Only 762 years of humanity left, according to mathematician.

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The core of Dr. Gott’s reasoning (independently advanced by two other physicists, Brandon Carter and Holger Bech Nielsen) is known to statisticians as the “German tank problem.” When the Allies were planning the Normandy landings, they wanted to know roughly how many tanks the Germans could be expected to have on D-Day. One clue was the meticulous consecutive numbering of German tanks and their components.

Army statisticians reasoned that captured tanks and parts could be regarded as randomly drawn from all of those that Germany produced. The serial numbers gave certain evidence of the minimum number (it couldn’t be less than the highest serial number captured). All the numbers taken together provided a statistical probability—though not a certainty—for how many more existed and, based on that, for how many more could likely be produced by D-Day. After the war, captured German records revealed that the statisticians’ estimates were almost exactly right.

To apply this to the future of humanity, the doomsday argument begins by asking us to imagine a list of all past, present and future people, sorted in their order of birth. No one alive knows how long the list is or where their own names fall in it, so we can consider ourselves randomly drawn. That means that statistically there is an equal, 50% chance that we are in the first half or the last half.

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Humans do not come with serial numbers, of course. But Dr. Gott recognized that demographers have already roughly estimated the number of humans so far. They put the total number of people who ever lived, from the beginnings of Homo sapiens to the present day, at about 100 billion. That means that my birth-order “serial number,” like that of anyone alive now, is somewhere around 100 billion.

Since it is equally likely that those of us living today are in the first or second half of all past and future human births, let’s say that we are in the second half—which would mean that there are no more than 100 billion births yet to come. There is a 50% chance that is true, which at the current global birthrate (about 131 million a year) translates to a 50% chance that we have at most 760 more years of births. A changing birthrate would modify that estimate, but the calculation is that simple.

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