Branching polymers, knot theory and Cantorian spacetime

Within the framework of classical statistical mechanics, we draw some nontrivial connections and analogies between the Bethe model and quantum physics in Cantorian spacetime as well as between knot theory, noncommutative geometry, four manifolds, quasicrystals and . In particular, we show that and space, although formally infinite-dimensional and appearing to be so, effectively have a finite Hausdorff dimension, d=4+φ3, where φ3=[(√5−1)2]3 which is a PV number with the continuous fracture representation .