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From: Matthew Donald <mjd1014.domain.name.hidden>

Date: Wed, 11 Oct 2000 13:36:01 +0100 (BST)

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''

***************************************************

Received on Wed Oct 11 2000 - 05:44:14 PDT

Date: Wed, 11 Oct 2000 13:36:01 +0100 (BST)

I wrote

Nick Bostrom <nick.domain.name.hidden> replied

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

Bostrom replied

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

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''

***************************************************

Received on Wed Oct 11 2000 - 05:44:14 PDT

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