Nick Bostrom writes:
>Suppose we change the example slightly. Now, an A universe contains
>10 humans and nothing else. A B universe contains 10 humans and one
>trillion trillion stones. There is a small C universe (of negligible
>size), and it spawns one thousand baby-univeses through a random
>process (like rolling fair dice) that has a 10% chance of yielding an
>A and 90% of a B.
>
>It seems clear that there will probably be about 100 A univeses and
>900 B universes. But that means about 90% of all humans will find
>themselves in an B universe. So if all you knew was the set-up and
>that you were a human, then you should believe that there was a
>90% chance that you were in an B universe.
>
>And yet, if you include stones in the reference class, then it seems
>you should believe you are in an A universe. For if you are in a B
>universe, then there exists in total at least one trillion trillion
>stones and then you would probably have been one of these stones
>rather than a human.
Let N = "trillion trillion", and assume there are exactly 100 A "universes" and 900 B "universes". Note that these are *not* "universes" in the sense I was using of "possible worlds." The entire construction of C + 100 As + 900 Bs is just one total space-time, a "possible world."
As described the only remaining uncertainty is where in this world I am. If I treat stone slots and human slots equally, there are 100*10 + 900(10+N) slots. If my prior is uniform across these slots, then conditioning on my being in a human slot, there is a 90% chance I'm in a B "universe," as you prefer.
>> >Similarly, I would say that finding that you are an observer does not
>> >give you reason for thinking that a large fraction of all slots in
>> >the universe is occupied by observers.
>>
>> Your error is to say "large fraction." The fact that life exists
>> on Earth *does* make it more likely that our universe has other planets
>> where life has evolved in a similar time. It just isn't enough to
>> conclude the fraction of Earth-like planets with life is "large."
>...
>And now you say that finding that life exists on Earth should
>not affect your beliefs about about the fraction of Earth-like
>planets with life.
But I said exactly the opposite in the quote above!
[More responses in next message. RH]
Robin Hanson
hanson@econ.berkeley.edu http://hanson.berkeley.edu/
RWJF Health Policy Scholar, Sch. of Public Health 510-643-1884
140 Warren Hall, UC Berkeley, CA 94720-7360 FAX: 510-643-8614