Sunday, May 31, 2009

The barber’s paradox

Here is an interesting paradox:

Suppose you walk past a barber’s shop one day, and see a sign that says

  “Do you shave yourself? If not, come in and I’ll shave you! I shave anyone who does not shave himself, and noone else.”

This seems fair enough, and fairly simple, until, a little later, the following question occurs to you - does the barber shave himself? If he does, then he mustn’t, because he doesn’t shave men who shave themselves, but then he doesn’t, so he must, because he shaves every man who doesn’t shave himself… and so on. Both possibilities lead to a contradiction.

Apparently this problem gave mathematicians like Bertrand Russel a big headache at the beginning of the 20th century, and almost made some people give up on life entirely.

I don’t think it is that big a deal, because the barber could just be a woman.

Paradoxes are kind of fun though, especially ones about God being all powerful and all.  One nice one goes “Could God create a burrito so big that even God could not eat it?” I like this one because it helps me imagine what an infinite burrito would be like, and it also helps me imagine God eating that burrito in an instant.  What this would do to the divine digestive tract is anyone’s guess.