That is disturbing, isn't it? I still think what I said is true. If you pick any unit vector in N-space as a reference, my intuition is that the dot product of a second, randomly chosen unit vector with the reference vector will follow a distribution more and more tightly centered on 0 as N increases. If this is true, then as Dan points out, for a large enough N, even if you pick a bunch of k different reference vectors, the random vector will tend to be near 90 degrees away from *all* of them. It may be that N has to increase dramatically to accommodate small increases in k, though. I don't think there is a logical contradiction here. Or my intuition may be completely misguided. On Thu, May 31, 2018 at 1:12 AM, Dan Asimov <dasimov@earthlink.net> wrote:
Trouble is, there are so many equators ...
—Dan
----- ... almost all the hypervolume is near the equator. -----
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