RE: Conditional probability & continuity of consciousness (was:

From: Jesse Mazer <>
Date: Thu, 06 Sep 2001 14:39:13 -0400

>From: Marchal <>
>To: <>
>Subject: RE: Conditional probability & continuity of consciousness (was:
>Date: Jeu, 6 Sep 01 10:53:17 +0100
>Charles Goodwin wrote:
> >
> >I don't see how you can talk about the "probability of being a particular
> >observer moment". The probability is 1 at that moment! We
> >don't get dropped into observer moments from some metaphysical realm
> >Fred Hoyle's flashlight-and-pigeonholes analogy in
> >"October the 1st is too late") - we ARE those observer moments. It's a
> >like the probability of me being born as me. The
> >probability was 1, because otherwise I wouldn't be me! Similarly for this
> >particular observer moment.
>So the question is "knowing that I am living (1-person view) this
>observer-moment, what can I expect (immediately)?
>The answer will be given by a measure on the 1- observer-moment
>described in some 3-person view.
>My feeling is that Charles and Jesse agree here.
>Unlike Jacques Mallah, but like Charles, I cannot give meaning to an
>absolute a priori probability on "observer-moment", but I can give,
>like Jesse conditional or relative probabilities. This is because
>the constraint of theoretical computer science are enough for
>isolating natural nearness relations bearing on computational states
>and histories.
>I agree with Jesse that my actual observer-moment is not a matter
>of definition. Nor will I appreciate, if I ask my doctor if there
>is a high chance of surviving a delicate operation, that he answers
>me that it is a matter of definition.

Hmm, I think we actually have a full spectrum of opinions here...Jacques
believes only in absolute probability, Bruno believes only in conditional
probabilities, and I believe in both. So, of course, I agree with what Bruno
said about the importance of conditional probabilities--what happens to me
after an operation is not a matter of definition--but I also think there
should be an absolute distribution to tell me how likely it is that I will
experience one type of observer-moment vs. another in the first place.

I don't really think there's some "other metaphysical realm" where we get
dropped from, but I do think that, as an analogy, the spotlight one is not
actually so bad. After all, if you think that you just *are* your current
observer-moment, how can you possibly become any other one? The
observer-moment itself doesn't transform--it's just sitting there timelessly
in Platonia among all other possible observer-moments. So, it's better to
think of "continuity of consciousness" as a spotlight moving between
different observer-moments, with the probability of going from one to
another defined by the conditional probability distribution.

Similarly, if you just *are* your current observer-moment with probability
1, nothing else can be said, so there doesn't seem to be any way to assign
meaning to an absolute probability distribution on all observer-moments. I
think it makes more sense to think of this distribution as the probability
that a randomly-selected spotlight will be shining on a particular
observer-moment, like in the Hoyle story. If we abandon the idea of an
absolute probability distribution, we have no hope of explaining why I am
this particular type of observer-moment experiencing this particular type of
universe, and we can only explain why my future experience will have a
certain amount in common with my current experience (assuming that's what
the conditional probability distribution actually predicts). But plenty of
observer-moments might find themselves experiencing universes with very
different laws of physics--why am I experiencing these laws as opposed to
some other set? Without a global probability distribution this can only be a
brute fact, unexplained by the TOE. Likewise, why am I experiencing this
particular era of the universe's history, or this unusual spatial region
(the surface of a planet containing complex life), or this particular
organism's point of view (a human vs. some other animal)? In all of these
cases I think the intuitive explanation is something like the "anthropic
principle" or the "self-sampling assumption" (this term is explained on by Nick Bostrom, for anyone who's not
familiar with it), and my hope is that the global probability distribution
would incorporate a formalized version of something like this. But without
such a global probability distribution, all this stuff becomes just more
brute facts.

Just because something has probability 1 from your current point of view, I
don't think that means it should be treated as a brute fact. If so, all
historical scientific theories would be pointless--cosmologists would be out
of a job, for example. As long as we can imagine that things *could* have
been different, we should try to explain why they are the way they are. Even
though I know with probability 1 that I am Jesse Mazer sitting in front of a
computer right now, I think I can imagine somehow that this could have been
different--that my current experience could have been that of Blackbeard the
pirate sailing the high seas, or that of a bat locating bugs through
echolocation, or even that of a 12-dimensional alien living in a universe
with very different laws of physics. The global probability distribution
would hopefully tell me something about which types of observer-moments my
"spotlight" is more likely to find itself shining on in the current moment.

