Is the universe full of

**advanced alien civilizations?** If it is, why don't we have overwhelming evidence of their existence? The

**Doomsday Argument** is a mathematical theory that aims to cast light on these questions.

Suppose that you are staying in a hotel, and you know that either

(a) the hotel contains 10 rooms, consecutively numbered 1 to 10, or

(b) the hotel contains a million rooms, consecutively numbered 1 to 1000000.

Suppose that in addition, you observe that you are in room number 7. Given this, which of possibilities (a) and (b) is more likely? If (a) is true, you have a 1 in 10 chance of being in room number 7. But if (b) is true, you have a 1 in a million chance of being in room 7. So it seems that (a) is much more likely.

The original

*Doomsday Argument* works like this, but with civilizations. Let's say that you are the 70 billionth person ever to have been born. Given this, what is more likely: that the number of people who will ever live is a few hundred billion, or that the number of people who will ever live is much bigger than this? Following the hotel room logic, it would seem reasonable to deduce that there will never be trillions of human beings.

However, this argument is incorrect, because it does not take into account the fact that you are much more likely to exist in a large civilization than in a small one. To correct for this, one needs to regard people as randomly picked from the set of all possible people. In his 2012 preprint

*The Doomsday Argument in Many Worlds* http://arxiv.org/abs/1209.6251 Austin Gerig goes further and regards people as randomly picked from the set of all possible people in all possible parallel universes, in which the copies of the "same" individual in the various universes are all identified as a single person. This new version of the argument fixes the aforementioned problem in the original argument.

Gerig asks some interesting questions about this scenario. Given that you are the 70 billionth person to be born, and that you do exist, which is more likely? Are there many advanced civilizations in the universe, or just one? And is it the case that civilizations tend to become extinct before producing trillions of individuals or not? The probabilities in the picture are calculated on page 11 of the paper; I am calling civilizations

*doomed* if they typically become extinct before producing trillions of individuals. The conclusions are very striking:

**it is overwhelmingly likely that there are many advanced civilizations in the universe, but also overwhelmingly likely that each one dies out before producing trillions of individuals.** In particular, the model in the paper predicts that our civilization will die out within a few centuries.

If this sounds too depressing, you may enjoy the recent article

*5 Insane Theories About Why We Haven't Discovered Alien Life* by Fernando Ramirez; it may be found at

http://www.cracked.com/article_20216_5-insane-theories-about-why-we-havent-discovered-alien-life.htmlIn summary, the five insane theories are:

5. If They Exist, They're Likely Too, Well,

*Alien*4. They Might Not Want to Screw Us Up

3. We Might Not Be Worth the Aliens' Time

2. We'd All Be Dead by the Time It Happens

1. Aliens May Not Exist at All

Ramirez cites Gerig's paper as justification for reason number 2. The article (seen via

+Jonah Miller) is entertaining, if speculative, and is worth reading

#mathematics #sciencesunday