Mathematics and Humor – Paradoxical Bridge

Paradoxical Bridge

The issue regarding similarities between humor and mathematics has been examined by John Allen Paulos in his book “Mathematics and Humour” (1988). Both mathematics and humor are a sort of an intellectual game; in mathematics the accent falls on the logical side, in humor – on the funny side. Logic, patterns, formulas, structures – they are the essence of not just mathematics but also humor. In humor logic is reversed, patterns destroyed, formulas broken, and structure shaken. All these transformations are not, however, purely coincidental. The story takes the listener to a new level of sense and order, very different from the original one. Moreover, both mathematics and humor are simple and economical. The beauty of a mathematical proof depends to some degree on its level of concision and elegance. Similarly, a joke loses its strength when it’s long and heavy.

The bridge between humor and mathematics come from paradoxes and puzzles. They have a more intellectual character than a joke but a less serious tone than mathematics. For example:


Two trains, set apart from each other by a distance of 300 miles, begin to move towards each other alongside the same tracks. The first train goes at a speed of 100 miles per hour, whereas the second – 50 miles per hour. At the moment the trains begin to move a bird flying at the speed of 200 miles per hour takes off from the top of the first train and flies toward the other. Having reached its destination the bird turns around and flies back to the starting point and then repeats its flight between the two trains. How far will the bird fly before the trains collide?

If a person attempting to solve the puzzle focuses on the length of the flight alone, they will face the complex task of adding each consecutive path. However, if somebody realizes that the necessary time for the trains to meet is 2 hours (since the trains are approaching each other at the speed of 100 + 50 = 150 miles per hour), then they would immediately calculate that the bird will cover the distance of 2 x 200 = 400 miles.

Deduction and logic play an equally important role in mathematics and humor. Some rudimentary knowledge of logic is necessary to, for example, understand jokes build on syllogism. Very often jokes follow a structure that can be easily represented using logical deduction. For example: the teller of the joke says “In what model the axioms 1, 2, and 3 are true?”. Listener replies: “In model M”. The teller retorts: “Not at all! It’s model N”.

This is a common structure for many humorous puzzles.

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