Interesting argument. Is it fair to summarise it as: (a) Mathematics models the deterministic and random aspects of reality; (b) Mathematics reduces to computat

Interesting argument. Is it fair to summarise it as: (a) Mathematics models the deterministic and random aspects of reality; (b) Mathematics reduces to computation; (c) Church-Turing says that all computation is equivalent; (d) Therefore a Turing machine[2] can fully model reality. "When you get deep enough, mathematics is in fact reducible to computation (paging Robert Harper)." Could you elaborate on that, as it seems to be a big jump? I'm not familiar with Harper's work (I'm assuming you mean this [1] Robert Harper). I'm also not a mathematician... [1] http://en.wikipedia.org/wiki/Robert_Harper_(computer_scientist) http://en.wikipedia.org/wiki/Robert_Harper_(computer_scienti... [2] Or, presumably, Lambda calculus or Godelian recursion.