?đ
The proof is in the paper âLearnability can be undecidableâ published in âNature Machine Intelligenceâ (đ) in 2019. doi.org/10.1038/s422... And I learned about it through the following related question posted on MathOverflow: mathoverflow.net/q/478719/17064 âą7/7đ
In particular, if X=â, it is undecidable in ZFC whether Alice and Bob have a winning strategy for any given 1<m<n (and for m=1 they definitely do not): the assertion that they have one for m=2 is exactly equivalent to the Continuum Hypothesis. đ€Ż âą6/7
(For k=0, for example, the strategy is very simple: we can assume wlog that X=â, and then Alice simply passes the m greatest elements of S to Bob, who then completes with all smaller elements. But it is worth thinking about how to do the case X=Ïâ and m=2.) âą5/7
(Of course, Bob doesn't know S, only SâČ â or this would be trivial.) So the question is: for which m,n and X do Alice and Bob have a strategy in this game? Well, the answer is very surprising: this is the case iff m>k where card(X) = â”_k (and there is no constraint on n). âą4/7
⊠And Bob, in turn, must respond with a finite set Sâł, and his goal is that SâłâS. In other words, Dr. No gives n elements of X to Alice, Alice can pass only m<n of these elements to Bob, and Bob's goal is to find finitely many elements including Dr. No's original ones. âą3/7
⊠having n elements of some infinite set X (e.g., X=â), where n and X are prearranged (known in advance to Alice and Bob); Alice must then select a subset SâČâS having m<n elements (where m is also a prearranged parameter), which is passed to Bob. ⊠âą2/7
A cute little puzzle illustrating an intriguing result in infinite combinatorics: evil Dr. No has captured two mathematicians (Alice & Bob) and challenges them the following game. After Alice and Bob agree on strategy, Dr. No will present Alice with a finite subset SâX ⊠âą1/7
White dwarf stars consist mostly of electron-degenerate matter.â€â€QUESTION: is there a (1st order? 2d order?) phase transition between this electron-degenerate matter and ordinary matter? If not, what is the phase (solid, plasmaâŠ)?
I also wonder if that existential unease is itself an emotion. Because sometimes I think my five basic emotions are something like âserendipityâ, âcompunctionâ, âmetaphysical longingâ, âexistential uneaseâ and, of course, âschadenfreudeâ. (Pixar, please do a film about these!)
Tonight I watched Disney/Pixar's âInside Out 2â movie, and I am now experiencing existential unease about whether my emotions have consciousness â each with their own set of emotion. What if my joy experiences disgust? And what if my joy's disgust itself feels anxious? đ€
There's a program called `update-xmlcatalog` but of course it doesn't have a --regenerate-from-scratch option and I have no idea what the authoritative data source is. And /etc/xml/catalog isn't marked as belonging to a particular package that I might simply reinstall
So one of my (Debian) Linux machines somehowÂč found itself with a corrupt (empty) /etc/xml/catalog file.â€â€âŁ HOW am I supposed to regenerate this /etc/xml/catalog to a sane content?â€â€1. Probably as a result of a mid-update crash: bsky.app/profile/gro-...đ
Renart n'est pas un pauvre bougre, il a son domaine de Maupertuis, sa femme Hermeline. Il s'en prend tout autant voire + aux vilains (c'est Ă dire aux paysans libres) qu'Ă son pair Ysengrin, ou au roi. Il ne fait pas ce qu'il fait par esprit de justice ni par vengeance, il le fait parce qu'il peut.
So this answers the questions earlier in this thread (except that I write âsurjectiveâ for âinjectiveâ, which doesn't help): bsky.app/profile/gro-...đ
And in fact, the answer is quite explicit: we can construct a continuous function F : D â {0,1} which does not extend to a continuous function {0,1}^S â {0,1}.
OK, thanks to an explanation by KP Hart on MathOverflow, I was able to write a full and satisfactory answer to my own MSE question: if D is countable and dense in {0,1}^S for infinite S, then ÎČD â {0,1}^S is never injective: math.stackexchange.com/a/4969756/84...đ
âWer mit Idioten verhandelt, mag zusehn, dass er nicht dabei zum Idiot wird. Und wenn du lange in eine Dummheit blickst, blickt die Dummheit auch in dich hinein.ââ€â€(Ich bitte Friedrich Nietzsche um Entschuldigung.)
A history of the notion of equivalence (as in: equivalence relations, equivalence classes) in mathematics, by Amir Asghari in âSyntheseâ. doi.org/10.1007/s112...đ
features you want in a new phone:â€-camera works betterâ€-longer batteryâ€-wonât shatter when you look at it wrongâ€â€features you get in a new phone:â€-photo is not photo you tookâ€-create image of hands made of butterâ€-recipe suggestion may be poisonous
I have the vague feeling it might be useful to see it as the Boolean algebra analogue of a functional analysis question like âgiven a subspace V â â^S dense for the product topology, is every continuous linear form on V the restriction of one on â^S (or sth)?â.
Gro-Tsen's law of zero duality: whenever someone feels the need to point out in an argument thatâ€â€âthe economy is not a zero-sum gameââ€â€you can be sure that their contribution to the discussion is a zero-worth trash.
there's currently massive unrest in the venomous snake hobbyist community bc some dumbfuck who owned an inland taipan in the US, encouraged free handling and didn't have anti-venom (insane) got bit and now he's in the hospital on a ventilator and also he posted this one (1) week agođŒïž
It is possible for Alice and Bob to agree on a common secret key (passphrase) they can use to later exchange secret messages which Eve cannot decipher, even if Eve gets to eavesdrop on every message that Alice and Bob send each other. en.wikipedia.org/wiki/Diffie%...đđ
⊠A related, easier to state, but perhaps not equivalent, question is: when is every clopen subset of D the intersection with D of a clopen subset of {0,1}^S (can we give a simple criterion for this)?
⊠this defines a map ÎČD â {0,1}^S: the latter is surjective precisely when D is dense (in the sense that for finitely many s_1,âŠ,s_k â S distinct and v_1,âŠ,v_k â {0,1} we can find hâD s.t. h(s_i) = v_i). But when is it surjective? âŠ
OK, I think the following is a better question to ask (than this đœ): let S be a set, and D â đ«(S)â {0,1}^S a set of subsets of S, maybe assumed closed under Boolean operations, which we endow with the subspace topology from {0,1}^S (itself with the product topology); âŠđ
I would just like to wish the inventors of DisplayPort - a type of display port that is called DisplayPort and that looks almost identical to HDMI, a completely different type of port for displaying - a very stubbed toe.
Oh wait! I was wrong to assume that D gets the same topology as a subspace of {0,1}^â and of {0,1}^â â so the equivalences asserted in the question might not be correct, and the assertion in the previous skeet is probably wrong. Now I'm even more confused. đ
One can say intelligent things about politics, but it requires space because the world is complex. All that will ever fit in a skeet is a stupid slogan whose real purpose is to gain more followers among people who think the same thing you do, and preach to the choir.
I mean, whom are you trying to convince? Whatever your political ideas, do you REALLY think someone is going to read your one post and think âoh noes! I had been led astray by communism/capitalism/whatever, but this has changed my mind and I now realize the error of my waysâ?
At any rate, if the answer is positive (I don't know what to believe), this is interesting because it gives a somewhat explicit subspace of {0,1}^â (clearly, D can be seen as such) whose Stone-Äech compactification would be exactly {0,1}^â.
Maybe I should have better asked on MathOverflow, because this is unlikely to get much attention on MSE. But I feel like I'm missing a very simple fact that would make the answer almost entirely trivial. đ€
I asked on Math StackExchange a question about the set D of characteristic functions of finite Boolean combinations of intervals with rational endpoints as a subspace of X := {0,1}^â (namely, whether it is C^*-embedded). math.stackexchange.com/q/4968033/84...đ
(I mean, for âlumberâ-vs-âplumberâ we can say âthe âbâ is silent in âplumberââ, but for âfingerâ-vs-âsingerâ we can't just say âthe âgâ is silent in âsingerââ whereas we could if they were spelled with âĆâ instead of ânâ.)
Exactly the same phenomenon happens in âlumberâ versus âplumberâ, but I suspect that it gets noticed more for âlumberâ-vs-âplumberâ than for âfingerâ-vs-âsingerâ simply because the alphabet lacks a symbol for a velar nasal (âĆâ) whereas it has one for a labial nasal (âmâ).
Much of the attention on the oddities of English pronunciation/spelling is devoted to vowels, but consonants can be weird too: I wonder how many people realize that the words âfingerâ and âsingerâ do not rhyme (well, they do rhyme, but not as far as you might think).
All of this is not to say that one can't be Duke of Fodderfolk and not be a good person. In fact there is at least one past hereditary member of the House of Lords whom I very much respect: en.wikipedia.org/wiki/Bertran...đ
It seems like they intend to keep the âLords Spiritualâ, though, so it would still be possible to be a legislator as Bishop of Scrumbridge.
www.theguardian.com/politics/art...â€â€Does this mean I'll no longer be able to snarkily point out that there's a supposedly modern democracy in Europe where someone can be a legislator merely by virtue of having been born Earl of Wibbleshire or Baron Crumplethwaite of Giggledon? đđ
In my case it was because I had produced a tar backup of my smartphone's filesystems, and I realized it was stupid to have lumped all of /data together, that I should at least separate /data/media from the rest, but I didn't want to redo the archiving, nor extract the files.
I wrote this little âtar filterâ utility for my own use, but maybe it could be useful for someone else: it takes a GNU tar archive and (without extracting it to the filesystem), outputs another tar file containing only the paths matching a given pattern. gist.github.com/Gro-Tsen/76e...đ
Du mĂȘme genre (mais pas la mĂȘme espĂšce):â€â€â colza/rutabaga, chou, navet, moutarde noire (Brassica),â€â€â courgettes/citrouilles et potirons (Cucurbita),â€â€â topinambour et tournesol (Helianthus),â€â€â pomme de terre, tomate et aubergine (Solanum),â€â€â tous les agrumes (Citrus).
⊠And gravity is something similar, except that instead of being a twisting in special dimensions that you cannot see, it is the curvature of ordinary space and time.â€â€(Again, take all of this with a galaxy-sized grain of salt.)
The electromagnetic field, for example, is a kind of twisting of certain dimensions in which the field can vibrate (the âU(1) gaugeâ); when this twisting propagates, it is electromagnetic radiation â but if it does not propagate, it is merely an electric or magnetic field. âŠ
⊠More precisely, the particles are the âpropagatingâ modes of vibration of this field (e.g., an electron is when the field vibrates in the âelectronâ directions, a muon when it vibrates in the âmuonâ directions, etc.); but the field can also deform in ways that aren't really vibrations.
Of course, mathematically it makes absolutely no difference to speak of two fields or one field with the sum of the dimensions of the value spaces. So if you prefer you can think that there's just one single (quantum) field, which can vibrate in different modes which we call âparticlesâ. âŠ
(Take this âexplanationâ with an enormous grain of salt, of course: I'm just putting very rough words on the math, and it may not âexplainâ anything.)
What we call âparticlesâ are vibrations in quantum fields (which permeate all of spacetime), and the very rough idea is that the state of one field displaces the equilibrium of another, so vibrations in one can have effects on another like hitting one piano string can cause another to vibrate.
(Et par ailleurs il est possible que Brassica napus soit un hybride naturel entre B. oleracea (chou, chou-fleur, broccoli, etc.) and B. rapa (le navet, donc). Donc tout ça reste terriblement proche.)
(The thing is, for this to explain dark matter, the GALAXIES of the other universes would have to be in the same place â so, as in ours â but the individual STARS would not be in the same place. A bit weird.)
I think we can probably refute this hypothesis because we'd have seen weird stuff in celestial dynamics due to objects of the other universe going through the solar system, but it could be an interesting plot idea for a science-fiction story.
Another related idea I had come up with concerning dark matter is this:â€â€What if there are ~10 different physical universes (inc. ours), all with the same laws of physics, all occupying the same space, but interacting with each other only through gravity? Would we know? How?đ
I think in the times when there were no disk caches and the filesystem used was FAT, defragmentation did something useful. But my guess would be: probably only in specific circumstances, and not as much as some utility vendor advertised.
Another âyou are old ifâŠâ test: do you remember the grinding noise of hard drive defragmentation, the bzwomm of monitor degaussing, the squeal of floppy drive ejection, the crackle of CRTs being turned on and the horrifying shriek of dot matrix printers? If so, you were born in the previous century.đ
⊠but it has fascinated me ever since that what seemed to 14-year-old-me the immediately very obvious candidate for dark matter was never taken too seriously â and it's even more hilarious if this explanation turns out to be correct and gets called the ânightmare scenarioâ!
⊠Now my father had some counterarguments about this possibility and/or the simplicity of the hypothesis (like, how would this particle have appeared in the early universe, or how it would have cooled down, I don't remember exactly), âŠ
I found this video about the ânightmare scenarioâ for dark matter funny because when I was 14 or so, my father told me about dark matter and my immediate reaction was: âisn't the most obvious explanation just a massive particle that interacts ONLY with gravity?â. ⊠www.youtube.com/watch?v=_P6W...đ
If they want to be able to change the format, that's precisely a reason to provide a tool to export the data it contains. Bottom line is, it's my data, I should be able to extract it into something usable if I want to be able to, say, search though it, filter it, or do stats on it. âŠ
⊠and most of which will probably cease to work when Signal decides to change or expand its format slightly.â€â€When you invent a format, you're supposed to provide basic tools to convert to and from that format, and do basic tasks on it like encryption and decryption!
Why the fđck doesn't @signal.bsky.social provide an official tool to decrypt and extract a Signal backup file? It's not super difficult (see jhnet.co.uk/articles/sig... for example) but this means that there are now a dozen half-baked such tools, none packaged by mainstream Linux distros, âŠđ
⊠Likewise, some apps had their in-app data kept, but for others it was wiped clean (and yet other apps weren't copied at all). So anyway, this saved me a bit of time, but I still had to go through page after page of settings trying to get everything on my new phone just like it was on the old one.
⊠So for some reason, all the image files in my âDownloadâ dir were copied, but not PDF files. Likewise, the âUSB debuggingâ system preference was kept, but not the (super useful) âshow arrow keys while typingâ one. Why??? âŠ
So, Android does have a mechanism for copying (migrating) data and preferences from a old phone to a new one, which works (more or less); but the set of stuff which gets copied seems very random: some system preferences were migrated, others weren't, and the logic escapes me. âŠ
The key, here, is that I have the useful âncâ command (netcat) on my phone from BusyBox (I don't know if all Androids have this, but Lineage OS has it), and adb lets you forward TCP ports on the USB link.â€â€TWRP backup was much better, of course, but it seems to be dead now.
# Connect phone through USB, then run:â€adb rootâ€adb forward tcp:5555 tcp:5555â€adb shellâ€# On phone:â€cd /â€tar cf - somedir | nc -l -p 5555â€# On computer, in a different terminal:â€nc 127.0.0.1 5555 > somedir.tarâ€# (Interrupt when finished.)
In case someone is, like me, trying to do a poor man's backup of an Android phone because Android still has no useful concept of âbackupâ, and if you are root, the following commands MAY be useful (âïžuse at your own risk, and only if you understand what they doâïž): đœ
Love this photo from đŹđ§ (saw this on X)â€â€Now imagine similar access across communities in Africa â€â€Thatâs what equity would look likeđŒïž
I think this is a bit unfair, though, as Norilsk, Russia, has so much to offer. But maybe it's in a different category?đŒïž
So for whatever reason I was searching for âugly cityâ in Google Images, and the very top result used to illustrate an article thetimes.com/travel/inspi... on the âten uglies cities in the worldâ, was one of:â€â€â” Charleroi, Belgium â”đŒïž
I am completely flabbergasted to learn that we know the internal body temperature of various species of dinosaurs to a good precision thanks to⊠<spoiler> the isotopic ratio and bonding of ÂčÂłC and ÂčâžO in apatite crystals in their bones. đČ www.youtube.com/watch?v=VNiJ...đ
The difference between a king and an emperor is that when France wants to get rid of a king, we just do a revolution; but when we need to get rid of an emperor, we have to ask our European neighbors for pest control, it annoys everyone and they charge a hefty fee.
Enfin, c'est un peu comme demander pourquoi les gens postent des liens vers des articles de journaux derriĂšre un paywall ou un subscribewall: oui, c'est agaçant, mais si l'info n'est pas disponible ailleurs, ben on le fait quand mĂȘme.
Ben parce que beaucoup de gens ont un compte lĂ -bas, justement, ne serait-ce que pour pouvoir lire, mĂȘme s'ils ne postent rien. Par ailleurs, un lien vers un tweet unique continue Ă ĂȘtre visible mĂȘme sans compte (mais effectivement, pour un fil, ça ne marche plus).
