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161 points isaacfrond | 1 comments | 16 Jan 25 09:57 UTC | HN request time: 0.214s | source

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danwills ◴[16 Jan 25 11:34 UTC] No.42724002[source]▶

I'd really love to know what the mathematicians are actually doing when they work this stuff out? Is it all on computers now? Can they somehow visualize 24-dimensional-sphere-packings in their minds? Are they maybe rigorously checking results of a 'test function' that tells them they found a correct/optimal packing? I would love to know more about what the day-to-day work involved in this type of research actually would be!

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1. scythe ◴[16 Jan 25 12:10 UTC] No.42724238[source]▶

>>42724002 #

In many cases you are "translating" the higher-dimensional geometry into something that is not geometric or which is much lower dimensional. You don't generally visualize 24 dimensions. You can get a decent intuition for 4 with practice but at some point this breaks down.

For example, the 24-dimensional packing corresponds to the Leech lattice which itself corresponds to the Golay code:

https://en.wikipedia.org/wiki/Leech_lattice

https://en.wikipedia.org/wiki/Binary_Golay_code

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