Doomsday argument Guide, Meaning , Facts, Information and Description

The Doomsday argument is a probabilistic argument that claims to predict the future lifetime of the human race given only an estimate of the present running total of the human population (perhaps 60 billion people born so far).

It was first proposed by the astrophysicist Brandon Carter in the 1980s and was subsequently championed by the philosopher John Leslie. It has since been independently discovered by Richard Gott III and Nielsen. This article follows Gott's development of the argument.

Table of contents

1 The Doomsday argument 2 Other versions 3 See also 4 External links

The Doomsday argument

Let us imagine our fractional position f=n/N along the chronological list of all the humans who will ever be born, where n is our absolute position from the beginning of the list and N is the total number of humans.

Assuming that we are equally likely (along with the other N humans) to find ourselves at any position n, we can assert that our fractional position f is uniformly distributed on the interval (0,1] prior to learning our absolute position. This is an example of the Copernican principle.

Let us further assume that our fractional position f is uniformly distributed on (0,1] even after we learn of our absolute position n. This is equivalent to the assumption that we have no prior information about the total number of humans, N.

Now, we can say with 95% confidence that f=n/N is within the interval (0.05,1]. In other words we are 95% certain that we are within the last 95% of all the humans ever to be born. Given our absolute position n, this implies an upper bound for N obtained by rearranging

n / N > 0.05

to give

N < 20n.

If we assume that 60 billion humans have been born so far then we can say with 95% confidence that the total number of humans, N, will be less than 20*60=1200 billion.

Assuming that the world population stabilizes at 10 billion and a life expectancy of 80 years, one can calculate how long it will take for the remaining 1140 billion humans to be born.

Thus we find the argument predicts, with 95% confidence, that mankind will disappear within 9120 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 will disappear rather soon.

Remarks

• A precise formulation of the argument requires the Bayesian interpretation of probability, which is widely, if not universally, accepted.

• The argument assumes no 'prior' knowledge on the distribution of N. This is not an unreasonable assumption for 'in principle' reasoning.

• The argument does make the implicit assumption that N is finite. This is because a uniform probability distribution cannot be defined over an infinite range of positions. As, in principle, there is no reason why N should not be infinite this seems like a pointer to a fundamental problem with the argument.

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.

See also

• An attempted Bayesian refutation of this argument has been published by Carlton M. Caves of the University of New Mexico (see below).

• This argument plays a central role in Stephen Baxter's science fiction book, .

• Technological singularity

External links

• Nick Bostrom's version of the argument
• A Critique of the Doomsday Argument by Robin Hanson
• A third route to the doomsday argument
• Caves' Bayesian critique of Gott's argument. C. M. Caves, "Predicting future duration from present age: A critical assessment," Contemporary Physics 41, 143-153 (2000).

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