Under what physical scenarios do the properties of high-dimensional spheres come in handy? If physics is 3 or 4-dimensional, when does one need to interest oneself in spheres of dimensionality higher than 4 and how is this useful? Does it happen when the underlying reality involves higher dimensions as in string theory, or in phase or parameter spaces that may have very high dimensions?
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Beyond string theory, I think wikipedia is correct when it says "All classical statistical physics is based on the concentration of measure", which follows from the "all mass is near the equator" property of very high dimensional spheres. – David Bailey Oct 21 '22 at 22:52