I just skimmed through a rebuttal of Penrose's argument, and I thought that I should bring to attention a novel and simple way of reaching non-computable states with computer networks. Therefore, not all real numbers are computable.
Lets call the ratio of the clock speeds R, which is a real number.
Suppose R is in fact one of these uncomputable numbers. Then these two computers can compute things that are traditionally non-computable. The two clocks running the computers are some sort of physical process. If one does not believe this, one must show that in nature, somehow only computable reals occur. Naively, it would seem that one doesn't, and one can't.