Robin Hanson wrote:
> 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."
Sure, my usage agrees with this.
> 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,
But the point of my example having a C universe etc. was that this prior is not a plausible one. The fair dice in the C universe, or rather let's say it's a fair coin, do you really want to say that the prior probability that this coin should land heads all thousand throws is almost one? That seems wrong.
> then conditioning on my being in a human slot, there is a 90% chance I'm
> in a B "universe," as you prefer.
But since that prior seems wrong, you don't get this result.
> >> >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!
Actaully, you didn't say anything about what we should believe about the *fractions*.
Suppose the only alternatives were (1): one in ten Earth-like planet evolve intelligent life; or (2) one in a thousand does. Suppose the prior probability is fifty-fifty.
Now you observer that the Earth has evolved life. Based on your clarification above, I now take it that you think this observation should increase your confidence in (1). Is this right?