Re: PhD-thesis on Observational Selection Effects

From: Matthew Donald <>
Date: Mon, 25 Sep 2000 10:46:41 +0100 (BST)

I wrote

> Under any interpretation of quantum theory, it really does look as
> if dice are being thrown. In my opinion, because of the way that
> instabilities are magnified in the normal functioning of the
> human brain, those dice affect every aspect of our behaviour on
> any timescale above a millisecond.

Nick Bostrom <> replied

> My belief is that the quantum nature of the chemicals in our
> brains is pretty irrelevant to our thinking. I think if you built an
> artificial neural network that didn't have any significant quantum
> properties, that it could be made to operate (and be conscious) in
> the same way as a human brain. Do you disagree with that?

I agree that the quantum nature of the chemicals in our brains is
pretty irrelevant to our thinking.

I also think that it is possible to imagine building an artificial
neural network without any significant quantum properties,
which would function in the same way as a human brain.

If my interpretation of quantum theory is correct however,
then being conscious is a matter of being a physical structure of a
precisely characterized type. Artifical networks may well not be
of that type, and so would be zombies.

Nevertheless, (unlike Penrose and Hameroff, for example), I do not
believe that consciousness depends on some peculiar large-scale
quantum coherence of neural chemicals. I not believe that there is
any evidence or necessity for such coherence. I also think that the
search for it is based on concepts (technically speaking, the idea of
pure normal states) which were developed for simple quantum
systems but which cannot be applied to the physically relevant
local quantum states in quantum field theory.

This does not affect my point that the natural instability of the
brain amplifies its underlying (quantum) uncertainties. (For an
artifical network to be a good human mimic at the level of
neural firings, you would need to make very extensive use of a
random number generator.)

I wrote

> Nevertheless, Eve still must expect to be typical as an observer.
> Otherwise, she has no reason to believe her physical theories. Her
> birth rank puts her in the position of someone who has tossed a
> fair coin 1,000 times and it has always come up heads. But she is
> tossing a million other coins at the same time so it isn't really
> that surprising.

Bostrom replied

> For all she knows, she may simply be one out of two humans -
> pretty typical.

I replied

> Eve should find her birth rank surprising because of her (assumed)
> knowledge of human biology. The question is whether she can
> deduce her own infertility from that surprise.

Bostrom replied

> Ok. However, you also said earlier that she is "tossing a million
> other coins at the same time" - I assume you mean that she
> exists on multiple branches of the universal wavefunction. Why
> would this make her observation any less surprising? She could
> think: "If that were true, how come I - this instance of me -
> would be observing something so atypical? Why am I not on one of
> those normal branches?"

What I'm trying to do here is some thinking aloud about whether
the Doomsday argument is correct and about what issues are raised
in an attempt to apply it in a many-minds framework.

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.

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.

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.

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.

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.

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.

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.

I suppose that the best one could imagine doing for Eve would be
something like this. Run a lattice simulation of the universe and
calculate the structures of all observers with complexity bounded
by a given fixed amount (in theory, given sufficient computer
power, this is possible because of the finiteness of my theory.)

Now analyse all those structures. Let P be the sum of the a priori
probabilities of those which are decided, by some criterion which
will certainly be imprecise, to be women of Eve's age with evidence
for early birth rank and let Q the sum of the a priori probabilities of
women of Eve's age without such evidence. Then a crude
estimate of Eve's current birth rank improbability is P/(P+Q). This
number will, I would think, be much smaller than 1.

Nevertheless, what Eve would really like to calculate would be a
ratio with numerator her own personal current a prior probability. I
do not believe that there is a sensible denominator for this except
that provided by the set of all other observers of her age
(age is equivalent in my theory to complexity and is effectively
definable). My claim is that the corresponding ratio is not
significantly smaller for Eve than for you or me.

Should Eve worry about the smallness of P/(P+Q)? As defined, it
may depend on the precise Hamiltonian used in the theory.
Should Eve attach more credence to Hamiltonians giving larger

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.

For Eve, I was trying to imagine the closest possible world to how I
think the real universe is, in which your scenario, based on the idea
that Eve knew her true birth rank, could work at all.

In my theory, all Eve has is her own mental history. This would be
unaffected if she lived on an isolated island but did not know about
the other islands. Indeed, in my version of the many-minds
interpretation, she would be the same observer in both cases; with
the possibility among her (multiple) futures of her discovering other

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

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.)

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 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.)

(This point revises what I said about Eve. Actually, (were she
plausibly to exist at all), because she has so little evidence of
prior species history, her individual a priori probability might well
be somewhat greater than yours or mine.)

Matthew Donald (
web site:
``a many-minds interpretation of quantum theory''

Received on Mon Sep 25 2000 - 02:49:03 PDT

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