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Originally Posted by BioSci
I will repeat one last time - that is not what the Carter probability is doing. It does not apply probability to multiple values of a specific "M" to estimate total "N." It applies a statistical argument to any one individual. There is no dependence on the value "M" for the argument.
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What you are failing to recognize is that applying it to an individual
is invoking an M value-- it is simply the birth number of that individual, and it is used to specify the entire catastrophe scenario. Let me put it another way. Let's say there are a million different intelligent species in the universe, all of whom think of the Carter catastrophe at some point. Let us go into the minds of the subclass of those individuals whose birth number is, say, 15 billion, which is kind of like our own. Now let us ask a simple question: do we expect that 90% of that subclass are living in the last 90% of the number of their kind?
The answer to this, if you understand probability, is:
no, we simply have
no idea what that fraction will be, which is easily verifiable by simply choosing some distributions of N for those million species and checking my claim that it will
not yield 90% (try it, really, you probably can't understand what I'm saying until you do). Saying that 90% is therefore the best we can do is like saying that anything can either happen or not, so everything has a 50% chance of happening if we know nothing else. That's wrong use of probability, which is different from correct use of probability in the absence of much information. The Carter argument, if it is applied to us at this moment in human history, i.e., to this M, is simply wrong use of probability.
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It simply uses the "the plainly obvious statement that 90% of beings live in the last 90% of any set from which they are generically chosen" and combines with our observed exponential growth to arrive at a simple statistical probability that the end is likely near.
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I already addressed the fallacy of "combining" that with any expectation of continued exponential growth. On what basis would we choose that combination, pray tell? But that's another issue, I prefer to think of the Carter conjecture in terms purely of birth number, for that requires less absurd assumptions and is therefore wrong for far more subtle reasons.
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If you use no other information, it is a valid statistical estimate.
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That's like saying that if I think of a number, and you try to guess it, you can either be right or wrong. Since there are two possibilities, and you have no other information to go on, the best you can do is assume you have a 50% chance of being right. Shall we call that a valid statistical estimate, and blame our lack of information? No, when we lack all information, we also lack the very meaning of probability.
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If you think there are other arguments for probable human life existence, that the shape of our population curve will change in the future, or that your specific birth order is somehow special (not generic), then the simple, Carter (no additional knowledge) estimate will not be accurate to the extent you believe your other knowledge is informative and/or likely to be correct.
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So Carter is using no information to say it will continue to be exponential, but I'm bringing in something new if I ask for a reason to accept that assumption? Not.