Le 12-juin-05, à 14:48, Stathis Papaioannou a écrit :


Bruno Marchal writes:

But the basic idea is simple perhaps: Suppose I must choose between

a) I am 3-multiplied in ten exemplars. One will get an orange juice and 9 will be tortured.

b) I am 3-multiplied in ten exemplars. One will be tortured, and 9 will get a glass of orange juice instead.

OK. Now, with comp, strictly speaking the 1-uncertainty are ill-defined, indeed. Because the uncertainty bears on the maximal histories. Without precision I would choose "b". But if you tell me in advance that all the 9 guys in "b", who got the orange juice, will merge (after artificial amnesia of the details which differ in their experience), and/or if you tell me also that the one who will be tortured will be 3- multiplied by 1000, after the torture, this change the number of relative histories going through the 1-state "orange-juice" or "tortured" in such a way that it would be better that I choose "a". Obviously other multiplication events in the "future" could also change this, so that to know the real probabilities, in principle you must evaluate the whole histories going through the states. To be sure, the reasoning of Stathis is still 100% correct with comp for what he want illustrate, but such probability calculus should not be considered as a mean to evaluate "real probabilities". When you look at the math, this can be described by conflict between local information and global information. It is all but simple. Today I have only "solve" the "probability 1" case, and it is enough for seeing how quantum proba could be justify by just comp. But even this case leads to open math questions. It is tricky in QM too.

I was with you until you proposed the tortured copy in (a) be multiplied 1000-fold or the 9 orange juice copies in (b) be merged. I would *still* choose (a) in these situations. I look at it in two steps. The first step is exactly the same as without the multiplying/merging, so at this point (a) is better. If you had then proposed something like, the orange juice copies will then be tortured, then that would have made a difference to my choice. What you in fact proposed is that the absolute measure of the tortured copies be subsequently increased or the absolute measure of the orange juice copies be subsequently decreased. I would argue that changing the absolute measure in this way can make no possible first person difference; or, equivalently, that multiplying or reducing the number of instantiations of an observer moment makes no possible first person difference - it's all the one observer moment.

Yes but this leads to paradoxes. It can be shown that all OM have the same measure in the running of the UD, or that there is no measure at all. The relative measure of OM2 relative to OM1 will be given by the density of computations going from OM1 to OM2.



What does make a difference is the *relative* measure of candidate successor OM's, and it is crucial that this refers to the transition from one OM to the next.

Strictly speaking I agree, but then I am taking the opportunity of the ambiguous nature of you statement.


This is simply because that is how our minds perceive the passage of time and construct the illusion of a single individual who maintains his identity over time.


I agree intuitively, but here I have a problem: for technical reasons I disbelieve in "intuition" at this stage. At this stage I cannot *not* take into account the "reversal" which makes the "passage of time" secondary from the way the 1-computations (the web of arithmetical "dreams") are coherent. Of course this is probably highly counter-intuitive and that's why I turn on the math. I have said this recurrently on the list. The thought experiments are good for making us doubt about many prejudices. But to build a theory, at some point it is necessary to be utterly clear on what we assume or not, and to be open that the consequences of the theory are in contradiction with what intuition told us. After all this happened already more than one time with modern physics. I am not sure at all I can follow you when you describe how our minds perceive the passage of time. I have learn to accept that the notion of single individual is less an illusion than time, space and all physical modalities. But I know it is counter-intuitive and that is the reason I have eventually decided to interview lobian machine to take into account the lob-godel incompleteness (which is counter-intuitive at its roots). Sorry if this looks a little bit like an authoritative argument, but I can explain all the details if you are willing to cure your math anxiety .... As I said once, common sense is the only tool we have to go a little bit beyond ... common sense.

Bruno

http://iridia.ulb.ac.be/~marchal/


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