Re: Doomsday Example

Robin Hanson (
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?

I accept that given your postulated prior, learning you are human strongly suggests you are in the universe made only of humans, rather than made mostly of stones.

>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.

Consider the analogy of death. Imagine in one universe I live for 100 years and another where I life for 50. The difference between the two universes is that, after 50 years are up, in one universe "I" would be alive and in the other universe, "I" would be dead. The atoms that would make up a living body are instead, for example, in a charred material preserved in the lava flow that enveloped me. That material is the material that would have been "me" had I been alive. There *is* an "I" associated with that dead rock.

Similarly, if some small event had never triggered life on Earth, the matter that would have me alive would instead be rock near Earth's surface. There is a sense it which it makes sense to ask which rock it would have been.

Yes, it would be a real pain to track down which atoms those would be. But I don't see any other way to make sense of the hypothesis that "I" might not have existed, other that to describe what would otherwise have become of the material and space-time I now occupy.

>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.

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."