Nick Boström have been trying to calculate the probability that we live in a computer simulation. His answer to how you go about this (below) if we live in an infinite universe with infinite simulations seems to fit how one could do probabilities in a multiverse with an infinite number of universes as well.
Lennart Nilsson "To deal with these infinite cases, we need to do something like thinking in terms of densities rather than total populations. A suitable density-measure can be finite even if the total population is infinite. It is important to note that we to use some kind of density-measure of observation types quite independently of the simulation argument. In a Big World cosmology, all possible human observations are in fact made by somebody somewhere. (Our world is may well be a big world, so this is not a farfetched possibility.). To be able to derive any observational consequences from our scientific theories in a Big World, we need to be able to say that certain types of observations are more typical than others. (See my paper Self-Locating Belief in Big Worlds for more details on this.) The most straightforward way of making this notion precise in an infinite universe is via the idea of limit density. Start by picking an arbitrary spacetime point. Then consider a hypersphere centered on that point with radius R. Let f(A) be the fraction of all observations that are of kind A that takes place within this hypersphere. Then expand the sphere. Let the typicality of type-A observations be the limit of f(A) as R--->infinity." -----Ursprungligt meddelande----- Från: everything-list@googlegroups.com [mailto:[EMAIL PROTECTED] För Brent Meeker Skickat: den 6 april 2006 18:21 Till: everything-list@googlegroups.com Ämne: Re: Do prime numbers have free will? Stathis Papaioannou wrote: > Tom Caylor writes: > > >>1) The reductionist definition that something is determined by the >>sum of atomic parts and rules. > > > So how about this: EITHER something is determined by the sum of atomic parts > and rules OR it is truly random. > > There are two mechanisms which make events seem random in ordinary life. One > is the difficulty of actually making the required measurements, finding the > appropriate rules and then doing the calculations. Classical chaos may make > this practically impossible, but we still understand that the event (such as > a coin toss) is fundamentally deterministic, and the randomness is only > apparent. > > The other mechanism is quantum randomness, for example in the case of > radioctive decay. In a single world interpretation of QM this is, as far as > I am aware, true randomness. Unfortunately there is no way to distinguish "true randomness" from just "unpredictable" randomness. So there are theories of QM in which the randomness is just unpredictable, like Bohm's - and here's a recent paper on that theme you may find interesting: quant-ph/0604008 From: Gerard Hooft 't [view email] Date: Mon, 3 Apr 2006 18:17:08 GMT (23kb) The mathematical basis for deterministic quantum mechanics Authors: Gerard 't Hooft Comments: 15 pages, 3 figures Report-no: ITP-UU-06/14, SPIN-06/12 If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes. The nature of the equivalence classes is further elucidated, as it follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model. >In a no-collapse/ many worlds interpretation > there is no true randomness because all outcomes occur deterministically > according to the SWE. However, there is apparent randomness due to what > Bruno calls the first person indeterminacy: the observer does not know which > world he will end up in from a first person viewpoint, even though he knows > that from a third person viewpoint he will end up in all of them. > > I find the randomness resulting from first person indeterminacy in the MWI > difficult to get my mind around. In the case of the chaotic coin toss one > can imagine God being able to do the calculations and predict the outcome, > but even God would not be able to tell me which world I will find myself in > when a quantum event induces splitting. And yet, I am stuck thinking of > quantum events in the MWI as fundamentally non-random. It's also unclear as to what "probability" means in the MWI. Omnes' points out that "probability" means some things happen and some don't. Brent Meeker --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
