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Originally Posted by grant hutchison
Exactly. So it would be odd to find yourself among one of the first balls. The number you find yourself to be therefore does allow you to make a statistical inference about how many balls there are.
Grant Hutchison
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Yes, but it would be meaningless. It focuses on one point and ignores many others. It would be odd if I was the first human. It would be odd if I was the last human. It would be odd if I were the middlest (?) human. It would be odd if my 'birthnumber' would be exactly a prime number. Yet, someone has to be (or will be or has been) one of these. For a species to exist 100 years, a specimen has to exist after ten years. For a species to exist 100 billion years, a specimen has to exist after ten years. As long as we don't know what the average lifetime of a species (or an intelligent species, or whatever distinction you like to make) is, we can't make any useful statistics.
Using 'your' statistics, the best chance for a long future of humanity would be to kill all humans except a hundred or so, and keep humanity at that number. That would mean that if my number 9 billion is an average number (which wouldn't be that odd compared to it being an early number), we could have 90 million generations more after this one. Reduce it to a couple that has two children and so on, and you'll have 4.5 billion of those couples before homo sapiens gets extinct! I think you'll see that this shows that statistics can 'prove' anything and that the basic premisse (of the peculiarity of us living now unless we are doomed fairly soon) is flawed.