  We discuss the extent to which numerical techniques for computing
approximations to Ricci-flat metrics can be used to investigate hierarchies of
curvature scales on Calabi-Yau manifolds. Control of such hierarchies is
integral to the validity of curvature expansions in string effective theories.
Nevertheless, for seemingly generic points in moduli space it can be difficult
to analytically determine if there might be a highly curved region localized
somewhere on the Calabi-Yau manifold. We show that numerical techniques are
rather efficient at deciding this issue.
