3 ms·
You got it backwards. His use of knots is a bit more complex than our current mathematics of knots can explain, if we talk about knots in the 3D space. In fact
by Shorel 4y ago
You got it backwards. His use of knots is a bit more complex than our current mathematics of knots can explain, if we talk about knots in the 3D space.
In fact, we don't have a predictive model of knots that can in the general case say if one knot has better tensile properties than the other knot.
Is this a critique of knot theory? Far from it. It is an open question, an invitation to do new theories, which can only be answered with exploration.
- kazinator 4y agoIf we talk about the engineering properties of real knots in 3D space, then that is something entirely different from the topology of ideal knots, which has to do with enumerating the unique ways in which they loop around an intersect themselves. Those properties don't change even if the knot is left entirely loose, so that the string never touches itself. Is it true that current mathematics cannot explain what's going on in a 3D knot in space? Even if a closed equation couldn't solve it symbolically, surely we must have have clever people who can build a finite element model of it and do it numerically.