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Originally Posted by grant hutchison
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
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And what is the chance that every generation of humans belonged to that 5 percent instead of the 95 percent? Well, that must be way smaller than the 5 % chance that we will be a long living species.
To say it in another way: the chance that we will be a long existing species is much bigger than the chance that we have made it thus far yet.
Just to put all this statistic spielerei into perspective...