At the beginning of the 20th century, the philosopher and mathematician Bertrand Russell presented the world with a problem that seemed like a simple word game, but actually concealed a catastrophic flaw in the foundations of modern mathematics.
It is known as “The Barber Paradox” and it presents the following situation:
In a distant village there is a single barber. In this place there is an absolute and unbreakable law: the barber only shaves men who do NOT shave themselves.
The problem arises when we ask ourselves the ultimate question: Does the barber shave himself?
- – If the barber shaves himself: He breaks the law, because the rule says that he can only shave those who do not shave themselves. Therefore, he should not shave himself.
- – If the barber does NOT shave himself: He immediately falls into the group of men who do not shave themselves. And since the law says that the barber shaves that group, then he is obligated to shave himself.
It is an infinite loop. If he does it, he cannot do it; and if he does not do it, he has to do it. Your brain just collapsed.
What is the real answer to the problem?
For years, people have tried to find loopholes in the story: “that the barber was a woman”, “that the barber was bald and had no beard”, or “that a barber from another village came by”. But in pure logic, those answers are cheats.
The true scientific and mathematical answer to the paradox is as simple as it is devastating: The barber does not exist. It is a logical impossibility.
Russell invented this story to demonstrate that the “Set Theory” used by the mathematicians of his time had a serious flaw. He showed that you can write a rule that sounds perfectly logical on paper, but when you try to apply it to reality, it destroys itself.
The paradox is resolved by accepting that the condition that defines the barber is contradictory; therefore, the existence of a character who fulfills that law is mathematically impossible.
Thanks to this headache, scientists had to rewrite the rules of modern mathematics to prevent these “black holes of logic” from happening again.