Consider a high-dimensional Gaussian probability distribution with unit variances and zero covariances. Most of the probability mass is concentrated in thin shell a considerable distance from the mean, and not concentrated a short distance around the mean. This counterintuitive result, the curse of dimensionality, is explored in the exercises of the first chapter of Bishop's "Neural Networks" textbook. Intuitively, there is a lot more space further away (from the mean point) in high dimensions.
The characteristics of a person, with many characteristics, might be a high-dimensional Gaussian (let's hope the nonzero covariances don't matter) bell curve. If so, the above result predicts very few people with characteristics all of which lie close to the mean. Most people are freaks.
"Why can't I ever just meet a normal person?"
HT : Brit (whose experience was the opposite, meeting so many people who are stuck in a rut of boring normalness)
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