Hi Bruno ----- Oorspronkelijk bericht ----- Van: "Bruno Marchal" <[EMAIL PROTECTED]> Aan: "Saibal Mitra" <[EMAIL PROTECTED]> CC: "Stathis Papaioannou" <[EMAIL PROTECTED]>; <everything-list@eskimo.com> Verzonden: Friday, May 27, 2005 04:08 PM Onderwerp: Re: Many Pasts? Not according to QM...

> Hi Saibal, > > Le 27-mai-05, à 14:29, Saibal Mitra a écrit : > > > ----- Oorspronkelijk bericht ----- > > Van: "Stathis Papaioannou" <[EMAIL PROTECTED]> > > Aan: <[EMAIL PROTECTED]> > > CC: <[EMAIL PROTECTED]>; <everything-list@eskimo.com> > > Verzonden: Friday, May 27, 2005 01:44 AM > > Onderwerp: Re: Many Pasts? Not according to QM... > > > > > >> Saibal Mitra wrote: > >> > >>> Quoting Stathis Papaioannou <[EMAIL PROTECTED]>: > >>> > >>>> On 25th May 2005 Saibal Mitra wrote: > >>>> > >>>>> One of the arguments in favor of the observer moment picture is > >>>>> that > > it > >>>>> solves Tegmark's quantum suicide paradox. If you start with a set > >>>>> of > >>> all > >>>>> possible observer moments on which a measure is defined (which can > >>>>> be > >>>>> calculated in principle using the laws of physics), then the > >>>>> paradox > >>>> never > >>>>> arises. At any moment you can think of yourself as being randomly > > drawn > >>>>> from > >>>>> the set of all possible observer moments. The observer moment who > >>>>> has > >>>>> survived the suicide experiment time after time after time has a > >>>>> very > >>>> very > >>>>> very low measure. > >>>> > >>>> I'm not sure what you mean by "the paradox never arises" here. You > > have > >>>> said > >>>> in the past that although you initially believed in QTI, you later > >>> realised > >>>> > >>>> that it could not possibly be true (sorry if I am misquoting you, > >>>> this > >>> is > >>>> from memory). Or are you distinguishing between QTI and QS? > >>>> > >>> That's correct. In both QTI and QS one assumes conditional > >>> probabilities. > >>> You just > >>> throw away the branches in which you don't survive and then you > >>> conclude > >>> that you > >>> continue to survive into the infinitely far future (or after > >>> performing > > an > >>> arbitrary > >>> large number of suicide experiments) with probability 1. > >>> > >>> But if you use the a priori probability distribution then you see > >>> that > > you > >>> the measure > >>> of versions of you that survive into the far future is almost zero. > >> > >> What does "the measure of versions of you that survive into the far > >> future > >> is almost zero" actually mean? The measure of this particular version > >> of > > me > >> typing this email is practically zero, considering all the other > >> versions > > of > >> me and all the other objects in the multiverse. Another way of > >> looking at > > it > >> is that I am dead in a lot more places and times than I am alive. And > >> yet > >> undeniably, here I am! Reality trumps probability every time. > > > > > > You have to consider the huge number of alternative states you could > > be in. > > > > 1) Consider an observer moment that has experienced a lot of things. > > These > > experiences are encoded by n bits. Suppose that these experiences were > > more > > or less random. Then we can conclude that there are 2^n OMs that all > > have a > > probability proportional to 2^(-n). The probability that you are one of > > these OMs isn't small at all! > > > > 2) Considering perforing n suicide experiments, each with 50% survival > > probability. The n bits have registered the fact that you have > > survived the > > n suicide experiments. The probability of experiencing that is 2^(-n). > > The > > 2^(n) -1 alternate states are all unconscious. > > > > > > So, even though each of the states in 1 is as likely as the single > > state in > > 2, the probability that you'll find yourself alive in 1 is vastly more > > likely than in 2. This is actually similar to why you never see a > > mixture of > > two gases spontaneously unmix. Even though all states are equally > > likely, > > there are far fewer unmixed states than mixed ones. > > > > Saibal > > > I agree in the case I could imagine all the "observer moments" in some > complete third person way, where the notion of "dying" can be given > some third person sense. > But the compi and the qti, relies, it seems to me, on the fact that we > cannot experience not being there. So that in both case the first > person probabilities are one, from first person points of view. They > are one, *almost* by definition, the very notion of "probabilitiy" > presupposes the ability to test the outcome of a (random) *experiment* > (this is still more plausible for an "observer-moment" first person > *experience*). > > Do you see what I try to say? > > That's why we need some "no cul-de-sac" hypothesis. > > [For those who knows the (Godel Lob Solovay) provability logics (G and > G*) : you can go from a provability logic Bp (= G; with cul-de-sac > accessible from all transitory obsever momente) to a probability logic > (without cul-de-sac) by *imposing* consistency: Bp ==> Bp & -B-p. (-B-p > = 'Consistent p' remember the dual of Bp is -B-p, and with Bp read as > 'Provable p', ('Beweisbar p', in German), -B-p is 'Consistent p'. And > if you remind Kripke Semantics, Con p, means there is at least one > observer moment (with p true) accessible from you current observer > moment. > Of course G* proves Bp <-> (Bp & -B-p), But G* proves also -B(Bp <-> > (Bp & -B-p)), so that from the machine point point of view, it will > change the provability logic, indeed, it changes it into a probability > logic.] > > In my 1988 paper, I argue that the qti is a confirmation of the compi. > (Given that the uda shows comp entails the no cul-de-sac hypothesis). > > Or you are (still) with the ASSA ? Or do I miss what you try to explain? > I'm actually still with the ASSA. I agree that if there is no cul-de-sac, you can always redefine an observer moment by including the information that he has survived a suicide experiment. But I would consider that observer moment to have a lower measure than the 'previous' one. Also, if you take the first person relative measure serious, then you have to deal with transitions between different persons. Time evolution in both classical and quantum mechanics of an isolated system will yield any state if you wait long enough. So, you will evolve into me (and everything else). Now you can cut away these states just like the unconscious states, but since the total number of OMs that you can consider to be 'you' is finite you then end up with an absolute measure over your 'reference class'. Saibal