Trails and Triality
On his octonion webpages John Baez discusses triality, namely non-degenerate triple maps t(u,v,w) into the reals. These are closely associated with the division algebras. When the triple takes the form (vector, L spinor, R spinor), each of which is acted upon by Spin(8), triality takes on a physical significance. The Dynkin diagram for Spin(8) looks like a trivalent vertex (4 nodes). In M-theory one also considers open and closed string vertices.
Many people seem to think I've gone completely crazy. Cool! Something happening. Make sure to look out for Carl Brannen's upcoming paper on the derivation of the lepton masses! And remember: what can be said in a line is not always trivial.