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i'm going to bed but let's try and set up a game 1. reply with an interest, a picture, a quote, whatever – something random that you'd like to talk about with someone. ask a question, state an observation 2. reply to someone else in the replies enjoy your new friends

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QC (in Berlin 7/29-??? w/ COVID

anyone wanna talk about how applying the central limit theorem to a random walk in 2D reproduces the euclidean metric starting from a *grid* it’s fucked up and wrong and i’m still trying to figure out what it means

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can u send me a link that explains this a lil past 280 characters i feel like i'm 80% towards understanding why this sucks

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QC (in Berlin 7/29-??? w/ COVID

idk a place where this is spelled out but like okay take a random walk on a 2D square grid where you go up, down, left or right with probability 1/4 each. sample the walk a bunch of times and make a plot of where you end up after like a million steps. you’ll get a 2D gaussian

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QC (in Berlin 7/29-??? w/ COVID

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and

which has radial symmetry: the probability that you end up in a certain small region depends only on how far you are from the origin, in the *euclidean* metric. this is despite the fact that the random walk itself is only defined knowing what up, down, left, and right are

1:20 AM · Sep 20, 2020Twitter for iPad

QC (in Berlin 7/29-??? w/ COVID

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and

i’ve wondered for years how important or meaningful this observation is and i still don’t know one way or the other

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ok yeah wow i do not know enough math to advise simply to sympathize and this sucks!!!!

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Hmm. So in what sense is the EM *reproduced*? I don’t think I see what exactly is reproducing it?

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QC (in Berlin 7/29-??? w/ COVID

in the negative log probability. you need to take a particular scaling limit to see it come out and the details are slightly annoying to write down unfortunately

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Replying to

and

Are you saying p = 1(root(x^2 + y^2))?

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QC (in Berlin 7/29-??? w/ COVID

the probability ends up being (a constant) exp(-(another constant)(x^2 + y^2)), this is the pdf of a 2D gaussian:

en.m.wikipedia.org

Multivariate normal distribution - Wikipedia

@aphercotropist

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Wtf

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QC (in Berlin 7/29-??? w/ COVID

yeah exactly it’s super weird i’m starting to realize in this discussion also that like... okay i vaguely expected people to be kinda familiar with CLT from hearing about bell curves but now i’m starting to realize probably way fewer people have seen CLT in multiple variables

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I like this idea as emergent geometry, but you don't get the Euclidean metric itself.

george smiley's man titties

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i understand what this means and i think i understand why it's fucked up and it's blowing my mind a little because i never would have thought of it as being fucked up without it being pointed out

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QC (in Berlin 7/29-??? w/ COVID

yes thank you! more math popularizers should talk about how fucked up stuff is maybe this can be my new niche

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