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
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