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 B and quantum physics in Cantorian spacetime E-(infinity) as well as between knot theory, noncommutative geometry, four manifolds, quasicrystals and E-(infinity). In particular, we show that E-(infinity) and B space, although formally infinite-dimensional acid appearing to be so, effectively have a finite Hausdorff dimension, d = 4 + phi(3), where phi(3) = [(root 5 - I)2](3) which is a PV number with the continuous fracture representation [d] = ((4) over bar)(-1). (C) 1999 Elsevier Science Ltd. All rights reserved.