  In any quantum theory of gravity we do expect corrections to Einstein gravity
to occur. Yet, at fundamental level, it is not apparent what the most relevant
corrections are. We argue that the generic curvature square corrections present
in lower dimensional actions of various compactified string theories provide a
natural passage between the classical and quantum realms of gravity. The
Gauss-Bonnet and $({\rm Riemann})^2$ gravities, in particular, provide concrete
examples in which inconsistency of a theory, such as, a violation of
microcausality, and a classical limit on black hole entropy are correlated. In
such theories the ratio of the shear viscosity to the entropy density,
$\eta/s$, can be smaller than for a boundary conformal field theory with
Einstein gravity dual. This result is interesting from the viewpoint that the
nuclear matter or quark-gluon plasma produced (such as at RHIC) under extreme
densities and temperatures may violate the conjectured bound $\eta/s\ge
1/4\pi$, {\it albeit} marginally so.
