knot #4d #math #dimensions

It's time for a dimension check. This knot I just tied tells me that I'm in 3D space, because it wouldn't be possible to tie this knot anywhere else. In 2D space, a line can't cross over itself, and nothing can be above or below other things, so knots can't be tied. And in 40 space, this knot would just fall out. The rope could move in the fourth dimension, avoiding this intersection entirely, and always slipping undone. In 40 space, though, instead of using string, we could tie knots in flat planes. 40 braids wouldn't be strands of hair, but planes of hair. Though the knotted planes would still fall out in 5D space.