The Contextual Computer

What kind of computer is the universe? Here we present three results. The first is a consequence of the Kochen-Specker theorem: If the predictions of quantum mechanics are correct, then the universe cannot be a non-contextual computer. We then show that, if we assume that the density of memory is bounded, then the universe cannot be a classical contextual computer. The third result singles out the universe among all possible contextual computers by exploiting a curious connection with graph theory: In the universe, the maximal contextuality of a set of propositions is given by the Lovász number of the graph representing their mutual exclusiveness.