Weird Things in High Dimensions

Some weird stuff happens in high-dimensions. Reference 1. High Dimensional Oranges Are Almost All Peel Consider an $n$-dimensional cube of side length 1 containing a smaller $n$-dimensional cube with side length $0.8$ (&ldquo;pulp&rdquo;) surrounded by a $0.1$-width border (&ldquo;peel&rdquo;). The volume of the pulp is $0.8^n$, which rapidly approaches 0 as $n$ increases: Dimensions Pulp Volume…