A few days ago I happened upon an online discussion of probability theory, and the issue of the doomsday argument came up. This is an odd bit of mathematics that seems to predict the end of the world is coming soon, and it has been bolstered in recent years by academic articles written by respected scientists and published in peer-reviewed journals. While I disagree with some of the arguments used in this calculation, it is still worth studying and understanding if for no other reason than to understand the mathematics behind it.

However I will also add a warning that some people should not read this article. Some people get very scared and depressed by this argument, when it really should not be taken so seriously. So if you are one who worries easily, you should probably quit reading now. I hear Youtube has several fluffy cat videos that are enjoyable.

Now back to the mathematics of Armageddon...

Assume that one day in the future, the human race will cease to exist. It could be next week, or it could be in a trillion years. Given that over 10 billion humans have already existed, what is the most likely number of humans that ever will exist?

Lets begin with smaller numbers. Suppose a small town decides to number their residents to determine its population. And suppose you receive the number 95. If the population of the town is 1,000,000, then the probability of receiving a two digit number is 0.009% . So that is probably not the population of the town. If the population of the town is 200, then the probability of getting a two digit number is 45%. And because you received a two digit number, you can guess that the town's population is around a few hundred people, but unlikely to be more than a few thousand people. (This is an application of Bayes Theorem for those who are interested in reading more about it).

So now we go back to the end of the world. Suppose that I know I am the ten billionth human who has ever been born. Using the same argument as above, I can infer that the maximum number of humans for all time will only number a few tens of billions. It would seem unlikely that if I am a random human among trillions of trillions, that I should just happen to be one of the first ten billion - the probability of that happening is infinitesimal.

So humanity will likely die out after another ten or twenty billion people have been born. Except that Earth currently adds on the order of 1 billion people per year - and so that means humanity is going to end in about ten to twenty years! There is suddenly a high probability that the human race will die out before I do!

The end is nigh!

Except it isn't. This is an entertaining exercise in mathematics, statistics, and philosophy, but there are equally valid arguments that counter it. For example a mathematician 500 years ago could have done the exact same argument and proven that life would end in his lifetime, but we know it didn't. We also know that even in a city of a million people, someone will always come first in the phone book, and many people will be on the first few pages. The probability that someone will get a small identifying number in the town example is of course 100%. And events that have a 1 in a billion chance of happening still happen hundreds of times every day.

Personally, I am not that worried about doomsday happening any time soon.