I still think my argument kills Carter; in order for a statistical argument to apply, the sample has to be taken at random; but we are not a random sample, and so statistical arguments cannot apply. We exist now, when an apparent exponential growth is occurring in the population; we did not exist in the Palaeolithic, when slow growth would indicate a distant doomsday, and we do not exist in the future, when a slowly rising interplanetary or interstellar population would indicate a distant doomsday.
We can only sample the population now, when the rapid rise in population seems to indicate a near-future doomsday, because we have only just developed the right statistical tools.
We did not have the statistical tools in the Palaolithic, so we were not concerned about Carter (and it would have indicated a distant doomsday back then anyway) and we do not yet exist in the future.
If we did exist in the future we would no longer be worried about Carter, because the population would be growing slowly again and this would extend the Doomsday ever further into the far future; additionally we would have a historical record of the period long ago when the Carter argument was first discovered, and would know that it loses its accuracy during periods of rapid growth.
In most cases Carter's Argument predicts a long, long existence for the human species; only now for a relatively brief and anomalous period, does the argument seem to indicate a near-future doomsday.
And what do you know? That is the exact same period that we discover the argument itself! This is not a coincidence; we discovered the benefits of civilisation, of science, mathematics and statistics all within a short period - this explosion in technology and knowledge has produced an explosion in population numbers, and also has produced the Carter-Leslie argument.
To recap; this statistical method requires that we are chosen from random from all humans that ever lived. That is not the case- we are self-selected and could not exist at any other period of time, not in the past or in the future.
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