Quantum-Geometrical Space (on the nature of space)
Let me say at the outset that I am not happy with this state of affairs in physical theory. The mathematical continuum has always seemed to me to contain many features which are really very foreign to physics. […] If one is to accept the physical reality of the continuum, then one must accept that there are as many points in a volume of diameter 10^13 cm or 10^33 cm or 10^1000 cm as there are in the entire universe. Indeed, one must accept the existence of more points than there are rational numbers between any two points in space no matter how close together they may be. (And we have seen that quantum theory cannot really eliminate this problem, since it brings in its own complex continuum.)
Roger Penrose, On the Nature of Quantum-Geometry
Quantum-Geometrical Space (the nature of space)The above section of Introduction to Quantum-Geometry Dynamics can be downloaded here. Or click here for the entire book.