# What is the ultimate paradox?

Here are three very good paradoxes – [The last one is my favorite!]**The paradox of Achilles and the tortoise:**

In the paradox of Achilles and the tortoise, Achilles is in a race with the tortoise. Achilles gives the tortoise a head start of 100 feet. If we assume that each runner starts running at a constant speed (one very fast and one very slow), after a definite time, Achilles will have run 100 feet, bringing him to the tortoise’s starting point. During this time, the tortoise has run a much shorter distance, say 10 feet. Achilles will then take more time to cover that distance, at which point the tortoise will have gone further; and then there is still more time to reach this third point, while the turtle moves forward. Therefore, each time Achilles reaches a place where the tortoise has been, he still has to go further. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never reach the tortoise. Of course, simple experience tells us that Achilles will be able to outrun the tortoise, so this is a paradox.

**The barber paradox:**

Suppose there is a city with only one male barber; and that all the men in the city keep themselves perfectly shaved: some by shaving themselves, others by going to the barbershop. It sounds reasonable to imagine that the barber obeys the following rule: he only shaves all the men in town who don’t shave themselves.

Under this scenario, we can ask the following question: Does the barber shave himself?

However, by asking this, we discover that the situation presented is in fact impossible:

-If the barber does not shave himself, he must comply with the rule and shave himself.

-If he shaves himself, according to the rule, he will not shave himself.

**The unexpected hanging paradox:**

A judge tells a convicted prisoner that he will be hanged at noon on a weekday the following week, but that the execution will come as a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day. Having reflected on his sentence, the prisoner comes to the conclusion that he will escape hanging. His reasoning has several parts. He begins by concluding that the “surprise hanging” cannot be on a Friday, since, if he had not been hanged by Thursday, there is only one day left, so it will not be a surprise that he is hanged on Friday. of the judge stipulated that the hanging would be a surprise to him, he concludes that it cannot happen on Friday, then he thinks that the surprise hanging cannot happen on Thursday either, because Friday has already been eliminated and if he has not been hanged on Wednesday night, the hanging must happen on Thursday, so a Thursday is not a surprise either. By similar reasoning, he concludes that the hanging cannot occur on a Wednesday, Tuesday, or Monday either. Joyfully, he retreats to his cell, confident that the hanging will not happen at all. The following week, the executioner knocks on the prisoner’s door at noon on Wednesday, which, despite all of the above, will still come as a complete surprise. Everything the judge said has come true. Tuesday or Monday. Joyfully, he retreats to his cell, confident that the hanging will not happen at all. The following week, the executioner knocks on the prisoner’s door at noon on Wednesday, which, despite all of the above, will still come as a complete surprise. Everything the judge said has come true. Tuesday or Monday. Joyfully, he retreats to his cell, confident that the hanging will not happen at all. The following week, the executioner knocks on the prisoner’s door at noon on Wednesday, which, despite all of the above, will still come as a complete surprise. Everything the judge said has come true.