  We discuss scaling relations in four dimensional simplicial quantum gravity.
Using numerical results obtained with a new algorithm called ``baby universe
surgery'' we study the critical region of the theory. The position of the phase
transition is given with high accuracy and some critical exponents are
measured. Their values prove that the transition is continuous. We discuss the
properties of two distinct phases of the theory. For large values of the bare
gravitational coupling constant the internal Hausdorff dimension is {\em two}
(the elongated phase), and the continuum theory is that of so called branched
polymers. For small values of the bare gravitational coupling constant the
internal Hausdorff dimension seems to be {\em infinite} (the crumpled phase).
We conjecture that this phase corresponds to a theory of topological gravity.
{\em At} the transition point the Hausdorff dimension might be finite and
larger than two. This transition point is a potential candidate for a
non-perturbative theory of quantum gravity.