But having something that is well supported by LineageOS is critical. I will be wasting enough time migrating each and every app because Android still doesn't have a backup/restore feature (đ), I don't want to add extra pain of discovering that many things are broken in AOSP.
I don't care much about features of any kind, I pretty much only use my phone for the GPS, for very basic photos, for browsing the Web (mostly Wikipedia) and for ConnectBot. So I don't want something too fancy, nor too bulky.
I just noticed that my current (Pixel 4a) smartphone's battery has started to swell, so I need to buy a new one.â€â€Does someone have recommendations to share for a recent-ish Android smartphone that is well supported under LineageOS (this is my primary criterion)?
This is from the paper by Robert Lubarsky, âOn the failure of BD-â and BD, and an application to the anti-Specker propertyâ, âJ. Symbolic Logicâ 78 (2013) 39â56 doi.org/10.2178/jsl....đ
âJust as we are more upset when religious leaders engage in even common sexual transactions than when lay people do, because we hold them to a higher standard, so are people who discuss constructive mathematics questioned about their use of [LEM].â đ Robert Lubarsky seems fun.đŒïž
âHave Swiss scientists made a chocolate breakthrough?â www.bbc.com/news/article... This news headline conjures in my mind the idea that there are chocolate researchers who attend chocolate conferences and publish their chocolate breakthroughs in chocolate journals â and I love every bit of it!đ
A very cursory glance through the argument suggests to me that the answer is ânoâ, but your guess would be as good as mine. If you want a more informed answer, try asking as a comment on mathoverflow.net/a/477708/17064 (where I learned this), or as a new question on MSE / MathOverflow.đ
Even after decades of study, mathematics never ceases to surprise: today I learned that ââ€â€âŁ There exists a continuous map f: đÂČ â âÂČ which preserves the length of every curve. đ±â€â€(Reference: arxiv.org/abs/1405.6606 theorem 4.1, aka âGromov's rumpling theoremâ)đ
Yow! I see you like VERSION NUMBERS so my version numbers have THEIR OWN VERSION NUMBERS. đ€Ą
Today I learned that there is something called âUSB4 version 2.0â and the only possible explanation for such an abomination is that whoever came up with that name was trapped in a mental torture facility somewhere and was trying to call out for help.
⊠soit active ou passive), et qu'il a un sens actif dans les verbes utilisant l'auxiliaire «ĂȘtre» et passif dans les verbes utilisant l'auxiliaire «avoir». C'est quand mĂȘme une observation vraiment basique qu'il est facile de rater, je trouve dingue qu'on ne l'enseigne pas clairement.
⊠Je pense que c'est assez courant dans les langues Ă alignement absolutif-ergatif en.wikipedia.org/wiki/Ergativ... (le basque en est une) puisque de telles genres assimilent, justement, l'objet d'un verbe transitif au sujet d'un verbe intransitif (les langues nominatif-accusatif font le contraire).đ
People are already submitting AI-generated or âimprovedâ photos to Wikimedia Commons, which serves them up as the âofficialâ image of a person or event. The almost-overnight destruction of photo-as-truth. www.theverge.com/2024/8/22/24...đ
The âShelterâ Android app looks like it could be useful: it claims to let you, among other things, install two copies of the same app on the same device. f-droid.org/en/packages/... Has someone tried it?đ
I posted a new answer to an already-answered question on MathOverflow about why the Stone-Äech remainder ÎČâââ is not extremally disconnected, noting that this is equivalent to saying that the Boolean algebra đ«(â)/fin is not complete. mathoverflow.net/a/477479/17064đ
I asked a question on Math StackExchange about what we can say about the map ÎČââÎČâ between the Stone-Äech compactifications of â and â that might help visualize it. math.stackexchange.com/q/4962042/84...đ
It is pretty alarming that, in ZF, Ïâ can be singular (i.e., a countable union of countable sets). In fact, â can be a countable union of countable sets (and the latter fact implies the former since we can surject ââÏâ as you had observed): see Jech, âThe Axiom of Choiceâ, theorem 10.6 for a proof.
(This is to connect with what I was saying 5 skeets above, not immediately above. So just to be clear, ZF+AD does not imply that Ïâ is singular: quite the contrary, ZF+AD implies that Ïâ is measurable, and in fact, that the closed unbounded filter on Ïâ is an ultrafilter.)
Also incidentally, as I've just learned, â”â â° 2^(â”â) (aka âevery well-ordered set of reals is countableâ) is a consequence of ZF+AD (because ZF+AD implies âevery uncountable set of reals contains a perfect setâ): Kanamori, âThe Higher Infiniteâ (2d ed, 2009), propositions 27.11(a) and 11.4(b).
It is pretty alarming that, in ZF, Ïâ can be singular (i.e., a countable union of countable sets). In fact, â can be a countable union of countable sets (and the latter fact implies the former since we can surject ââÏâ as you had observed): see Jech, âThe Axiom of Choiceâ, theorem 10.6 for a proof.
I suppose âÏâ â€â Bâ is supposed to be âÏâ â€â ââ, i.e., ââ surjects on Ïââ, and â unlike the statement that âÏâ â€á”ą ââ, i.e., âÏâ injects in ââ bsky.app/profile/gro-... â you are correct that this holds in ZF (by mapping the real coding a well order type on â to the latter's ordinal).đ
The part that says Ïâ injects in â without AC is incorrect: for your diagonalization to work you need to choose a countabilization of every ordinal <Ïâ, and this requires some form of Choice. In fact ZF does not prove â”â †2^(â”â) as explained by Asaf Karagila in math.stackexchange.com/a/43877/84253đ
I think there are several typos in the last two skeets and I can't guess what you actually meant to say, so I'll let you fix them first. But this bit should at least clarify a few things concerning the standard terminology: bsky.app/profile/gro-...đ
⊠The alephs, of course, are well-ordered. Cardinalities are partially ordered (by Schröder-Bernstein), and IIRC it turns out their order can be pretty much anything. Also, there is another not very well-behaved relation defined by surjections: mathoverflow.net/a/322029/17064đ
For the general terms without AC: âa cardinalityâ refers to an equivalence class of sets under bijection (some people just say âa cardinalâ), and âan alephâ refers to the cardinality of a well-ordered set, i.e., of an ordinal. So AC says âevery cardinality is an alephâ. âŠ
What you asked made perfect sense. Your definition of Ïâ is correct and it is indeed not obvious to decide how to formulate CH without AC. You may want to look up âHartogs numberâ (and âLindenbaum numberâ) as well. bsky.app/profile/gro-...đ
I think the standard form of CH without AC would be âthere is no cardinality đȘ such that â”â < đȘ < đ (where đ = 2^(â”â) is the size of the continuum)â. Clearly I'm using more than this. However, it is known that GCH implies AC and related stuff: see mathoverflow.net/a/173091/17064 and passim.đ
⊠while Bob thinks to himself âno matter what x is, there are only countably many y such that yâŒx, so my probability of winning is 1â. So if both players choose their number at random, it looks like both players have probability 1 of winning the game! đ”âđ« âą5/5
⊠Alice draws a random number x uniformly between 0 and 1, and Bob likewise draws y. Alice wins if yâŒx for that order and Bob wins if xâșy. Alice thinks to herself âno matter what y is, there are only countably many xâșy, so my probability of winning is 1â, ⊠âą4/5
If you think the answer is âyesâ, consider the following different situation. Assume the Continuum Hypothesis. Then there exists a total order âș on [0,1] such that {xâ[0,1] : xâșy} is countable for every yâ[0,1]. Now consider the following game: ⊠âą3/5
⊠Question: what is the probability that v=u?â€â€Would you say that it is Âœ or that it is undefined? Of course, âșafterâș t (and hence u) has been chosen, the probability that v=u is Âœ no matter what t (or u) is. But beforehand? Can we conclude that it is Âœ as well?â€â€âą2/5
A mathematico-philosophical question:â€â€Fix Eâ[0,1] a non Lebesgue measurable set. Alice draws a random number t uniformly between 0 and 1. If tâE, let u:=0; otherwise, let u:=1. Bob throws an unbiased coin. If it lands on tail, let v:=0; otherwise, let v:=1. âŠâ€â€âą1/5
That âD(aâb, ab) > Δâ in the penultimate line of the second paragraph should clearly be âD(aâb, ab) < Δâ, though. No wonder the guy didn't pursue this any further. đ€
The author of this paper is famous for⊠other things, and I admit I had no idea he had published something on group theory / geometry, and in âAnnals of Math.â no less. jstor.org/stable/1968716đŒïž
This is from Lubarsky, âSeparating the Fan Theorem and its Weakenings IIâ, âJ. Symbolic Logicâ 84 (2019) 1484â1509. jstor.org/stable/26873... The paper is completely serious, and, for those who will understand why I'm saying this, does not mention broccoli anywhere.đ
I⊠did not expect to read this in a math paper. đź And I certainly did not expect an appeal to Kant's âDing an sichâ, or a comparison with a black hole, to justify the technical change of adding nodes representing â„ in Kripke semantics of linear logic. đđŒïž
Actually, the story of how the notion of âcompactnessâ (which is arguably one of the most important notions in all of mathematics) emerged and why it was thusly named is something that entire papers have been written about: âŠ
No: large cardinal properties are boring because they're pretty much totally ordered (at least by consistency strength, if not by logical implication). Sure, they have colorful names, but you don't really need to scratch your head to invent sth which coheres with the zillion preexisting notions.
You just need a nice diagram and all will become clear. đ [Taken from Kunen & Vaughan (eds.), âHandbook of Set-Theoretic Topologyâ (1984), chapter 9 âCovering Propertiesâ by Dennis Burke, §4]đŒïž
Actually I think there is an interesting sociological/psychological study to be made on how mathematicians name things, especially in domains like general topology where there are already a zillion names around for a zillion confusingly similar concepts, so you try to reconstruct their logic first.
Actually I think there is an interesting sociological/psychological study to be made on how mathematicians name things, especially in domains like general topology where there are already a zillion names around for a zillion confusingly similar concepts, so you try to reconstruct their logic first.
Wait until you hear about the âWeak Lesser Limited Principle of Omniscienceâ (e.g., Berger, Ishihara, Schuster, âThe Weak KĆnig Lemma, Brouwer's Fan Theorem, De Morgan's Law and Dependent Choiceâ ejournals.eu/en/journal_a... )
We can also check that any continuous map ââX is constant: I'll leave this as an exercise. I don't know what can be said about continuous maps XâX, however: maybe they're worth investigating. âą14/14
(More advanced remark: this means that the Stone-Äech space of X is ÎČX = ÎČâ. I shouldn't call it a âcompactificationâ, however, because while XâÎČX is continuous and injective, it is not a homeomorphism onto a subspace! This is because X is Urysohn but not Tychonoff.) âą13/14
⊠so we have |f(z_n)âf(x)|<η, so by passing to the limit, |f(y)âf(x)|â€Î·. So in fact f:Xââ is continuous in the usual sense âââ; and the converse is obvious. So continuous maps Xââ are the same as continuous maps âââ. âą12/14
Now consider a continuous map f:Xââ. This means that for any xâX and η>0 there is ÎŽ>0 such that if z is rational and |zâx|<ÎŽ then |f(z)âf(x)|<η. But now if |yâx|<ÎŽ with y arbitrary, then y is the limit (in X or â) of a sequence of rationals z_n with |z_nâx|<ÎŽ, ⊠âą11/14
⊠and since the complement of A is also open and closed in X, that complement is also open for the usual topology, so A is closed for the usual topology. This shows: clopen subsets of X are in fact clopen in â, and since â is connected, this shows that X is connected. âą10/14
Concerning separation: it is easy to see that X is Tâ (=Hausdorff). On the other hand, it can't be Tâ (=regular) because âââ is closed and it's easy to see that any open set (in X) containing âââ will obviously meet any open neighborhood (in X) of 0. âą8/14
As I mentioned, â is open and dense in X and has its usual (order) topology. As for âââ, the situation is completely different: it is closed and discrete. So intuitively I guess we should imagine X as being â in which every irrational has been âisolated from othersâ. âą7/14
Note that we can reason with sequences in X because every point has a countable neighborhood basis. A sequence (y_n) converges to x in X when for every Δ>0 there is a point after which each y_n is either equal to x or rational and within distance Δ of x. âą6/14
As for the closed sets of X, they are the Fââ such that whenever they contain a sequence of RATIONALS converging to x (in the usual sense), they also contain x. And the closure operation adds to a set all limits of sequences of rational sequences. So â is dense in X. âą5/14
Well, the open sets of X are the subsets Uââ which, whenever they contain some xââ, also contain all RATIONAL numbers within some distance Δ>0 of x. So for example, â is an open subset of X, and it has its usual topology as a subspace of X. So is ââȘ{â2}, say. âą4/14
So, it has â as underlying set, but the topology on this space X is finer than the usual topology on â (that is, Xââ is continuous): the neighborhoods of xâX are the sets containing x as well as some RATIONAL open interval around x. What are open and closed sets of X? âą3/14
Note that I didn't invent this example, I just ârediscoveredâ it, as many people probably have. It turns out to be counterexample #68 (the âPointed Rational Extension of ââ) in Steen & Seebach's celebrated âCounterexamples in Topologyâ (1978). âą2/14
⊠Maybe this is because âultranormalâ is equivalent to ânormal and strongly zero-dimensionalâ (but âstrongly zero-dimensionalâ, despite being more standard, is less obvious to define). Anyway, this note by Joseph Van Name explains things rather well: arxiv.org/abs/1306.6086đ
A Hausdorff topological space X in which any two disjoint closed sets A,B are separated by a clopen one (i.e., there is C clopen s.t. AâC and Bâ(XâC)) is sometimes called âultranormalâ. But almost nobody seems to discuss, or even mention, this property. âŠ
The authors of this math paper aren't listed in alphabetical order. I wonder what we are to make of this! đ€â€â€âŁ Robert S. Lubarsky & Hannes Diener, âSeparating the Fan Theorem and its Weakeningsâ, âJ. Symbolic Logicâ 79 (2014) 792â813: www.jstor.org/stable/43303...đ
⊠he was told he should attend a physics class, so he enrolled in one at the Sorbonne; and one of the first things the professor said was âgentlemen: what some people call the âatomic theoryâ has no place in this classâ (this was in 1952!) â so of course Cartier never went back.
I remember talking to him when I was a student at the ENS because I wanted to discuss some ideas I had; then he gave me a ride back to my parents' house in Orsay, and he told me a number of anecdotes about his own studies when he was my age. I remember this one: âŠ
The passing of Pierre Cartier this saturday is a great loss, not just for mathematics, but also for the history of mathematics, because he always had a story to tell about everything and everyone, and he was so nice and entertaining to listen to. en.wikipedia.org/wiki/Pierre_...đ
Also, this completely demolishes the arguments in freedesktop.org/wiki/Softwar... (âthe case for /usr mergeâ) which claims it won't break things: well, it does, it breaks libpng12. So either fix this or don't go ahead.đ
And of course the really inexcusable shđt isn't so much the conflict itself than the fact that âaptâ has no tool to tell you âthe reason I'm trying to remove this package on upgrade is that it depends on this other one which conflicts with this oneâ.
I am being forced to set boundaries in my marriageâ€Me : âyou *cannot* send me more than one video per day featuring unusual animal friendshipsââ€Him five minutes later : âthere is a fantastic video of a pelican and dog who are friends. If I canât send it to youâŠcan I describe it to you?â
Yeah, both are used. What led me to the remark is the video www.youtube.com/watch?v=Lm9M... which says that a satellite has been launched into the âAllâ. The difference seems about as slim (and maybe similar to) the difference between âspaceâ and âthe cosmosâ in English.đ
We're in the (largely avoidable) mess we are with Mpox due to a toxic combination of homophobia, pharma greed, and neo-colonialism as well as other factors.â€â€Not because there's a conspiracy to obscure the route of transmission.
I love it that space, in German, is called âAllâ (and, yes, AFAICT, it's cognate with the identical English word: so it's really âAllâ as in âthe Universeâ).â€â€It sounds so much better to say that you're sending a rocket in the All than to say you're sending it in space.
Oh great. One of my servers crashed just halfway while I was upgrading from Debian 11 âBullseyeâ to Debian 12 âBookwormâ. This is going to be a nightmare to fix.
Ne pas confondre: la variole du singe, qui est une maladie qu'on ne veut pas attraper, et la raviole de singe, qui est un plat qu'on ne veut pas manger.
