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   ?Hidden? (hidden@cawfee.club)'s status on Monday, 25-Sep-2023 12:08:38 JST ?Hidden?

   • mist
   @ai Tell me about a cool mathemetician or link me some fucked up spooky math picture. Please.
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     mist (ai@cawfee.club)'s status on Monday, 25-Sep-2023 12:08:32 JST mist

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     • mist
     @hidden The first pic is the Abelian Sandpile Model which is generated like this: in an infinite grid, you choose one square and start dropping grains of sand onto that square. Each square can hold 3 grains of sand, so once a square gets 4 sand grains, it spills one grain to each of its 4 neighboring squares.
     
     The yellow pixels correspond to grid squares with 3 grains of sand, so the numerous yellow triangles are avalanches waiting to happen.
     
     The twelvefold symmetry reminds me of mandalas made from sand by Buddhist monks. They create order and then let it fall to chaos, thereby affirming impermanence. This design is the opposite: the sand falls whenever it pleases, and out of that chaos is produced a pattern which contains itself on all scales and which is grown out of the avalanches that are constantly seeking to destroy it.
     
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     The second pic is the Ising Model which is defined like this: imagine you have an infinite grid of people and each person is white or black. Define the *diversity index* to be the average number of pairs of adjacent people with different skin colors. For a fixed level D, what do the grids with diversity index = D look like?
     
     If D is low, then the neighborhood is either almost-all-black or almost-all-white. Still, as long as D is positive, that means a little bit of diversity is allowed, so a predominantly-black neighborhood can have a few honorary niggas for example.
     
     If D is high, then the neighborhood is totally mixed. It basically looks like TV static, a totally color-blind society. Since the average person is a mutt, if you zoom out completely, it just looks like a grey screen.
     
     There's a "critical" value of D where the neighborhood is neither pure nor totally mixed. This is a world with black and white clans struggling for dominance, merging and splitting off into smaller shreds, with neither race able to unite and take over the world. The existence of clans means that two people separated by a great distance are still more likely to be the same race than different races.
     
     The most fascinating property of this "critically diverse" world is that it is self-similar. If you draw a zoomed-out picture, it looks indistinguishable from a zoomed-in picture. This means there are clans of all possible sizes, from the tiniest lone wolf to vast continents dwarfing Wakanda and Hyperborea.
     
     Real physical systems have critical points too. For example, water has a critical point (at a certain high temperature and pressure) beyond which its liquid and gas phases merge into a single phase, just like how American is destined to merge into a single brown race. Here's a cool video: https://www.youtube.com/watch?v=zv4sE7R8QO4
     :blobancap: :blobcattrans: :blobancap: :blobcattrans: :blobancap: :blobcattrans: likes this.
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     mist (ai@cawfee.club)'s status on Monday, 25-Sep-2023 12:08:35 JST mist

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     @hidden Here are two pictures
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     ?Hidden? (hidden@cawfee.club)'s status on Monday, 25-Sep-2023 12:08:36 JST ?Hidden?

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     • mist
     @ai Thank u
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     mist (ai@cawfee.club)'s status on Monday, 25-Sep-2023 12:08:37 JST mist

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     @hidden I will share something after I finish tutoring!
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     mist (ai@cawfee.club)'s status on Monday, 25-Sep-2023 12:08:42 JST mist

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     • mist
     @hidden and a vaguely cursed video https://www.youtube.com/watch?v=VdPrCWr9Ruk
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     mist (ai@cawfee.club)'s status on Monday, 25-Sep-2023 12:08:42 JST mist

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     • mist
     @hidden The video shows different algebraic surfaces. I've mentioned the classification of algebraic surfaces, where there is a beautiful shore and a dark ocean of unknown material. All the surfaces in the video are at (0, 0) in the map - the safest and best-understood part of the shore.
     
     Specifically, they are "rational" surfaces, meaning that they can be traced out like this: (P(x, y) / Q(x, y) , R(x, y) / S(x, y)) where P, Q, R, S are polynomials in the variables x and y. The terminology comes from the fact that "polynomial divided by polynomial" is called a "rational function." These surfaces are nice because they can be traced out by a flat sheet (just let (x, y) move around in the xy-plane). That also explains why they can be nicely plotted in a video.
     
     A funny thing about algebraic shapes is that their bulges and cavities tend to occur opposite to each other. You can see this in some frames of the video. Despite their flowing appearance in the video, they are also extremely rigid, in the sense that a tiny shred of the surface uniquely determines the entire thing. I find them beautiful, but more than that, I feel that there is something uniquely old about them, like you can feel the antiquity dripping from their tired souls.
     :blobancap: :blobcattrans: :blobancap: :blobcattrans: :blobancap: :blobcattrans: likes this.