4 ms·
I believe it's because in high dimensions, most of the "volume" is near the center, whereas in low dimensions, most of the volume is near the surface.
by Zaak 16y ago
I believe it's because in high dimensions, most of the "volume" is near the center, whereas in low dimensions, most of the volume is near the surface.
- cperciva 16y agoNot at all. The expected distance between the center of an n-ball and a random point in the ball is n/(n+1) times the radius. Now, if you look at an n-sphere with respect to orthogonal axes, you find that moving along an axis you get out as far as (1, 0, ... 0) and moving "away" from the axes you only get to (1/sqrt(n), 1/sqrt(n), ... 1/sqrt(n)); but this isn't due to the sphere being spiky -- rather, it's because orthogonal axes are spiky.