Jerry Clark <[EMAIL PROTECTED]> writes:
> I don't think that it means anything to say whether one is in a universe with
> an infinite future or not: In an all-universe model there are many universes
> which have identical copies of 'you' in them and there is no meaning to saying
> which one of these universes 'you' are in.
Let me try to restate the argument, as I understand it from the earlier
discussions on this list. I'll also eliminate the infinities since that
introduces irrelevant complications.
Suppose there are two possibilities: you live in a universe where there
will be 100 billion people total, or in a universe where there will be
100 trillion people total, and a priori you think there is a 50-50 chance
which one is the case. You check your birth order and find that you are
about number 50 billion.
Now, that would be pretty likely if you were in the 100-billion universe,
but it would be very unlikely if you were in the 100-trillion universe.
Hence by Bayesian reasoning you find you are more likely to be in the
100-billion universe, and therefore the human race is likely to end
relatively soon. This is the Doomsday argument.
However introducing the all-universe model and the self-selection
assumption (that you are a random individual from among all individuals in
all universes) then a priori the chances that you are in the 100-trillion
universe are ten times greater than that you are in the 100-billion
universe. This exactly counters the shift which you made in the Doomsday
argument, based on your birth order, which made you think you were more
likely to be in the 100-billion universe.
The net result is that you have no information about which universe you
are in; you are equally likely to be in either universe, or in fact in
any universe which has at least 50 billion people in it. Hence the
Doomsday argument doesn't work in this model, and you can't conclude
that we are likely to experience Doom Soon.