Carter's Carter's Doomsday Doomsday

Carter's Doomsday is a mathematical argument that claims to predict the end of the world. The fundamental idea that powers this argument is quite simple.

Consider 2 boxes, containing numbered balls. The first box contains only 10 balls, numbered 1-10 Whereas the second box contains 10000 balls, numbered 1-10000 Now suppose you are handed a ball numbered 5, and told that the ball was taken from one of the 2 boxes Which box do you think the ball came from? It seems that it is far likelier for the ball to have come from the box with just 10 balls right? Now let us extend this idea to the earth. Assume that there are 2 identical earths with one that would support life up to the 200 billionth human, after which the world will end, a near doomsday And the second earth allows up to the 200 trillionth human, a far doomsday Now given that you are amongst the first 100 billion humans alive, which earth do you think you would belong to? Similar to the first example it would seem that near doom scenario is much likelier, but by how much?

To calculate this, we can use Baye's theorem. Now consider the 2 scenarios, near doom (denoted N) where the world will end after 200 billion humans, and far doom (denoted F) where the world will end after 200 trillion humans. If we are given no further information about these scenarios, the probability of these two events would be 50-50 We can set this as our original belief. Baye's theorem allows us to update our beliefs in light of new evidence Now let's consider the evidence that we are amongst the first 100 billion humans alive The probability that we are amongst the first 100 billion humans given that only 200 billion humans will ever exist, (denoted P(E|N)) is simply 1/2 Similarly, the probability that we are amongst the first 100 billion humans given that 200 trillion humans will exist, (denoted P(E|F)) is 1/2000 Now if we plug these values into Baye's theorem, we get the probability that the world will end after 200 billion humans are born is 1000/1001 or 99.9%. Assuming the current birth rate will continue, this theorem suggests that the world is 99 9 percent likely to end within the next 1000 years. This argument seems scarily convincing, but should we accept it as fact? Should we start bracing for a mathematically prophecied apocalypse within this millennium?

Well, maybe not just yet. Carter's doomsday is subject to intense mathematical debate with dozens of papers disputing the claim, and dozens disputing the disputes to the claim. So let's not spend too much time worrying about the end of the world, rather let's spend time coming up with other weird ways to apply mathematical ideas