Le 08-déc.-05, à 22:21, George Levy a écrit :


Bruno Marchal wrote:
Le 05-déc.-05, à 02:46, Saibal Mitra a écrit :


I still think that if you double everything and then annihilate only the
doubled person, the probability will be 1.



Actually I agree with this.



So far we have been talking about splitting universes and people. Let's consider the case where two branches of the universe merge.



Of course this is the an hard and interesting question ... I would say that Everett, Deutsch, Hartle somehow answer it in the quantum realm. I would say that empirically or "apparently", at the bottom there is neither elimination of information, nor duplication of information.
Irreversibility and non cloning.
I believe comp entails this too. Got evidence from the interview with the Lobian Machine, but also from some intuitive way to put (first person) measure on the computational histories generated by the UD.





In other words, two different paths eventually happen to become identical -

At the bottom I don't think this can happens. Like Deutch I think that both bifurcation and fusion are really differentiation and dedifferentiation by *apparent* lack of memory.

Remember Y = II If you "bifurcate" I think you just grow the measure on your past. If you fuse consistently you don't change the measure. To be sure I have also different arguments in favor of an increase of measure when you fuse (loosing memory makes greater your possible histories, like substracting equations in a system of equations augments the possible number of solutions (the Galois connection).
All this is very difficult, that I think we should take benefit of Godel, Lob, Solovay and the discovery of the (modal) logic of self-reference G and G* to ask the opinion of a universal machine ...



Of course when this happens all their branching futures also become identical.

This is not so obvious. You should define a notion of identity for the branches, path, etc.



Would you say that such a double branch has double the measure of a single branch even though the two branches are totally indistinguishable? How can you possibly assert that any branch is single, double, or a bundle composed of any number of identical individual branches?

Indeed, how? And from which point of view?


Bruno

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

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