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What do numbers look like?

johnhw.github.io

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Re: What do numbers look like?

#11

Post by O_H_E »

Jtsummers wrote: post #3
qwertyuiop_ wrote: post #2

Can someone explain to me like I am 5 ?

Convert numbers to a vector space represented by their prime factors: 2 => [1 0 0 0...] 3 => [0 1 0 0...] 4 => [1 0 0 0...] And map that high dimensional space back down to two dimensions (using some technique I haven't dug into yet). Colors are assigned by some scheme, later images help to illustrate how the particular clusterings happen like one where primes are rendered in white.

ahem .... explain like I am 0.5

Re: What do numbers look like?

#15

Post by krick »

I don't get it. So, do all these clusters mean anything at all? It feels like that should be telling us something eerily important about numbers. Granted, I don't really understand UMAP, but still, if it's any good for dimensionality reduction at all (and it appears to be), then clusters are clusters. This seems to have way too distinct structure to be essentially just a weird artifact of UMAP itself. Or is it?

Re: What do numbers look like?

#16

Post by quakeguy »

tunnuz wrote: post #9

This is one of the most beautiful things I have seen in 2022 on the Internet, and there were some very good contenders. This provokes in me an immediate sense of beauty, and I'm compelled to read and understand as much of it as I can. Thanks for sharing this, I'm fascinated and amazed.

Sadly merely artifacts .

Re: What do numbers look like?

#19

Post by glotchimo »

quakeguy wrote: post #16
tunnuz wrote: post #9

This is one of the most beautiful things I have seen in 2022 on the Internet, and there were some very good contenders. This provokes in me an immediate sense of beauty, and I'm compelled to read and understand as much of it as I can. Thanks for sharing this, I'm fascinated and amazed.

Sadly merely artifacts .

Can’t those artifacts be beautiful in and of themselves? Whether or not this represents some deep reality about dimensions, it’s cool to see something like this emerge from a program when working with a bunch of numbers.
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