On Penrose view of transfinite sets and computability and the fractal character of E-infinity spacetime

The Penrose view of transfinite sets, fractal character of E-infinity spacetime and the Cantor space of descriptive set theory were discussed. It was found that the P-Adic form of the electromagnetic fine structure constant taken to be the prime umber 137 was equal to the coupling constant of a Planck mass. The Cantorian spacetime was not distinguished from the flat four dimensional space of quantum and classical mechanics at low resolution. Analysis shows that the transfinite fine structure appears only when the resolution is increased at very small distances.