February 4, 2011

We are almost certainly wrong

As individuals, and as societies, we rightfully dismiss a bunch of crazy theories. However, we can't dismiss them with 100% confidence. We are pretty sure that the moon landing wasn't faked, that UFOs aren't stashed at Roswell, that we are not part of a computer simulation (à la Matrix), etc. Let's say there are 100 of these crackpot theories, and that we are 95% certain that each one is incorrect. That seems pretty good, right? We are 95% sure that all of those theories are incorrect, right?

This is where things get strange. Even though we are 95% sure that each of the crackpot theories is incorrect, we shouldn't be 95% confident that all of the theories are wrong. If there is a 5% chance that each one is correct, then the chance that all 100 theories are incorrect is actually only 0.6%! In other words, at least one of the theories is almost certainly correct, and probably quite a few of them are correct.

So does this mean that you should start believing crackpot theories? No - and that's the craziest part of all. The key is that we don't know which of our beliefs are wrong. It is rational to disbelieve all of the crackpot theories and believe that some of your beliefs are wrong.