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RE: Hyperspheres - What are They? How does one visualize them?
Do you mind providing more information about those 'truths' in 8 and 24 dimensions? I am a bit curious here :)
PS: I can't watch the video at the moment.
Well, the sphere packing arrangements are not known for any other dimensions up from 3, except 8 and 24. You can find much more information about this in the following article: https://www.quantamagazine.org/sphere-packing-solved-in-higher-dimensions-20160330
The following excerpt from the article gives some further insight:
"Finding the best packing of equal-sized spheres in a high-dimensional space should be even more complicated than the three-dimensional case Hales solved, since each added dimension means more possible packings to consider. Yet mathematicians have long known that two dimensions are special: In dimensions eight and 24, there exist dazzlingly symmetric sphere packings called E8 and the Leech lattice, respectively, that pack spheres better than the best candidates known to mathematicians in other dimensions."
I got the main ideas. Thanks for providing the information, the link, and indirectly the references in the link.
Symmetries as always :)