710: Collatz Conjecture
Title text: The Strong Collatz Conjecture states that this holds for any set of obsessively-hand-applied rules.
The Collatz conjecture is a longstanding unsolved problem in mathematics. It states that repeating the sequence of operations described in the comic will eventually lead to the number 1. The description in the comic starts out accurate, then veers into the joke.
The comic illustrates the sequence with a graph in which an arrow connects each number to its successor. For example, the number 22 is even, so the next number in the sequence is 22 ÷ 2 = 11, and there is an arrow from 22 to 11. On the other hand 11 is odd, so the next number is 3 × 11 + 1 = 34, and there is an arrow from 11 to 34.
According to the title text, Cueball is obsessively writing out the graph by hand, and is so preoccupied with the task that he has stopped socializing with his friends. He will be busy for a very long time, because the Collatz conjecture has been confirmed for all starting values up to 5 × 1018.
The Strong Collatz Conjecture in the title text is a humorous extension of the Collatz Conjecture. Some other mathematical conjectures and axioms also have normal and Strong variants, where the Strong variant gives a more general rule.
- [Cueball sits in a chair at a desk, papers piled on top, writing furiously. Depicted above are apparently the writing, a series of nodes in various Collatz sequences (starting with 7, 21, 24, 29, 106, 176 and 256), all eventually leading back to 1.]
- The Collatz Conjecture states that if you pick an number, and if it's even divide it by two and if it's odd multiply it by three and add one, and you repeat this procedure long enough, eventually your friends will stop calling to see if you want to hang out.