# 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] https://www.phasespacecomputing.com/ 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.