Conditional probability & continuity of consciousness (was: Re: FIN Again)

From: Jesse Mazer <>
Date: Wed, 05 Sep 2001 17:45:08 -0400

>From: "Jacques Mallah" <>
>Subject: Re: FIN Again (was: Re: James Higgo)
>Date: Thu, 30 Aug 2001 17:51:46 -0400
>>From: "Jesse Mazer" <>
>>I don't understand your objection. It seems to me that it is perfectly
>>coherent to imagine a TOE which includes both a universal "objective"
>>measure on the set of all observer-moments and also a relative conditional
>>probability which tells me what the probability is I'll have experience B
>>in the future if I'm having experience A right now.
> "You" is just a matter of definition. As for the conditional effective
>probability of an observation with characteristics A given that it includes
>characteristics B, p(A|B), that is automatically defined as p(A|B) = M(A
>B) / M(B). There is no room to have a rival "relative conditional
>probability". (E.g. A = "I think I'm in the USA at 12:00 today", B="I
>I'm Bob".)

Well, I hope you'd agree that which observer-moment I am right now is not a
"matter of definition," but a matter of fact. My opinion is that the global
measure on all observer-moments is not telling us something like the "number
of physical instantiations" of each one, but rather the probability of
*being* one particular observer-moment vs. some other one. I would be
interested to hear what you think the measure means, though, since my
version seems to require first-person facts which are separate from
third-person facts (i.e., which observer-moment *I* am).

In any case, I'm pretty sure there's room in a TOE for a "conditional
probability" which would not be directly deducible from the global
probability distribution. Suppose I have a large population of individuals,
and I survey them on various personal characteristics, like height, IQ, age,
etc. Using the survey results I can create a global probability function
which tells me, for example, what the likelihood is that a random individual
is more than 5 feet tall. But If I then want to find out the conditional
probability that a given individual over 5 feet tall weighs more than 150
pounds, there is no way to deduce this directly given only the global
probability distribution. In this example it may be that p(A|B) = M(A and B)
/ M(B), but the point is that M(A and B) cannot be found simply by knowing
M(A) and M(B).

And a TOE could conceivably work other ways too. Suppose we have a large
number of interconnected bodies of water, each flowing into one another at a
constant rate so that the total amoung of water in any part stays constant
over time. In that case you could have something like a "global measure"
which would tell you the probability that a randomly selected water molecule
will be found in a given body of water at a given time, but also a kind of
conditional probability that a water molecule currently in river A will
later be found in any one of the various other rivers that river A branches
into. This would approximate the idea that my consciousness is in some sense
"flowing" between different experiences, splitting and merging as it goes.
Just as the path of a given molecule is determined by the geographical
relationships between the various bodies of water, so the path of my
conscious experience might be determined by some measure of the "continuity"
between different observer-moments...even though an observer-moment
corresponding to my brain 5 seconds from now and another one corresponding
to your own brain at this very moment might have equal *global* measure, I
would presumably be much more likely to flow into a future observer-moment
which is more similar to my current one.

Most generally, we can imagine that a TOE defines both a global measure on
individual observer-moments, but also a "conditional measure" on ordered
pairs of observer-moments, or perhaps longer ordered chains. There would
probably be some kind of mathematical relation between the two types of
measure, but it wouldn't necessarily have to be of the form p(A|B) = M(A and
B) / M(B) as you said. Do you see anything inherently contradictory about
this idea?

>>self-sampling assumption--what does it mean to say that "I" should reason
>>as if I had an equal probability of being any one of all possible
> It means - and I admit it does take a little thought here - _I want to
>follow a guessing procedure that, in general, maximizes the fraction of
>those people (who use that procedure) who get the right guess_. (Why would
>I want a more error-prone method?) So I use Bayesian reasoning with the
>best prior available, the uniform one on observer-moments, which maximizes
>the fraction of observer-moments who guess right. No soul-hopping in that
>reasoning, I assure you.

I'm not sure it's possible to take a third-person perspective on the
self-sampling assumption. For one thing, the reasoning only works if I
assume *my* observer-moment is randomly selected--I can't use anyone else's
or I may get incorrect results, as if I reasoned from Adam and Eve's point
of view in the doomsday argument. Then there is what Nick Bostrom calls the
"problem of the reference class," and I think there is a very good case to
be made that the problem can only be solved by making reference to some sort
of objective measure of the "consciousness level" of a particular
observer-moment. For example, suppose I find that I was created as one of
two "batches" of humans, the first batch containing 950 members and the
second containing only 50. One batch is all-male and the other is
all-female, and I know that which batch is which sex was determined by a
coinflip, so that a third-person observer would say there is a 50% chance
that the large batch is the male batch. However, since I observe myself to
be a male, I use the self-sampling assumption to reason that there is
actually a 95% chance that the large batch was all-male, simply because I'm
assuming that I'm as likely to be any human as any other, and 95% of the
humans were members of the large batch.

