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Counterintuitive Properties of High Dimensional Space (2018)
(people.eecs.berkeley.edu)
247 points
nabla9
| 2 comments |
13 Oct 24 21:09 UTC
|
HN request time: 0.423s
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bmitc
◴[
14 Oct 24 00:42 UTC
]
No.
41833078
[source]
▶
>>41831617 (OP)
#
Actually, the most counterintuitive is 4-dimensional space. It is rather mathematically unique, often exhibiting properties no other dimension does.
replies(3):
>>41833147
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>>41833346
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>>41833385
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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.
replies(1):
>>41835256
#
1.
ngruhn
◴[
14 Oct 24 07:56 UTC
]
No.
41835256
[source]
▶
>>41833385
#
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
#
ID:
GO
2.
madcaptenor
◴[
14 Oct 24 14:37 UTC
]
No.
41837953
[source]
▶
>>41835256 (TP)
#
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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