Here at NeoTeo we love to melt brains, and one of our favorite ways to do that is by presenting paradoxes. Some hit close to home, such as the paradox of choice, while others affect robots exclusively.
Today we bring you a paradox you can easily reproduce at home. All you need is a pair of identical coins, placed in contact and in the same position. If you roll one coin around the circumference of the other, how many rotations does it complete?
The coin rotation paradox is usually associated with a question that appeared in an old SAT exam in 1982: A circle called "A" has one-third the radius of the larger circle "B". Circle "A" rolls along the entire circumference of circle "B" until it returns to its starting position. The question is: How many complete rotations did circle "A" make?
Almost all participants chose "3" as the answer, because circle "B" has three times the circumference of circle "A". At first glance, anyone would agree, however, the exercise had two problems: the correct answer is not 3, and it wasn't even available in the multiple choice. So... what's the trick?
The Coin Rotation Paradox
To discover it, you need to use two identical coins and roll one around the other, just as in the circle exercise. The surprise (so to speak) is that the coin completes one rotation halfway, and once it returns to the original position, the final rotations are two. The coin paradox in all its splendor.
What's happening here is that there are two movements in play: rotation and revolution. The moving coin completes one revolution around the central coin, but it also rotates on its axis while doing so.
For that reason, if you come across a similar exercise in an exam, the answer is "n+1", that is, you have to add one revolution at the end. That will allow you to escape the paradox easily, regardless of the size of the circles.
Want more paradoxes or dilemmas to keep going? If so, you can review a classic like the prisoner's dilemma, the thought experiment of the Chinese room, the birthday paradox, and why it's a bad idea to split the bill at dinner.
