In article <76r4a6$nlr$1...@pravda.ucr.edu>, ba...@galaxy.ucr.edu (john baez) wrote: >Don't get mixed up by the difference between topology and geometry. Alas, >it's probably hopeless discussing this without me actually looking at that >stocking. Some things just don't work well in writing. If you tried to >explain *in writing* how you tie your shoelaces, for me to understand it >would be a major intellectual feat, worthy of an Einstein. It's probably >best to save both our brain cells for something a bit more useful.
Speaking about tying your shoelaces, I and some friend was able to develop an interestiong thoery why some tie good knots and other don't. Perhaps some physicist can give the full theoretical explanation:
If one carefully pulls in the shoelace loops of the tied shoelace knots out so that the result is a knot (instead of untying the shoelaces), then there are two variations that can occur, the reef-knot and the granny's knot. The former shoelace knot will hold well, but the other will not.
So here is an explanation why every second ties a good shoelace knot and every second generation ties bad one: When mom teaches the child to tie the knot, she stands in front of the child; the child first ties the simple crossing of laces, but when mom shows the child doing the complicated shoelace knot loops, the child is taught the mirror reversed variation. So every second generation it switches between a reef-knot and a granny's knot.
>(By the way, I've read that Einstein didn't wear socks, and he once >painted his toes black to camouflage some holes in his shoes. The man >was obviously a genius. But I digress....)
I have not tried this; it probably generalizes to covering up holes in socks as well. But a mathematican would probably prefer to use cohomology theory. (As in an earlier article in this thread, where cohomology was likened with studying the behavior around holes, and socks with holes were likened topological surfaces with holes.)