It only takes 2-3 orders of magnitude to get a very impressive rotational symmetry from a cubic lattice; e.g., do a high-quality anti-aliased rotation of a hi-def image on your computer screen. Many PDE's are successfully simulated on cubic lattices and faithfully reproduce isotropy "more or less". But experiments of this type suggested in the arxiv paper are wonderful; we need as many of these experiments as we can get. I am certain that discrepancies will eventually appear, but perhaps not from a simplistic cubic lattice model of space. I'm quite intrigued by the holographic model, because it starts getting at quantum issues like entanglement, which have the possibility of saving bits; there aren't nearly as many bits or degrees of freedom in a holographic model as a simple cubic lattice model might suggest. Taking inspiration from Maxwell/Boltzmann/Planck/Bekenstein, it should be possible to push the entropy/information equivalence much harder to better characterize where information resides and flows in the holographic model. At 04:27 PM 2/9/2013, meekerdb wrote: It would be nice to have physical theories that didn't assume real numbers, and of course in any actual calculation or measurement only rationals are used. But experimental attempts to measure the discreteness of spacetime, as hypothesized by loop quantum gravity for example, have come up empty - even down close to the Planck scale, http://arxiv.org/pdf/1109.5191.pdf