kogasa

@kogasa@programming.dev

• ⁨Comment⁩ on ⁨Listen here, Little Dicky⁩ ⁨⁨2⁩ ⁨days⁩ ago⁩:

  1. I also have a masters in math and completed all coursework for a PhD. Infinitesimals never came up because they’re not part of standard foundations for analysis. I’d be shocked if they were addressed in any formal capacity in your curriculum, because why would they be? It can be useful to think in terms of infinitesimals for intuition but you should know the difference between intuition and formalism.

  2. I didn’t say “infinitesimals don’t have a consistent algebra.” I’m familiar with NSA and other systems admitting infinitesimal-like objects. I said they’re not standard. They aren’t.

  3. If you want to use differential forms to define 1D calculus, rather than a NSA/infinitesimal approach, you’ll eventually realize some of your definitions are circular, since differential forms themselves are defined with an implicit understanding of basic calculus. You can get around this circular dependence but only by introducing new definitions that are ultimately less elegant than the standard limit-based ones.

• ⁨Comment⁩ on ⁨Listen here, Little Dicky⁩ ⁨⁨2⁩ ⁨days⁩ ago⁩:

  Ok, but no. Infinitesimal-based foundations for calculus aren’t standard and if you try to make this work with differential forms you’ll get a convoluted mess that is far less elegant than the actual definitions. It’s just not founded on actual math.

• ⁨Comment⁩ on ⁨Listen here, Little Dicky⁩ ⁨⁨2⁩ ⁨days⁩ ago⁩:

  No 👍

• ⁨Comment⁩ on ⁨Listen here, Little Dicky⁩ ⁨⁨2⁩ ⁨days⁩ ago⁩:

  It doesn’t. Only sometimes it does, because it can be seen as an operator involving a limit of a fraction and sometimes you can commute the limit when the expression is sufficiently regular

• ⁨Comment⁩ on ⁨Listen here, Little Dicky⁩ ⁨⁨2⁩ ⁨days⁩ ago⁩:

  The other thing is that it’s legit not a fraction.

• ⁨Comment⁩ on ⁨Anon loves The Lord of the Rings⁩ ⁨⁨6⁩ ⁨days⁩ ago⁩:

  Sounds like a skill issue. If that ruined the game for you, I dunno what to say. Might be a replicant?

• ⁨Comment⁩ on ⁨Anon loves The Lord of the Rings⁩ ⁨⁨6⁩ ⁨days⁩ ago⁩:

  I agree with them, that game is a masterpiece. Didn’t you love it?

• ⁨Comment⁩ on ⁨Order of magnitude is a hell of a drug⁩ ⁨⁨2⁩ ⁨weeks⁩ ago⁩:

  It’s a number and complexity refers to functions. The natural inclusion of numbers into functions maps pi to the constant function x -> pi which is O(1).

  If you want the time complexity of an algorithm that produces the nth digit of pi, the best known ones are something like O(n log n) with O(1) being impossible.

• ⁨Comment⁩ on ⁨The Legends is among us⁩ ⁨⁨2⁩ ⁨weeks⁩ ago⁩:

  It’s got a very high barrier to entry. You kinda have to suffer through it for a while before you get it. And then you unlock a totally different kind of suffering.

• ⁨Comment⁩ on ⁨Anon predicts the future⁩ ⁨⁨3⁩ ⁨weeks⁩ ago⁩:

  The last time I had fun with LLMs was back when GPT2 was cutting-edge, I fine-tuned GPT2-Medium on Twitch chat logs and it alternates between emote spam, complete incoherence, blatantly unhinged comments, and suspiciously normal ones. The bot is still in use as a toy, specifically because it’s deranged and unpredictable. It’s like a kaleidoscope for the slice of internet subculture it was trained on, much more fun than a plain flawless mirror.

• ⁨Comment⁩ on ⁨Baldur's Gayte⁩ ⁨⁨3⁩ ⁨weeks⁩ ago⁩:

  What specifically constitutes a hole is somewhat ambiguous, but if you pull on the thread a bit, you’ll probably agree that it’s a topological quality and that homotopy groups and homology are good candidates. The most grounded way to approach the topic is with simplicial homology.

• ⁨Comment⁩ on ⁨nyet⁩ ⁨⁨5⁩ ⁨weeks⁩ ago⁩:

  You can imagine tracing a path along a Klein bottle to see that it only has one side. To get more precise than that requires some topological context. If you slice it down the middle it turns into two Möbius strips and an orientation of the Klein bottle would induce an orientation of the strips, which are non-orientable. Alternately it has zero top integer homology, which you can get from looking at a triangulation. The orientable double cover of a Klein bottle is a torus, which is connected (if it were orientable, the double cover would be two disconnected Klein bottles).

• ⁨Comment⁩ on ⁨Don't ask for more pixels⁩ ⁨⁨1⁩ ⁨month⁩ ago⁩:

  As long as we can put an upper bound on gayness (or more specifically on each totally ordered subset of people under the is-gayer-than relation) this follows from Zorn’s lemma.

  It’s also true by virtue of the fact that the set of all people who will have ever lived is finite, but “the existence of a maximal element in a poset” just screams Zorn’s lemma.

