# Re: Doomsday Example

Robin Hanson (hanson@econ.berkeley.edu)
Sun, 23 Aug 1998 20:47:22 -0700 (PDT)

Nick B. writes:
>> >Well, suppose there were two possible worlds, A and B, that are a
>> >priori equally probable. In A there are a hundred humans and nothing
>> >else. In B there are a hundred humans and a million stones. If you
>> >know this and nothing more except that you exist and are a human,
>> >what would you say the posterior probabilities are for the two
>> >worlds?
>> >
>> >I would say 1/2. Finding myself being a human would give me no
>> >information as to the number of stones.
>> >
>> >But in order to get this result we need to assume that there was a
>> >zero chance that you would have been a stone.
>...
>But in the present example, A and B were postulated to be a prior
>equally probable. Do you deny that this is a coherent assumption?

>What you are doing is you define a state to be:
>Si = "u is the real universe and I occupy slot x in u."
>where u is a member of U, the set of possible universes, and x is a
>spacetime slot in u. ...
>
>One thing that I find problematic is your use of the indexical "I" in
>the definitions of the states. Are you using this term as a rigid
>designator that denotes the same individual in all possible worlds
>where that individual exists? What if anything does it refer to in
>those worlds where you do not exist? For example, in "* is the real
>universe and I occupy slot A1 [where there is a rock]" - here it
>seems more like you're using "I" as variable ranging over all slots
>in a given universe. ...
>I would say that there are no "I"s associated with dead rocks. In
>order to be the sort of thing that could be referred to by the term
>"I" you have to be a person, and rocks are not persons. So the prior
>probability that I should be a rock must be zero. If you replace "I"
>with "this thing here-and-now" then it's really clear that this
>doesn't refer to anything in particular except if it is
>accompanied by an act of pointing. But if this is what you mean then
>in order to make sense of the state descriptions we have to
>understand "I" as a rigid designator. If we do that, then do you
>really think there is a fact of the matter, in a world containing ten
>similar rocks and nothing else, as to which one of these rocks is
>"really" you? Are there then ten physically identical possible worlds
>in each of which you are really a different rock? Sounds very
>metaphysical to me.

>We observe that evolution on Earth yielded intelligent life pretty
>quickly (~ 4 b. years, within the main sequence of the sun). Shall
>we therefore conclude that a large fraction of Earth-like planets
>give rise to intelligent life in about ~4 b. years? I say: no,
>bececause whatever the fraction of Earth-like planets give rise to
>intelligent life in ~4 b. years, we were sure to find ourselves
>originating from a planet that did.
>
>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.