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A mathematical side note: I might be woefully ignorant but I thought it's not possible to make a Klein bottle in the real world...? This is not to belittle Sto
by chx 5y ago
A mathematical side note: I might be woefully ignorant but I thought it's not possible to make a Klein bottle in the real world...?
This is not to belittle Stoll's work, it might be a model or approximation... or I'm just missing something.
- cperciva 5y agoYou are correct. Stoll makes a projection of Klein bottles into 3-space which results in them being self-intersecting.
- CliffStoll 5y agoYep, exactly.
- onion2k 5y agoI might be woefully ignorant but I thought it's not possible to make a Klein bottle in the real world...? I think Cliff Stoll sells 3D models of Klein bottles rather than the impossible 4D version.
- fortran77 5y agoThe 4D version is not impossible in 4D space.
- taneq 5y agoNow you've got me wondering if it'd be possible to build a 4D klein bottle by animating a 3D shape.
- jcl 5y agoI imagine you could, and that it might not even be that exciting... Since a Klein bottle is just a cylinder with its ends glued together a particular way, I think one way to sweep out a Klein bottle through time would be to have a rubber band split into two, then have each band travel along a trajectory that brings them back together with the correct orientation. The self intersection is easily avoided by having one of the bands travel faster than the other.
- onion2k 5y agoThe self intersection is easily avoided by having one of the bands travel faster than the other. They'll still meet up again. It'll just take more revolutions to get there. That doesn't avoid it.
- sundarurfriend 5y agoAn experimental test for N-D space string theories then!