• ⁨Comment⁩ on ⁨Data speaks for itself⁩ ⁨⁨1⁩ ⁨month⁩ ago⁩:

  I thought at first the point was that murders had gone down because they were suddenly technically legal. The inverted scale thing is worse

• ⁨Comment⁩ on ⁨Anybody?⁩ ⁨⁨2⁩ ⁨months⁩ ago⁩:

  Math builds up so much context that it’s hard to avoid the use of shorthand and reused names for things. Every math book and paper will start with definitions. So it’s not really on you for not recognizing it here

• ⁨Comment⁩ on ⁨Anybody?⁩ ⁨⁨2⁩ ⁨months⁩ ago⁩:

  🍕(–, B) : C -> Set denotes the contravariant hom functor, normally written Hom(–, B).

  In this case, C is a category, and B is a fixed object in that category. For any given object X in C, the hom-set Hom(X, C) is the set of morphisms X -> B in C. For a morphism f : X -> Y in C, the Set morphism Hom(f, B) : Hom(Y, B) -> Hom(X, B) is defined by sending each g : Y -> B to gf : X -> B. This is the mapping C -> Set defined by Hom(–, C), and it’s a (contravariant) functor because it respects composition: if h : X -> Y and f : Y -> Z then fh : X -> Z and Hom(fh, C) = Hom(h, C)Hom(f, C) sends g : Z -> B to gfh.

• ⁨Comment⁩ on ⁨Anybody?⁩ ⁨⁨2⁩ ⁨months⁩ ago⁩:

  It’s not nonsense, although there is a typo that makes it technically unsolvable. If you fix the typo, it’s an example calculation in the wikipedia page on cohomology rings.

• ⁨Comment⁩ on ⁨Anybody?⁩ ⁨⁨2⁩ ⁨months⁩ ago⁩:

  It’s real projective space

• ⁨Comment⁩ on ⁨what is the truth⁩ ⁨⁨2⁩ ⁨months⁩ ago⁩:

  Some of it looks like topology. The curvy horizontal lines turning into curvy vertical lines are symbols relating to the Kauffman bracket, which belongs to knot theory. Other diagrams look like they might be from Floer homology which is related under the umbrella of low-dimensional topology.

  encyclopediaofmath.org/…/Kauffman_bracket_polynom…

  figures.semanticscholar.org/…/10-Figure5-1.png

• ⁨Comment⁩ on ⁨The science is divided⁩ ⁨⁨4⁩ ⁨months⁩ ago⁩:

  No, that’s what induction is. You prove the base case (e.g. n=1) and then prove that the (n+1) case follows from the (n) case. You may then conclude the result holds for all n, since we proved it holds for 1, which means it holds for 2, which means it holds for 3, and so on.

• ⁨Comment⁩ on ⁨The science is divided⁩ ⁨⁨4⁩ ⁨months⁩ ago⁩:

  It’s not actually claiming that all horses are the same color, it’s an example of a flawed induction argument

• ⁨Comment⁩ on ⁨Manifolds⁩ ⁨⁨4⁩ ⁨months⁩ ago⁩:

  Not really, you need to have a basic understanding at least

• ⁨Comment⁩ on ⁨Manifolds⁩ ⁨⁨4⁩ ⁨months⁩ ago⁩:

  You might be thinking of a [connection of an affine bundle](en.wikipedia.org/wiki/Connection_(affine_bundle). You could learn it through classes (math grad programs usually have a sequence including general topology, differential topology/smooth manifolds, and differential geometry) or just read some books to get the parts you need to know.

• ⁨Comment⁩ on ⁨Manifolds⁩ ⁨⁨4⁩ ⁨months⁩ ago⁩:

  Manifolds and differential forms are foundational concepts of differential topology, and connections are a foundational concept of differential geometry. They are mathematical building blocks used in modern physics, essentially enabling the transfer of multivariable calculus to arbitrary curved surfaces. I think the joke is that physics students don’t typically learn the details of these building blocks, rather just the relevant results, and get confused when they’re emphasized.

• ⁨Comment⁩ on ⁨Generative A.I. a Parasitic Cancer⁩ ⁨⁨5⁩ ⁨months⁩ ago⁩:

  I don’t think you need permission to send someone an email directly addressed to and written for them. I don’t have context for the claims about Kagi being disputed, but I’d be frustrated if someone posted a misinformed rant about my work and then refused to talk to me about it. I might even write an email. Doesn’t sound crazy.

• ⁨Comment⁩ on ⁨Fuck geometry⁩ ⁨⁨6⁩ ⁨months⁩ ago⁩:

  You’re talking about a metric tensor on a pseudo-Riemannian manifold, I’m talking about a metric space. A metric in the sense of a metric space takes nonnegative real values. If you relax the condition that distinct points have nonzero distance, it’s a pseudometric.

• ⁨Comment⁩ on ⁨mathposting⁩ ⁨⁨6⁩ ⁨months⁩ ago⁩:

  It’s (co)homology, not Cartesian algebra. There’s also a typo in the meme. I have a fixed version and solution somewhere.

• ⁨Comment⁩ on ⁨Fuck geometry⁩ ⁨⁨7⁩ ⁨months⁩ ago⁩:

  The distance between two complex numbers is the modulus or their difference, a real number

• ⁨Comment⁩ on ⁨Fuck geometry⁩ ⁨⁨7⁩ ⁨months⁩ ago⁩:

  Metric, not measure. Metrics are real by definition.

• ⁨Comment⁩ on ⁨Fuck it, we're doing eggs this.weekend. Behold: Scotch eggs.⁩ ⁨⁨7⁩ ⁨months⁩ ago⁩:

  Yes, the egg needs to be barely cooked before battering and frying, which makes it really annoying to shell + batter + fry them