I have to say, the one good thing about Zuckerberg is the way he acts as a repeated and decisive rebuttal of the notion that the world would be a better place if only the techbros had some sort of education in Classics and the Humanities more generally. www.bbc.com/news/article...đ
For the same reason, we shouldn't put up statues of people. Because at some point we ARE going to discover that that person did something awful â or come to understand that something we already knew they did is, in fact, awful. And then there will be a fuss about whether to keep the statue.
For the same reason, we shouldn't put up statues of people. Because at some point we ARE going to discover that that person did something awful â or come to understand that something we already knew they did is, in fact, awful. And then there will be a fuss about whether to keep the statue.
We should not idolize anyone. Not because everyone is terrible, but because you just don't know. By all means admire specific accomplishments, and think of people as role models for specific roles. But it's a trap to think that because someone is awesome along one axis they are awesome along all.đ
I asked a question on MathOverflow about why it is so hard to give examples of extremally disconnected spaces, and why those we have always seem impossible to visualize. mathoverflow.net/q/476947/17064đ
The idea that the contracts big corporation force us to sign (making us effectively their vassals) are âfreely consentedâ when, as individuals, we have zero say in negotiating their contents â is the most horrific of legal fictions.đ
Binding arbitration is, indeed, possibly the most twisted evil contract clause ever to have been invented. Even when you sign your soul to the Devil, does the Devil not require this. No sane legal system should allow contracts like this to stand.
Disney is arguing they can't be sued for a woman dying of nut allergies at their restaurant after promising it was safe, because her widower had a Disney+ trial 4 years before - with its terms meaning you can't take Disney or its partners to court:â€â€lawandcrime.com/lawsuit/bord...đŒïž
I asked another question on MathOverflow about surreal numbers, and what makes them special among other âsurreal-likeâ fields. (I'm afraid my question is once again a bit rambling, though.) mathoverflow.net/q/476921/17064đ
Je pense que je peux me permettre d'y manger une fois tous les 25 ans.
Does anyone have a clue what the âentry=ttuâ and âcoh=<number>â parameters which Google Maps and/or Google Street View like to add at the end of URLs mean?
This is an unpopular opinion I know but I personally feel that the Olympics has strayed too far from its roots. It used to be all nude Greek men. Now there are no nude Greek men. There should be at least some nude Greek men there. They donât have to be competing, they could just be hanging around
People saying we need more regulation of social media need to answer: what should be legal offline but illegal on social media? Or alternatively, what is currently legal on social media or elsewhere that should be made illegal on social media?
Plus en amont, certainement. Mais en aval de Poissy (et jusqu'au confluent de l'Epte), lĂ d'oĂč je parle, je ne vois vraiment pas ce que ça donnerait d'absurde de mettre la limite Ă la Seine, surtout qu'elle est difficile Ă franchir Ă cause du peu de ponts.
Je pense à des communes du Vexin français comme Drocourt, Lainville-en-Vexin, Jambville ou Tessaincourt-sur-Aubette, dont on se demande ce qu'elles font dans les Yvelines plutÎt qu'en Val d'Oise. Mais aussi, le long de la Seine (rive droite): Limay, Gargenville, Meulan.
I asked a question on MathOverflow about whether complete Boolean algebras which are countably compact are countably distributive, or vice versa. (I suspect there's something wrong with the âcountably compactâ notion, but I can't see it.) mathoverflow.net/q/476589/17064đ
(Cette personne va juste recevoir une tonne de messages disant «euh, j'ai vu un pigeon⊠il avait l'air de vouloir à manger⊠enfin, comme tous les pigeons, quoi».)
I am now lost in a maze of twisty topological properties, all alike:â€â€âŁ âcountable intersections of dense open sets have dense interiorâ,â€â€âŁ âcountable intersections of open sets are openâ,â€â€âŁ ânonempty countable intersections of open sets have nonempty interiorââ€â€â etc. đ
I asked a question on MathOverflow about topological spaces in which countable intersections of dense open sets have dense interior (equivalently: meager sets are nowhere dense). This is much stronger than âBaireâ. mathoverflow.net/q/476300/17064đ
I'm definitely throwing a lavish party to celebrate my One Hundred Billionths birthday. My only concern is that, as it falls on a Tuesday, I may have trouble getting people to come. But you're all invited!
Immortality sucks because after 10^(31536000000000000) years, merely saying your age out loud takes about a billion years. And after 10^(10^(31536000000000017)) years, merely saying how long it takes to say your age takes about a billion years.â€â€(Don't talk to mathematicians about large numbers. đ)
Immortality sucks because after 10^(31536000000000000) years, merely saying your age out loud takes about a billion years. And after 10^(10^(31536000000000017)) years, merely saying how long it takes to say your age takes about a billion years.â€â€(Don't talk to mathematicians about large numbers. đ)
So stretching things just a bit (but what would be the fun in not doing so?), we can say that carrots are orange because the Sanskrit name of an unrelated plant happens to sound slightly like the Latin name of a place in France to which a Dutch leader inherited a title. âą15/15
The name of that âOrangeâ, in France, comes from the Provençal âAurenjoâ, from the Latin âArausioâ, perhaps of Gaulish origin (sources differ). But certainly unrelated to the fruit or the color. âą14/15
Orange was a principality in the Holy Roman Empire (enclaved in the papal state of the Comtat Venaissin, near Avignon). Aforementioned William of Orange inherited it from a cousin who died without children. Orange was ceded to France in 1713, but the house kept the name. âą13/15
The House of Orange (later Orange-Nassau, which came to rule England after the Dutch invasion â cough cough â âglorious revolutionâ), meanwhile, owes its name to the (now) French city of Orange, whose name in French is identical to that of the color (again, this is a coincidence). âą12/15
The name of the color didn't exist in English until fairly late. When a word was needed, it was called something like âyellowredâ. The word âorangeâ became common when the fruit of Citrus Ă sinensis (or C. Ă aurantium?), the âorangeâ, became common. âą9/15
But of course the âorangeâ in âHouse of Orangeâ and in the color have no relation. It's an accidental similarity in the word which gave rise to the association. âą8/15
⊠one of the leaders of the Dutch revolt against the Habsburgs, which ultimately led to the independence of the United Provinces in 1648. The same House of Orange produced many Dutch heads of state (stadhouders) and the color became associated with the country. âą7/15
But wait, why is orange associated with the Netherlands, when it's not even on their (modern) national flag? That's because of the House of Orange, whose founder (in its current incarnation) was William of Orange (Willem van Oranje, 1533â1584), ⊠âą6/15
(The importance of this effect is disputed. It's hard to know how munch people liked them for their taste and how much for their color, and, id the latter, how much the âDutch national colorâ played a role. But as they say: se non Ăš vero, Ăš ben trovato.) âą5/15
To be sure, orange carrots have been around since forever, and they've been selected because people liked them. But 17th century Dutch farmers played a role in popularizing the vegetable through Europe, and especially the orange variety. Orange was the Dutch national color. âą4/15
You might be tempted to say that carrots are orange because that's just how the plant is (the carotene pigment is orange), but wild Daucus carota (pictured below) isn't so much orange as it is white. Carrots are orange because we humans selected the orange cultivars. âą3/15đŒïž
Ok, this was meant in jest, but it's not entirely facetious, nor perhaps completely wrong: let me explain the reasoning: [this is copied from a Twitter thread I wrote in 2022] đ§”â€”ïž âą2/15
THE REASON CARROTS ARE ORANGE is that the Sanskrit (and ultimately, Dravidian) name âà€šà€Ÿà€°à€à„à€â for Citrus Ă aurantium(?) happens to vaguely resemble the Latin (ultimately, Gaulish) name âArausioâ for a city (now) in France where a family of Dutch stadhouders had a principality. đ âą1/15
This European Citizens' Initiative might interest some of my gamer mutuals. It demands that the EU put up some kind of regulation prohibiting videogame editors from remotely disabling their game. You can sign it at: eci.ec.europa.eu/045/public/#...đŒïž
I asked a (probably too long and rambling) question on MathOverflow about the geometrical structure of the set of monomial orders on â^k. But even if the question isn't interesting, it cites an interesting theorem by Robbiano on the subject. mathoverflow.net/q/476147/17064đ
thinking about how far off the deep end the NFT thing was. every A-list celebrity at least said they were going to do one. and it was nothing. literally nothing. at least with tulip fever there were tulips
The New York Times currently has a mathematically interesting interactive gadget where you choose your own weight on the medals' worth and it ranks the countries according to those weights (with graphs of where they rank in the weight plane). www.nytimes.com/interactive/...đ
The New York Times currently has a mathematically interesting interactive gadget where you choose your own weight on the medals' worth and it ranks the countries according to those weights (with graphs of where they rank in the weight plane). www.nytimes.com/interactive/...đ
Well, some people do sort by deglex, i.e., count the total number of medals first and foremost, so yes, they do think 3 bronze medals is better than 2 gold ones. This ordering currently places the US on top, IIUC, so of course they're going to count that way. Whereas China is on top by lex ordering.
Unless I made a silly mistake somewhere, all three orders I describe agree on the fact that 1 gold > 1 silver > 1 bronze, i.e., (1,0,0) > (0,1,0) > (0,0,1). Where it gets more interesting is when you start comparing (2,0,0) with (0,7,0) and (1,0,6) or that sort of things.
⊠But I am, for my part, disappointed in the lack of success of:â€â€â degrevlex: (2,0,0) > (1,1,0) > (0,2,0) > (1,0,1) > (0,1,1) > (0,0,2) > (1,0,0) > (0,1,0) > (0,0,1)â€â€(Sort by total number of medals and, if equal, by number of gold+silver, then just gold.)
I will use this as an example if I ever need to teach how monomial orders (for Gröbner bases) work.
The only fun part of the Olympics is seeing people argue about the best total order (compatible with the monoid structure) on âÂł.â€â€(How do you compare countries based on their number of gold, silver and bronze medals?)
⊠I'm really tired of seeing skeets/tweets promoting a cause I care about, but which are written in a way that is guaranteed to have no impact because most ppl won't understand what the fuss is (e.g., âlaw XYZ is about to pass! please RTâ when most people have no idea what âlaw XYZâ is).
⊠You have ONE MESSAGE to catch attention and then maybe 3 to explain what the fuss is about (and provide a link). Make it count! It needs to be understandable to EVERYONE. If you use jargon or abbreviations common to your Cause, you will only reach ppl who already support it. âŠ
â ïž An important message to all who want to use Bluesky (or Twitter, ThreadsâŠ) for some kind of activism or to promote a cause: —ïžâ€â€It's vitally important that your message provide CONTEXT so ppl who are potentially sympathetic, but ignorant, can understand what this is all about. âŠ
Was asked to fill in a survey about the academic methods I use. Couldn't find 'thinking' on the list.
I asked on Math StackExchange for a reference for the fact that a topological space in which every regular open set is closed is, in fact extremally disconnected (viê«. the closure of an open set is open). math.stackexchange.com/q/4952039/84...đ
Tout ça n'est pas trÚs surprenant de la part d'un film dont toute la promo consistait à faire du queerbaiting alors qu'on sait trÚs bien qu'ils ne montreront rien de plus entre Deadpool et Wolverine que des sous-entendus pour en tirer des blagues.
The ultimate French pastime is making other people (above all other French people) angry. So yes, we are forced to admit, this opening ceremony was quintessentially and delightfully French.đŒïž
I was really angry at the Olympics for their cost and all the disturbance in Paris, and I didn't watch the opening ceremony; but the howls of the crazies who think it was âsatanicâ, âwokeâ or I know not what else make me think it might have been worth it for the schadenfreude. đđŒïžđŒïžđŒïž
⊠But IIUC, Holmes himself seemed to say his proof technique for NF was highly technical and not really interesting, so I don't think there's much analogy between the ZFU-versus-ZF situation for violating Choice and the NFU-versus-NF situation.
⊠its universes are in no way cumulative; models of NFU are constructed from models of Z using a little trick due to Jensen, which has the unfortunate consequence of producing lots of atoms, so consistency of NF is harder just because that trick won't work. âŠ
I'm not sure it's related, though. Violating Choice is easier in ZFU than in ZF because atoms are ad hoc things you can impose symmetries on, whereas the cumulative hierarchy of pure (âgenuineâ) sets is rigid. But NF/NFU is a different kind of beast: âŠ
PS: AFAICT, if âform 3â := âfor every infinite X, |X|=|2ĂX|â, the statement âform 3 does not imply ACâ is non-transferable, so the 1976 Halpert-Howard paper (announced in 1974) only gives this for ZFU. But the Howard-Rubin book seems to reference it for ZF also, so maybe I'm confused. âą12/(11+1)
Whatever the case, if this interests you, the book to turn to is Jech's short book âThe Axiom of Choiceâ (1973). It's available in standard cosmic ray sources and has also been reprinted on dead trees by Dover. It explains both permutation models and basics of forcing for symmetric models. âą11/11
⊠so if you just want an easy understanding of some constructions you can't hope to do without a form of Choice, not a detailed reverse-mathematics of what lies between ZF and ZFC, then permutation models of ZFU are the right thing to learn. âą10/?
⊠but even this will only get you so far, e.g. you can't prove things about real numbers that way. Still, permutation models are intuitively clearer than the more complicated constructions of forcing (which also involve creating and breaking symmetries, but âon the truth valuesâ so to speak), ⊠âą9/?
There is a so-called âtransfer theoremâ (Jech-Sochor) which lets you transfer some independence statements from ZFU to ZF (essentially by encoding the atoms by âgenuineâ sets to a certain degree of approximation), e.g., âit is consistent that there is an amorphous setâ is transferable, ⊠âą8/?
This is a really simple techniques for constructing violations of various forms of Choice, and it was know before Cohen, but the drawback is that it applies only to the sets constructed on the atoms, not âgenuineâ sets of the cumulative hierarchy over â . âą7/?
⊠then the sets in your permutation model are those which, hereditarily, âfixâ only finitely many of the atoms: so the atoms themselves are in it, the set of atoms is in it, but all sets of atoms must be either finite or cofinite â the set of atoms becomes amorphous in the permutation model. âą6/?
⊠and Choice implies breaking a lot of symmetries. For example, it's almost trivial to get an amorphous set like that: you start with an infinite set of atoms, its symmetries are all permutations thereof, and you declare that you can break them only by fixating finitely many: ⊠âą5/?
⊠This gives you a model of ZFU which, typically, will not satisfy Choice, because, intuitively, you have this symmetry group of the atoms which you're allowed to break-but-only-so-much (âonly so muchâ being determined by the subgroups you chose), ⊠âą4/?
⊠in most cases this will be something like the [subgroups containing the] pointwise stabilizers of finite sets, or something of the sort. Then inside the boring model you keep only those sets which, hereditarily, are âsufficiently symmetricâ in that their stabilizer is in the chosen bunch. ⊠âą3/?
⊠this gives you a boring model of ZF with urelements (ZFU). But now the âpermutationâ part is that you take a permutation group acting on your atoms (âsymmetriesâ) and a bunch of subgroups (technically a ânormal filter of subgroupsâ) which are deemed âsufficiently symmetricâ: âŠ
Urelements (=atoms) make it much easier to construct models that refute the axiom of Choice: in a nutshell, you start with a set of atoms (which are things which aren't sets but which you can collect into sets), you construct the cumulative hierarchy (iterated powerset) on them: ⊠âą1/?
(This is in ZFU, i.e., ZF with Urelements/Atoms, however.)â€â€For more implications or nonimplications, you need to consult the Howard-Rubin book, where your statement is âform 3â.
The 184-page paper is if you want a proof that it doesn't imply Countable Choice. If you just want a proof that it doesn't imply AC, this 10-page paper by Halpern and Howard from 1976 (âThe Law of Infinite Cardinal Addition is Weaker âŠâ) gives you a permutation model: www.ams.org/tran/1976-22...đ
I think the answer is somewhere in Jech's book on the Axiom of Choice, or, if not, certainly in Howard and Rubin, âConsequences of the Axiom of Choiceâ (but that one is about as fun as a phonebook to read). IIRC, âX.|X|=|XÂČ| is equivalent to AC, but âX.|X|=|2ĂX| is notably weaker.
Sur L'Autre Siteâą, j'apprends que dans un passage du Nouveau Testament, Paul livre un sermon si long qu'un type s'endort, tombe par la fenĂȘtre et se tue. Paul va alors le ressusciter puis REPREND SON SERMON, ce qui devrait en faire le saint patron des podcasteurs.â€â€saintebible.com/lsg/acts/20....đ
Elon Musk's daughter Vivian Wilson was interviewed by my colleague David Ingram at NBC News after Musk deadnamed her & made claims about her childhood: "If youâre going to lie about me, like, blatantly to an audience of millions, Iâm not just gonna let that slide..." â€www.nbcnews.com/tech/tech-ne...đ
⊠et en fait il n'y en a pas tant que ça (pour une correspondance exacte): arrĂȘt, bĂątard, forĂȘt, hĂąte, hĂŽpital, hĂŽtel, Ăźle, pĂąte, pĂąture â et plein de faux amis (p.ex., tĂąte en français n'a pas le sens de taste en anglais!). Certes, si on autorise des petites variations, y'en a plus (quĂȘte, p.ex.).
