Georges Quenot writes: > I would be interested in reading the opinions of the participants > about that point and about the sense that could be given to the > question of what "happens" (in the simulated universe) in any non- > synchronous simulation "when" the simulation diverges ?
I'll make two points. First, you're right that there are other ways of computing a universe than simply starting with some initial conditions and evolving "time" forward step by step, computing the state of the universe at each subsequent instant. You list several ways this might happen and I agree that this concept makes sense. We might call this "non-sequential" or "non-temporal" simulation. But, given the specific temporal structures that exist in our universe, there are limitations to how this computation can be done. Specifically, we are able to construct physical computers in this universe which perform complex calculations. And among these calculations are those which are believed to be inherently sequential and lengthy, calculations for which the answer cannot be computed without spending a great deal of time from the initial values. Given that our universe contains systems like this, it constrains the amount of computation which must be done in any kind of non-sequential simulation. Specifically, the non-sequential simulation must do at least as much computation in order to produce our universe as the more traditional kind of sequential simulation. This demonstrates a limit on the power of non-sequential simulation. My second point is with regard to your specific question, what would happen if we tried to simulate a universe which diverged in some space-time region from the conventional physical laws? This is our often-discussed "flying rabbit" paradox (we have other names as well), where it seems that if all universes exist, we might as well be living in a universe which was lawful everywhere except in some small region, or up until a certain time, as in one where the laws are truly universal. Your question is whether this concept makes sense in a non-sequential simulation, or whether it assumes sequential simulation. I think it makes just as much sense in the context of non-sequential simulation. The non-sequential simulator is trying to find or create a universe which satisfies certain physical laws. It may be iteratively solving a differential equation or using some other non-temporal method, but that is its goal, its mechanism. The case at hand is simply a matter of defining the physical laws to be different in different regions of space-time. We could define the physical laws which the non-sequential simulator is trying to solve in some such terms. We'd say, observe these laws in this region, but these other laws in that region. For example, we might say to observe the true laws of our universe (whatever they turn out to be) up to simulated time T, and then to observe other laws after time T. Or similarly we could have one set of laws up to spatial coordiate X, and another set of laws on the other side of X. The non-sequential simulator would have no more difficulty in creating a universe which satisfied such non-uniform physical laws than in one where the laws were the same everywhere. So I'd say that the issue of sequential vs non-sequential simulation is irrelevant to the question of the existence of "flying rabbit" universes and does not shed light on the issue. Hal Finney
