kogasa
@kogasa@programming.dev
- Comment on Emma Watson banned from driving for speeding 1 week ago:
So I’m not advocating for speeding, and I think getting a ticket for going 38 in a 30 is reasonable enough, she should be more careful. But “the probability of death given a collision” is an astronomically low contributor to the risk to pedestrians compared to “the probability of a collision.” We all know getting hit by a car is extremely dangerous even at low speeds. The risk of hitting a pedestrian doesn’t go up much between 38mph and 30mph under normal conditions, so the risk to pedestrians doesn’t change much. It’s probably within typical margins considering the difference between drivers who may be older, have slower reaction times, have slept less that day, etc.
- Comment on Emma Watson banned from driving for speeding 1 week ago:
it’s not like you can accidentally go around 30% over the limit
When that 30% is 8mph, yes you can
- Comment on UwU brat mathematician behavior 1 week ago:
In the context of differential forms, an integral expression isn’t complete without an integral symbol and a differential form to be integrated.
- Comment on UwU brat mathematician behavior 1 week ago:
The mathematician also used “operative” instead of, uh, something else, and “associative” instead of “commutative”
- Comment on Dunkin' Donuts Drinks 2 weeks ago:
Everything changed when they removed ham from the menu
- Comment on Listen here, Little Dicky 3 weeks ago:
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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.
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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.
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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.
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- Comment on Listen here, Little Dicky 3 weeks 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 3 weeks ago:
No 👍
- Comment on Listen here, Little Dicky 3 weeks 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 3 weeks ago:
The other thing is that it’s legit not a fraction.
- Comment on Anon loves The Lord of the Rings 3 weeks 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 3 weeks 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 5 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 5 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 5 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 1 month 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 1 month 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 2 months 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 2 months 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 3 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 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 5 months ago:
Not really, you need to have a basic understanding at least
- Comment on Manifolds 5 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 5 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 6 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.
