The Futurama Theorem

Only once in the history of television has a mathematical theorem been created for the sole purpose of entertainment. The series was “Futurama,” the theorem, the aptly named “Futurama Theorem,” and its creator was show writer Dr. Ken Keeler, Ph.D. The doctorate held by Keeler is in applied mathematics, (didn’t I tell you in my previous post that Matt Groening’s writers rooms are simply mobbed by multitudes of mathematical minds?).

In season seven, episode ten, “The Prisoner of Benda,” Dr. Farnsworth and Amy create a device that permits a pair of people to trade minds with each other. The catch? The mind-switching machine will only allow the same two people to exchange minds once. Chaos and hilarity ensues as minds are passed from body to body. It eventually requires the “funky mathematics” of the Harlem Globetrotters, (they’re aliens from another planet, didn’t you know?) to remedy the situation. The theorem employed by the extra-terrestrial-trotters is as follows:

The Futurama Theorem, by Dr. Ken Keeler, as presented by the extra-terrestrial Harlem Globetrotters

The Futurama Theorem, by Dr. Ken Keeler, as presented by the Harlem Globetrotters

It’s all Greek to me. In fact, I can pick out a Greek letter or two within that incomprehensible jumble. A better person than I provided it in layman’s terms:

Step 1: Have everybody who’s messed up arrange themselves in circles, each facing the body their mind should land in (e.g., if Fry’s mind is in Zoidberg’s body, then the Zoidberg body should face the Fry body).

Step 2: Go get two “fresh” (as of yet never mind-swapped) people. Let’s call them Helper A and Helper B.

Step 3: Fix the circles one by one as follows:

3.0) Start each time with Helper A and Helper B’s minds in either their own or each other’s bodies

3.1) Pick any circle of messed-up people you like and unwrap it into a line with whoever you like at the front

3.2) Swap the mind at the front of the line into Helper A’s body

3.3) From back to front, have everybody in the line swap minds with Helper B’s body in turn. (This moves each mind in the line, apart from the front one, forward into the right body)

3.4) Swap the mind in Helper A’s body back where it belongs, into the body at the back of the line. Now the circle/line has been completely fixed. The one side effect is that for each time a circle is fixed, the Helpers’ minds will switch places, but that’s OK, see below

Step 4: At the very end, after all the circles have been fixed, mind-swap the two Helpers if necessary (i.e., in case there was originally an odd number of messed-up circles)

In the words of Jesse Pinkman…


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