  Recent computations of scattering amplitudes show that N=8 supergravity is
surprisingly well behaved in the ultraviolet and may even be ultraviolet finite
in perturbation theory. The novel cancellations necessary for ultraviolet
finiteness first appear at one loop in the guise of the "no-triangle
hypothesis". We study one-loop amplitudes in pure Einstein gravity and point
out the existence of cancellations similar to those found previously in N=8
supergravity. These cancellations go beyond those found in the one-loop
effective action. Using unitarity, this suggests that generic theories of
quantum gravity based on the Einstein-Hilbert action may be better behaved in
the ultraviolet at higher loops than suggested by naive power counting, though
without additional (supersymmetric) cancellations they diverge. We comment on
future studies that should be performed to support this proposal.
