## 25 June 2007

### The Simpsons use decimal numbers

In The Simpsons, people have four fingers on each hand. Eight fingers in total. Therefore, shouldn't they use numbers in base 8?

(The reason that they have four fingers is the same reason that most animated characters have four fingers -- it's easier to draw. In at least one episode, God appears; God has five fingers.)

This occurred to me while watching the episode The Canine Mutiny, in which "After using his credit card to buy another dog, Bart must choose between his new wonder-pooch and the bumbling but loyal Santa's Little Helper." Bart gets the credit card in the name of his old dog, Santa's Little Helper; to order the new dog from a catalog, he has to dial an 800 number. He says "I don't think our phone goes up to 800", which got me thinking about what kind of numbers they use in Simpsons-world.

simpsonsmath.com, by Sarah Greenwald and Andrew Nestler, has a list of mathematical references on the Simpsons. This is not one of them.

It's actually possible to prove that the Simpsons universe has numbers in base 10. The baseball attendance figures in Marge and Homer turn a Couple Play are 8191, 8128, and 8208. The use of 9 indicates that we're in base at least 10. If we assume this is supposed to be a mathematical joke, 8191 and 8128 are immediately recognizable as 213-1 (Mersenne prime) and (27-1)26 (a perfect number.) 8208 is also 213 + 24, but more importantly it's the sum of the fourth powers of its digits. This would only be true in base 10. (Incidentally, most mathematicians regard properties of numbers that are based on their digits as not worthy of investigation, because they are basically accidents of the fact that we have ten fingers.)

#### 1 comment:

Pseudonym said...

That, BTW, isn't the only reason why cartoon ("animated" is more general) characters have four fingers on each hand. It's also easier to read the broad cartoony motions and poses that they adopt when there's less to look at.

(Incidentally, this isn't true of The Simpsons, which doesn't use a lot of cartooniness, but tends to rely on dialogue.)