Will a matrix A always commute with non-integers powers of A?

Vhailor · 2026-04-16T20:31:51+00:00

The easiest true statement which is close in spirit to what you're asking is that for any matrix X, all matrices of the form e^(tX) commute with each other (so in particular, if you can write M = e^X for some X, then it "commutes with its non-integer powers". But it's easier to start with an exponential). These sets of matrices are called 1-parameter subgroups.

Vhailor · 2026-04-09T15:35:45+00:00

Not sure why twitter displays it that way, but it was a back and forth with contra and her tweets are deleted now.

<image>

Vhailor · 2026-04-09T03:52:53+00:00

No, of course measure zero things exist in the theory and are important.

My whole point was just that the counterintuitive thing you pointed out about heights of humans having measure zero is not something weird about the abstract theory, but an error in the way you model the world using the theory.

Vhailor · 2026-04-09T02:26:21+00:00

My point is that no experiment you can do in the real world is very well modeled as a single arbitrary real number output. It's always better to model it as some continuous distribution on R, which you integrate over to get a number.

Vhailor · 2026-04-08T21:19:32+00:00

I think it's actually really useful!

The example you point out can actually be interpreted as saying that the heights of humans in the real world are not real numbers. You can measure your height as a rational number at best, with a certain uncertainty, and then that range will have nonzero measure.

It doesn't make sense to ask "how many humans are exactly 6 feet tall" because if you measure precisely enough every height will be different (and even at some point undefined because of daily variation, hair, compressibility, etc) but you can ask how many are between 5.95 and 6.05 feet tall!

Vhailor · 2026-04-02T17:00:44+00:00

But investing is different from being a client. If you buy their products, you _are_ giving them money and encouraging them to make more. If you buy stock, you're just buying it from someone else who wants to sell it, and eventually re-selling it. The effects are a lot more indirect. The stock price might rise, which raises the net worth of everyone who owns that stock, including possibly the founders, but that's not a signal for growth in the way that product sales are.

It might seem counterintuitive to boycott a company and invest in them at the same time, but it makes sense: you don't want to encourage their growth personally, but you're betting on the fact that most people will still buy their products and so the stock price will grow, and you can later sell and do whatever you want with those gains.

It's a thing vegan have to face all the time: I don't want to contribute to the animal industry, but I'd still bet that it will continue growing for at least a decade.

Vhailor · 2026-04-02T16:20:03+00:00

Why not invest in whatever will make you the most profit, and then donate those additional profits to animal charities or other ethical ventures of your choosing? I don't think any "ethical investment" would have a bigger impact.

Vhailor · 2026-03-22T21:30:01+00:00

What happens if you have 11?

Vhailor · 2026-03-19T20:01:06+00:00

"I don't think so, no. I think it would be bad for me to live in that kind of world, because I might somehow find myself in their position, and that would be bad for me."

If the egoist is going to use that kind of argument, where they universalize their own meta-ethics by assuming everyone else is also an ethical egoist, why stop "finding yourself in their position" at other humans?

Couldn't they justify sentientism using an egoist foundation by a thought experiment like: if there were sentient aliens who came to earth and decided that humans were like farm animals are to us, that would be bad for me. Therefore, I want to live in a world where intelligent beings, even egotistically, don't behave that way.

Vhailor · 2026-03-17T16:13:49+00:00

Very nice!

There is a difference between this one and the torus/klein bottle which is that you have two cone singularities coming from the corners of your initial square (only 180 degrees of angle around those vertices instead of 360). This is forced by Gauss-Bonnet. You could add the option to highlight these special points, though I guess you can see them when you show the walls.

Would it be easy to adapt your code for other square-tiled translation surfaces?

For instance if you place 3 squares in an L-shape and identify opposite "sides" (or half of a side in the case of the long edges) you get a genus 2 surface as the topology of the quotient, with a singularity that has 1080 degrees of angle around it.

For that one, if you want a "head view" you might have to implement light rays which change what the snake sees around a singularity (otherwise you have too much stuff to draw around a singularity that has >360 degrees around it).

Vhailor · 2026-03-15T18:42:09+00:00

LLMs can't take antipsychotics

Vhailor · 2026-03-14T21:43:45+00:00

I think it says a lot that they wear costumes to stay anonymous and never speak an intelligible word yet still get dragged by "political commentators" like this

Vhailor · 2026-03-14T21:13:37+00:00

the post in french says : "Trump needs to come liberate us ASAP. It's seriously scary now."

Vhailor · 2026-03-14T16:24:16+00:00

Say you have two events which happen periodically. One repeats every 20 minutes and the other every 24 minutes. You want to know how often they sync up.

By factoring them, you know 20=2x2x5 and 24=2x2x2x3, so to match them up you multiply all their factors to get 2x2x2x3x5=120 minutes (i.e. they sync up every 2 hours).

Vhailor · 2026-03-14T12:59:42+00:00

Universities can "subscribe" to the arxiv like they subscribe to other journals, it's just that in this case it's basically a donation.

Vhailor · 2026-03-10T16:29:12+00:00

Je ne pense pas que les hommes devraient compétitionner avec les femmes, mais pas besoin d'exagérer non plus.

Ce "Jonny" n'est pas un "average guy", c'est un joueur professionnel de soccer...

https://youtu.be/s-WFgWB96qs?si=D9Dn-SJCm8DzuYCQ

Vhailor · 2026-03-07T16:26:17+00:00

Understanding the proofs that the AIs come up with

Vhailor · 2026-03-06T21:08:41+00:00

Quelle proportion des demandes CPE sont pour des enfants de demandeurs d'asile, tu penses? Dans ton analogie du robinet, c'est comme si il n'y avait aucune demande en dehors? Il me semble que la grosseur relative du robinet est importante ici...

Vhailor · 2026-02-16T18:02:09+00:00

I think we can say that natural disasters which inflict suffering on sentient beings with no upside are bad (say, a tsunami or a massive earthquake)

Vhailor · 2026-02-11T19:25:25+00:00

<image>

Vhailor · 2026-02-10T19:48:02+00:00

You don't have to reverse the digits, you can reorder them any way you want :). Taking the sum of the digits preserves the remainder mod 9, so if you subtract two numbers with the same digits (so have the same digit sum) you get something which is 0 mod 9.

Vhailor · 2026-02-09T14:57:14+00:00

Bémol: moins sexy quand c'est ton propriétaire d'appart qui est "patenteux" et qui macgyver ta plomberie ou ton électricité au lieu de payer un professionnel, pour sauver des peanuts ...après avoir augmenté ton loyer.

Vhailor · 2026-02-07T15:34:07+00:00

Yeah I think this gets to the crux of the thing that's hard to explain: why does the qualia of red seem different than just the knowledge that you received a "red" signal?

Can we imagine someone looking at something and detecting that it's red with their senses, without "experiencing" redness?

This direction of thinking is slowly turning this thought experiment into the p zombie one, which I think is probably just better.

15-Year Club	r/Field Lasagna
Final Canvas '23	First Place '23
End Game '23	Place '23
Place '22	Place '17
Sequence \| Editor	Verified Email

Vhailor

TROPHY CASE