Doomsday argument

The Doomsday argument is an argument, purely from probability theory, that purports to show that humanity will probably go extinct sometime within the roughly foreseeable future, possibly less than one thousand years.[1] It is extremely controversial, both in professional and lay circles.

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“”Almost everyone who hears this argument immediately sees something wrong with it.

The problem is, everyone thinks it's wrong for a different reason. And the more they study it, the more they tend to change their minds about what that reason is.
—Randall Munroe of xkcd, Twitter Timeline Height

Of tanks and humans

The argument has its roots in the German tank problem, which was the attempt by the Allies during World War II to determine how many tanks Germany was producing purely by examining the serial numbers of the tanks that they were able to observe. While it's of course impossible to determine such a number with complete accuracy, if you get four tanks and they all have numbers under twenty, there probably aren't more than twenty of them; and similarly if the numbers have five digits apiece, there are probably tens of thousands of them. Thus we can make a rough guess as to how many there are. (This ignores the fact that you can fake serial numbers, which was a problem for the German tank study but isn't one for the Doomsday argument.)

If we have just one such number, we can make a very rough guess that the number we have is probably about half of the total. If we're looking at tank number twelve, there are probably not 600,000 tanks. Statistically, if there were that many, we would get something with six digits.

The Doomsday argument applies this to the human race. In the entire history of our species, there have been about one hundred billion humans so far. If the human race were to continue to survive for thousands of years hence, and maintained the current increase in reproduction, the total number of humans would be far greater; on the order of the high trillions or even the quadrillions. This would mean that we are observing humanity in its infancy, which is statistically unlikely. The argument therefore concludes that we're in the "middle" of the human timeline and, extrapolating from current population growth, that timeline will end roughly within the next thousand years.

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  • Wikipedia's articleFile:Wikipedia's W.svg has more detail on the math behind it, including Bayesian probability stuff, and lots of counterarguments. Including snarky ones like "Presently, only one person in the world understands the Doomsday argument, so by its own logic there is a 95% chance that it is a minor problem which will only ever interest twenty people, and I should ignore it."
  • Primer on the Doomsday Argument goes into more detailed explanation via analogies.

References
  1. Based on current population growth, the end would occur inside of a millennium. However, more optimistic models predict a stabilization of the growth rate, which would extend the duration of humanity by as much as nine thousand years, while not altering the total number of humans.
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