Check out what i found...

I was trying to work out what the dickens one of the boasts in Khovanov's paper was about

...the Penrose-Kauffman q-spin networks calculus, of which the Jones polynomial is a special instance...

and I stumbled on this: it's supposedly a classic paper on the topic and it's pretty accessible- in fact it's the paper Penrose uses to give the very first formulation.

It's kinda cool, the idea is to think of a system of particles as linked bundles of undefined angular momentum, which quantum physics says is either 'up' or 'down', together forming a larger angular momentum (also undefined). Then we ask exactly how undefined its angular momentum actually is...

The answer, it turns out, blends graph theory, quantum physics, probability and geometry. Looks like a cool Dg on the brew...

Still haven't got the foggiest how to get the jones polynomial out though.