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The Doomsday argument is a probabilistic argument that claims to predict the future lifetime of the human race given only an estimate of the total number of humans 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 H. B. Nielsen. Similar theories predicting an end to the world from population statistics were proposed earlier by Heinz von Foerster, among others.
This article primarily follows Gott's development of the argument.
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 (Leslie's figure) 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 is likely to 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. In principle there seems to be no reason why we must assume the prior existence of some finite upper bound to our position n which suggests that there is a fundamental problem with the argument.
- One can arbitrarily choose, depending on one's definition of "human", the total number of humans having been born so far, and arrive at completely different answers.
Simplification
Here is a simplified version of the argument, based on A refutation of the Doomsday Argument by Korb and Oliver (http://www.findarticles.com/p/articles/mi_m2346/is_n426_v107/ai_20550244).
Assume for simplicity that there are two possible numbers for N, the total number of humans who will ever be born: either N=60 billions, or N=6 000 billions. Now, you have no a priori knowledge of your position in the history of humanity, so you decide to compute how many humans have been born before you. It turns out that you are human #59 854 795 447, i.e. one of the first 60 billions.
Now, if in fact N=60 billions, the probability that you were in the first 60 billions is 100%, of course. However, if N=6 000 billions, then the probability that you were in the first 60 billions is only 1%. Therefore, it is more likely that N=60 billions (although it is not certain). In fact, N is monotonously less probable as it grows larger. It is possible to compute the probability for each N and then to compute an average. Taking the numbers above, it is 95% certain that N is smaller that 1200 billion.
Other versions
This argument has generated a lively philosophical debate, and no consensus has yet emerged on its solution. Leslie's argument differs from Gott's version in that he does not assume a 'vague' prior probability distribution for N. Instead he argues that the force of the argument resides purely in the increased probability of an early Doomsday once you take into account your birth position regardless of your prior probability distribution for N. In fact the use of a vague prior distribution of the form P(N)=1/N seems well-motivated as it assumes as little knowledge as possible about N. As mentioned above, it is in fact equivalent to the assumption that the probability density of one's fractional position remains uniformly distributed even after learning of one's absolute position.
Singularity
Heinz von Foerster argued that humanity's abilities to construct societies, civilizations and technologies do not result in self inhibition. Rather, societies' success varies directly with population size. Von Foerster found that this model fit some 25 data points from the birth of Jesus to 1958, with only 7% of the variance left unexplained. Several follow-up letters (1961, 1962, …) were published in Science showing that von Foerster's equation was still on track. The data continued to fit up until 1973. The most remarkable thing about von Foerster's model was it predicted that the human population would reach infinity or a mathematical singularity, on Friday, November 13, 2026.
Many Worlds
The problem with the argument might lie in its implicit assumption of a pre-determined linear timeline. The many-worlds interpretation of quantum mechanics suggests that time has a network-like structure with many actually-occurring pasts merging into each present moment and many actually-occurring futures branching from each present moment. The apparent linearity of time is due to the fact that our memories are consistent with only one past. It has been suggested that a generalized form of the argument, in which all finite values of total population size are realized in different futures, avoids both the prior assumption of a finite upper bound to our birth position and also any correlation between our present position and a particular future total population size that we experience should we live long enough to see Doomsday.
See also
External links
References
- John Leslie, The End of the World: The Science and Ethics of Human Extinction, Routledge, 1998, ISBN 0-415-18447-9.
- J. R. Gott III, Implications of the Copernican Principle for our Future Prospects, Nature, vol. 363, pp. 315-319, 1993.
- J. R. Gott III, Future Prospects Discussed, Nature, vol. 368, p. 108, 1994.
- This argument plays a central role in Stephen Baxter's science fiction book, , Del Rey Books, 2000, ISBN 0-345-43076-X.
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