Trippy Trees

Tony Smith, who likes octonions and Clifford algebras a lot, has a nice page on the surreal numbers. The further one moves up the tree, the more rational numbers one gets!

We've also seen trees in phylogenetics and knot theory, but most importantly in Batanin's operads. Recall that 1-level trees represented the Stasheff associahedra. These turn up everywhere, such as in tiling the real moduli M(0,n) of genus zero surfaces.