Or am I wrong to assume that the type genus of an order is also automatically the type genus of whatever family it belongs to?
Zoological nomenclature legalese:â€â€What is the type genus of the order Anseriformes? âAnasâ or âAnserâ? In the former case, the name is irregular (historical?); in the latter case, âAnserâ should also be the type genus of the family âAnatidĂŠâ, shouldn't it?, but it isn't.
âQuis backupet ipsos backupes?â (âWho will backup the backups themselves?â)
⊠But then, of course, the âsomebookâ reference shouldn't have a page number. Except if it's actually âsomepaperâ which can have a page range. (And let's not even get into the issue when âsomepaperâ is a chapter in âsomebookâ, which is a mess unto itself.)
⊠Some articles have different ânotesâ and âreferencesâ sections, which is more tedious but I think makes more sense when you need to cite the same paper/book several time: so you can have a note saying â[somebook] theorem 1.2.3 (p. 42)â and another saying â[somebook] corollary 1.2.4 (p. 43)â. âŠ
I think it's better if you can cite the theorem/exercise number rather than (just) the page number, because it tends to be more stable across editions. But I don't know how this is supposed to interact with Wikipedia's citing style. âŠ
â Alexander S. Kechris, âClassical Descriptive Set Theoryâ (Springer GTM 156, 1995), chapter I, exercise 7.12 (p.40)â€â€â Jan van Mill, âThe Infinite-Dimensional Topology of Function Spacesâ (Elsevier 2001), theorem 1.9.6 (p. 76)â€â€[Engelking and Kechris are classics; van Mill gives a proof]
Also, my head exploded before I could understand how to use Wikipedia's completely crazy way of writing citations, but you might add the following refs:â€â€â Ryszard Engelking, âGeneral Topologyâ (1989), exercise 6.2.A(d) (p. 370)
It does seem to be missing from Wikipedia. But it's surprisingly little known even to mathematicians (so: don't feel bad!), despite being a fairly straightforward analogue of the analogous theorem en.wikipedia.org/wiki/Cantor%... for linear orders. I'm not even sure I know a book reference.đ
⊠you can do some âinterestingâ things at level â€, but it is still VERY different from the levels âȘ and â , or even âĄ/âą/⣠I defined above: it is not a magical power, and we can find some more discerning challenges than the list below. âą23/23 x.com/ESYudkowsky/...đ
Anyway, my point is that physical feasibility, perfect knowledge, computational power, and âintelligenceâ (whatever that may be), are all different things, and we have very little idea which one is the limiting factor in any slightly complicated situation, so probably ⊠âą22/23
⊠on Mars within ten yearsâ â is this possible at level â , let alone â€? I suspect not. But what if we allow one tweet per year? Per month? Per day? At some point it probably becomes doable, depending on the difficulty level, but of course we have no idea. âą21/23
We have no idea, of course, and it's pretty silly to speculate. Just like for some other strange tasks I could set, like âyou're allowed to write one single tweet, which will be inserted in the feed of 1000 random people, and using this you must put a living human ⊠âą20/23
⊠make them fear some kind of reprisal if they don't follow your instructions. But at level âĄ, with no prior interaction? Probably not. But what if there are some interactions allowed? How many do you need, at each level, to get the person to perform a certain task? âą19/23
But what about a human? You get to show the human one image, and your goal is to get them to do something silly that they ordinarily wouldn't want to do. Well, at level â I'm pretty sure you can: you know all of the person's dirty secrets, so you can certainly ⊠âą18/23
If you think the cat challenge was too easy, try getting an earthworm to tie itself into a knot by showing it a single image: that one, I believe we can reasonably say, is impossible even at level â (because earthworms are blind). âą17/23
⊠that, operating at level â , you know down to the molecular level. On the other hand, it probably isn't possible at level ⥠or higher: even if there is suck a hack, you don't have enough information, by just seeing the cat, to reconstruct its detailed brain structure. âą16/23
⊠(at level âȘ the question isn't even really meaningful, because the challenge limits you to just displaying one image on a computer screen); but maybe it IS possible by activating lots of quirky pathways in the cat's brain, ⊠âą15/23
But we can come up with some more fun and less strictly scientific challenges! Can you make an image that, if shown to a cat on a computer monitor, will cause the cat to stand on its hind legs and walk in circle? I suspect this is impossible even at level â ⊠âą14/23
⊠but of course it might conceivably be the case that there's a flaw in SHA-512, so maybe there's a smart way to attack it, and the superintelligent AI could find it. So maybe it is doable at level †â we really don't know. âą13/23
⊠on the other hand, we believe that SHA-512 is genuinely algorithmically hard, so even a superintelligent AI running on a planet-sized supercomputer (so, level â€) couldn't perform the ~2^512 computations required to meet this challenge; ⊠âą12/23
How about âfind a tweet-long text whose SHA-512 cryptographic hash consists entirely of zeroesâ? This is more tricky, but probably it exists, so it is trivially doable at level âą or less, and even ⣠because the search is parallelizable; ⊠âą11/23
Another example: âcompute the 100 decimals of Ï, starting at number Ackermann(100,100)â, where Ackermann(100,100) refers to a Ginormous number. This is obvious to do at level âą or less, but probably can't be done (in reasonable time) at level ⣠or more. âą10/23
⊠but still can't be done at level ⥠or more because the weather system is chaotic so even if you have perfect computing abilities, your ability to predict is limited by your input data, and the predictability horizon is approximately 2 weeks, so 2 months is way off. âą9/23
Here's a more interesting challenge example: âpredict the detailed weather over all of Earth, two months from now, with a 1°C accuracy at worstâ: this is trivial at level â (at least if the laws of physics are deterministic), and of course at level âȘ, ⊠âą8/23
Something doable at level âȘ but not at level â would be, say, to teleport the entire galaxy at a wholly different place in the Universe. This is not too interesting, so I won't dwell upon such examples here. âą7/23
Now we can look at a few different tasks (challenges) and, of each one, wonder if it is doable at each of the aforementioned levels. For example, the task âprove that 2+2=5 in Peano arithmeticâ is (presumably!) impossible even at level âȘ because such proof does not exist. âą6/23
Level âŁ: you have access to a nondeterministic Turing machine, so basically you can perform any kind of parallel search, solve all NP problems in polynomial time. Level â€: you have (or âareâ) a supercomputer the size of a planet, running some kind of superintelligent AI. âą5/23
Level âĄ: you have perfect knowledge of all mathematical truths, but not physical ones (for that, you need to rely on your senses). Level âą: you have access to the Halting Oracle, so basically you can perform any finitistic computation instantaneously. âą4/23
⊠in other words you have perfect knowledge of all mathematical truths and all physical truths relating to this universe (i.e., you always have the most precise meaningful description of the state of the physical universe, down to its elementary particles). âą3/23
First, a typology of difficulty, in decreasing order of powerfulness given to you. Level âȘ: you are omnipotent; in other words, you can do everything that is logically possible, including altering the laws of physics. Level â : you are omniscient, ⊠âą2/23
OK, that đœ was a bit dismissive, so to make amends let me propose a typology and a few possible interesting thought experiment challenges for a superintelligent AI. đ§”â€”ïž âą1/23đ
Here's another fun fact: â[ââ1] = {a+b·ââ1 : a,bââ} and â[â2] = {a+b·â2 : a,bââ} are isomorphic as groups (obvious!), and also as topological spaces (viê«., homeomorphic: see at.yorku.ca/p/a/c/a/25.htm for proof), but NOT isomorphic as topological groups (there is no bicontinuous group isomorphism).đ
Here's another fun fact: â[ââ1] = {a+b·ââ1 : a,bââ} and â[â2] = {a+b·â2 : a,bââ} are isomorphic as groups (obvious!), and also as topological spaces (viê«., homeomorphic: see at.yorku.ca/p/a/c/a/25.htm for proof), but NOT isomorphic as topological groups (there is no bicontinuous group isomorphism).đ
As Goethe said: âMathematicians like Frenchmen: if one speaks to them, they translate it into their own language, and forthwith it is something completely different.â đ
Slightly rephrased from a MathOverflow comment:â€â€âThe entire digital technology depends on the (obvious) fact that the free monoid with countably many generators embeds in the free monoid with two generators.ââ€â€mathoverflow.net/questions/43...đ
⣠Thomas Russell, âSymplectic geometry: The natural geometry of economics?â, âEcon. Lett.â 112 (2011) 236â238 doi.org/10.1016/j.ec... reformulates and reinterprets Samuelson's area ratio condition in terms of symplectic geometry (see the above-cited MO question for why).đ
Thanks to MathOverflow mathoverflow.net/q/207820/17064 I just learned of two papers on economics that, for once, seem to explain things in terms that I (as a mathematician) can actually understand: —ïžđ
⊠so even if such a thing even makes sense (dubious!), I see no reason to believe it could predict human actions on a large scale, which, apologies to Asimov, are probably largely random; let alone manipulate them to its wishes, like these guys casually take for granted.
Side note: I've always been amazed how the supposedly hyper-rational Yudkowsky fans have a naĂŻve, almost childish idea of what âintelligenceâ is, like a kind of super-power from comic books. A âsuperintelligentâ AI couldn't predict the weather a month from now: âŠ
⊠J'ai souscrit pour un an le 25 juillet 2023. Donc il dure jusqu'au 24.»â€â€N: «C'est pas un an, c'est 52 semaines. Donc jusqu'au 22 juillet.»â€â€M: «Vous avez le texte du contrat?»â€â€N (fouille, puis lit): «âŠpour 52 semainesâŠÂ»
Maybe forward this reply, though, which seems to say there's at least one actual use of these glyphs. (And personally I think that now the characters have been in Unicode for so long it's best not to touch their reference glyphs.) bsky.app/profile/eggr...đ
Note that there is a different proposal unicode.org/L2/L2023/232... (not yet in Unicode) to incorporate some different symbols for âStein-Zimmermannâ microtonalities with names such as MUSICAL SYMBOL HALF SHARP, that are provisionally assigned starting at 1D1EB but not yet approved.đ
The original proposal to add these Western musical symbols into Unicode seems to be here unicode.org/L2/L1998/980... by Perry Roland in 1998 but I can't find any serious discussion of these particular symbols or their origin.đ
A question for musicians and/or Unicode geeks: does anyone know the origin of the glyphs shown in the image below? They are supposed to be a quarter-tone sharp (đČ) and quarter-tone flat (đł) respectively, but I wonder if anyone ever really uses them.đŒïž
OK, this thread blew up, so I need to mute it now. But I wrote a fu2 of sorts answering some of the most common points like âwhy are you whining?â, âthis was entirely predictableâ and âantiterrorism measures are obviously necessary!â. đ§”đœ âą20/(19+1) bsky.app/profile/gro-...đ
Il n'y est pour rien. Le prolongement analytique de la fonction ζ, et notamment le fait que ζ(â1) = â1/12, c'est dĂ» Ă Riemann, bien avant Ramanujan.
What is not beside the point, however, is that normal life in a large city is more important than ANY kind of event that would severely disrupt this. So if you can't hold Olympics without severely disrupting normal city life, then⊠just stop! It's that simple. â âą15/15
Personally I don't care about professional sports of any kind: I think it's a sick display of drugs and money â the only sports I care about are the ones practiced by amateurs who have nothing to gain but having fun and improving their health. But that's BESIDE the point. âą14/15
So: if you can't guarantee safety from terrorism during the Olympics without crazy security measures, then the answer is to NOT HOST THE OLYMPICS: do not bid for them, and if you realize you can't do it, then retract your bid, or provide an alternative venue. âą12/15
We can argue about what sacrifices should be made to ensure safety, i.e. of the importance of â· versus âž, and that is a different debate, but one thing is certain, namely that the Olympics (â¶) is far less important than EITHER. âą11/15
⊠I mean, if (IF!) you can't have all three ofâ€âŁ ⶠhosting the Olympics,â€âŁ â· adequate security against terrorism, andâ€âŁ âž a normal life in the city,â€â then one of them has to go, and one which should be sacrificed is the least important, which is â¶, not âž.â€âą10/15
Now another point that has been raised several times is âof course authorities need to take drastic measures: there is a very high terrorism threat, and this requires strong security measures!â. But this just highlights the absurdity of hosting the Olympics in Paris! ⊠âą9/15
So, no, I'm not surprised by anything I wrote in the thread: I very well knew that this was going to happen, and I protested at the time (in French), and try to get people to realize that it would be that way. Now I'm trying to provide ammo against future Olympic bids. âą8/15
⊠this is what happens when you host the Olympics, esp. in a large city where there is a terrorist threatâ â this is why I'm writing in English, not French: so what I write can, hopefully, be used as arguments against future Olympic bids in other cities and countries. âą7/15
⊠obviously I realize I'm not going to get the Paris 2024 Olympics cancelled one week ahead of the opening ceremony. đ I did what I could to raise alarms when there was still time, and obviously I failed then. So now my point is to say âsee? this is what happens â ⊠âą6/15
A number of people said things like âstop whiningâ or âstop complainingâ. I think it's a bit ironic to complain that other people are complaining, but let's ignore that. The broader point is that my point was not so much to complain as to document: ⊠âą5/15
Anyway, my thread was not meant to be a comprehensive critique of the Paris 2024 Olympics. This will be left for journalists and, I hope, a parliamentary inquiry some day. ⧠But what did some replies to the thread say? â€”ïž âą4/15
Or how the price of metro tickets has been suddenly doubled(!) for the games. Admittedly this is more of a tourist tax, because locals typically have monthly cards or could buy their tickets well in advance, but this is still crazy from a supposed public service. âą3/15
First, there are number of things that I forgot to mention. Like how many homeless people were forcibly removed from Paris ahead of the games, or students being told to vacate their residence because they would be used as lodging for the games. âą2/15
OK, this đœ blew up (and I'll need to mute the thread). I can't respond to every reply individually, but there are a few common ones that deserve specific attention. So here are a few followup points I should add. đ§”â€”ïž âą1/15đ
So, now we get to pay billions to host a big business show to which we're very emphatically not invited, we're told to leave the city or stay at home (and also please don't be sick) during that time. As you can imagine, not everyone is very happy with this whole affair. âą19/19
For months now the authorities have been running ad campaigns telling Parisians to âplan in advanceâ for the games. Basically this meant: try to leave Paris for the summer, or if you need to be here, stay at home and work remotely. (And don't get anything delivered.) âą18/19
When she campaigned for election in 2014, Paris mayor Anne Hidalgo said she didn't want the city to bid to host the games. For some reason she changed her mind shortly after being elected, and a number of Parisians who elected her are a bit unhappy about this. âą17/19
I'm not even going to get into the cost of the games, because that's not really my point here: but I'd like to recall that France is already heavily in debt, and Paris's finances are alarming, and we really didn't need this extra burden. âą16/19
And because basically all the French police reserves are being mobilized in Paris, any sort of large-scale event that is not the Olympics is impossible: so lots of music festivals, not just around Paris but all around France have been canceled. âą15/19
And of course this is still not the end of the story: there are policemen everywhere in Paris, and the authorities have deployed security cameras on a massive scale and an experimental AI-based video-surveillance system that would make president XĂ jealous. âą14/19
Also, barriers have begun sprouting all over the place in Paris. Nobody seems to know exactly what they're for. And if you're in a wheelchair, well, I guess that's too bad for you. âą13/19 x.com/EricKLein_/s...đ
On the day of the opening ceremony, things are even more insane: all planes are barred from taking off, landing, or flying near Paris, and even ALL TRAINS have been canceled. Basically the opening ceremony will have the effect of a city-scale nuclear bomb test. âą12/19
And when they close a station, it doesn't just mean you can't get on or off there: you can't even change lines there â because reasons. So the Paris metro is now an incomprehensible maze of disconnected lines and randomly closed stations which changes every day. âą11/19
Some have been closed well ahead of the olympics, and nobody knows why: âConcordeâ has been closed since the 17th of JUNE, and there has been exactly zero explanation of why it needed to close so early. âą10/19
Now maybe you don't drive a car (in Paris this is a bad idea anyway, if you can avoid it) and you prefer to take public transit? Well, surprise: lots of metro stations are closed as well. The list is incomprehensibly large and illogical. âą9/19
An even larger area than the red one is the âblueâ one which is closed to most, but not all, road traffic. But also, most of the highways connecting Paris to the surrounding suburbs, have special âParis 2024â lanes, reserved for Olympics officials, ⊠âą7/19
Of course this is not the only restriction. Around this âanti-terroristâ no-go zone, there is a much larger âredâ zone which is âonlyâ closed to all road traffic. Not as catastrophic, but if you're a business or need to get something delivered, you're in big trouble. âą6/19
Now keep in mind that this is a week before the opening ceremony (why do they need to close the entire area days before the ceremony? nobody knows!). During the ceremony itself, access to the hospital will be completely forbidden to anyone. This is insane! âą5/19
Also, there's a hospital within that off-limit perimeter, with some people requiring vital care there. Patients may apply for a permit, but again that's not automatically granted. âą4/19
Getting the permit is no sure thing: apparently some people have had their application denied (no explanations given), so they're not allowed to go where they work, or even where they live. Nobody knows what's supposed to happen to them. âą3/19
The different levels of security perimeters are incomprehensible, but basically all areas within ~100m of the Seine are now completely off-limits. You can only go there, even by foot, if you live there or work there, and you need to get a special permit in advance. âą2/19
I think non-French and non-French-speaking readers should be told about how utterly insane things are now in and around Paris because of the Olympics are. The opening ceremony is one week away and they've already barred any access to the Seine! đ§”â€”ïž âą1/19
A curious thing about bidirectional text: suppose I write the sentence «he wrote: âhe wroteâ» and translate either the first (=outer) âhe wroteâ or the second (=inner) âhe wroteâ into Arabic. What do I get? âŠ
Et pour le deuxiĂšme, Braun-Pivet a aussi eu son nouveau boulot qui est aussi son ancien boulot â Ă 13 voix prĂšs.â€â€(Si on voulait donner deux signaux que voter ne permet pas de faire changer les choses, on pouvait difficilement faire plus clair.)
