Quote in context
I myself have sketched an attempt along these lines that utilizes the rich notion of dimension, and there is probably no better place than here to sketch it. Specifically, I've developed a mathematical metaphor for the old chestnut "There are two kinds of people in the world: those who are very strange and those whom you don't know well." In other words, I'm suggesting that each of us is actually very strange and not a completely integrated personality, and there is a way in which higher dimensions can illustrate this.
[He goes on to calculate the percentage of an N-square that is more than 5% from both edges, e.g. for a line of length 10 inches "Consider the part within a half inch of aside of this square and call this border the extreme part of the square." The normal part is (10 - 2*0.5)^2 = 9^2 = 81 square inches. Taken as a percentage, one has for an N-dimensional square 0.9^N, and evidently this shrinks as N increases. Line: 90%; square: 81%; cube: 72.9%; hypercube: 65.61%; etc. "For one hundred dimensions, the interior or normal part shrinks to only 0.0027 percent of the total volum"
