Le 10-mai-05, à 12:25, Stathis Papaioannou a écrit :
I should add that I don't believe in QTI, I don't believe that we are guaranteed to experience such outcomes. I prefer the observer-moment concept in which we are more likely to experience observer-moments where we are young and living within a normal lifespan than ones where we are at a very advanced age due to miraculous luck.
Aren't the above two sentences contradictory? If it is guaranteed that somewhere in the multiverse there will be a million year old Hal observer-moment, doesn't that mean that you are guaranteed to experience life as a million year old?
With some ASSA perhaps, but with the RSSA it makes sense only if those "old Hal OM." have the right relative proportion to the young one.
SSA self-sampling assumption (by Nick Bolstrom)
ASSA idem but conceived as absolute
RSSA idem but conceived as relative
OM = Observer Moment
Is the SSA even relevant here? The SSA says that I should consider each OM as if randomly sampled from the set of all possible OM's. In the MWI, although it is certain that there will be a million year old version of me, the distribution of OM's is greatly skewed towards younger versions of me, so that the measure of million year old versions is very close to zero; in fact, it should have the same numerical value as the probability of my reaching this advanced age in a single world interpretation of QM. Therefore, if I pick an OM at random from my life, it is extremely unlikely that it will be one where I find myself to be a million years old.
I accept the above reasoning as sound, but I don't think it disproves QTI. The probability that a randomly chosen OM from all possible OM's available to me will be experienced as a million year old version of me is *not* the same as the probability that I will experience life as a million year old at some point. The former probability may be very close to zero, but the latter probability, if MWI is true, should be exactly one.
Here is a somewhat analogous example to show the difference. Suppose that there is only one universe and that my life expectancy in this universe is about one hundred years. Consider the one second time interval between August 10 2005, 10:00:00 AM and August 10 2005, 10:00:01 AM. Counting all the one second intervals available to me in a one century lifespan, assuming I sleep eight hours a day, gives about 2 billion. The probability that a random one second long OM in my life coincides with the above interval on August 10 is therefore about 1/2 billion. The probability that I will live through this time interval, on the other hand, is hopefully very close to one.
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