Doomsday argument
The Doomsday argument is an argument advanced by some which predicts an unexpectedly early end to the human race.
Some scholars have used an estimate of the running total of the human population (perhaps 20 billion people) to help forecast the end of man. This article describes one version of the argument, put forth by Richard Gott III. A Bayesian refutation of this argument has been published by Carlton M. Caves of the University of New Mexico (see below).
The Doomsday argument
Assuming the following (held out to be valid computations of probability):
- If you pick a number uniformly at random in a set of numbers from 1 to N, where N is a finite number unknown to you, and if we name that number j, then:
- Your unbiased estimate of N is 2 * j,
- You can say with 95% confidence that N is between 40/39 * j and 40 * j.
The Copernican principle says that you do not occupy a special place in the universe, in time or space. So, your birth rank in the history of mankind is random, i.e. not special in any way, and you can say that your birth has been selected uniformly from the set of all births. Then your best estimate for the total number of humans ever to live is 40 billion (based on the estimate that 20 billion have lived so far). And you could say with 95% confidence that it would not exceed 800 billion.
Assuming that the world population stabilizes at 10 billion and a life expectancy of 80 years, the end of humanity can be estimated to be A.D. 2160, and you can say with 95% confidence that mankind will disappear in 1,600 years.
Depending on your projection of world population in the forthcoming centuries, your estimates might vary, but the main point of the argument is that mankind would disappear rather soon.
This sort of reasoning requires the Bayesian interpretation of probability, which is not universally accepted. It also ignores any 'prior' knowledge on the distribution of N.
Other versions
This argument has generated a lively philosophical debate, and no consensus has yet emerged on its solution. Gott's argument has been improved in various ways, in particular to take into account the 'prior' probability distribution of N; the argument then shows that the probability of an early doomsday is significantly increased once you take into account your birth rank.
This argument plays a central role in Stephen Baxter's science fiction book, Technological singularity
