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This reminds me of the well-known counterintuitive result that in high dimensions, most of the weight of a distribution is in the tails rather than towards the center. Possibly related I think.
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That particular point is so simple it may be hard to dig up a citation (assume unit vectors uniformly distributed, rotate so that one is (1,0,0,0...), what's the average squared value of a single coordinate of the other?).
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