My thoughts on a computational universe: If time dilates with the amount of entropy then perhaps the universe can indeed fit an infinite amount of it without collapsing. However infinite precision seems like it requires exponentially more entropy than a single infinity. I term that as infinite and unbounded entropy. Perhaps Hilbert space is another term for that configuration. In that space Boltzmann brains are probable, so it is not very interesting to study. A more interesting configuration is infinite and bounded entropy where the universe needs to make do with finite precision, perhaps rational and transcendental numbers but not the Real numbers. I'd like to coin a term; anti-inertial entropy. Perhaps it would explain how pilot wave theory works. This would be the quantity by which an unfamiliar form of entropy is measured. This entropy is a form of matter which does not obtain mass from the Higgs mechanism, and its salient property is that there is a bounded amount of it causing its state to converge when there exists two states which are very close to one another. The closeness metric changes depending on how much how much the universe has available for choosing future and past histories. In this world a curious form of fate exists, and old people arguing about what happened in the past are both right, but their pasts have diverged so that the universe may save precision storing it. It is a strange universe, but it is mine and I like it. =)