The Simpsons and Their Mathematical Secrets

by Simon Singh

  After telling me the story about how he was recruited to join The Simpsons, Burns drew some parallels between puzzles and jokes, and suggested that they have a great deal in common. Both have carefully constructed setups, both rely on a surprise twist, and both effectively have punch lines. Indeed, the best puzzles and jokes make you think and smile at the moment of realization. And perhaps that is part of the reason why mathematicians have proved to be such valuable additions to the writing team of The Simpsons.

  As well as bringing their love of puzzles to the series, the mathematicians have also brought a new way of working. Burns has observed that his nonmathematical colleagues will generally offer fully formed gags created in a moment of inspiration, whereas the mathematicians on the writing team have a tendency to offer raw ideas for jokes. These incomplete jokes are then bounced around the writers’ room until they have been resolved.

  As well as using this group approach in order to invent jokes, the mathematicians also rely on it to develop storylines. According to Jeff Westbrook, Burns’s writing colleague on The Simpsons and another ex-mathematician, this enthusiasm for collaboration harks back to their previous careers: “I was a theoretician in computer science, which meant I was sitting around with other guys proving lots of mathematical theorems. When I came here, I was surprised to discover that it is the same kind of thing in the writers’ room, because we’re also just sitting around throwing out ideas. There’s this common creative thread, which is that you’re trying to solve problems. In one case, it’s a mathematical theorem that’s a problem. In the other case, it’s a story issue. We want to break the story down and analyze it. What is this story all about?”

  With this in mind, I began to ask other writers why they thought so many mathematically inclined writers had found a home at The Simpsons. As far as Cohen is concerned, mathematically trained comedy writers are more confident and comfortable exploring the unknown armed only with their intuition: “The process of proving something has some similarity with the process of comedy writing, inasmuch as there’s no guarantee you’re going to get to your ending. When you’re trying to think of a joke out of thin air (that also is on a certain subject or tells a certain story), there’s no guarantee that there exists a joke that accomplishes all the things you’re trying to do . . . and is funny. Similarly, if you’re trying to prove something mathematically, it’s possible that no proof exists. And it’s certainly very possible that no proof exists that a person can wrap their mind around. In both cases—finding a joke or proving a theorem—intuition tells you if your time is being invested in a profitable area.”

  Cohen added that training in mathematics helps give you the intellectual stamina required to write an episode of The Simpsons: “It sounds fun and easy, but there’s a lot of pounding your brain against the wall. We’re trying to tell a complicated story in a short amount of time and there are a lot of logical problems that need to be overcome. It’s a big puzzle. It’s hard to convince somebody of the pain and suffering that goes into making these shows, because the final product is fast moving and lighthearted. Any given moment in the writing process can be fun, but it’s also draining.”

  For a contrasting perspective, I then spoke to Matt Selman, who had studied English and history before joining the writing team. He identifies himself as the “guy who knows least about mathematics.” When asked why The Simpsons has become a magnet for people with a penchant for polynomials, Selman agreed with Cohen that the scripts are essentially a puzzle and that complicated episodes are “a real brain burner.” Also, according to Selman, the mathematical writers do have a particular trait: “Comedy writers all like to think that we’re great observers of the human condition and that we understand pathos, bathos, and all the -athoses. If you wanted to disparage the mathematicians, then you could say that they are cold and heartless, and that they don’t have great jokes about what it’s like to love or to lose, but I disagree. However, there is a difference. I think the mathematical mind lends itself best to writing very silly jokes, because logic is at the heart of mathematics. The more you think about logic, the more you have fun twisting it and morphing it. I think the logical mind finds great humor in illogic.”

  Mike Reiss, who worked on the very first episode of The Simpsons, agrees: “There are so many wrong theories about humor. Have you ever heard Freud on humor? He’s just wrong, wrong, wrong. However, I realized an awful lot of jokes work on false logic. I’ll give you an example. A duck walks into a drugstore and says, ‘I’d like some ChapStick, please,’ and the druggist says, ‘Will you be paying cash for that?’ and the duck says, ‘No, put the ChapStick on my bill.’ Now if incongruity was what made comedy, then it would be funny that a duck walks into a drugstore. It’s not incongruity, but it’s the fact that there’s a false logic to it, which brings all the disparate elements of this story together.”

  Although the writers have offered various explanations of why mathematical minds lend themselves to writing comedy, one important question remains: Why have all these mathematicians ended up working on The Simpsons rather than 30 Rock or Modern Family?

