http://users.ox.ac.uk/~tweb/00001/
Roger Penrose: "I had, for a good many years earlier, been of the
opinion that the SPACE-TIME CONTINUUM picture of reality would prove
inadequate on some small scale."

http://www.perimeterinstitute.ca/pdf...09145525ca.pdf
Albert Einstein: "I consider it entirely possible that physics cannot
be based upon the field concept, that is on CONTINUOUS structures.
Then nothing will remain of my whole castle in the air, including the
theory of gravitation, but also nothing of the rest of contemporary
physics."


Just in order to answer in a scientific way :
Look at the page 574 he
http://www.alainconnes.org/docs/book94bigpdf.pdf

That describes a model in which the space is not continuous, and which
embed, however, the Einstein's gravitation.

More generally, look at page 196 he
http://www.alainconnes.org/docs/bookwebfinal.pdf

Of course, non commutative gegometry is only one way out of 10.000 to
extend general relativity using non-continuous spaces. An other is
quantum loop gravity :
http://xxx.lanl.gov/abs/gr-qc/9905087v1

What you point out is only the fact that Einstein has not the
mathematical tools to express his theory in a non-continuous space-
time. Now we have.

Does it answer you concern ?

Good afternoon
Laurent