Bon alors pour le premier, von der Leyen a eu son nouveau boulot qui est aussi son ancien boulot â et mĂȘme avec plus de voix qu'il y a 5 ans. www.bbc.com/news/article...đ
Je suppose qu'une telle note juridique constitue un document administratif communicable au public: ce serait mieux si l'Administration la publiait d'elle-mĂȘme au lieu d'attendre que qqn la lui exige, ou qu'elle fuite par voie de presse et/ou circule sous le manteau!
Il n'y a pas un article qui dit «les membres en question continueront Ă faire office de ministres pour la gestion des affaires courantes jusqu'Ă la nomination d'un nouveau gouvernement»?đź Comment on sait que ce sont eux qui gĂšrent les affaires courantes? legifrance.gouv.fr/jorf/id/JORF...đŒïž
Of course, the real issue is that Web browsers should support self-signed certificates, and DNSSEC-based authentication so anyone can set up an https site without having to rely on the existence of something like LetsEncrypt. (The whole https certification business is a mafia.)
Really, though, what bugs me is that if LetsEncrypt breaks or goes out of business, I would be left scrambling for an alternative (which might not be free). If they provided a certificate valid for 1âŻ000 years (which should really be MY choice, not theirs), I'd be less hesitant.
Lots of people are telling me I should switch my Web site from http to https because LetsEncrypt makes this âso easyâ, but several people I know who use it keep having all sorts of problems with certificate renewal.
⊠but sup(x,y) cannot be said to belong to {x,y}, so I think denoting it by âmax(x,y)â is absurd and will just confuse everyone (even more so as there does not seem to be a reasonable general definition of max(S) which would give this for S={x,y}).
The issue is that in constructive math, â cannot be said to be totally ordered in the sense âxâ€y âš yâ€xâ (note that it is still so in the sense âÂŹ(xâ€y) â yâ€xâ). The âsupâ operation on pairs of reals is well-defined, and does look A BIT like a max, âŠ
Trying to convince the writers of the HoTT book that it's insane to use the notation âmax(x,y)â for something that may fail to be equal to x or y. github.com/HoTT/book/is...đ
I see your Pâ NP and I raise you this paper which solves Every Problem at Once with a simple equation âS=666â: article.sapub.org/10.5923.j.ij... â this is simply The Ultimate Paper.đ
An interesting exercise in constructive mathematics: assume (the âWeak Limited Principle of Omniscienceâ for the (Dedekind) reals),â€â€âŁ âxââ. (x=0 âš ÂŹ(x=0))â€â€â and use it to prove the âsignedâ version of the same:â€â€âŁ âxââ. (x=0 âš xâ0 âš xâ0)â€â€where âuâvâ means âÂŹ(uâ€v)â.
Mostly talking about what I don't really understand: I answered a question on MathOverflow about foundations of mathematics that are conservative over Peano arithmetic, by pointing out that Feferman defined such a system by formalizing ideas by Weyl. mathoverflow.net/a/474931/17064đ
(This means that if the reader has trouble remembering what âcommuting withâ means, or grasping the notation, each one will help with the other. And if there's a typo or misprint, or if the text is blurry, it will very much help correct or fill the gap. A kind of error-correcting code!)
When writing a math text, I think it's really useful to basically write everything twice, in English and in symbols, especially definitions, e.g.:â€â€âThe centralizer of x in G, denoted C_G(x) or just C(x), is the set {yâG : x·y = y·x} of elements which commute with x.â
(If you need a recap: T. gondii is a brain-infecting parasite that makes mice less fearful of cats because it needs the mouse to get eaten by a cat in order to reproduce. It infects humans as well, mainly by exposure to cats excrements, and causes them to be less risk-adverse.)
From the abstract: âFinally, [âŠ] we found that [T. gondii] infection prevalence was a consistent, positive predictor of entrepreneurial activity and intentions at the national scale, regardless of whether previously identified economic covariates were included.â
Ah je ne dis pas Ă 100%. Le taux d'imposition peut trĂšs bien ĂȘtre >100%, par exemple 1000% d'impĂŽts: tu dois payer 10 fois tout ce que tu gagnes. Manifestement ce n'est pas tenable. Donc problĂšme. Donc revenu nul.
Unix systems are already a nightmare of incoherent config files in /etc but Debian adds another level of perversity by hiding a good deal of config in /var/cache/debconf/config.dat where nobody would think to look (let alone back up!).
I'm just saying it's a bit too long to fit in the margin, or in most other media. But I will welcome the version of Bluesky when we get 10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^10)))))))))))) chars per skeet.
⊠and also, it's not even clear what âknowingâ the value of BB(6) means, as it is known to be larger than 10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^10))))))))))))), so it's not like you can hope to write it down explicitly.
It is likely that the value of BB(6) (let alone any further one) will never be known. First, this would require radical progress in mathematics as there is at least one known 6-state machine whose halting is equivalent to a Collatz-type problem, âŠ
A rather interesting article (written for the general public, in âQuantaâ) about the âBusy Beaverâ problem and the recently completed computation of BB(5) (which has a value of 47âŻ176âŻ870), and what it means to prove this. www.quantamagazine.org/amateur-math...đ
âLawrence Berkeley National Laboratoryâ is not named in honor of a guy called âLawrence Berkeleyâ, but Ernest Lawrence and the city itself named after George Berkeley. #ContextClub
Or as Isaac Asimov onceÂč put it: âThe closer to the truth, the better the lie, and the truth itself, when it can be used, is the best lie.ââ€â€1. âFoundation's Edgeâ (1982), chapter 12 (§6).
One very important thing to keep in mind, especially in politics, is that it is entirely possible to lie by telling only the truth: because the lie can be not just in the content of what is being said but also the selection of what to say and what to omit.
Alors qu'en vrai tout est de la faute de François Guizot.
Very nice result proved yesterday by Will Brian on MathOverflow: there exists an infinite set of real numbers which is not homeomorphic to any of its proper subsets. (Sadly, the proof is deeply non-constructive.) mathoverflow.net/a/474173/17064đ
This advice about how academics should talk to pseudohistorians/pseudoarchaeologists applies to many other fields of academia: most of it can be taken pretty much verbatim to apply to pseudoscience, and he makes many good points. www.youtube.com/watch?v=G0us...đ
⊠De mĂȘme qu'il doit arriver que les rĂšgles de la religion catholique entrent en conflit avec celles de la France, plaçant les catholiques français devant un cas de conscience. Le fait que ça PUISSE arriver ne signifie pas qu'on doit interdire Ă tout français d'ĂȘtre catholique ou vice versa.
⊠So by now everyone knows there is no Nobel prize in mathematics and thinks there is one in economics; and people even tell stories about how this is because Mittag-Leffler had an affair with Nobel's wifeÂč or some silly such urban legends.â€â€1. (In fact, Nobel never married.)
⊠Meanwhile, mathematicians named their analogous prize the âAbel prizeâ, but since the Fields medal was already often described as âa sort of Nobel prize but for mathâ, nobody considers the Abel prize to be a Nobel prize, which it is just as much as that for economics. âŠ
Economists are more shrewd tacticians than mathematicians: there was no Nobel prize in economics so they created a âSveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobelâ, which is such a mouthful that everyone just says âNobel prize in economicsâ. âŠ
Without looking it up, do you know what is (currently!) the most deadly infectious disease on Earth, killing roughly 1.5M to 2M people per year (nearly as much as covid did in 2020 â but EVERY year; and yes, you know its name)?â€â€If not, please watch this: www.youtube.com/watch?v=GFLb...đ
Il n'y a pas plus de contradiction entre le fait que je sois français et le fait que je sois canadien qu'il n'y en a Ă ce qu'on puisse ĂȘtre, par exemple, français ET catholique (on va prendre cette religion au pif pour l'exemple đ ): ⊠âą13/22
Oui, je suis aussi canadien, je ne peux pas renier ce fait pas plus que je ne peux renier ma famille qui vit lĂ -bas. Mon pĂšre m'a fait enregistrer Ă l'ambassade Ă ma naissance pour que je puisse toujours aller les voir. Oui, je suis sujet du roi du Canada (Charles). âą9/22
Wait, there's a FILM ADAPTATION of âThe Master and Margaritaâ? This could be the absolute best or the absolute worst thing in the Universe. Or anything in between. www.imdb.com/title/tt1453...đ
I wrote something of a rant on Reddit trying to explain what the point of constructive mathematics is. reddit.com/r/math/comme...đŒïž
I would add this thought: authoritarianism is like a pathogen that infects societies, and like all pathogens that might elicit an immune response, it tries not to be too virulent â at first! â because this maximizes its ability to spread and infect others.
âLife in authoritarian states is mostly boring and tolerableâ: provocative title but insightful piece from âVoxâ some years back, about how democracy ends not with a bang (a coup, like most people tend to imagine) but a whimper.đ
⊠mais que ce sera de toute façon le Premier ministre qui aura le vrai pouvoir jusqu'à la fin de son mandat, y compris si ce Premier ministre vient du camp auquel il [Macron] appartenait. En gros, «n'en faites pas un referendum contre moi, moi de toute façon je me retire».
S'il a pu s'imaginer une seconde que parler trois fois par semaine pendant la campagne â alors que les candidats de son camp en sont Ă effacer son image partout â pouvait aider, non, il ne comprend pas du tout. âŠ
If he did this, Harris would become 47th president for a few days (and first woman president, which might even be a plan in itself even if Trump is elected), and Biden (or Trump) would become 48th. Right?
So if Biden is reelected the counter remains at 46, but if Trump is reelected the counter increases to 47. Weird.â€â€This also raises the following question: if reelected, could Biden theoretically resign from the end of his 2021â2024 term without resigning from his 2025â2028 term?
Does the numbering of US presidents (the one which currently takes the value â46â) have official status? Because it's a bit strange: two consecutive terms count as one, but non-consecutive terms count as two (so Cleveland is 22 & 24).
If I am not mistaken, it is equivalent to asking: in a positive semidefinite matrix with a diagonal of 1, given the coefficient (i,j) and the coefficient (j,k), what bounds can we place on the coefficient (i,k)?
I asked a question on Math StackExchange: given the Pearson correlation coefficient of X and Y and that of Y and Z, what bounds do we have on that of X and Z? Surely this is a well-known problem! math.stackexchange.com/q/4931463/84...đ
Donc en gros, r>0 signifie que quand il y a beaucoup de votes pour une des deux listes dans une circonscription il y en a aussi beaucoup pour l'autre, plus r est grand plus cet effet est fort; et r<0 signifie au contraire que beaucoup de votes pour l'une se traduit par peu pour l'autre. âą7/14
OK, this comic is funny, but the QR-code points to the Android download page for WeChat (WÄixĂŹn), and one might wonder whether this is intentional.đ
Oui enfin, majoritaire sur le secteur Paris-Centre (4 premiers arrondissements), qui contient notamment l'Ăźle Saint-Louis. Il est fort possible qu'elle ne soit pas majoritaire sur l'Ăźle, je n'en sais rien, je n'ai pas carte plus fine.
Mais au moins, si quelqu'un veut faire une introduction rapide Ă l'utilisation de cet assistant de preuve, il pourra l'appeler «Rocq in short», ou, en français, «Rocq en court». đ„
En effet, je ne vois pas Ă quel mot de ce monde-ci tu peux penser. En anglais on dirait «termwise» pour des suites/vecteurs (ou «pointwise» dans le contexte des fonctions: «pointwise multiplication» est trĂšs courant), mais je ne vois pas de verbe utilisable. âŠ
⣠Et si la personne avec qui on veut parler se considÚre de droite, il ne faut surtout pas non plus se dire de gauche, parce que sinon il va juste passer une heure à vous expliquer que depuis 1990 on sait que le communisme est une faillite monumentale, autre perte de temps.
Et surtout, le bandeau ne rappelle mĂȘme pas le fait sans doute le plus important et que je dis plus haut: IL Y A FORCĂMENT PLUS D'ARGENT PERDU PAR LES JOUEURS QU'IL N'Y EN A DE GAGNĂ.
â Referencing webcomics is second nature to us geeks, so it's easy to forget that the average person probably only knows the xkcd comics âTen Thousandâ and âStandardsâ.â€â€â And âDuty Callsâ, of course.â€â€â Of course.
You're right: it's easy to forget that the average person probably only knows how to perform proof-theoretic ordinal analysis on PRA and Kripke-Platek set theory. (And first-order Peano, of course.)
Actually, even to condemn, it might make sense to allow for a single dissenter (i.e., require unanimity-less-at-most-one), and keep the tally secret: so that every juror gets plausible deniability (you can never be sure that THIS particular person voted to condemn).
In fact, the requirement of unanimity can also be worth discussing. France requires a supermajority to condemn, but a minority to acquit (there is no âhung juryâ): requiring unanimity to acquit seems a bit bizarre if the prosecuting case is to be made âbeyond a reasonable doubtâ.
It seems to me this secrecy is important to avoid pressures, even if the requirement of unanimity means that, in the end, we can be sure that everyone eventually came to the same opinion (except in the case of a hung jury, where divulging who was doing the hanging can matter).
I don't know about US civil trials, but where I am (France), not only are criminal juries sworn to secrecy (there are no civil juries), but even academic juries (i.e., the committee that awards a diploma, say, a doctorate) are supposed to keep deliberations secret.
One of the surprising features of the American criminal trial by jury, for me, is that (at least in some states?) the jurors are apparently not sworn to secrecy after the trial is over. So they're free to tell the press that juror X convinced everyone else, or stuff like that.
But perhaps this is an interesting way to have a political discussion: imagine a genie grants you the power to change society in any plausible way provided you BOTH agree to the same terms of the wish â can you negotiate something jointly desirable?
The society we live in is a shitty compromise between many different utopias and the very fat turd that is Reality. So of course we have a hard time finding common ground. But even if we remove the necessity of reality, many visions of society are irreconcilable just as dreams.
Perhaps the most politically revealing and instructive question one can ask anyone is: what is your dream society? what kind of utopia would you like to live in?â€â€And sadly, many political divergences come from the fact that one person's utopia is another's dystopia.
⊠One depressing thought is that fundamental rights maybe only really make significant progress when our collective consciousness is deeply shaken by something horrific like WW2 and the holocaust. I hope this is wrong!
⊠so it behooves to understand when, where and how authoritarianism declines. But in every case I feel at least somewhat informed about, it seems that democracy, human rights and the rule of law are declining. Is this an observational bias, or a general worldwide trend? âŠ
Are there any countries on Earth that have, in recent (say, 5â10) years, moved away from authoritarianism and toward the rule of law, rather than the other way?â€â€That democracies, not all the fruit of revolutions, even exist, suggests that this at least sometimes happens, âŠ
Possibly stupid medicine question:â€â€There seem to be far more pathologies (cancer, inflammations, etc.) of the oesophagus, stomach and colon than of the SMALL intestine. Is this correct? If so, can this be explained?
