The Barber Paradox

The Barber paradox is a paradox that relates to mathematical logic and set theory. The paradox considers a town with a male barber who shaves daily every man who does not shave himself, and no one else. Such a town cannot exist:

• If the barber does not shave himself, he must abide by the rule and shave himself.
• If he does shave himself, according to the rule he will not shave himself.

Thus the rule results in an impossible situation.

This paradox is attributed to the Bertrand Russell, a British logician who in 1901 constructed Russell's paradox to demonstrate the self-contradictory nature of Georg Cantor's naive set theory by formalizing the Barber paradox. The paradox also underlies the proof of Gödel's incompleteness theorem as well as Alan Turing's proof of the undecidability of the halting problem.

The Barber Pole

Barbers often have a red-and-white striped pole outside of their shops. This symbol of the barber dates back to medieval times and earlier, when barbers would perform a variety of medical tasks, including surgery and bloodletting. To show their experience, barbers would hang the bloody cloths of their operations on the pole, creating the red-and-white symbol of modern barbers.