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247 points nabla9 | 3 comments | 13 Oct 24 21:09 UTC | HN request time: 0.596s | source

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bmitc ◴[14 Oct 24 00:42 UTC] No.41833078[source]▶

Actually, the most counterintuitive is 4-dimensional space. It is rather mathematically unique, often exhibiting properties no other dimension does.

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1. dullcrisp ◴[14 Oct 24 01:34 UTC] No.41833385[source]▶

>>41833078 #

Well I’m sure 2- and 3- dimensional space are also mathematically unique and interesting by the same token, but they’re nearer to our experience and intuition.

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2. ngruhn ◴[14 Oct 24 07:56 UTC] No.41835256[source]▶

>>41833385 (TP) #

I‘ve heard that knots only exist in 3 dimensions. In 2D you can’t entangle anything and in 4D+ you can always untangle everything.

replies(1): >>41837953 #

3. madcaptenor ◴[14 Oct 24 14:37 UTC] No.41837953[source]▶

>>41835256 #

It's been a while since I studied any topology, but if I'm remembering correctly you can knot an (n-2)-dimensional surface in n-dimensions.

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Counterintuitive Properties of High Dimensional Space (2018)