Today’s insights

I was going to write about some new insights here. I posted a picture. Then later added more pictures, to which I need a quick URL in order to refer to them elsewhere. So the new insights never came. But I think I still know what they were. Maybe I’ll write about them another time.

1000 points uniformly distributed on the sphere using the Archimedes theorem method (z is uniform [-1, +1]
2 “t-slices” of a uniform random sample (x, y, z, t) from S^3
Empirical historgram, and theoretical density of, t
“t-slices” of a uniform random sample (x, y, z, t) from S^3. N = 100 000. Delta t = 0.01. Red, radius 0.3. Blue, radius 0.8.
Histogram of x-coordinate of sample of ca. 52000 uniformly distributed points in 3-ball. Theoretical density = parabola. Also drawn: density of x-coordinate of uniformly dist points on 3-sphere = semicircle.
(x, y, z) coordinates of sample of size 1000 of uniform random points (x, y, z, t) on the 3-sphere.
1000 (x,y,z) points from uniform random sample of points (x,y,z,t) on 3-sphere.

1 thought on “Today’s insights

  1. Richard Gill Post author

    Today I had a large number of quite stunning insights. Later I might fill in, above, what some of them were, and also how it came that they came so many all at once. For the moment the first insight of today is: emptyness. If you are a mathematician, you can think of the empty set.


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