beautiful movies! I have heard that making the units of string repel each other, while keeping the arc length constant, seems to be a good heuristic for unknotting unknots. However, since telling whether a knot is an unknot or not is believed to be computationally hard (even showing it's in NP is pretty challenging) such a heuristic shouldn't work in all cases --- there should exist knots where it gets stuck. A similar issue arises in numerical general relativity: it shouldn't be easy to tell whether two 4-manifolds are equivalent (it's undecidable because of the word problem!) but there are no known examples where numerical algorithms that try to tell whether a 4-manifold is just a sphere get stuck for a long time. Does anyone know of references on either of these? Cris On Dec 30, 2013, at 1:58 PM, Warren D Smith <warren.wds@gmail.com> wrote:
I've posted before about knots are really machines and should be analysed as such. This idea turns out not to be new. Here is a paper
http://arxiv.org/abs/1002.1723
with computer simulations of knots trying to find the "tightest" form of each knot type. You can see movies of the tightening process for many knots & links here:
http://www.jasoncantarella.com/movs/
Many questions suggest themselves...
-- Warren D. Smith http://RangeVoting.org
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun