  Is there a number for every bit of spacetime, or is spacetime smooth like the
real line? The ultimate fate of a quantum theory of gravity might depend on it.
The troublesome infinities of quantum gravity can be cured by assuming that
spacetime comes in countable, discrete pieces which one could simulate on a
computer. But, perhaps there is another way? In this essay, we propose a
picture where scale is meaningless so that there can be no minimum length and,
hence, no fundamental discreteness. In this picture, Einstein's Special
Relativity, suitably modified to accommodate an expanding Universe, can be
reinterpreted as a theory where only the instantaneous shapes of configurations
count.

General Relativity and Quantum Cosmology