Morning thought: 2x2 diagrams work so well because a random pair of vectors in a high dimensional space are orthogonal with probability ~1 @vgr
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Proof by example
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to make it clearer, 4 runs at increasing dim with histograms plotted on fixed x axis ranges to show the progressive narrowingpic.twitter.com/adDiDdN22K
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Another random high dimensional probabilistic observation – the limit as n -> inf of the location of a random infinitesimal chunk of mass in a homogeneously dense n-dim sphere is on the sphere's surface
End of conversation
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This sounds like the classic curse of dimensionality, although that usually features points drawn from a multivariate Gaussian. I'm pretty it would give similar results, although I don't feel like running the experiment right now.
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not surprising
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