  Peculiar phenomena appear in the discretization of a system invariant under
reparametrization. The structure of the continuum limit is markedly different
from the usual one, as in lattice QCD. First, the continuum limit does not
require tuning a parameter in the action to a critical value. Rather, there is
a regime where the system approaches a sort of asymptotic topological
invariance ("Ditt-invariance"). Second, in this regime the expansion in the
number of discretization points provides a good approximation to the transition
amplitudes. These phenomena are relevant for understanding the continuum limit
of quantum gravity. I illustrate them here in the context of a simple system.
