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.
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