# Doomsday Argument

The Doomsday argument (DA) is a probabilistic argument that claims to predict the number of future members of the human species given only an estimate of the total number of humans born so far. Simply put, it says that supposing the humans alive today are in a random place in the whole human history timeline, chances are we are about halfway through it.

It was first proposed in an explicit way by the astrophysicist Brandon Carter in 1983, from which it is sometimes called the Carter catastrophe; the argument was subsequently championed by the philosopher John A. Leslie and has since been independently discovered by J. Richard Gott and Holger Bech Nielsen. Similar principles of eschatology were proposed earlier by Heinz von Foerster, among others.

Denoting by N the total number of humans who were ever or will ever be born, the Copernican principle suggests that humans are equally likely (along with the other N − 1 humans) to find themselves at any position n, so humans assume that our fractional position f = n/N is uniformly distributed on the interval prior to learning our absolute position.

f is uniformly distributed on (0, 1] even after learning of the absolute position n. That is, for example, there is 95% chance that f is in the interval (0.05, 1], that is f > 0.05. In other words we could assume that we could be 95% certain that we would be within the last 95% of all the humans ever to be born. If we know our absolute position n, this implies an upper bound for N obtained by rearranging n/N > 0.05 to give N < 20n.

If Leslie's Figure is used, then 60 billion humans have been born so far, therefore it can be estimated that there is a 95% chance that the total number of humans N will be less than 20 × 60 billion = 1.2 trillion. Assuming that the world population stabilizes at 10 billion and a life expectancy of 80 years, it can be estimated that the remaining 1,140 billion humans will be born in 9,120 years. Depending on the projection of world population in the forthcoming centuries, estimates may vary, but the main point of the argument is that it is unlikely that more than 1.2 trillion humans will ever live. This problem is similar to the famous German tank problem.

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