  The familiar theories of physics have the feature that the application of the
theory to make predictions in specific circumstances can be done by means of an
algorithm. We propose a more precise formulation of this feature --- one based
on the issue of whether or not the physically measurable numbers predicted by
the theory are computable in the mathematical sense. Applying this formulation
to one approach to a quantum theory of gravity, there are found indications
that there may exist no such algorithms in this case. Finally, we discuss the
issue of whether the existence of an algorithm to implement a theory should be
adopted as a criterion for acceptable physical theories.
