  We argue that the torus partition sum in $2d$ (super) gravity, which counts
physical states in the theory, is a decreasing function of the renormalization
group scale. As an application we chart the space of $(\hat c\leq1)$ $c\leq1$
models coupled to (super) gravity, confirming and extending ideas due to A.
Zamolodchikov, and discuss briefly string theory, where our results imply that
the number of degrees of freedom decreases with time.
