I see your point, but I don't quite agree...
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Originally Posted by grant hutchison
Once the population curve becomes a level line leading off to infinity, we're just as likely to find ourselves anywhere under that line (because there's no bulge to "concentrate lives" in one temporal region), and so we can't infer anything about survival time in the future.
Either we have exponential growth, and Carter's right, and we're likely to be living in the End of Days; or we level out our population, and Carter can't make any deductions about the future - the areal midpoint under an infinite level curve is anywhere.
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First, as the urn/ball example shows, exponential grow is not a necessary prerequisite for the basic argument; it just lets The End draw closer to the present point in time.
Second, the population curve is finite at least at one end (the past), so we have an asymmetry which makes a populated future "unlikely".
I just think trying to beat the Carter argument on its own premises is missing the point; my basic gripe ist still that the argument makes a statistical statement based on a sample size of precisely one...
But, heck, why am I arguing with you anyway? Probably you dont even exist! I know that Switzerland is roughly 200km across. The fact that I'm Swiss would be very, very unlikely if the World was seizably bigger than, say, 1000km. So, in all likelyhood, anything beyond the English Channel must be a figment of my Imagination!
Madalone