I won't dispute the main point of the article but a couple minor errors bug me. First, he kept referring to a Gaussian distribution as being the unit sphere, when of course the radius depends upon the parameters of the Gaussian (the standard deviation). If not, then it wouldn't be invariant under which units you chose. A bizarre mistake to repeat many times throughout the article.
Less importantly, the last paragraph says that the probability that two samples are orthogonal is "very high". Being precisely orthogonal is technically a probability zero event. There author means "very close to orthogonal."
There was a good discussion about this problem in the context of Monte Carlo simulations in (1).