I wrote
> 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.
Nick Bostrom <nick.domain.name.hidden> replied
> 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[s] over all
> observer-branch-moments which she, for all she knows, might
> currently be.
This looks like a natural suggestion but it is not possible in my
version of the many-minds interpretation.
The problem here, relevant to any ``theory of everything'' or
any theory potentially compatible with a quantization of general
relativity, is to what extent the observer-moments of different
observers can be ordered.
In the simple version of my many-minds theory, the probabilities of
different observer-histories can be calculated, given a quantum
field theory and a quantum state omega. Omega is Everett's
``uncollapsing'' ``universal wave-function''. It can be thought of as
an initial state, and I postulate that it is a particularly simple
state -- a vacuum state, for example.
Individual observer histories arise as possible sequences of
apparent ``wave-packet collapses'' each beginning separately from
omega.
Because this is a many-minds theory, each individual observer
carries in his own history all the information which makes him who
he is. Part of that information is his idea of past history prior to
his birth. For us, therefore, the individual dinosaurs roaming the
earth millions of years ago are like so many Schroedinger's cats:
until we observe specific traces, their lives and deaths are
undecided possibilities. The traces of them that we may potentially
observe in our futures are also undecided possibilities and so are
the number of our ancestors, the number of planets with observers,
the precise age and size of the universe, and our exact birth rank.
Thus we cannot define ``birth rank as [ ] position in the class of all
[ ] observer-branch-moments''. The best we can do is to look at an
observer's own personal current evidence as to his birth rank. This
can be quite ambiguous and, in general, will be a matter for
interpretation rather than mathematical definition.
I wrote
> 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.
Bostrom replied
> 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.
When I said ``undefinable'', I was speaking as a mathematician. I
meant that I believe that there is no conceivable algorithm which
could take elements of the set of observers as I define it
(well-defined and countable although that is) and attach
unambiguous birth ranks to each one of them. It is even less
plausible that there is an algorithm which will tell us whether a
possible observer is ``like Eve'' or not. And even at the handwaving
level, I claim that ``like Eve'' can only be interpreted either
in a wide sense as ``like a woman'' or in a much more narrow sense
as ``like a woman who has considerable and lifelong evidence of
social isolation''. This implies that, although it may be
reasonable for Eve to find her birth rank or social isolation
improbable, she should not expect to be able to define a precise
quantification of that improbability.
Moreover, we understand probability best when it is applied to
situations in which we can distinguish sequences of simple repeated
events with different possible outcomes which have occurred, or at
least could occur, under the observation of a single individual. My
comments are also intended to stress how little Eve's social
isolation is like that paradigm.
Bostrom wrote
> 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.
As I see it, *the question* is rather ``Given what I have learned
from my life up to now, how should I predict my future?''
To answer this question, I do have to consider how improbable my
past observations would be under different possible physical
theories. I can accept a considerable amount of personal
improbability either if it is inevitable -- I do have to be born
somewhen -- or as the price of a beautiful and simple overall
theory.
Matthew Donald (matthew.donald.domain.name.hidden)
web site:
http://www.poco.phy.cam.ac.uk/~mjd1014
``a many-minds interpretation of quantum theory''
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Received on Wed Oct 11 2000 - 05:44:14 PDT