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A comment on Geometry from Another Universe. Parent comment

Re:Geometry from Another Universe by melissalobos on Thursday January 20, 2022 @10:37AM (#30010169)
> everything was happening in lower dimensional manifolds curving through that space where β€œall the action was.”

I feel like this would have to be true in a very high dimensional space, since an infinite dimensional orange is all skin.

> systems obeyed solid state physics type laws: stars formed an outer lattice and planets in small lattices around stars.

This sounds really fun, could you try explaining a bit more about it?

Thanks for sharing.

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Re:Geometry from Another Universe by mark_l_watson on Thursday January 20, 2022 @12:32PM (#30011936)
Sort of like the manifold hypothesis in deep learning.
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Re:Geometry from Another Universe by Jeff_Brown on Thursday January 20, 2022 @11:08AM (#30010696)
> an infinite dimensional orange is all skin

Huh?

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Re:Geometry from Another Universe by jerf on Thursday January 20, 2022 @01:55PM (#30013004)
As you increase the dimensionality of a sphere, an ever-increasing proportion of the sphere is within epsilon of the surface.

This 3Blue1Brown video addresses enough related stuff that the rest should become reasonably comprehensible: https://www.youtube.com/watch?v=zwAD6dRSVyI This particular result is tossed in as a side note around 23:25, so it's not addressed directly, but it'll help.

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