Conversation

Sep 19, 2020

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

)

@QiaochuYuan

Sep 20, 2020

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

Emily

@the_aiju

Sep 20, 2020

random walks have a funny habit of introducing square roots

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

Replying to

and

the square roots are whatever, what fucks me up is the random walk has a discrete symmetry and its scaling limit has a much bigger continuous symmetry

1:24 AM · Sep 20, 2020Twitter for iPad

Replying to

and

Surely the square roots are intimately related to the symmetry? I'm thinking about how distance is calculated in 2D

Replying to

and

lol reminds me of the nightmare that is renormalisation theory you get results that defy dimensional analysis which is spooky af scaling is wizardry

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

)

@QiaochuYuan

Sep 20, 2020

one of these days i am going to actually understand statistical mechanics and hopefully when i do that will include some kind of understanding of wtf conformal field theory has to do with critical points

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Replying to

and

i get where the translations come from but where do the rotations come from?

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

)

@QiaochuYuan

Sep 20, 2020

you mean where do they come from in the limit? the limiting distribution (after appropriate scaling) is a gaussian with density something like exp(-x^2 -y^2) and that exponent is what i’m pointing at

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