Geometry both discrete and continuous at once, like information--Kempf It is possible for a geometry to be both discrete and continuous. We don't know if our universe's geometry is like that, but it could be. Video of a talk at Perimeter by Achim Kempf, describing this, was put online yesterday. http://pirsa.org/09090005/ Spacetime can be simultaneously discrete and continuous, in the same way that information can. It refers to this paper published in Physical Review Letters http://arxiv.org/abs/0708.0062 On Information Theory, Spectral Geometry and Quantum Gravity Achim Kempf, Robert Martin 4 pages (Submitted on 1 Aug 2007) "We show that there exists a deep link between the two disciplines of information theory and spectral geometry. This allows us to obtain new results on a well known quantum gravity motivated natural ultraviolet cutoff which describes an upper bound on the spatial density of information. Concretely, we show that, together with an infrared cutoff, this natural ultraviolet cutoff beautifully reduces the path integral of quantum field theory on curved space to a finite number of ordinary integrations. We then show, in particular, that the subsequent removal of the infrared cutoff is safe." and also to this paper Kempf recently posted on arxiv: http://arxiv.org/abs/0908.3061 Information-theoretic natural ultraviolet cutoff for spacetime Achim Kempf 4 pages (Submitted on 21 Aug 2009) "Fields in spacetime could be simultaneously discrete and continuous, in the same way that information can: it has been shown that the amplitudes, [tex]\phi(x_n)[/tex], that a field takes at a generic discrete set of points, [tex]x_n[/tex], can be sufficient to reconstruct the field [tex]\phi(x)[/tex] 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." Jal says the PIRSA video is of the same talk that Kempf gave in Vancouver last month, at the EG4 conference.