⊠as far as I see it, the really interesting thing about Selman's theorem is that from such a non-uniform hypothesis (details don't matter much) we get a single (viê«. uniform) program that lets us enumerate A from an oracle which is only guaranteed to enumerate B, no further details guaranteed.
I think you're making matters needlessly complicated here. It's pretty obvious that if we can do something with an oracle that enumerates B then (non-uniformly) we can do that something with an oracle that computably lets us enumerate B: this is just transitivity of reductions; âŠ
(That's assuming I didn't mess this up. Don't take my word for it, I haven't slept much last night. Or cf. the footnote of the paper by Miller I mentionedđœ: MuÄnik reducibility is non-uniform whereas Medvedev reducibility is uniform.) bsky.app/profile/gro-...đ
I think you need to add at least a short intuitive explanation about why it's a uniformity result. Something like this: assume that with any oracle enumerating B we can write a program that enumerates A: then there is a single (uniform) program that enumerates A from any oracle that enumerates B.
⊠but there he gives a reference to a 1997 paper by Kate Copestake doi.org/10.1002/malq... which appears to be much more readable (and pretty much identical to the one described by @jeanas.bsky.social in his answer to my MSE question above?).đŒïž
Update: proofs of this theorem are annoyingly hard to find. Selman's original 1971 proof is hard to read. There's a 1978 proof by Rozinas, but it's in Russian. Cooper's proof quoted above appears incomplete. Exactly the same is found in his book chapter doi.org/10.1007/BFb0... âŠ
One of the brilliant ideas, I find, is how you can make use of Earth-based observations to test theories about the motion of Mars around the Sun⊠you select the observations where the Sun, Earth and Mars are aligned! đ€Ż
This is really fascinating to watch, and it goes into a lot of details. All I knew was âthe Greeks had invented epicycles, Tycho Brahe made some precise observations, and Kepler used them to discover his lawsâ but I knew nothing of the details, nor the concept of âequantâ.
I came across these two extremely interesting videos about how Johannes Kepler actually discovered his first two laws of planetary motion, by a combination of brilliant thinking, lucky guesses, mishaps, and tedious computation.â€â€Here's the first part: youtube.com/watch?v=Phsc...đ
I asked a question on MSE about a proof of Selman's theorem on enumeration reducibility found in Cooper's book on computability, which I can't quite make sense of: math.stackexchange.com/q/4925064/84...đ
Maybe I should have made the remark that if S is finite with cardinality â„1, then sup S always exists, although constructively it might fail to belong to S (as sup{u,v} belongs to {u,v} iff uâ€v or vâ€u).â€â€See đœ for the definition of sup and lub. bsky.app/profile/gro-...đ
My MO question (quoted above) was about finding nice conditions to add to âS is inhabitedâ and âS has an upper boundâ such that sup S exists. But of course one can legitimately ask for conditions for lub S to exist (S need not be inhabited, as the previous example illustrates). âą3/3
It's clear that x = sup S implies x = lub S. But a lub need not be a sup, as shown by:â€â€âŁ S = {0 : pâšÂŹp} (for p a truth value)â€â€Then lub S = 0 (exercise! remember that xâ€z means ÂŹ(x>z)). However sup S = 0 implies pâšÂŹp. (So âlub S = sup S for all Sâ implies LEM.)â€â€âą2/3
Following comment by @jeanas.bsky.social, a clarification on the notions of âsupremumâ (sup) vs âleast upper boundâ (lub) of a set of reals Sââ in constructive math:â€â€âŁ x = sup S means âyâS. (yâ€x) and âz<x. âyâS. (zâ€yâ€x)â€â€âŁ x = lub S means âyâS. (yâ€x) and âz. ((âyâS. (yâ€z)) â xâ€z)â€â€âą1/3đ
I asked a question on MathOverflow about what nice condition we can add to âinhabitedâ and âbounded aboveâ on a set of (Dedekind) reals in constructive math to ensure that it has a supremum (with a discussion about locatedness): mathoverflow.net/q/472243/17064đ
âCow cuddling: Cognitive considerations in bovine-assisted therapyâ doi.org/10.1079/hai....â€â€Now this is the sort of research I think deserves more funding! đâ€â€(In fact, if you're looking for volunteer subjects, đ.)đŒïž
Very interesting video on the history of chemistry, concerning the discovery of argon, helium, krypton, neon, xenon and radon in rapid succession (and how William Ramsay earned a Nobel prize in Chemistry). www.youtube.com/watch?v=loqu...đ
Ne pas confondre:â€â€âŁ «Mon +1 me fait des bisous Ă chaque fois que je le vois.» â đ„°đâ€â€âŁ «Mon N+1 me fait des bisous Ă chaque fois que je le vois.» â đ±đ€Źâ€â€#ClubContexte
⊠I'd add the information myself but, of course, this is the sort of thing for which I don't have a source (and you're not allowed to say: âjust listen to the music! it's obvious!⊠and it's also very well knownâ).
⊠or conversely that the âin popular cultureâ section of the article on this famous sarabande doesn't mention the connection (like it does mention that it's used in Kubrick's âBarry Lyndonâ â although this is a direct use, not a mere citation of the theme). âŠ
I'm surprised that the Wikipedia article on Miyazaki's animated film âNausicaĂ€ of the Valley of the Windâ doesn't mention that the musical score by Joe Hisaishi makes prominent use of the theme from the sarabande in HĂ€ndel's keyboard suite #4 in D minor (HWV 437), âŠ
En anglais, tous ces mots ont une seule ânâ partout:â€â€âŁ functional â functionalityâ€âŁ personal â personalityâ€âŁ proportional â proportionalityâ€âŁ constitutional â constitutionalityâ€âŁ rational â rationalityâ€âŁ national â nationalityâ€âŁ tonal â tonality
âCarnap then attended the University of Jena, where he wrote a thesis defining an axiomatic theory of space and time. The physics department said it was too philosophical, and Bruno Bauch of the philosophy department said it was pure physics.ââ€â€Nothing new under the sun. đđ
I asked a question on MathOverflow about whether we can find a formula for the line connecting two points in the projective plane over a[n associative] division ring (=skew field) analogous to the very simple formulas over a field. mathoverflow.net/q/471711/17064đ
⊠This is very bad. Courts of justice can maintain their clout in society only if a majority respects their wisdom, and don't have preconceived ideas about what the outcome should be, but rather trust the judges to generally make the right call.
⊠Sadly, for many âpoliticizedâ cases, this is not at all what happens. Everyone seems to have prior idea of what the court should say: some will be happy they âwonâ, others angry that they âlostâ (and blame âbiasedâ judges), but nobody actually defers to the judges' opinion. âŠ
⊠before rendering judgement; then most people (though perhaps not the parties themselves), learning the decision of the Court, should think âI didn't know what to think about the case, but the Court took a lot of time to consider it, so I now defer to their opinionâ. âŠ
The way a healthy justice system is supposed to work is that, in a case they aren't involved in, most people should have no preconceived idea about what the ârightâ outcome is: so we have judges, whose job it is to be impartial, who listen carefully to all parties involved âŠ
On passe ensuite dans le parc paysager Ă l'anglaise, qui est vraiment impressionnant: nous avons fait trĂšs attention en marchant Ă ne pas abĂźmer l'herbe, on aurait cru qu'on marchait sur une moquette. âą6/20đŒïžđŒïžđŒïžđŒïž
So now I'm listening to his imitation of a French accent in English (which isn't as funny), something I hear a lot of for obvious reasons. He's good, but it's not perfect â but I can't quite put my finger on why (his /l/'s are too dark, maybe?). youtube.com/watch?v=2ce5...đ
This video on how to sound German when speaking English is both phonetically accurate and pretty funny â and it ends in a parody of Monty Pythons' âFawlty Towersâ. youtube.com/watch?v=rEhX...đ
it is time again for my favorite sisyphean story: olympics organizers attempting to put all of the most physically fit 18-30 year olds on earth under one roof and prevent them from fucking each otherđ
Similarly, all texts written about the work will be about its analysis, metaphorical meaning, historical importance or I don't know what else, but nothing about how good it is, because it's a classic so you're not allowed to say any of the things normally found in a critic. âą3/3
⊠by notes written by Pr. Jones, renowned Shakespeare expert, and an introduction by Mr. Wright, famous stage director, but it won't tell me what the play itself is about (because somehow you're supposed to know that already â but wait, why are you reading it, then?). ⊠âą2/3
One of the problems with classics is that, because they are deemedâclassicsâ, nobody is ever willing to review them in a candid way. Suppose, for example, that I'm considering reading a play by Shakespeare: the back cover will tell me that this edition is accompanied ⊠âą1/3
I don't remember whence I got this link so I'll repost it here: âWhat technically happened at Chernobylâ â a somewhat detailed presentation by a nuclear engineer of how RBMKs are supposed to function, the problems they have, and what went wrong in 1986. www.youtube.com/watch?v=YRPu...đ
It seems to be a bug that only occurs with certain window-manager and focus mode combinations (in my case, fvwm2 with FocusFollowsMouse), which is probably why it hasn't been detected/fixed: bsky.app/profile/jean...đ
Your mouse cursor wasn't captured on the video, so I can't tell if your behavior differs from mine, but you're getting what I call âmerely suggestsâ below: bsky.app/profile/gro-...đ
⊠If you can't reproduce, maybe it's because it depends on one of the many settings of Gtk+, or on my window manager (I use fvwm2 with focus-follows-mouse, so maybe the dropdown menu gets focus in an unexpected way and this confuses Gtk+, or something).
⊠This second behavior is very annoying because I want to just type â/the/file/nameâ and not have to pay attention to the point where it became unique and suddenly I need to stop typing. For me it happens when (and only when?) the mouse cursor is over the dropdown list where completions are shown. âŠ
⊠or it âforcefully insertsâ, meaning that the completion is inserted after my cursor as soon as it is unique, but the cursor jumps to the end, so if I continue typing I will get something like â/the/file/namemeâ because the new characters I type are appended to rather than replace the completion. âŠ
⊠because there is only one path component matching. Then Gtk+ inserts that unique completion, but it can do so in 2 different ways: either it âmerely suggestsâ, meaning it inserts-but-highlights, so if I keep on typing what is already selected it will just work (I can ignore the insertion) âŠ
It's not easy to describe in few words, but what I do is open a Gtk+ file chooser (typically to select an image to attach to a post on BlueSky or that more musky clone of it), start typing â/the/file/nameâ because I know exactly what it is. At some points the completion becomes unique âŠ
In 2D this is not so obvious. But in 3D, the points U,V,W lie in the plane of both triangles, so they lie in the intersection of these two planes, which is a line, so they are aligned! It's that simple. And the 2D version then follows from the 3D version.
The theorem says: if triangles AâBâCâ and AâBâCâ have a âperspector pointâ O, meaning AâAâ, BâBâ and CâCâ meet in O (green), then they have a âperspectrix lineâ, meaning the points U,V,W where BâCâ&BâCâ, CâAâ&CâAâ, and AâBâ&AâBâ meet, are aligned (blue).
I'm pretty happy with this pair of illustrations I created to illustrate how the theorem of Desargues becomes almost trivial if we move up to 3 dimension. [The left-hand image is hand-written SVG, the right is made in POV-Ray; and they are superimposable.]đŒïžđŒïž
When the mouse cursor is over the dropdown menu showing the possible completions, completions will be forcefully filled in, when it's elsewhere they will merely be suggested. This is still annoying as hell, but at least I now know what causes it. đ«€ âą3/3
This second behavior is extremely annoying and confusing. Suggesting a completion for something I'm typing is OK, but forcefully inserting it under my cursor really breaks my typing habits. Well it turns out the difference depends on the MOUSE CURSOR position. âą2/3
I finally understood something about the Gtk+ (Gnome toolkit) file chooser that had been bugging me for ages: file completion seems completely unpredictable. When you type a file name, sometimes it suggests a completion for you, and sometimes it automatically fills it. âą1/3
Unicode hack for people who are both evil AND desperate: if your browser or whatever persists in deleting your U+00A0 NO-BREAK SPACE characters and you want something wider than U+202F NARROW NO-BREAK SPACE, you can use U+2800 BRAILLE PATTERN BLANK instead. đż
You know mathematicians mean to issue a serious warning when they italicize âabsolutely sureâ and they tell you it will be painful if you try. mathoverflow.net/a/471142/17064đŒïž
I've made a number of contributions to the OEIS, but I think my favorite is still A100002 (which also makes an interesting âcode golfâ exercise): oeis.org/A100002đ
This makes for an interesting âcode golfâ question: write the prettiest/shortest program, in your favorite programming language, to generate this sequence.
I got a new sequence published in the Online Encyclopedia of Integer Sequences: A372325, the list of numbers whose binary expansion has an even count of 1's among positions in the list in question (0, 2, 5, 7, 8, 10, 13, 15, 16, 18, 21, 23, 24âŠ). oeis.org/A372325đ
A detailed and pretty interesting account of the âKryptosâ code that forms part of an artistic installation (by Jim Sanborn) in front of the CIA headquarters in Langley, Virginia, and how 3 of its 4 parts were deciphered by code-breakers. youtube.com/watch?v=jVps...đ
The Desargues configuration can also be seen as a pair of âmutually inscribedâ pentagons, meaning each vertex of one is on (the extension of) an edge of the other. The same 10 points and 10 lines can be seen in 6 different ways as such a pair of mutually inscribed pentagons:đŒïžđ
I also made an animated gif of the 10 figures, which helps make it clear that the 10 points and 10 lines are really the same each time, but I couldn't figure out how to post it on BlueSky. So here's the link to the post on the Musky Place: twitter.com/gro_tsen/sta...đ
On a different thread (đ§”đœ), here's an illustration of the 10 different ways the same set of points and lines as in the figure above can be seen as an application of the theorem of Desargues â this is what I mean by its âcombinatorial symmetryâ. bsky.app/profile/gro-...đ
⊠notice anything about these 10 figures? It's always the same set of 10 points and 10 lines which is shown in each of them! (So for example each of the 10 points is the perspector exactly once.) This illustrates the symmetry of the Desargues configuration. bsky.app/profile/gro-...đ
OK, I spent waaaaay too much time producing these 10 figures, but I'm really happy with the result. These are 10 illustrations of the theorem of Desargues: in each, the two shaded triangles have a perspector point (in green) and a perspectrix line (in blue). BUT WAIT! âŠđŒïžđ
This statement (and the figure above), however, hides the combinatorial 5-fold symmetry of the Desargues configuration (formed by the 10 points and 10 lines involved in the theorem) following from the description in my first post (which can also be used to prove the theorem).
The theorem of Desargues states that two triangles ABC and AâČBâČCâČ (shaded in above figure) have a perspector point (intersection of AAâČ, BBâČ and CCâČ, shown in green above) iff they have a perspectrix line (alignment of ABâ§AâČBâČ, BCâ§BâČCâČ and CAâ§CâČAâČ, shown in blue). en.wikipedia.org/wiki/Desargu...
Take 5 points in general position in (3-dimensional) space: they define 10 lines and 10 planes. Intersect these with a (sufficiently general) plane: this gives you 10 points and 10 lines in the plane. These form a so-called âDesargues configurationâ. en.wikipedia.org/wiki/Desargu...đŒïž
So, the answer is (đ„) the 1779 play âNathan the Wiseâ by G. E. Lessing. Now the next question is whether these similarities between âNathan the Wiseâ and âStar Warsâ are coincidental or not. scifi.stackexchange.com/q/287822/174...đ
Well, I mentioned it a few times on my blog, but apparently never in connection with âStar Warsâ. However, grep did tell me that I called the author âGottlobâ instead of âGottholdâ some 20-ish years ago, and it's never too late to correct my mistakes. www.madore.org/~david/weblo...đ
Ah, that is interestingly close. But the brother-sister thing doesn't seem to be there, and I believe the work I'm thinking of is more widely famous (and certainly more often played).
No, I got 021f53379f2a4afa28213de6d9c6c3f0f355c8151fa8c643d9fe508407cc4595 from `echo -n "${name}, ${title}" | sha256sum`, name and title being as written in the German Wikipedia. Still, I would be âșextremelyâș surprised if you had found a different work with the same plot points!
The original is in German. (But of course, it has been translated into English and very many of the world's languages. If this is any indication of worldwide celebrity, the Wikipedia article concerning it exists in 21 languages.)
Indeed. Now next question: if I tell you I was in fact thinking of a much older (as in: 18th century) work, would your working hypothesis be that this is a coincidence or that the older work influenced the later one?
⊠and also that they are the powerful lord's next-of-kin, and the lord in question turns out to be not so evil after allâ, what famous classic work of fiction do you think I have in mind?
