3 ms·
A sphere of course have sum of the squares of all points equal to one. So in high dimensions, it’s clear that most points have to be close to 0. Hence the “spik
by petters 2y ago
A sphere of course have sum of the squares of all points equal to one. So in high dimensions, it’s clear that most points have to be close to 0. Hence the “spikes”
Boxes are more intuitive
- figure8 2y agoYes. I appreciate the article because it gets people to think about high dimensional geometry. But I think the right takeaway is that in high dimensions, cubes have huge volume compared to the enclosed sphere. So the sphere is not spikey at all. Instead realize that the diagonals and volume of the cube get very large compared to the sphere.
- zardo 2y agoThe 'spikes' depend on an arbitrary choice of coordinate system.
- petters 2y agoYes, that is true