@GabrielDuquette A manifold is a shape like a hollow sphere, mobius strip, klein bottle. Something you could sew together out of...
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Replying to @St_Rev
@GabrielDuquette ...pieces of fabric. (Or of space, or of 4-d space, or of 5-d space...) We often think of manifolds as sitting inside...1 reply 0 retweets 0 likes -
Replying to @St_Rev
@GabrielDuquette ("embedded in") higher-dimensional space, like how a beach ball sits in ordinary 3-d space and a Klein bottle...1 reply 0 retweets 0 likes -
Replying to @St_Rev
@GabrielDuquette ...*doesn't* fit in 3-d space (it's forced to intersect itself) but is OK in 4-d space. So you'd call a beach ball...1 reply 0 retweets 0 likes -
Replying to @St_Rev
@GabrielDuquette ...a 2d manifold (sewed together from patches of cloth) embedded in a 3d manifold (the universe).1 reply 0 retweets 0 likes -
Replying to @St_Rev
@GabrielDuquette You can extend this metaphor to 'clusters in thingspace' by thinking of a good compression device as scrunching up...1 reply 0 retweets 2 likes -
Replying to @St_Rev
@GabrielDuquette ...a complicated/high-dimensional space of possibilities into a lower-dimensional subspace (submanifold).1 reply 0 retweets 2 likes -
Replying to @St_Rev
@GabrielDuquette Here 'lowering the dimension' is a more or less literal metaphor for 'taking away variables/moving parts'.1 reply 0 retweets 1 like
@GabrielDuquette I have no fucking idea what the rest of that post is on about though.
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.