>Whether knots are the key to physics, I can't say. Certainly there
>are suggestive notions that particles might be some kind of knots in
>spacetime (of some dimensionality)...
Interesting! Chromosomes make knots, also.
But my reading of Louis Kauffman, a great enthusiast and a great pedagogue,
makes me believe that knots could be much more:
-Knots could be "type" of multiverse! (multi-histories "skeleton").
Much more:
-Invariant of knots could be quantum statistical abstract physical theories!
As you know perhaps I get a proof that with the comp hyp, the mind-body problem
is partially reduced into a derivation of physics from machine's psychology:
poetically: physical realities is a web of infinite machine dreams(*).
Machine's psychology can be approximated (at least) by the many possible
intensionnal (modal) variant of the Godel Lob logic of Self-reference
(restricted to the \Sigma_1 arithmetical sentences (= genuily accessible
by the Universal Dovetailer when true)).
This gives the Z logics. Normaly the Z logics should give ... a skeleton
of physical theories. Knots will perhaps provide the missing link.
Knots would give a shortcut between comp psychology and
quantum physics (or quantum psychology?).
Toposes and monoidal/braided categories are most probably
important part of the big drama in the middle term run.
Aaaaaaaah... knots are so cute, also :-)
(I'm afraid I am not vaccinated against the mathematical sirens, perhaps)
-Bruno
(*) IN case you are interested, here are relevant links to a step by step
version of the basic uda proof (conversation with Joel Dobrzelewski):