All right so far. But suppose I now find out that one of the two batches was
genetically engineered to lack a brain, having no consciousness whatsoever?
Or, if you prefer, suppose that one batch is not made of real humans at all,
but just marble statues of them. Can I still assume I am as likely to be any
individual as any other? I don't think so--I think some kind of "anthropic
principle" must come into play here, guaranteeing that I will be a conscious
individual rather than an unconscious one. So, even if the small-batch was
the all-male one, I would still be guaranteed to find myself a male, simply
because all the "females" in this experiment are going to totally lack
consciousness. It's just the same as how I can't assume I'm "randomly
sampled" from the set of all computations being implemented in the universe,
because the vast majority of computations, associated with things like the
random collisions of gas molecules in a nebula, will not lead to any
high-level conscious experiences...only the very rare ones associated with
biological brains which have evolved on planets with just the right
conditions will have these sorts of experiences (or so I'd assume, anyway).
Again, the anthropic principle must be taken into account.

I think this should be a matter of degree, rather than an all-or-nothing
affair. I think other animals, at least other mammals and birds, almost
certainly have some kind of high-level conscious experience, so there is
"something it is like" to be them, but I don't think I should reason as if I
was randomly sampled from the set of all these animals, either. Indeed, I
don't think it's just a lucky break that I find myself to be a member of
what is probably the most intelligent species that has ever existed on
planet earth, despite the fact that the number of animals who have ever
lived probably vastly outweighs the number of homo sapiens who have ever
lived. I think some sort of graded anthropic principle is likely to be
responsible here...the usual self-sampling assumption perhaps needs to be
replaced by some kind of weighted self-sampling assumption, with the
"weights" on an observer-moment having something to do with the complexity
of the consciousness involved. Indeed, I think it would be particularly
elegant if the whole global measure function turned out to be nothing but
this sort of weighted self-sampling assumption, although the weights would
probably have to be determined by more than *just* the level of
consciousness (after all, an observer-moment experiencing a white rabbit
could be just as complex as a 'normal' one). In other words, I think a TOE
should incorporate a "theory of the anthropic principle" rather than just
adding it onto a sort of global "physical" measure as in theories like Max
Tegmark's. The anthropic principle/physical measure distinction seems to me
to be another version of the old mind/body duality, and it would be nice if
a TOE could erase this distinction.

So I guess I should repeat the question, when you talk about a global
measure on all observer-moments, what do you think this measure means? Does
it just represent the "number of instantiations" in the multiverse, so that
if the vast majority of observer-moments/computations turned out to be of a
very simple nature, we might need to make additional recourse to the
anthropic principle to explain why we find ourselves to be experiencing
these particularly complex type of observer-moments? Or do you think, as I
do, that the global measure tells us the actual probability that "my"
current experience will be a given observer-moment, and in that case do you
agree that the global measure function must already take into account
something along the lines of the anthropic principle?

>>if I am about to step into a machine that will replicate one copy of me in
>>heaven and one copy in hell, then as I step into the imaging chamber I
>>be in suspense about where I will find myself a moment from now, and if
>>conditional probability of each possible future observer-moment is 50%
>>given my current observer-moment, then I will interpret that as a 50/50
>>chance that I'm about to experience torture or bliss.
> That depends on the definition of "you". In any case, one copy will be
>happy (the one partying with the succubi in hell) and the other will be sad
>(the one stuck hanging out with Christians). So your utility function
>should be about even. I assume you'd care about both future copies at that

Well, you're assuming that reality itself has no opinion on the definition
of "me," that it all depends on my own choice of utility function. Likewise,
perhaps someone might have a TOE in which there is no "objective" global
measure on the set of all observer-moments, that each observer-moment would
have his own measure defined by what he believes to be real.

But I think that in both cases the TOE should give me an answer which does
not depend on my own preferences--as Phillip K. Dick once said, "reality is
that which, when you stop believing in it, doesn't go away." I don't think I
could "save myself" from a hellish fate simply be redefining my utility
function so that only those copies which go to heaven are defined as
"me"--whether I find myself in heaven or hell seems to be something imposed
on me by external reality, unless the flow of consciousness is a complete
illusion. I talked about this question in an earlier post called "3 possible
views of consciousness:"

These were the 3 I mentioned:

>1. Consciousness is not "real"--our decision to call a system "conscious"
>or not is based only on subjective aesthetic criteria, like "cuteness"
>(Daniel Dennett's example). The only facts about reality are third-person
>facts, in this view.
>2. Consciousness is real, but the feeling of continuity of consciousness
>over time (the 'flow of related thoughts in time' above) is not. In this
>view, only moments of experience exist, but nothing flows between these
>3. Consciousness is real, and so is continuity of consciousness over time.
> Proponents of this view may still believe that identity can split or
>merge though (think of many-worlds, or replicator experiments).

Presumably you'd choose either 1 or 2, although I'm not quite sure which.
But do you think view #3 is "crazy," or is it just quantum immortality
specifically that you find crazy? It would be possible to believe in #3
without believing in quantum immortality, of course...I do think that once
you accept #3, as well as the "splitting" and "merging" of
consciousness-streams, then are some thought-experiments which make quantum
immortality very plausible. But they're only plausible if you already find
view #3 to be plausible in the first place.

