kogasa
@kogasa@programming.dev
- Comment on Order of magnitude is a hell of a drug 3 days 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 5 days 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 6 days 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 1 week 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 3 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 4 weeks 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? 1 month 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? 1 month 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? 1 month 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? 1 month 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.
- Comment on The science is divided 3 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 3 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 3 months ago:
Not really, you need to have a basic understanding at least
- Comment on Manifolds 3 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 3 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 6 months ago:
The distance between two complex numbers is the modulus or their difference, a real number
- Comment on Fuck geometry 6 months ago:
Metric, not measure. Metrics are real by definition.
- Comment on Fuck it, we're doing eggs this.weekend. Behold: Scotch eggs. 6 months ago:
Yes, the egg needs to be barely cooked before battering and frying, which makes it really annoying to shell + batter + fry them
- Comment on Fuck geometry 6 months ago:
That’s not a metric. In any metric, distances are positive between distinct points and 0 between equal points
- Comment on Fuck geometry 6 months ago:
That’s not relevant to what they said, which is that distances can’t be imaginary. They’re correct. A metric takes nonnegative real values by definition
- Comment on Het! 6 months ago:
R^(3) specifically
- Comment on Het! 6 months ago:
Did they teach you how to formulate thought experiments in the shop?
- Comment on Het! 6 months ago:
Yeah, basic graduate level math is a lot more useful than whatever you do with your life to warrant such an attitude.
- Comment on Het! 6 months ago:
Specifically, the thing that exists is a regular homotopy of immersions from the standard embedding to its opposite. The “rules” aren’t supposed to be self evident, they’re part of a broader context in topology
- Comment on Het! 6 months ago:
It’s interesting because it’s highly counter-intuitive that such a thing is possible. It’s not supposed to be useful except as an example of a false intuition, which can remind us to be careful in our reasoning.
