I love the counter-intuition of high-dimensional spaces, seems to be making the rounds on my feeds these days. One of the harder generalizations to develop int

I love the counter-intuition of high-dimensional spaces, seems to be making the rounds on my feeds these days. One of the harder generalizations to develop intuition for is the fact that the measure of a d-sphere tends to 0 as d approaches infinity, even though for all d = 0, 1, 2, 3 that our meager brains can visualize, the opposite is true! Geometry goes crazy.