In 3D space, a sphere can touch 12 other identical spheres without overlapping. In 24-dimensional space, this number is 196,560 (!)

For noisy neural codes, this means there are a LOT of distinguishable directions you could point a vector

https://www.quantamagazine.org/mathematicians-discover-new-way-for-spheres-to-kiss-20250115/

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