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Counterintuitive Properties of High Dimensional Space (2018)

(people.eecs.berkeley.edu)
247 points nabla9 | 1 comments | 13 Oct 24 21:09 UTC | HN request time: 0s | source
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remcob ◴[14 Oct 24 04:17 UTC] No.41834128[source]▶
The distance between two uniform random points on an n-sphere clusters around the equator. The article shows a histogram of the distribution in fig. 11. While it looks Gaussian, it is more closely related to the Beta distribution. I derived it in my notes, as (surprisingly) I could not find it easily in literature:

https://xn--2-umb.com/21/n-sphere

replies(2): >>41834590 #>>41834640 #
7fYZ7mJh3RNKNaG ◴[14 Oct 24 05:51 UTC] No.41834590[source]▶
beautiful visualizations, how did you make them?
replies(1): >>41834925 #
1. remcob ◴[14 Oct 24 06:57 UTC] No.41834925[source]▶
The first one IIRC with Geogebra, all the rest with Matplotlib. The design goal was to maximize on 'data-ink ratio'.