Bruno Marchal wrote:
>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...
Jesse
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Received on Tue Feb 03 2004 - 23:17:12 PST