  In perturbative QED, the approximation is improved by summing more Feynman
graphs; in non-perturbative QCD, by refining the lattice. Here we observe that
in quantum gravity the two procedures may well be the same. We outline the
combinatorial structure of spinfoam quantum gravity, define the continuum
limit, and show that under general conditions refining foams is the same as
summing over them. The conditions bear on the cylindrical consistency of the
spinfoam amplitudes and on the presence of appropriate combinatorial factors,
related to the implementation of diffeomorphisms invariance. Intuitively, the
sites of the lattice are points of space: these are themselves quanta of the
gravitational field, and thus a lattice discretization is also a Feynman
history of quanta.
