Morning thought: 2x2 diagrams work so well because a random pair of vectors in a high dimensional space are orthogonal with probability ~1
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okay this was intriguing enough I had to check it out. Kinda checks out. The dot product of 2 random 10,000 element unit vectors has a mean peak at zero and the whole distribution pretty tight around zero.
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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 narrowing
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
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