>>Surely you agree that there is nothing *mathematically* incoherent about
>>defining both absolute and conditional probability measures on the set of
>>all observer-moments. So what's your basis for calling the idea "crazy?"
> I've explained that in other posts, but as you see, the idea is indeed
>mathematically incoherent - unless you just mean the conditional effective
>probability which a measure distribution defines by definition. And _that_
>one, of course, leads to a finite expectation value for ones's observed age
>(that is, no immortality).

The "expectation value" is a problem, but as I said it's possible to accept
#3 without accepting quantum immortality. For example, there could be a
"null observer-moment" (death) which any given observer-moment has a small
probability of becoming at any given time, and this probability could become
large given enough time. Another interesting possibility is that whatever
"conditional probability" we choose will be nonzero for *any* pair of
observer-moments, so that there is some tiny probability that my next
observer-moment will be completely unlike my current one--in situations
where the probability of my physical death is large (like observing myself
falling off a cliff), perhaps the combined conditional probability of my
next moment being fairly similar to my current one is smaller than the
combined conditional probability of a dissimilar next moment, so that I may
suddenly find myself waking up from a dream of falling as a totally
different person in a different region of the multiverse. In this way my
conscious experience could be infinite even if at any given time I find
myself as a finite organism with a finite memory.

Finally, if conditional measure and global measure mutually determine each
other in some way, there might be a way in which "young" observer-moments
could have greater global measure than "old" ones. Imagine an experiment
where I am duplicated, as in Bruno Marchal's example, once in Moscow and
once in Washington. Then a year later, if a democrat wins the U.S.
presidency, the Washington twin will be duplicated 1000 times; if a
republican wins the presidency, the Moscow twin will be duplicated 1000
times. Even though this subsequent duplication happens a year after the
original Moscow/Washington split, I think it could have an effect on my
original first-person probability of finding myself in Moscow vs. Washington
(since after all this is done, 1000 out of 1001 descendants of the original
person will remember having ended up in the city corresponding to the future
president)...we might then have the strange effect that I would have a
pretty good idea of who was going to win the presidency a year from now
based on whether I found myself in Washington or Moscow, even though this
prophecy would be useless to everyone else since they'd have no way of
knowing which twin has a lower measure/probability of being experienced.
What this might mean is that the global measure on a particular-observer
moment would be found by doing some sort of "path integral" over all
possible future histories, which would perhaps be weighed both by their
internal consistency (determined by the conditional measure--a history where
my experience leaps around between radically different observer-moments
might contribute less than a more 'seamless one') and by their objective
probability (determined by the global measure of all the constintuent
observer-moments, which would hopefully make white rabbit experiences very
unlikely). Now, there's obviously something a bit circular about this, since
it would involve finding the "objective probability" of experiencing a
particular observer-moment by doing something like an integral over all
possible first-person histories containing that observer-moment, and these
histories would be weighted by internal consistency *and* the "objective
probability" of all the other experiences in all these possible histories.
But perhaps this would allow you to bootstrap a unique global probability
distribution into existence, like solving a large set of simultaneous
equations to get unique values for each variable.

If the global probability distribution depends on the possible future
histories of each observer-moment, then it might change how we should think
of quantum immortality. For instance, instead of the immortality guarantee
only "kicking in" at the last possible moment (as the guillotine is
dropping, say), we might have a situation where the most likely
observer-moments are precisely those that can most "reasonably" be expected
to survive long periods of time (so that I'd be less likely to go to the
guillotine in the first place). Just as there may be a whiff of the
anthropic principle in the fact that I find myself to be a human rather than
one of the many other animals which has ever lived on earth, I think
something like the anthropic principle may also be involved in the fact that
I find myself at this particular point in human history, on the verge of a
possible "technological singularity" which could make my indefinite survival
seem entirely natural (see ).
And beings who are among the first to upload having their memories most
widely distributed in the future evolution of a cybercivilization spreading
throughout the universe, since they will have the most time to "expand their
minds", make large numbers of copies of themselves, etc. Thus, "young"
observer-moments on the cusp of the singularity might have much higher
global measure, just as the twin about to be duplicated 1000 times might
have had higher global measure than any of his subsequent "descendents."
Alternately, even if you ignore the possibility of such a singularity, if
you think of the MWI in terms of "splitting histories" then young
observer-moments might be more likely for similar reasons.

So, there are a variety of ways I can imagine solving the "expected age"
problem without having to throw out quantum immortality. I expect you'll
find them all somewhat crazy...that's why, for now, I'd rather focus on the
more general question of whether you think it's completely impossible that
the correct TOE would make continuity of consciousness into something
"objective" rather than something defined only by our own choices about
utility functions. I don't entirely rule out the possibility that continuity
of consciousness is a kind of illusion, but I still don't see how you can
have grounds to be sure that it is.


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Received on Wed Sep 05 2001 - 14:51:13 PDT

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