John D. Cook has a couple of blog posts about non-intuitiveness of high-dimension geometry [1][2] and this article [3] expands on the very observation that you

John D. Cook has a couple of blog posts about non-intuitiveness of high-dimension geometry [1][2] and this article [3] expands on the very observation that you described. Quote: "In his article “An Adventure in the Nth Dimension,” Brian Hayes explores how in high dimensions, balls have surprisingly little volume. As the dimension n increases, the volume of a ball of radius 1 increases until n = 5. Then for larger n the volume steadily decreases." [1] https://www.johndcook.com/blog/2017/07/13/concentration_of_measure/ https://www.johndcook.com/blog/2017/07/13/concentration_of_m... [2] https://www.johndcook.com/blog/2017/07/19/corners-stick-out-more-in-high-dimensions/ https://www.johndcook.com/blog/2017/07/19/corners-stick-out-... [3] https://www.johndcook.com/blog/2012/10/23/dimension-5-isnt-so-special/ https://www.johndcook.com/blog/2012/10/23/dimension-5-isnt-s...