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Mathematicians discover new way for spheres to 'kiss'

(www.quantamagazine.org)
161 points isaacfrond | 2 comments | 16 Jan 25 09:57 UTC | HN request time: 0.456s | 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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davethedevguy ◴[16 Jan 25 11:54 UTC] No.42724129[source]▶
Likewise!

In higher dimensions, are the spheres just a visual metaphor based on the 3-dimensional problem, or are mathematicians really visualising spheres with physical space between them?

Is that even a valid question, or does it just betray my inability to perceive higher dimensions?

This is fascinating and I'm in awe of the people that do this work.

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bux93 ◴[16 Jan 25 11:59 UTC] No.42724167[source]▶
I have a hard time visualizing even 3 dimension, but 4 dimensions and up, I just think of it as a spreadsheet where each thing has 4 or more columns of data rather than 3. Whether a 4th column is time, spin, color, smell or yet another coordinate.
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1. nejsjsjsbsb ◴[16 Jan 25 12:22 UTC] No.42724307[source]▶
It sort of like the visualizable 3D "kissing spheres" is the story that makes it interesting, captivating and accessible and therefore competitive/social which makes it interesting even more, but basically at higher dims it's a bunch of equations as it is impossible to visualise on human wetware.

You could do kissing starfish but no one cares as there is no lore. A bit like 125m world record doesn't matter. 100m is the thing.

This is not a knock ... it is interesting how social / tradition based maths is.

Another example is Fermat's Last Theorem. It had legendary status.

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2. ndsipa_pomu ◴[16 Jan 25 12:26 UTC] No.42724335[source]▶
However, the use of spheres means that it is applicable to error correcting codes, whereas "kissing starfish" wouldn't be useful.