If I say âa young orphan chivalrous knight fighting a powerful lord meets a wise old man who will serve as his mentor, and saves a young lady who was also adopted; he starts falling in love with her, but they eventually discover that they are, in fact, brother and sister, âŠ
(Surely it has to be a joke: the exact same argument he uses to show that the Holy Spirit is the categorical product of the Father and the Son works for any permutation of the three, and I'm sure this is not at all theologically standard.)
I honestly can't tell if this paper is meant to be serious, a kind of literary exercise, or a complete joke, but the explanation of the âfilioqueâ by a commutative diagram, and the sentence âin God, all things are one up to isomorphismâ (in Latin!) are just infđ€Łckingcredible.
After I suggested this on Twitter as a joke, I learned that someone wrote a serious(âœ) paper on the use of mathematical category theory to describe the Christian Holy Trinity, and it absolutely BLOWS MY MIND. đ€Ż link.springer.com/chapter/10.1...đŒïžđŒïžđŒïžđŒïž
Everyone knows about the trolley problem, but I swear when I was your age almost nobody did. The phrase was coined in 1976! What happened around 2003 to inject it into popular discourse?đŒïž
Je ne connaissais mĂȘme pas. Ăa a l'air d'ĂȘtre un truc complĂštement niche que personne n'utilise, au moins pour l'instant â je ne peux pas en dire plus.
1970s: Giant building-size computers and remote connections are required for almost every single task.â€â€1990s: WOOO I CAN FINALLY MAKE A SPREADSHEET WITHOUT A SERVERâ€â€2020s: Giant building-size computers and remote connections are required for almost every single task.
Ben on peut aussi aller Ă pied n'importe oĂč. La question est Ă quel moment on considĂšre que le temps de trajet est tellement ridiculement long qu'il est inacceptable.
«Mais surtout : je vois un parser de fichier .XCompose dans GTK, et un autre dans IBus, et il y a des fonctions qui sont textuellement identiques entre les deux...»â€â€đ”
⊠par exemple je sais que pour avoir les bindings Emacs dans les widgets Gtk, j'ai un fichier `.config/gtk-3.0/settings.ini` qui ditâ€â€[Settings]â€gtk-key-theme-name = Emacsâ€â€â mais sous Gnome ça ne marche pas il faut faire autre chose (ou alors c'est le contraire je ne sais plus). Quel chaos!
Par contre, ce qui est vrai, c'est que Gnome met en place plein de choses (des variables d'environnement, je suppose, et sans doute des services D-Bus) qui vont affecter le comportement de Gtk de façon possiblement subtile: âŠ
Surtout, ce n'est pas trop difficile d'ajouter ses propres combinaisons Ă la table de Compose. On ne peut pas en dire autant pour tout le fatras des input methods dont personne ne semble savoir au juste comment il s'agence. đœ bsky.app/profile/jean...đ
⊠par exemple les guillemets anguleux â«â/â»â avec compose+<+< / compose+>+> et les guillemets courbes âčââș/âčââș avec compose+<+" / compose+>+" je m'en sers pas mal, ou le signe de multiplication âĂâ avec compose+x+x. J'en apprends un de temps en temps comme ça. âŠ
â Ă chaque fois que le site change, il faut mettre le programme Ă jour. (Ăa arrive plus ou moins souvent selon le site. Arte est trĂšs stable, par exemple.) Globalement, Ă chaque fois qu'on soupçonne un problĂšme â mise Ă jour de yt-dlp.â€â€âŠ
«â€Neither a borrower nor a lender be;â€For loan oft loses both itself and friend,â€And borrowing dulls the edge of husbandry.â€This above all: to thine ownself be true,â€And it must follow, as the night the day,â€Thou canst not then be false to any man.â€Â»â€?
Gro-Tsen's third law of politics: for every stupid idea in politics there is an opposite and even more stupid idea.â€â€Gro-Tsen's scholium on the third law: Gro-Tsen's third law of politics applies recursively.
So of course it doesn't mean anything to say that an element âisâ stable or unstable. What is meaningful is that a certain value of Z (here Z=43) has no stable (or billion-year-lasting) isotope. There are some bits of explanation for technetium here on Wikipedia: en.wikipedia.org/wiki/Isotope...đ
The Event Horizon Telescope has measured the *polarized* radiation from our friendly neighborhood black hole, Sgr A*! Press release: eventhorizontelescope.org/blog/astrono..., papers in next skeet đđ§ȘđŒïž
Start with an interval of length t>0 and repeatedly remove a random uniformly distributed subinterval of length 1 if there is one: what is the expected duration of this process, asymptotically as t gets large? mathoverflow.net/q/467793/17064đ
You know well, David, that the real reason for logicians to be is that when an evil supervillain tries to destroy the Universe by proving 0=1 from Peano's axioms, we can all band together as superheroes and save existence from annihilation by the power of Gentzen's âšTRANSFINITE RECURSION UP TO Δââš.
En tout cas, ça conserve, d'ĂȘtre un noble anglais: l'actuel Lord Elgin (11e du titre) vient de fĂȘter ses 100 ans: en.wikipedia.org/wiki/Andrew_...đ
#TIL that during the sack of the YuĂĄnmĂng YuĂĄn (Summer Palace of the QÄ«ng dynasty), the British looters seized, inter alia, a small Pekingese dog, who was brought to England and offered to Queen Victoria as a pet â and given the name âLootyâ. en.wikipedia.org/wiki/Looty_%...đ
«â€â€Q: Why are the pyramids in Egypt?â€â€A: Because they were too heavy to be moved to the British Museum.â€â€Â»
I have no idea how historically/scientifically accurate they are, or even how they were done, but these images attempting to reconstruct what Tenochtitlan (now Mexico City) looked like in 1518, are impressive and breathtaking: tenochtitlan.thomaskole.nlđ
âWolfskehl actually missed his supposed suicide time because he was in the library studying the Theorem. Upon realizing that, he concluded that the contemplation of mathematics was more rewarding than a beautiful woman so he decided not to kill himself.â en.wikipedia.org/wiki/Paul_Wo...đ
My main issue with HTML is that this format doesn't provide any decent and well-supported way to generate a self-contained file (with all CSS + images + fonts + JS included). So PDF sucks because it forces the page layout, but HTML sucks because you can't really save and browse locally.
Just in case you don't know: if you take the link to an arXiv abstract â e.g. arxiv.org/abs/2106.03061 â and replace the âxâ by â5â â e.g. ar5iv.org/abs/2106.03061 â this tries to generate an HTML5 version from the TeX source. Sometimes buggy, but often useful!
Just in case you don't know: if you take the link to an arXiv abstract â e.g. arxiv.org/abs/2106.03061 â and replace the âxâ by â5â â e.g. ar5iv.org/abs/2106.03061 â this tries to generate an HTML5 version from the TeX source. Sometimes buggy, but often useful!
Many PDF readers offer the option of displaying even and odd pages side by side horizontally. What I'm talking about here would be a kind of inverse option: split a single page into two halves and display them vertically. This shouldn't be hard. Why isn't it available everywhere?
Alternatively, since 2-column PDF files do exist and will never go away, how come is it that PDF reader software doesn't provide an easy layout option that will display the right half of the page below the left half, so we can read by easily scrolling down?đ
⊠causing a lot of completely unnecessary vertical scrolling and confusion, whereas for 1-column layout you just scroll down uniformly and conveniently.â€â€If you are a journal/conference editor, please lobby your publisher to stop this silly practice of 2-column layout. đ
⊠To read a 2-column PDF on a screen, you need to either fit to height, which is wasteful as our screens are landscape-sized and the page is portrait-sized, so the font ends up too small to conveniently read, or you need to scroll up when you reach the bottom of a column, âŠ
Dear people typesetting scientific papers (esp. in physics and computer science): please STOP IT WITH TWO-COLUMN LAYOUT. It may be slightly better for printing on actual dead tree pulp, but we spend much time reading âpapersâ on screen, and 2-col layout is awful for that. âŠ
Some people have advocated celebrating it on the 22 of July, a.k.a., â22/7â.â€â€Myself, being utterly committed to the ISO-8601 standard for dates, I will only celebrate pi day on the 92th day of the 15th month of the year 3014.
Remarkably interesting History of Medicine video about penicillin, that goes well beyond its serendipitous discovery by Fleming: how its safety and efficiency were tested in vivo, how it started being used as a drug, and how it got to be produced. www.youtube.com/watch?v=mhXm...đ
⊠These guys are supposed to be evil geniuses with human computers (âmentatsâ) at their service, they have the Emperor himself onboard, and the best they can come up is this ridiculously contrived plan that just screams WHAT COULD POSSIBLY GO WRONG? (Spoiler: đ !) Come on! đ
⊠and the best plan they all come up with is to give house Atreides control of THE MOST IMPORTANT AND VALUABLE PLANET IN THE ENTIRE UNIVERSE and hope that they (Atreides) will make such a mess that they (Harkonnen) can use this as a pretext to conquer it back. âŠ
Is the political premise of âDuneâ (any version) supposed to make the slightest bit of sense? Because to me it doesn't.â€â€So we have great noble house Harkonnen that wants to get rid of the rival house Atreides, somehow gets the emperor on board with their scheme (why, again?), âŠ
The reason this is happening all over the place, btw, is that large pre-2023 corpora of text written by actual humans is the low-background steel (en.wikipedia.org/wiki/Low-bac... ) of LLMs right now -- if LLMs continue to exist in another 5, 10 years, they will be forever frozen in 2023.đ
Leibniz, the original Sokal hoaxer. His first job was as secretary to an alchemical society. He knew next to nothing about alchemy but somehow bulshitted himself into the job as described here.đŒïž
But is there an operational difference (apart from the name) between â¶a nonpartisan primary followed by a general election in which only two candidates get to participate, and â·a two-round election with only two people in the runoff? You seem to imply there is, but I can't see it.
The Office of the United Nations High Commissioner for Human Rights has an entire booklet www.ohchr.org/Documents/Pu... about âthe Rights of Non-Citizensâ, but it says disappointingly little about freedom of expression.đŒïž
Are there any legal scholars around who might enlighten me about various doctrines and theories (and precedents in various countries and jurisdictions) concerning the right of non-citizens to free speech and expression? Any recommended readings on the subject?
You mean unusual for the US. Having a two-round election system where the top two candidats in the first round participate in the second round (or ârunoffâ) is very common in many countries. The French presidential election works that way, for example.
I mean, I have no idea who gets a notification if I reply to a postÂč. The default on X (viê«. âthe author of every ancestor post until nowâ) is shitty, but âjust the author of the parentâ with no choice available, would be even more shitty. Which is it?â€â€1. What are they even called? âSkiesâ?
On some other social media (generic brand, let's call it âXâ), when person B replies to person A and then person C replies to B, while posting C gets the option of notifying either B alone or both A and B (sadly, default is âeveryoneâ, but having the option is good).â€â€How do things work here?
I made an edit to Wikipedia but I have a hard time finding an adequate reference: I added to the page en.wikipedia.org/wiki/Millenn... about the Clay âMillennium prize Problemsâ in mathematics that:â€â€Â«The seven problems were officially announced by John Tate and Michael Atiyah âŠđ
I asked a question on Reddit AskHistorians about the extent to which the trial and execution of Charles I of England was used as model and precedent (or, on the contrary, counter-model) for those of Louis XVI of France. www.reddit.com/r/AskHistori...đ
Alors il y a clairement un fantasme dans l'histoire, mais je ne crois pas que âfurryâ soit le bon. La chauve-souris a beau avoir des plumes et le rouge-gorge des plumes, il est plus questions de muscles et de latex, lĂ . đł www.independent.co.uk/arts-enterta...đŒïž
Job opportunity! "Research Associate in Mathematical Epidemiology" - come and work with our friendly team on the relationship between community viral prevalence and disease burden in vulnerable settings.â€â€www.jobs.manchester.ac.uk/Job/JobDetai...đ
Oh yeah, one of the main things that makes Twitter shitty is that the douchebag-in-chief over there decided that mentioning any other social medium would be outright forbidden, or get you shadowbannedâŠâ€â€âŠlet's import this censorship rule on BlueSky to make it just as shitty! đ
Next time I run out of Latin letters in my math formulas, I'm going to consider using IPA symbols: like âlet (u,ÉŻ,v,w)âââŽâ, âlet f,g,h,É,Ê be five functionsâ, âso the functor Ê is left adjoint to Êâ, âlet us call É the neutral element of this groupâ, etc. đ
C'est pas juste! Sur le plateau de Saclay on est loin de tout et au milieu d'espaces immenses, et nous n'avons quand mĂȘme rien de tout ça. (Il paraĂźt qu'il y a une espĂšce de crapaud rare, mais elle se cache.)
I asked a question on MathOverflow about the volume and surface measure (and possibly other intrinsic volumes) of the set of positive semidefinite matrices with trace 1 (aka âspectraplexâ): mathoverflow.net/q/463282/17064đ
I realizeÂč that the question reads a bit like an ad for propositional realizability. That's on purpose. đâ€â€1. Pun unintended.
I asked a question on MathOverflow about what is known about propositional realizability for Kleene's second algebra and other PCAs (or, in fact, anything other than Kleene's first algebra): mathoverflow.net/q/463183/17064 (NB: the question gives all relevant definitions)đ
The title is misleading: there is nothing secret, just that buildings grew organically to fill the spaces left by other buildings, leading to a highly labyrinthine structure where you could get from hence to thither by different paths. This gets compared to Deleuze and Guattari's ârhizomeâ.
Interesting video about the architecture of prisons, and how it relates to their security, efficiency, humanity and overall philosophy; from a fictional in the sci-fi series âAndorâ, and Bentham's Panopticon, to the real world prison of Halden in Norway: www.youtube.com/watch?v=Yfo2...đ
Very interesting video imagining traveling back in time through prehistoric earth to find a point where a human could (sustainably) survive â an excuse to describe how these past eons and epochs âlooked likeâ. www.youtube.com/watch?v=XMQK...đ
Couches-salopettes pour pigeon domestique! đđ
I don't know who needs to hear this, and it seems that everyone's experience is different in this matter, but this Tampermonkey script (i.e., JavaScript snippet) seems to me to be the best ad blocker blocker blocker for YouTube: github.com/TheRealJoelm...đ
Uber: we can't make money if we have to follow the lawâ€â€Google: we can't make money if we're not allowed to be a monopolyâ€â€Nestle: we can't make money without using slave laborâ€â€OpenAI: we can't make money if we can't stealâ€â€media: should shoplifters be executed?
My daughters and I are feeding cows 10,000 pounds of macadamia nuts each because we are simple farm folk who love culinary adventure and that's what makes us so relatable and makes it so clear we don't need to be taxed at 98+ percent of our income.đŒïž
French as well. I don't think «chez le boucher» sounds weird at all. But for some reason I do find «chez le pharmacien» weird. (Maybe because I picture the butchery as having a well-defined head but not the pharmacy?) So I guess⊠YMMV or something.
Now because of you I don't know what I say. But Google Ngrams books.google.com/ngrams/graph... suggests that while âchez e boucherâ is less frequent than âĂ la boucherieâ, it's far from nonexistent.đ
âNiklaus Wirth has lamented that, whereas Europeans pronounce his name correctly (Ni-klows Virt), Americans invariably mangle it into (Nick-les Worth). Which is to say that Europeans call him by name, but Americans call him by value.â [fortune]
So all that's left to do is run pA(qA), pB(qB) and pC(qC) in parallel, wait for any one to terminate and output one of the labels A,B,C (necessarily one will eventually do this), and, when this happens, we know that this is the label of a safe door. âą25/(12+13)
To sum up, we've constructed (post 16 or 20) three programs, qA,qB,qC, such that if we run pA,pB,pC on them respectively, NO ONE will ever return the label of the dragon door, and AT LEAST ONE will terminate and return a safe door. âą24/(12+13)
And of course if X is the dragon door, then pX(qX) will always terminate and return Y or Z, never X, as that was the assumption on pX (no matter what qX does, so here we don't care how it was constructed). So in all cases, pX(qX) does NOT return the dragon door. âą23/(12+13)
⊠indeed, if X is a safe door, and we assume w.l.o.g. the dragon door is Y, then pX(qX) can never return Y, because if it does, qX returns Z (since it flips Y and Z), so pX(qX) returns Z (since Z is the only safe door â X, by assumption on pX): contradiction! âą22/(12+13)
So at this point I defined three programs, qA,qB,qC (in post 16 or 20), which I will give as input to pA,pB,pC. Note that pX(qX) might perhaps fail to terminate (or return something that's not a door label), but it can NEVER return the dragon door as output: ⊠âą21/(12+13)
In short, you'd do the trick thusly: let r be the program that takes an input s (assumed to be a program) and runs pX on s(s) (i.e. on s fed with s itself), then exchanges Y and Z in the output; now qX is r(r). This does what I claimed. âą20/(12+13)
⊠and the programs in question are known as âquinesâ. I wrote a long page, ages ago, about how to do this trick: www.madore.org/~david/compu... â but the bottom line is, it works in all programming languages: you can always refer to the very program you're defining. âą19/(12+13)đ
⊠(although it is, in fact, not at all due to Quine, but to Turing taking inspiration on Cantor and Gödel, and formalized as âKleene's [second] recursion theoremâ en.wikipedia.org/wiki/Kleene%... ), ⊠âą18/(12+13)đ
How and why is the program q allowed to refer to the program q itself in its own definition? Well, maybe the programming language allows you to do that, but even if not, it's a standard trick in computability, sometimes known as âQuine's trickâ ⊠âą17/(12+13)
⊠qX runs the program pX on qX itself (I'll point out next post why this is legitimate), and, if pX terminates and outputs Y or Z, it [viê«. qX] exchanges Y and Z and returns that (where {X,Y,Z}={A,B,C}; any other output is just returned; only Y and Z are flipped). âą16/(12+13)
And the trick is to run the program on âitself with outputs exchangedâ; more precisely, assuming pX is one of our three hint programs (pA,pB,pC), we define a program qX as follows: ⊠âą15/(12+13)
So, the program at the dragon door will always give us a good answer, but we don't know which one it is. So let's concentrate on this: what input q should we feed to a safe-door program to make sure it DOES NOT output the dragon door (no matter what else it does)? âą14/(12+13)
OK, I promised I'd post the answer on Bluesky, so here it goes. â€”ïž But note that I wrote a longer explanation on my blog (in French) at www.madore.org/~david/weblo... (Google Translate should work well if you don't know French), so turn to that for more details. âą13/(12+13)đ
⣠compilers output code in archaic machine languages, where processors have to do magic to recognize all sorts of patterns and guess the compiler's intentions so as to execute them efficiently.â€â€[Shamelessly stolen from a friend.]
