3 ms·
> everything was happening in lower dimensional manifolds curving through that space where “all the action was.” I feel like this would have to be true in a ve
by melissalobos 5y ago
> everything was happening in lower dimensional manifolds curving through that space where “all 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.
- Jeff_Brown 5y ago> an infinite dimensional orange is all skin Huh?
- jerf 5y agoAs 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 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.
- mark_l_watson 5y agoSort of like the manifold hypothesis in deep learning.