Science Lounge

[stankeylegjones]

Mathematicians Just Found a Hidden 'Reset Button' That Can Undo Any Rotation

A simple scaling trick can rewind even the most tangled motion back to its start.

www.zmescience.com

This is pretty neat. I haven't had chance to read the paper yet, but planning to do so.

 

[Ddseddse]

This is pretty neat. I haven't had chance to read the paper yet, but planning to do so.

Yeah. To the extent I understand it (not really all that much), it sounds ingenious. A factor exists that if you scale the preceding steps by it and repeat them twice you end up where you were before you started the preceding steps. Crazy.

Reminds me a bit (not really) of the old brain teaser: you travel a mile south, a mile west, and a mile north, and you arrive back at the same location, where on the earth might you be? (no just a singe solution, multiple locations are possible).

 

[stankeylegjones]

Yeah. To the extent I understand it (not really all that much), it sounds ingenious. A factor exists that if you scale the preceding steps by it and repeat them twice you end up where you were before you started the preceding steps. Crazy.

Reminds me a bit (not really) of the old brain teaser: you travel a mile south, a mile west, and a mile north, and you arrive back at the same location, where on the earth might you be? (no just a singe solution, multiple locations are possible).

Yes. They take a loop in SO(3), lift it to a path in SU(2). They then scale it by 1/2 and concatenate it with itself, giving a loop in SU(2). Since \pi_1(SU(2)) is trivial, when projected back down you get a contractible loop. Very cool!