if we lived in 4 spatial dimensions our cables would never get tangled. really makes you think
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wouldn’t they just get tangled worse...?
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they have more space to pass "through" each other. you can sort of visualize it by taking color to be a fourth dimension. you can move stuff in that dimension by changing its color and that lets you pass parts of cables "through" each other
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yea i get that, just as being able to move things through the 3rd dimension allows you to tidy up 2d messes by picking up objects "out" of the field and reinserting them elsewhere – but it also introduces a whole new kind of potential mess, no? in that same sense?
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i don't think so but i haven't thought about it super carefully. the point is that the "passing through" move i'm describing is totally "local"; you can do it whenever two cables are near each other and you only need to move each cable around a little bit
as opposed to untangling cables in 3d where you may need to make a "global" move of going all the way to one end of one of the cables
what does happen in 4d is that 2d shapes (surfaces) can get all tangled up in interesting ways tho
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so you get knots made out of cloth (bendy planes?) instead of cord? (bendy lines?)
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