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Originally Posted by Fram
But for the Carter catastrophe to be correct, you could take an imaginary 1 million species to start with. After 1 generation, only X (let's say 100,000) would still exist. Of those, 20,000 gets to a third generation, and perhaps 5,000 to a fourth one, and so on. So the chance that we have reached here is of course 100%, but the chance that a first generation species has survived as long as we did is 1 in 1,000,000 (random number, again). So it is much more amazing that we exist, according to the same hypothesis, than it is to suppose that we will exist for a very long time afterwards...
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Carter's calculation necessarily applies to a
single species, the species of the observer. Otherwise the observer would not be a random sample from all possible individuals in the population.
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Originally Posted by Fram
Another criticism / point of view. An alien visits the earth, and sees just one generation of people. The chance that it sees us is bigger if only a few more generations will survive than if we will live for millioàns of generations (thus far, standard Carter).
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Carter doesn't say anything about this, and it doesn't seem to make sense, probabilistically.
Carter says only that an alien who
did encounter us might be able to make some prediction about how long we will survive in the future, based on how many individuals of our species have lived so far. An alien passing at random is always more likely to encounter a long-lived species than a short-lived one, and to encounter a species somewhere in the middle 90% of its existence rather than at its start or finish.
Note: I say "might be able to make some prediction", because for the alien's random sampling in
time to strictly correspond to Carter's random sampling in
lives, the population would have to be stable across time, with the same number of individuals living at any given moment.
I've realized I didn't think this through properly the first time, when I introduced my visiting alien in discussion with
eburacum. The same proviso would pertain when I suggested we might be able to apply Carter's reasoning to lemmings ... lemmings were a
very bad example indeed, since their population is notoriously unstable.
Grant Hutchison