  Fields in spacetime could be simultaneously discrete and continuous, in the
same way that information can: it has been shown that the amplitudes,
\phi(x_n), that a field takes at a generic discrete set of points, x_n, can be
sufficient to reconstruct the field \phi(x) for all x, namely if there exists a
certain type of natural ultraviolet (UV) cutoff in nature, and if the average
spacing of the sample points is at the UV cutoff scale. Here, we generalize
this information-theoretic framework to spacetimes themselves. We show that
samples taken at a generic discrete set of points of a Euclidean-signature
spacetime can allow one to reconstruct the shape of that spacetime everywhere,
down to the cutoff scale. The resulting methods could be useful in various
approaches to quantum gravity.
