A related point from geometry is that high-dimensional spheres are "spiky". (https://news.ycombinator.com/item?id=3995615)

E.g. if you have a set of things which vary in many dimensions (even if each element is no more than a set "distance" from normality), very few elements will belong in the "centre" (normal on all dimensions) and most will belong on a spike (wildly extreme in 1 or 2 dimensions).