Doomsday argument

The Doomsday Argument (DA), or Carter catastrophe, is a probabilistic argument that claims to predict the future population of the human species based on an estimation of the number of humans born to date. The Doomsday argument was originally proposed by the astrophysicist Brandon Carter in 1983, leading to the initial name of the Carter catastrophe. The argument was subsequently championed by the philosopher John A. Leslie and has since been independently conceived by J. Richard Gott and Holger Bech Nielsen. Similar principles of eschatology were proposed earlier by Heinz von Foerster, among others. A more general form was given earlier in the Lindy effect, which proposes that for certain phenomena, the future life expectancy is proportional to (though not necessarily equal to) the current age and is based on a decreasing mortality rate over time. The premise of the argument is as follows: suppose that the total number of human beings that will ever exist is fixed. If so, the likelihood of a randomly selected person existing at a particular time in history would be proportional to the total population at that time. Given this, the argument posits that a person alive today should adjust their expectations about the future of the human race because their existence provides information about the total number of humans that will ever live. If the total number of humans who were born or will ever be born is denoted by , then the Copernican principle suggests that any one human is equally likely (along with the other humans) to find themselves in any position of the total population , so humans assume that our fractional position is uniformly distributed on the interval [0,1] before learning our absolute position. is uniformly distributed on (0,1) even after learning the absolute position . For example, there is a 95% chance that is in the interval (0.05,1), that is . In other words, one can assume with 95% certainty that any individual human would be within the last 95% of all the humans ever to be born.