In the answer to Explanation for this event on a high-dimensional dataset it is stated that: "almost all the surface area of a sphere in d -dimensional Euclidean space Ed is concentrated around its equator." and it is supposed that the equator is relative to an arbitrary point on the sphere.
What if a different random point on the sphere is now selected as the "north pole"? My understanding is that a new equator is now defined where the volume of the ball is concentrated.
This seems to create a paradox: how can it be that the ball's volume is concentrated on two different equators simultaneously? Or is it alternatively that the selection of an arbitrary "north pole" subjectively creates the corresponding concentration at the equator?