June 6, 2023

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# Futurama Theory: In my friend’s body

### The solution is in sight!

In the series, it is better to save the heroes from the “Globetrotters”: talented basketball players with brilliant scientific skills. In Bender’s Body, Professor Farnsworth watches with admiration two players, Sweet Clyde and Bubblegum Tate, solving the problem on the board. Finally, there’s Keeler’s guide – visible to all viewers for the first time when it aired on August 19, 2010. If that wasn’t open source.

Keeler abstracted the problem by asking himself n Presented objects are arranged in wrong order, such as (2, 3, 4, 5, …, Ii + 1, …, n, 1). The goal is to find the set (1, 2, 3, …, n) to restore by pairing objects with two new items x And the y Reverse. This swap can be made by (IAnd the x) note; I And the x Then switch positions. So you have a new group (2, 3, 4, 5, …, Ii + 1, …, n1, xAnd the y).

Keeler found that the group must first be divided into groups ranging from 1 to I Running, another by I+1 for n he goes. Then one exchanges each incorrectly placed item in the first group x And each of the second group with y. You change in the end x with I+1 and y With 1 out: (1, x) (2), x) (3), x) … (I, s) · (I+1, y) (I+2, y) … (n, y) · (I+1, x) 1 , y). No matter how I Choose, after these permutations, one ends up with an ordered set (ignore x And the y): (1, 2, 3, …, IAnd the I+1, …, n). In fact, it doesn’t matter how things were originally arranged. The method always works.

To see Keeler’s proof in action, see the Futurama episode. To do this, you first have to record the initial position in a table to get an overview of who is in his body. In the diagram, circles correspond to the person’s mind and rectangles to the outside: