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.




This is simply a consequence of
using the absolute measure.



Ah ? I am not sure this makes sense. If this makes sense, then the Absolute Measurer and the Relative one are closer than I was used to think.






The idea is that the future is ''already out
there''.



Again I agree, but I would say the 2^aleph_0 futures are "already out there". That's why we need a measure. I could say that the mathematical shape of that measure should be absolute (the same in all the worlds of the multiverse). The value of the measure with respect to the choice of some experiment is relative. Would you agree?





So, the correct picture is not that suddenly the plenitude is made
larger because a copy of the person plus (part of) his universe is appended to the plenitude. The plenitude itself is a timeless entity, containing all possible states. If someone wants to carry out a duplication experiment then
the results of that are ''already'' present in the plenitude.


I agree if you are talking about the 3-plenitude. For the 1-plenitude, the question is more delicate. (G* can show that the 1 and 3 notions of plenitude are the same, but from the machine point of view (either 1 or 3 view) this in not the case at all: the 1-plenitude will look much vaster than the 3-plenitude. This is akin to the Skolem paradox in axiomatic set theory, but also to some carrolian or monthy-python like fantasies where some place look tiny as seen from outside and very big from inside :)



When death can be ignored then the apparent time evolution can be described by a relative measure which is given as the ratio of absolute measures taken before and after an experiment (as pointed out by George Levy in a previous
reply).


Yes but as far as I remember older posts by George Levy, we need also to take into account some fusion of histories, by amnesy or "quantum" erasure, and this prohibits trust in the use of intuitive probabilities. Then the interview of the Universal machine explains somehow why things are counter-intuitive there (self-reference limitations).




Note that the locality of the laws of physics imply that you can
never directly experience the past.


Yes but then you should make clear if you assume the laws of physics just for illustration or as a fundamental hypothesis. From you other recent post I guess you don't assume the physical laws, just the algorithm (and I add the "mathematical execution of those algorithm in platonia. OK?





So, if you measure the z-component of a
spin polarized in the x-direction, you will find yourself in a state where
you have measured, say, spin up, while you have a memory of how you
prepaired the spin of the particle, some time before you made the
measurement. One thus has to distinguish between the three states:

S1: the experimenter prepaires the spin of the particle

S2: the experimenter finds spin up while having the memory of being in S1

S3: the experimenter finds spin down while having the memory of being in S1

These three states are ''timeless'' elements of the plenitude. They have their own intrinsic measures. I challenge people on this list to explain why this is not the case. If you have a plenitude you have everything. So, S1,
S2 and S3 are just ''out there''.



OK.




The measure of S2  and S3 are half that of
S1. The probability of being in either S2 or S3 is thus the same as being in
S1.


OK (relatively). 3-point-of- view talk.



But if measuring spin down leads to instant death, then the probability
of being alive after the experiment is half that of being alive before the
experiment.


Except that "death" has no 1-meaning, and should not be taken into account for evaluating a probability question. Here too George Levy argued some time ago that, strictly speaking the probability to find oneself 1-alive is always 1. But here too it is a little delicate because it is a typical "pure theological truth", it belongs to G* \ G.

I recall G formalizes correctly and completely what sound machines can prove about themselves, and that G* formalizes correctly and completely what is true about the sound machine, but not necessarily provable (that's mainly Solovay theorem). G* \ G literally axiomatizes what sound machines can "correctly hope" about themselves.

Your post makes me doubt the difference between Absolutist and Relativist, about measure, is less big than I was used to think.

Bruno

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

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