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. 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. 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.
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