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Originally Posted by grant hutchison
We know that only one ball is extracted, in this analogy. You live only once, and therefore you represent one ball.
You have no control over the time at which the ball is selected. You simply come into existence, and check your position in the birth order. If there are a very large number of balls, then you're unlikely to find yourself in the first few.
Grant Hutchison
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If you are number 7, then you are very likely to be in the first few
This is a variation on the strong vs. weak anthropogenic principle. You have to make the distinction between an outsider who has the choice from all balls and picks out a low number, or a ball itself, which has a number, period. I am ball number 7, and that says nothing at all about the chances for survival of humanity in the next 100, 1000 or billion years. I can not pick any ball I want, and so the "choice" of a ball is no choice at all.
To expand my slowly filling barrel analogy to make it more resemble reality. The barrel is slowly filling and even more slowly emptying again. You are allowed one moment to pick one ball. If you get a low number, then this only proves that the barrel didn't exist very long yet. This says nothing at all about how long it will exist in the future.
It's like madalone says:
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my basic gripe ist still that the argument makes a statistical statement based on a sample size of precisely one...
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