I start from a part of this post from David Barrett-Lennard (Mon, 3 Nov 2003 19:48:49) but I could probably hev selected several similar other ones:
> Given the "source code" for the simulation of our universe, it would > seem to be possible to add some extra instructions that test for a > certain condition to be met in order to tamper with the simulation. > It would seem likely that there will exist simulations that match our > own up to a certain point in time, but then diverge. Eg it is > possible for a simulation to have a rule that an object will suddenly > manifestitself at a particular time and place. The simulated conscious > beings in such a universe would be surprised to find that induction > fails at the moment the simulation diverges. It seems to me that there is a very strong assupmtion here which is that there should be some synchronicity between the "time" in the postulated computer into which the universe would be simulated and the time inside that simulated universe (as this is typically the case when an electronic device is simulated). But such an assumption not only does not seem necessary in any way but it also does not seem possibly consistent (or it would be very arbitrary at least) with a universe like ours for what we know of the implications of general relativity (it does not seem possible to define any global time in any consistent way in our universe). Many other way of simulating the universe could be considered like for instance a 4D mesh (if we simplify by considering only general relativity; there is no reason for the approach not being possible in an even more general way) representing a universe taken as a whole in its spatio-temporal aspect. The mesh would be refined at each iteration. The relation between the time in the computer and the time in the universe would not be a synchrony but a refinement of the resolution of the time (and space) in the simulated universe as the time in the computer increases. Alternatively (though both views are not necessarily exclusive), one could use a variational formulation instead of a partial derivative formulation in order to describe/build the universe leading again to a construction in which the time in the computer is not related at all to the time in the simulated universe. It seems to me finally that the simulations in which there is a synchrony between the time in this universe and the time in the computer simulating it are very specific (if even existing) among all other possible simulations of the same universe (at least for the kind of relativistic universe we live in). I would even conjecture that the measure of the set of synchronous simulations is null within the set of all possible simulations of a given (not so trivial) universe (if one can give a sound sense to this). 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 ? Georges.