Bruno Marchal wrote:
>
>At 20:17 03/02/04 -0500, Jesse Mazer wrote:
>
>>Personally, I would prefer to assign a deeper significance to the notion
>>of absolute probability, since for me the fact that I find myself to be a
>>human rather than one of the vastly more numerous but less intelligent
>>other animals seems like an observation that cries out for some kind of
>>explanation.
>
>
>
>I am not sure about that. Suppose a teacher has 10^1000 students. Today
>he says to the students that he will, tomorrow, interrogate one student of
>the
>class and he will chooses it randomly. Each student thinks that there is
>only
>1/(10^1000) chance that he will be interrogated. That's quite negligible,
>and
>(assuming that all student are lazy) none of the students prepare the
>interrogation.
>But then the day after the teacher says: "Smith, come on to the board, I
>will
>interrogate you".
>I hope you agree there has been no miracle here, even if for the student,
>being
>the one interrogated is a sort of (1-person) miracle. No doubt that this
>student
>could cry out for an explanation, but we know there is no explanations...
>Suppose the teacher and the student are immortal and the teacher
>interrogates
>one student each day. Eternity is very long, and there will be arbitrarily
>large
>period where poor student Smith will be interrogated each days of that
>period.
>Obviously Smith will believe that the teacher has something special against
>him/her.
>But still we know it is not the case ...
>So I don't think apparent low probability forces us to search for an
>explanation
>especially in an everything context, only the relative probability of
>continuation
>could make sense, or "ab initio" absolute probabilities could perhaps be
>given for the
>entire histories.
>
But your example assumes we already know the probabilities. If Smith has two
different hypotheses that a priori both seem subjectively plausible to
him--for example, "the teacher will pick fairly, therefore my probability of
being picked is 1 in 10^1000" vs. "I know my father is the teacher's
arch-nemesis, therefore to punish my family I expect he will fake the random
draw and unfairly single me out with probability 1", then if Smith actually
is picked, he can use Bayesian reasoning to now conclude the second
hypothesis is more likely (unless he considered its a priori subjective
likelihood to be less than 10^-1000 that of the first hypothesis).
This is a better analogy to the situation of finding myself to be a human
and not one of the much larger number of other conscious animals (even if we
restrict ourselves to mammals and birds, who most would agree are genuinely
conscious, the number of mammals/birds that have ever lived is surely much
larger than the number of humans that have ever lived--just think of how
many rodents have been born throughout the last 65 million years!) Even if I
a priori favor the idea that I should consider any observer-moment equally
likely, unless I am virtually certain that the probabilities are not biased
in favor of observer-moments with human-level complexity, then finding
myself to actually be experiencing such an observer-moment should lead me to
shift my subjective probability estimate in favor of this second sort of
hypothesis. Of course, both hypotheses assume it is meaningful to talk about
the absolute probability of being different observer-moments, an assumption
you may not share (but in that case the Smith/teacher analogy should not be
a good one from your perspective).
Another possible argument I thought of for having absolute probabilities as
well as conditional probabilities. If one had a theory that only involved
conditional probabilities, this might in some way be able to explain why I
see the laws of physics work a certain way from one moment to the next, by
describing it in terms of the probability that my next experience will be Y
if my current one is X. But how would it explain why, when I examine records
of events that happened in the past, even records of events before my
subjective stream of consciousness began, I still see that everything obeyed
those same laws back then as well? Could you explain that without talking
about the absolute probability of what type of "universe" a typical
observer-moment is likely to percieve himself being in, including memories
and external records of the past?
Jesse
_________________________________________________________________
Create your own personal Web page with the info you use most, at My MSN.
http://click.atdmt.com/AVE/go/onm00200364ave/direct/01/
Received on Mon Feb 09 2004 - 16:30:43 PST