I wrote something about two different meanings of the "anthropic principle"
in another post a while ago (at ) which might be relevant
here. The idea was that the weak anthropic principle can be used in two
slightly different ways--one version is just to say that I know with
probability 1 that I am a particular type of intelligent organism, and that
I use this to reason backwards and make deductions about what the universe
must be like, given that fact. But the second version actually tries to go
the other way and explain *why* I find myself to be an intelligent organism,
by starting from a universe/multiverse large enough to contain at least a
few intelligent organisms somewhere, no matter how rare, and then saying
that in some sense I am guaranteed to find myself in one of those rare
intelligence-containing regions since otherwise I wouldn't be an "I" at all.
Here was the section of the post where I talked about the distinction:

"I think we need to distinguish between two kinds of anthropic reasoning
here. The first version just says "I observe that I exist, so I know with
probability 1 that I must occupy a time and place where my existence is
possible." Obviously this is completely uncontroversial. In this version,
though, it's not really important that you say "I exist" or "intelligent
observers capable of anthropic reasoning exist"--you could just as easily
have made up the "star-thropic principle" which says that you know with
probability 1 that stars exist, so you must be in a time and place where
star formation is possible.

As originally envisioned by Carter, both the "strong" and "weak" anthropic
principles were versions of this idea. In "Modern Cosmology & Philosophy,"
John Leslie writes that "Carter's weak principle reminds us of the obvious
but oft neglected truth that our place and time must, granted that we are in
fact there, be a place and time where observers can exist: they are not, for
example, fried immediately, as they would be shortly after the Big Bang.
Carter's strong principle similarly reminds us that our universe must--as we
do exist in it, don't we?--be a universe whose nature is not
life-excluding...the 'must' is in both cases like that of 'The photo is
marked WIFE, so *must* be of a woman.' No suggestion that the photo *had to
be* of a woman or that it is somehow especially easy to be a woman!"

But there's another version of "anthropic reasoning" which, although it
perhaps deserves a different name, seems to me to be valid as well. This
version says that, given that at least some observer-containing regions
exist, "I" must find myself in one of these regions. In this case "I" is
like the "I" in the Doomsday argument, which says "I" could have been born
at any time in history, despite the fact that I wouldn't be the same person
if I'd been born at some other time. In this version the fact that we're
talking about "observers" is important--it wouldn't work with stars or
anything else.

If I win the lottery, I'm pretty "lucky"--I could just as easily have been
one of the losers. On the other hand, despite the fact that physically
realized genetic codes occupy only a tiny fraction of the space of all
possible human DNA sequences, I wouldn't say I'm "lucky" to have an existing
sequence rather than a nonexisting one--it isn't possible to "be" a
nonexistent person, so of course I'm one of the existing ones (assuming for
the moment that these other sequences aren't realized in a parallel universe
or something). This is an application of the second version of anthropic

The distinction between these two versions still may not be entirely clear.
Another way to put it is that the second version, when coupled with the
assumption of multiple universes/regions, allows you to *explain* why you
find yourself in what is possibly a quite unlikely set of circumstances.
For instance, if we assume that many physical constants are indeed set
randomly, then it seems the fact that our universe's constants are
fine-tuned to allow life becomes less puzzling if we assume multiple
universes (or multiple regions with different constants). In this case, the
"explanation" for the apparent fine-tuning is that at least one
correctly-tuned universe is likely to exist, and the second version of the
anthropic principle says that's the universe that "I" must find myself in.
In contrast, the first version can't explain anything at all--it's just a
statement about your prior knowledge.

An even clearer way to distinguish the two versions is that the second
version allows you to make new inferences about reality, while the first
only describes what you already know. For example, if we find that our
universe is indeed fine-tuned, then by a version of Bayesian reasoning we
can say we should be more inclined to believe in the existence of other
universes with different constants, in order to explain the "coincidence" of
observed fine-tuning (to make this more obvious, feel free to assume we know
a priori that there's a 50% chance God created a single universe and a 50%
chance he created a multiverse).

This is similar to "copernican" reasoning, like the Doomsday argument, which
also allows you to infer new things about reality just by observing your own
position in it. In fact, I'd make a case for distinguishing the two
anthropic principles by saying the second is identical to what's sometimes
called the "copernican anthropic principle." For example, most people who
say fine-tuning increases the probability of multiple universes would also
say that we're more likely to find ourselves in a universe where observers
(or observer-moments) are more common rather than one where they are rare,
assuming the number of each kind of universe is about equal."


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Received on Thu Sep 06 2001 - 11:40:48 PDT

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