@El'endiaStarman hehe:)

@flawr XD

I learned about hyperuniformity earlier today and this stuff is fascinating. quantamagazine.org/…

Thanks indirectly to this paper about hyperuniformity in large stretches of primes. arxiv.org/pdf/1802.10498.pdf

PDS :)

actually a friend just sent me an article about that this morning!

princeton.edu/news/2018/09/05/…

@flawr Likewise! Except my friend sent me an IFLS link, but the content is similar.

> Similar math might explain the emergence of hyperuniformity in bird eyes, the distribution of eigenvalues of random matrices, and the zeros of the Riemann zeta function — cousins of the prime numbers.

O_O

Waaaahhhhh?!?!

My understanding of Riemann zeta is a bit Rusty, but isn't finding the zeroes effectively looking in a 1-dimensional space, not two?

Can hyperuniformity exist in an arbitrary number of dimensions?

@DJMcMayhem if the RH is true :)

@DJMcMayhem why not? :)

Idk

@flawr Well it's not proven false

@DJMcMayhem It's defined for complex numbers, hence it actually is 2D.

@DJMcMayhem it isn't proven true either

@El'endiaStarman But the only known zeroes are all along the same line

@El'endiaStarman it is a 1d complex vector space:)

@DJMcMayhem Why does that mean all of them have to be?

If the RH is false, then there's at least one zero not on that line.

@flawr That's a concept I'm slowly understanding more over many years. It's hard to ignore all the 2D representations of complex numbers in particular to think of functions on a single complex number being 1D in that field.

@El'endiaStarman The question of dimensionality of one field over a subfield as a vectorspace (or module, if you're looking at the corresponding rings of integers) pops up a lot in algebraic number theory, and you can do a lot of fun stuff with that:)

@El'endiaStarman Maybe I'm reading too much in to that sentence, since they didn't really go into any detail. But it sounded like they were saying that the patterns in known 0's form a HU (Hyper uniform) distribution. I was just thinking that it would have to be a 1D HU since there aren't any known 0's outside of that line to analyze the distribution of

Actually I'm still convince that complex numbers should be taught way earlier in school, as they are such a fundamental topic and let you do so many cool things!

Like you can't say "All of the 0's form a 2D pattern!" because they'd have to be including the 0's that (haven't been found yet || don't exist)

@DJMcMayhem they are probably assuming that RH holds

What flawr said and they can certainly analyze the known zeros and see that they exhibit hyperuniformity (or not).

At least I think we do already know a lot about the distribution of zeros

In fact it is not too difficult to see that the nontrivial ones are within the strip 0 <= Re(z) <= 1

@El'endiaStarman Yeah, so the known ones, or any pattern in them, is effectively 1D

(of course ignoring the trivial ones)

I'm pretty sure the trivial ones are also (trivially) hyper uniform :)

No, they're lattice :P

Feels strange to refer to zeros as ones.

Perfectly even distribution

I really enjoy this room, and I've always found math super enjoyable and interesting. But whenever people who actually know math well start talking, I feel waaaaay out of my league. Like, anything above Algebra/simple Calc and I'm just totally lost. People break out mathjax? I'm useless. This message from flawr reads like a foreign language to me.

I really wish I could comprehend the higher level stuff better.

@DJMcMayhem Do not feel bad! And don't stop asking questions! I really enjoy this room too, but it is difficult to judge who knows what. If you want I'll try to explain it, but not right now as I have to got to bed :)

(I like explaining stuff:)

@DJMcMayhem For what it's worth, that one's hard for me to follow too. :P

Mathematics is vast and full of abstract ideas that require jargon to efficiently communicate which makes it easily incomprehensible if you aren't familiar with the topic.