As a demonstration of the non-intuitiveness of measures in high dimensions, I think this is still a decent example, no? I agree that n=5 [sic on my part above]

As a demonstration of the non-intuitiveness of measures in high dimensions, I think this is still a decent example, no? I agree that n=5 [sic on my part above] isn't special, but seeing the Gamma function should be cause enough for worrying your intuition. It might be misleading, but I'd hope that it wouldn't beg the question of what's special about n=5, but instead what's wrong with your views about high dimensional space. I agree with the comments on MathOverflow though.