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248 points nabla9 | 1 comments | 13 Oct 24 21:09 UTC | HN request time: 0.214s | source

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brazzy ◴[14 Oct 24 12:29 UTC] No.41836884[source]▶

> The volume of the unit -sphere goes to 0 as grows! A high dimensional unit sphere encloses almost no volume! The volume increases from dimensions one to five, but begins decreasing rapidly toward 0 after dimension six.

What the absolute fuck?

That one caught me truly off guard. I don't think "counterintuitive" is a strong enough word.

replies(1): >>41943758 #

1. Anotheroneagain ◴[25 Oct 24 09:57 UTC] No.41943758[source]▶

>>41836884 #

I don't think this is actually true - the actual volume of the sphere grows, but the volume of one grows even faster.

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Counterintuitive Properties of High Dimensional Space (2018)