Thank you Jesse for your clear answer. Your comparison of your use of both ASSA and RSSA with Google ranking system has been quite useful. This does not mean I am totally convince because ASSA raises the problem of the basic frame: I don't think there is any sense to compare the probability of "being a human" or "being a bacteria" ..., but your "RSSA use of ASSA" does not *necessarily* give a meaning to such strong form of absolute Self Sampling Assumption, or does it?
No, I don't think it's *necessary* to think that way. Nick Bostrom gives a good example of the use something like the "absolute self-sampling assumption" in the FAQ of anthropic-principle.com, where two "batches" of humans would be created, the first batch containing 3 members of one sex, the second batch containing 5000 members of the opposite sex. If I know I am the outcome of this experiment but I don't know which of the two batches I am a part of, I can see that I am a male, and use Bostrom's version of the self-sampling assumption to conclude there's a 5000:3 probability that the larger batch is male (assuming the prior probability of either batch being male was 50:50). One way to look at this is that if the larger batch is male, "I" have a 5000/5003 chance of being male and a 3/5003 chance of of being female--but presumably since you don't think it makes sense to talk about the "probability" of being a bacteria vs. a human, you also wouldn't think it makes sense to talk about the "probability" of being a male vs. being a female. So, another way to think of this would just be as a sort of abstract mathematical assumption you must make in order to calculate the conditional probability that, when I go and ask the creators of the experiment whether the larger batch is male or female, I will have the experience of hearing them tell me it was male. This mathematical assumption tells you to reason *as if* you were randomly sampled from all humans in the experiment, but it's not strictly necessary to attach any metaphysical significance to this assumption, it can just be considered as a step in the calculation of probabilities that I will later learn various things about my place in the universe.
In a similar way, one could accept both an absolute probability distribution on observer-moments and a conditional probability distribution from each observer-moment to any other, but one could view the absolute probability distribution as just a sort of abstract step in the calculation of conditional probabilities. For example, consider the two-step duplication experiment again. Say we have an observer A who will later be copied, resulting in two diverging observers B and C. A little later, C will be copied again four times, while B will be left alone, so the end result will be five observers, B, C1, C2, C3, and C4, who all remember being A in the past. Assuming the probable future of these 5 is about the same, each one would be likely to have about the same absolute probability. But according to the Google-like process of assigning absolute probability I mentioned earlier, this means that later observer-moments of C1, C2, C3 and C4 will together "reinforce" the first observer-moment of C immediately after the split more than later observer-moments of B will reinforce the first observer-moment of B immediately after the split, so the first observer-moment of C will be assigned a higher absolute probability than that of B. This in turn means that A should expect a higher conditional probability of becoming C than B. So again, you can say that this final answer about A's conditional probabilities is what's really important, that the consideration of the absolute probability of all those future observer-moments was just a step in getting this answer, and that absolute probabilites have no meaning apart from their role in calculating conditional probabilities. I can't think of a way to justify the conclusion that A is more likely to experiencing becoming C in this situation without introducing a step like this, though.
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. But I think this is more of a philosophical difference, so that even if an ultimate TOE was discovered that gave unique absolute and conditional probabilities to each observer-moment, people could still differ on the interpretation of those "absolute probabilities".
I think also that your view on RSSA is not only compatible with the sort of approach I have developed, but is coherent with "Saibal Mitra" backtracking, which, at first I have taken as wishful thinking.
What is the "backtracking" idea you're referring to here?
OK you make me feel COMP could be a little less
frightening I'm use to think.
Well, if I've spared you some sleepless nights I'm glad! ;)
Concerning consciousness theory and its use to isolate a similarity
relation on the computational histories---as seen from some first person
point of view, I will try to answer asap in a common answer to
Stephen and Stathis (and you) who asked very related questions.
Alas I have not really the time now---I would also like to find a way to explain
the consciousness theory without relying too much on mathematical logic,
but the similarity between 1-histories *has* been derived technically in the part
of the theory which is the most counter-intuitive ... mmh I will try soon ...
Yes, I definitely hope to understand the details of your theory someday, I think I will need to learn some more math to really follow it well though. My current self-study project is to try to learn the basic mathematical details of quantum computation and the many-worlds interpretation, but after that maybe I'll try to study up a bit on mathematical logic and recursive function theory. And even if I do, there's the little problem of my not knowing French, but I'll cross that bridge when I come to it...
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