This "density - idea is the first one that brings me a bit "less far" from the big (infinite?) number idea. It is still not reaching to the problem, how number qualia can turn into other meaning qualia - without outside (other) input.
Thanks Lennart John M --- Lennart Nilsson <[EMAIL PROTECTED]> wrote: > > 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. > === message truncated === --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
