Matthew Donald wrote:
>My first point is just a matter of setting probabilistic scales:
>
>Even with her property of seeing herself as having birth rank 2,
>Eve exists on many many branches of the universal wavefunction.
>These include, for example, lots of equiprobable branches in which
>she sees stars in different constellations. She also exists on
>atypical branches in which her nuclear physics is incorrect because
>whenever she has placed Uranium near a Geiger counter it has failed
>to decay and even on branches in which there are particular
>circumstances in which she has seen heat regularly flow from
>hotter to colder without energy input. We only deduce that such
>branches are atypical from our assumption that our branch is
>typical. Eve too needs to assume (rightly or wrongly) that her
>branch is typical. The chance of her seeing the laws of
>thermodynamics disobeyed significantly (assuming our beliefs about
>them are correct) is much much smaller than the chance of her
>seeing the constellations in the precise way that she does, but even
>that is much much smaller than 2 in a trillion.
I think I agree with all of that.
>My second point is that knowledge of atypical birth rank is not a
>simple branch-causing property. Information relevant to birth rank
>is distributed all over Eve's possible histories, and in different
>ways in different histories. It is not possible to take birth rank as
>a fact independent of any of the other properties which make Eve
>who she is.
Take each Eve-observer-branch-moment, i.e. each point in time on each
branch containing Eve, and define its birth rank as its position in the
class of all such observer-branch-moments. As to what Eve should think,
she then average over all observer-branch-moments which she, for all she
knows, might currently be.
>Of course, I do not dispute that Eve is correct to see her birth rank
>as interestingly atypical. The question is whether that knowledge
>should lead her to believe that she is incapable of becoming
>pregnant, or, more plausibly, should lead her to believe in the
>immanence of inevitable planetary catastrophe.
That would depend on the prior probabilities. If, prior to her taking
the Self-Sampling Assumption into account, she thought it more probable
that she would not get pregnant than that the planet would soon be
destroyed, she should continue to believe that after accounting for SSA.
>My first point says that Eve's birth rank is not even close to
>being as improbable as lots of other (in general less interesting)
>specific facts which any observer knows about herself.
Sure, but something improbable happening is by itself not a remarkable
fact. Every specific sequence of outcomes of one thousand coin tosses is
extremely improbable (2^-1000), but only a small subset (all heads;
alternating heads and tails; etc.) are surprising. The key is instead to
look at the conditional probabilities of the observed event given each
of the rival hypotheses. The conditional probability of being among the
first two observers is greater given that there are two observers than
given that there are billions. (Assuming all these observers would
belong to the same reference class - which I would question.)
>The second says that on a technical level, Eve cannot simply apply
>Bayes' theorem to prior probabilities of conception and subsequent
>information about birth rank.
>
>Firstly, the prior probabilities will be branch-dependent, being, for
>example, smaller in branches in which Eve is amenoretic.
The prior Eve should use is simply the weighted average of all the
branches she, for all she knows, might be on (assuming she is 100%
convinved about MWI).
>Secondly, only if there was a class of observers all of whom are
>like Eve except that they have different birth ranks would there be
>an objective probability which Eve could use as a genuine measure
>of the improbability of her birth rank. But such classes are
>undefinable, even in my theory in which the set of all observers is
>well-defined and countable, because hints about her birth rank have
>been built into everything Eve has ever known about herself.
That wouldn't make it undefinable, just small. But for reasons spelled
out in my dissertation, I think observer-moments should be grouped in
the same reference class even when they are subjectively
distinguishable, and I'm aware of no reason to limit this only to
observer-moments that are subjectively distinct only regarding their
knowledge of their birth ranks but not in other ways.
>By analogy, there might be an objective probability for me to
>win the British national lottery next week, but I do not believe that
>there is an objective probability for me being able to communicate
>in a language with a vocabulary significantly influenced by more
>than one prior language. My knowledge of word pairs from different
>sources; dog/canine, book/literature, meal/banquet is pretty
>well-worked into my mental life but, even with a perfect
>description of my early mental life, you couldn't say with any
>accuracy when it became clear that that was the sort of language I
>was learning.
You've lost me here.
>I wrote
>
>> One cannot separate birth rank from the other facts about Eve's
>> mental life. Birth rank is not the sort of fact that one could
>> imagine Eve ever being asked to guess, as if she had no idea of the
>> answer. As long as she has been aware, she has had lots of clues
>> that her birth rank was expectional, just as we have always had
>> lots of implicit clues of our birth rank (e.g. the taste of
powdered
>> baby milk).
>
>Bostrom replied
>
>> I, for one, am quite uncertain about my birth rank. It looks like
>> there have been infinitely many observers before me, but what
>> cardinality I do not know. Even if the world were finite, I'd
still
>> not know my rank, since I don't know (even approximately) how
>> many intelligent aliens have existed before me.
>
>> In the case of Eve, it is very easy indeed to describe a situation
>> where she is utterly ignorant as to her rank - just imagine she is
>> living on an isolated island, and she doesn't know whether there
>> are other islands in the world and if so whether they are
>> inhabited.
>
>These look like fairly good arguments for saying that the Doomsday
>Argument, for example, is empty in your cosmology.
Yes, I've been stressing that for years. Even in the best (worst!) case,
it has very limited empirical power in its original form.
>Whatever her future, Eve currently has reason to believe that she
>has an interesting birth rank, based for example on the purity of the
>air she breathes, the lack of archaeological remains around her, and
>what she has been told by her partner. Whether she is correct or
>not about her birth rank, she is certainly isolated. Should she
>deduce from that that most humans are as isolated, and that
>therefore her island will never be crowded with lots of her
>descendants?
Yes, that would rather be the conclusion.
>We also seem to be somewhat isolated in as far as, if our
>species were to continue indefinitely, then we might expect most
>humans to live in societies in which the past appeared
>interminable; with origins at best mythic and most of history
>unknown. (Fictions by Gene Wolfe come to mind.)
Basically, we should think a non-negligable fraction of all observers in
our reference class observe the same kind of things that we observe.
>I do suspect that it is possible that our species will continue
>indefinitely. Nevertheless, I don't think that this makes us
>infinitely improbable, because, in my theory, in which observers are
>defined entirely by their mental lives, there can only be finitely
>many possible observers of complexity less than any given bound. In
>particular, I do not suppose that observers can always be
>distinguished by spatial-temporal position. (I suspect that this
>hypothesis may well be needed if we are ever to understand what
>quantization of general relativity might mean.)
I have some as yet unarticulated ruminations that seem to resemble what
you are saying here, perhaps.
>I am also not sure whether observers with long species histories
>are not a priori less likely than observers with short species
>histories on the grounds that longer species-histories means more
>possible different histories with each of these possibilities made
>less likely precisely by its greater detail. (Information always
>costs probability in many-minds theory.)
Well, you know what you are; no matter how improbable, you just have to
take that for granted. The question is what else is true about the
world.
Nick Bostrom
Department of Philosophy
Yale University
Personal Homepage:
http://www.nickbostrom.com
Email: nick.domain.name.hidden
Received on Sat Oct 07 2000 - 22:52:41 PDT