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Originally Posted by Sam5
... it seems to me that based on the basic premise of the story, every generation would be just as much “near the end”, if we think that “this” generation is “near the end.” Or to put it another way, every generation would have just as much a chance of being “near the end” as any other.
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That's exactly right. If the population curve were exponential from the very start, each generation would assume, with 95% certainty, that they were close to the Carter Catastrophe. That level of certainty implies that 5% of those who made that deduction would be wrong, and 95% would be right. But because of the exponential growth in population, the first 5% (the ones who're wrong) are strung out over most of history, and the last 95% crowd into the last few generations before the extinction.
So (like everyone else who's ever lived) we can use Carter's argument to deduce with 95% certainty that we're close to the End of Days. But there's a 5% chance that we're wrong, and in fact ahead of us is a vast bulge containing more than 95% of all the people who'll ever live.
They'll be the 95% who're right, and
we'll be in the 5% who're wrong, along with everyone else in history so far.
Grant Hutchison