Get the latest tech news
Counterintuitive Properties of High Dimensional Space (2018)
Marc Khoury Our geometric intuition developed in our three-dimensional world often fails us in higher dimensions. Many properties of even simple objects, such as higher dimensional analogs of cubes and spheres, are very counterintuitive.
Given the rather unexpected properties of high dimensional cubes and spheres, I hope that you'll agree that the following are somewhat more accurate pictorial representations. Figure 9: As the dimension increases the width of the band necessary to capture 99% of the surface area decreases rapidly. Nearly all of the surface area of a high dimensional sphere lies near the equator.To provide some intuition consider the situation in two dimensions, as shown in Figure 10.
Or read this on Hacker News