Computer engineering is wonderful:â€â€âŁ humans write code in archaic programming languages, where compilers have to do magic to recognize all sorts of patterns and guess our intentions so as to translate them efficiently,â€â€âŠ but then âŠ
Let me add a very short definition of these trees:â€â€âŁ The height n+1 tree is a node at Âœ connected to two copies of the height n tree mapped by the functions L (left) and R (right) on [0,1], whereâ€â€âŁ Dyadic: L(x) = x/2, R(x) = (x+1)/2â€â€âŁ S-B: L(x) = x/(x+1), R(x) = 1/(2âx)
The binary dyadic tree (left) versus the Stern-Brocot tree (right) on the interval [0,1]. âŹïžâ€â€(x is to scale, but y is arbitrary.)â€â€I couldn't find a nice way to consistently scale and place the labels, so it's ugly, but I think it's still nice to see them side by side.đŒïžđŒïž
But remember that, if the dragon is at A, door B's program is only guaranteed to terminate (and output C) provided its input itself terminates and outputs C. So if you feed door A's program to door B's, and the former outputs B, the latter can do anything it wants.
Regarding your second question, yes, you can consider giving to one door's program another door's program (you can also build a wrapper around it to give it an input and/or change the output).
âNo inputâ can be considered as âthe trivial program as inputâ if you want. So yes, you can do that, and then: â the program from the dragon door will terminate (naming one of the two other doors), and âĄanother program might do anything it wants.
I think Raymond Smullyan would have loved this riddle. I'll post the solution in a few days and explain how I came up with it (it's a rephrasing of a theorem I read: I didn't want to read the proof but solve it by myself). I can provide hints or clarifications if needed. âą12/12
(You don't need to determine which door has the dragon, only one which is safe.) You can take the time you want, but it must be finite, i.e., your algorithm has to terminate (for any pA, pB, pC satisfying the constraints) and return some safe door. âą11/12
I hope the rules are perfectly clear. Now you are given these three programs, pA, pB and pC, and your goal is to find a safe door. Of course you should also do this algorithmically, i.e., write an algorithm taking such pA, pB and pC as input and returning a safe door. âą10/12
Note for example that pB is perfectly allowed to simply run its argument q and return the latter's output (since the only constraint is: if q returns C then pB(q) returns C). However pA (the dragon door's program) must ALWAYS terminate and return B or C. âą9/12
On the other hand, the program pB attached to door B will terminate and return C but only PROVIDED its input q is a program which ITSELF terminates and returns C. In any other case, it (that is, pB) can do anything it wants (not terminate, output A or B or C or 42 or whatever). âą8/12
Assume door A has the dragon. Then the program pA attached to door A will always terminate and return either B or C, no matter what its input is (the output might depend on the input, but it will always terminate and output either B or C). ⊠âą7/12
⣠The program attached to a safe door will terminate and return the label of the other safe door PROVIDED you give it as input a program which itself (takes no input and) terminates and returns the label of that other safe door(!).â€â€Let me rephrase this for clarity: ⊠âą6/12
⣠The program attached to the door with the dragon behind it will ALWAYS terminate (no matter what the input), and will return the label of one of the two other doors (note that they are both safe, since we're talking about the dragon door). âą5/12
⊠(I write âpossiblyâ because the program might run forever or misbehave if you give it the bad input.) The idea is that each might tell you a safe door; but things aren't that simple! Because the program takes an input.â€â€Your guarantees are as follows: ⊠âą4/12
⊠since this is a very modern dungeon, each hint takes the form of a computer program (which you have the computer to run or, if you wish, inspect).â€â€Each of these three programs takes an input and possibly returns the label of one of the two other doors. ⊠âą3/12
⊠lead to safety. Your goal is to open a safe (=non-dragon) door. Of course you don't know which one has the dragon, and the doors are identical except for the letter marking.â€â€But fortunately, a hint has been left for you attached to each door: ⊠âą2/12
It took me days to solve this one, so now I've got to tell the world about it:â€â€âïž A riddle about dragons and computability đâ€â€You are in a dungeon. There are three doors (A,B,C) in front of you. Behind one is a dragon who will eat you if you open it. The other two ⊠âą1/12
3 French Hens for the Elven-kings under the sky,â€7 Swans A-swimming for the Dwarf-lords in their halls of stone,â€9 Ladies Dancing for the Mortal Men, doomed to die,â€And a Partridge in a Pear Tree for the Dark Lord on his dark throne,â€In the Land of Christmas where the rest of the gifts lie.
Great thread đâ€â€Maybe one day a story about a deadly outbreak in Africa will be a story about a deadly outbreak in Africa rather than that the outbreak might come to rich countries but today is not that day.đ
Yes. Barendregt's exposition doesn't pinpoint the exact difference, the exact rule allowed in one and not in the other where the naĂŻve attempt to interpret the CoC λ-term into a proof will fail. I suspect it's another âProp versus Typeâ, aka predicativity, issue, but I'm utterly confused.
The statement I'm asking about is the one stated and proved below in Barendregt's chapter âLambda Calculi with Typesâ [I cropped irrelevants parts of page 264]:đŒïžđŒïž
I asked a question on the Computer Science Theory StackExchange about what it means intuitively that the Calculus of Constructions is not conservative over Higher-Order Logic: cstheory.stackexchange.com/q/53656/17747đ
This can't possibly be a bug: in the HTML source, image 3 comes before image 2. You can't make something like this without actually wanting to organize the images that way.
It is, as I feared, a gratuitous incompatibility: so, on TSNFKAT images should be read like English text, i.e., lines from top to bottom and from left to right on each line, whereas here images should be read like⊠uh⊠Mongolian?, viê«. columns from left to right and from top to bottom on each. đ
The four images below have been added to this post in the order 1, 2, 3, 4. If things are as I suspect, they will be arranged columnwise, whereas that-other-social-network-with-a-more-musky-smell-that-this-one-imitates uses a rowwise order. Confusing!đŒïžđŒïžđŒïžđŒïž
I think we can consider the case of the Voynich manuscript closed since the paper âA possible generating algorithm of the Voynich manuscriptâ by Timm & Schinner (âCryptologiaâ 44 (2020)) doi.org/10.1080/0161... â which gives a convincing stochastic algorithm for generating Voynichese text.đŒïž
I think we can consider the case of the Voynich manuscript closed since the paper âA possible generating algorithm of the Voynich manuscriptâ by Timm & Schinner (âCryptologiaâ 44 (2020)) doi.org/10.1080/0161... â which gives a convincing stochastic algorithm for generating Voynichese text.đŒïž
⊠and say w.l.o.g. it returned a C. Then we can realize ÂŹAâC: indeed, given a promise that A is uninhabited, we now know that our own promise to p was good (a promise is information-free!), so it returned a good C, so we can return âœthatâœ, and the realizability contract is fulfilled. â Very nice!
⊠one of these promises may be a false promise, but no matter; we feed them to p and q respectively: necessarily one of them will get a good promise, so it must terminate; so we can wait for the first to terminate (note that it still may be over a false promise, though!): say w.l.o.g. it is p, âŠ
And the proof of realizability is really nice, too. We are given: a promise that A and B cannot both be inhabited, and two programs, p resp. q, that take a promise that A resp. B is uninhabited and return an element of C or D. Now we make two promises, one that A is uninhabited and one that B is: âŠ
⊠so we can write a program that witnesses (realizes) this formula, but this CANNOT be done by typing, as there is no term having this type in the simply typed lambda calculus.â€â€I think this is mind-blowing. đ€Ż
I wrote a length addendum to my MO question [link in previous post], pointing out that there are propositional formulas such asâ€â€(ÂŹ(Aâ§B)â§(ÂŹAâ(CâšD))â§(ÂŹBâ(CâšD))) â ((ÂŹAâC)âš(ÂŹBâC)âš(ÂŹAâD)âš(ÂŹBâD))â€â€which are realizable but not provable: âŠ
⊠with myself as deaf as the audience (and the composer!), but sufficiently trained in musical theory that I know it would sound beautiful if any of us could hear it!â€â€[This comparison has limits, of course, so take it with a grain of salt, but it gives some idea.]
The frustrating thing about mathematics is: there is stupendous beauty in it, but we can experience this beauty only indirectly and after considerable technical training.â€â€It's a bit like trying to explain to a deaf audience how the score of a Beethoven symphony is beautiful âŠ
OK, I got an answer elsewhere: the U+002E FULL STOP here is a special syntax called a ârefutation caseâ, which specifically instructs the compiler to âtry harderâ to refute a pattern matching case: v2.ocaml.org/manual/gadts...đ
Joy to the world,â€Peace on Earth,â€Seize the means of production.đŒïž
Apparently this is how you do an empty pattern match in OCaml:â€â€type void = |â€let exfalso = fun (r:void) -> match r with _ -> .â€;;â€â€I don't understand what this â.â is doing here. Can someone explain? (My problem is purely syntactic.)
I rebooted and Windows 11 put an AI copilot button beside the start button without asking. The first thing I asked it was how to turn it off, and it answered incorrectly. Twice. Then I asked it who I was married to and it hallucinated a new job for Jenn, a son, and a dog - with fake referencesđŒïž
Asked in a lengthier way on MathOverflow: mathoverflow.net/q/459683/17064 (I hope the question there makes it clearer what relation I see between the two and what I would like to understand)đ
I know about Kleene's realizability and various generalizations thereof (including categorical formulations like the effective topos), and I know about the C-H correspondence, it's clear that they have much in common, but I don't know how to frame them in a common way.
Both realizability and the Curry-Howard correspondence are ways to make precise the Brouwer-Heyting-Kolmogorov interpretation of intuitionistic logic.â€â€Can we unify them in some way? Do they admit a common generalization?
So I asked a question on the Theoretical Computer Science StackExchange about complexity classes defined by genericity instead of randomness. (The question begins with a lot of motivations and background definitions, so it's a bit long.) cstheory.stackexchange.com/q/53598/17747đ
One reference is Sacks, âDegrees of Unsolvabilityâ (1963), §10, theorem 1 (p. 154) (as follows: «let A be a non-recursive set; then the set of all sets in which A is recursive has measure zero»).â€â€Surely there are more modern references!â€â€In fact, why is this not in EVERY textbook on computability?
Rephrased: «If f:âââ is computable with a random oracle with probability >0, then in fact f is computable (without oracle).»â€â€Rephrased: «If {α â {0,1}^â : f is Turing-reducible to α} has positive measure, then f is computable.»
What is a standard modern reference for the following fact (which is, or should be, well-known):â€â€Â«â€If f:âââ is a function such that for a set of positive measure of α in {0,1}^â the function f is computable with α as oracle, then in fact f is computable.â€Â»
In fact, this phenomenon is explained by the "House curve", the insights from which are soon to be available for a fee from my consultancy alongside output from AI-powered multi-omics digital twins.đ
The definition of the (3-variable) Ackermann function used here is:â€âŁ A(m,n,0) = m+nâ€âŁ A(m,0,1) = 0â€âŁ A(m,0,k) = 1 if kâ„2â€âŁ A(m,n,k) = A(m, A(m,nâ1,k), kâ1) if kâ„1 and nâ„1â€â€(so A(m,n,1)=m·n, A(m,n,2)=m^n âand so onâ).
(The crucial point in the above code is that the function âackermann_boundedâ of four arguments m,n,k,b returns the value of the Ackermann function A(m,n,k), provided the latter is â€b, without any recursion or unbounded loops, showing it to be primitive recursive.)
Fun fact: the Ackermann function (here with 3 arguments, but no matter), while not primitive recursive, becomes primitive recursive if you give it a fourth argument which is an upper bound on the value. (In particular, the GRAPH of the Ackermann function is p.r.)đŒïž
Ah oui, lĂ je suis bien d'accord que c'est complĂštement absurde.
Note to self: since I write in both English and French, whenever I post something on Blue Sky, I need to remember to correctly select the language in which it was written.â€â€(This is annoying. Autodetection can be wrong sometimes, but autodetection + manual override would be ideal.)
⊠but a hint is given in the table of contents of the (already 165-page long) volume 1 which is essentially an âoutlineâ of the proof (theorem Câ is there, but no mention of Câ*, so I guess a complication was discovered?): âŹïž. (That volume 1 looks fairly interesting, actually!)đŒïžđŒïž
So 29 YEARS after the project to REwrite the proof started, and 4060 pages later, it seems that we've finished âtheorem Câ and theorem Câ*, case Aâ. Good.â€â€I don't know how many volumes remain before the proof is finally complete (my guess would be 2±1), âŠ
If you want a feel of how complex the proof of the Classification of Finite Simple Groups is, look no further than the TITLE of this 570-page volume, which is volume 10 (the latest, I think) of an ongoing effort to simplify and streamline(!) the proof: bookstore.ams.org/view?Product...đ
I asked a question on the Computer Science Theory StackExchange about how encoding of values affects what Turing machines can compute: cstheory.stackexchange.com/q/53559/17747 (maybe it's a stupid question! you tell me)đ
I asked a question on the Computer Science Theory StackExchange on the precise connection between strong normalization of the simply typed λ-calculus, and cut elimination for propositional logic. cstheory.stackexchange.com/q/53551/17747đ
(Article 369 de la Constitution de l'an III. L'article 165 dispose de mĂȘme pour les membres du Directoire. Cette constitution est la plus bizarrement pointilleuse qu'ait jamais eu la France. www.madore.org/~david/weblo... )đ
Quel genre de livre? Texte scientifique? Vulgarisation? Manifeste politique? Roman policier? Science-fiction? Recueil de poĂšmes? Recettes de cuisine? Recettes informatiques?
I should probably link this here and not just on Twitter:â€â€Is there someone who can clarify the relationship between Martin-Löf's type theories and the pure type theories of Barendregt's âlambda cubeâ? cstheory.stackexchange.com/q/53507/17747đ
Beaucoup de gens doivent se dire que quand on a 140Ă plus de followers sur Twitter sur Bluesky (c'est mon rapport actuel, je ne sais pas combien il est typique), mĂȘme en sachant que >90% sont des comptes devenus inactifs, c'est plus tentant d'initier une conversation sur Twitter.
Cabin crew: Is there a Dr on board?â€â€Me: I am a Drâ€â€Cabin crew: Thank God. We have a question about the 18th century textile trade in Northern Africaâ€â€Me: Ah. I'm afraid my PhD is in the ceramics of Northern Europe, 1672 - 1701
âIf youâre angry about THIS, but not about THATââ â€â€Bro Iâm gonna have to stop you there, I am angry about so many things all of the time, I have never in my life been angry about just one thing at a time, my capacity for âthings to be angry aboutâ is as wide and as deep as the sea
OK, it appears that this place is so similar to Twitter that we even get the same bots with bogus female names and avatars randomly liking posts. Good, I won't be too disoriented! đđŒïž
This account will be used for testing purposes until I learn more about how this Twitter clone social network operates.