  We review lessons from the AdS/CFT correspondence that indicate that the
emergence of locality in quantum gravity is contingent on considering
observables with a small number of insertions. Correlation functions where the
number of insertions scales with a power of the central charge of the CFT are
sensitive to nonlocal effects in the bulk theory, which arise from a
combination of the effects of the bulk Gauss law and a breakdown of
perturbation theory. To examine whether a similar effect occurs in flat space,
we consider the scattering of massless particles in the bosonic string and the
superstring in the limit where the number of external particles, n, becomes
very large. We use estimates of the volume of the Weil-Petersson moduli space
of punctured Riemann surfaces to argue that string amplitudes grow factorially
in this limit. We verify this factorial behaviour through an extensive
numerical analysis of string amplitudes at large n. Our numerical calculations
rely on the observation that, in the large n limit, the string scattering
amplitude localizes on the Gross-Mende saddle points, even though individual
particle energies are small. This factorial growth implies the breakdown of
string perturbation theory for $n \sim (M_{pl}/E)^{d-2}$ in d dimensions where
E is the typical individual particle energy. We explore the implications of
this breakdown for the black hole information paradox. We show that the loss of
locality suggested by this breakdown is precisely sufficient to resolve the
cloning and strong subadditivity paradoxes.
