Nick B. writes:
>> But nothing else could have been me exactly. The only thing that
>> could be me exactly is something born when I was, and which then
>> did everything I did afterward, including writing this message.
>How does that support your claim that it makes sense to say that you
>could have been a rock?
We are talking counterfactuals here. I am male, but could I imagine being female? Yes. Could I imagine being born in 1400? Yes. Could I imagine being a chimp? Yes. Can I imagine being a rock? Yes. I see no boundary beyond which I can't imagine the variation. They all seem like reasonable counterfactuals to me. What reasons can you offer for rejecting some counterfactuals and accepting others?
>> >> What prior would you assign to world * in my example?
>> >That depends on such things as simplicity etc. If the three worlds
>> >are equal in these repects, I would say P(*) = 1/3. This would be the
>> >absolute prior. Then you take account of the fact that you exist, and
>> >you rule out world * (though I'm not sure what do about the monkeys).
>> >Then you renormalize and get P(#) = P(@) = 1/2.
>> But your *prior* is before you take information into account, and you
>> seem to prefer p(*) = 1/3, p(#) = 7/20, p(@) = 3/20. I instead prefer
>> all three being 1/3. You say:
>But I too would say all absolute priors three are 1/3. But these are
>the probabilities you should assign if you knew absolutely nothing,
>not even that you existed. In practice, you will always know you
>exist. If you conditionalize on this information then you get
>p'(*)=0, p'(#)=p'(@)=1/2. Now if you want you can call this new
>probability distribution, p'=p( _ | "I exist."), your "prior".
We seem to disagree on the math here. And since one of the reasons for precise models like this is so we can agree on such things, we really aught to get this clear. I say that since the probability of existing conditional on being in universes # and @ is different, you can't have equal probabilities for these universes BOTH for an absolute prior AND after you condition on existing. If they are equal to 1/2 after conditioning on existing, they cannot be both equal to 1/3 before conditioning. Could you please recheck your calculations?
>> "I'm not sure how many stones a universe has, but I expect universes
>> that have more stones in one region to have more stones in other regions
>> as well. If I look in one spot in this universe and I find a stone, that
>> suggests I'm more likely to find stones at other spots in this universe
>> as well."
>Sure, but this reasoning only works for things that may or may not be
>present where there are observers. Stones are a good example. But
>many other phenomena are correlated with the presense of observers
>and then this reasoning doesn't work. For instance, as you yourself
>has argued in your "Must early life be easy?"-paper, it would be
>wrong to use the observation that evolutionary processes here on
>Earth were fairly quick to infer that quick evolutionary processes
>are common in the universe; for we would not have existed if the
>particular evolutionary process we observe had not been quick enough
>to happen before the sun becomes a red gigant.
But my paper does things exactly the way I'm reccomending here. I choose a prior to have nice natural independence properties, without assuming that I exist. I then condition on my existing and find posterior probabilities are no longer independent in the way one might naively expect. If I had chosen independence conditional on existing I wouldn't have gotten any of the results I did.