Counterintuitive Properties of High Dimensional Space
A simple observation that makes these properties a bit less counterintuitive is that the diameter of an n-dimensional unit cube (Euclidian distance between two opposite corners) is √n while the diameter of a unit sphere is always 1. So as the number of dimensions grows, the diameter of the unit cube can become arbitrarily large and the corners of the unit cube move further and further away from the unit sphere.