M Theory Lesson 26
We can therefore think of these knot crossings as being embedded in a canonical manner in the real moduli space. That is, one crossing for each generation of the particle zoo. The trefoil knot traces out a loop through these idempotents. The non-planarity of knots is thus associated with the non-planarity of complexification in the tiling of moduli.
But we need to get to quaternions and octonions before all this makes sense. Just remember that the numbers don't get put in by hand. They always come from diagrams. Bar-Natan points out that integers can come from Khovanov morphisms for empty links.