  Al Jean has one possible explanation, which emerged as he recalled his teenage years and his relationship with laboratories: “I hated experimental science because I was terrible in the lab and I could never get the results correct. Doing mathematics was very different.” In other words, scientists have to cope with reality and all its imperfections and demands, whereas mathematicians practice their craft in an ideal abstract world. To a large extent, mathematicians, like Jean, have a deep desire to be in control, whereas scientists enjoy battling against reality.

  According to Jean, the difference between mathematics and science is paralleled by the difference between writing for a live-action sitcom versus writing for an animated series: “I think live-action TV is like experimental science, because actors do it the way they want to do it and you have to stick within those takes. By contrast, animation is more like pure mathematics, because you have real control over exactly the nuance of the line, how the lines are delivered, and so on. We can really control everything. Animation is a mathematician’s universe.”

  Some of Mike Reiss’s favorite jokes rely on mathematics: “I like these jokes. I savor them. I’m just thinking of this other great joke I heard when I was a kid. It’s about these guys who buy a truckload of watermelons at a dollar apiece and then they go across town and sell them for a dollar apiece. At the end of the day, they have no money and the one guy says, ‘We should have bought a bigger truck.’”6

  Reiss’s vignette is part of a long tradition of mathematical jokes, ranging from trivial one-liners to intricate narratives. Such jokes might seem bizarre to most people, and indeed they are not the sort of material that you might typically hear in a stand-up comedian’s usual repertoire, but they are very much part of the culture of mathematics.

  The first time I encountered a sophisticated mathematical joke was as a teenager, while reading Concepts of Modern Mathematics by Ian Stewart:

  An astronomer, a physicist, and a mathematician (it is said) were holidaying in Scotland. Glancing from a train window, they observed a black sheep in the middle of a field. “How interesting,” observed the astronomer, “all Scottish sheep are black!” To which the physicist responded, “No, no! Some Scottish sheep are black!” The mathematician gazed heavenward in supplication, and then intoned, “In Scotland there exists at least one field, containing at least one sheep, at least one side of which is black.”

  I stored that joke in the back of my head for the next seventeen years and then included it in my first book, which discussed the history and proof of Fermat’s last theorem. The joke was a perfect illustration of the rigorous nature of mathematics. Indeed, I was so fond of the joke, I would often recount the tale of the black sheep while lecturing, and afterward members of the audience would sometimes approach me and tell me their own jokes about π, infinity, abelian groups, and Zorn’s lemma.

  Curious about what
else was making my fellow geeks chortle, I asked people to e-mail me their favorite mathematical jokes, and for the past decade I have received a steady flow of comedic offerings of a nerdy nature, ranging from dismal puns to rich anecdotes. One of my favorites is a story that was originally told by the historian of mathematics Howard Eves (1911–2004). The tale concerns the mathematician Norbert Wiener, who pioneered cybernetics:

  When [Wiener] and his family moved to a new house a few blocks away, his wife gave him written directions on how to reach it, since she knew he was absentminded. But when he was leaving his office at the end of the day, he couldn’t remember where he put her note, and he couldn’t remember where the new house was. So he drove to his old neighborhood instead. He saw a young child and asked her, “Little girl, can you tell me where the Wieners moved?” “Yes, Daddy,” came the reply, “Mommy said you’d probably be here, so she sent me to show you the way home.”

  However, anecdotes about famous mathematicians and jokes that rely on the stereotypical characteristics of mathematicians offer only limited insights into the nature of mathematics. They can also become repetitive, as highlighted by this well-known parody:

  An engineer, a physicist, and a mathematician find themselves in an anecdote, indeed an anecdote quite similar to many that you have no doubt already heard. After some observations and rough calculations the engineer realizes the situation and starts laughing. A few minutes later the physicist understands too and chuckles to himself happily as he now has enough experimental evidence to publish a paper. This leaves the mathematician somewhat perplexed, as he had observed right away that he was the subject of an anecdote, and deduced quite rapidly the presence of humor from similar anecdotes, but considers this anecdote to be too trivial a corollary to be significant, let alone funny.

  By contrast, there are many jokes in which the humor relies on the actual language and tools of mathematics. For example, there is one well-known joke that was apparently created during an exam by a mischievous student named Peter White from Norwich, England. The question asked students for an expansion of the bracket (a + b)n. If you have not come across this type of question previously, then all you need to know is that it concerns the binomial Theorem and the correct answer ought to have explained that the rth term of the expansion has the coefficient n!/[(r – 1)!(n – r + 1)!]. This is quite a technical answer, but Peter had a radically different interpretation of the question and an inspired solution:

  Peter’s imaginative answer got me thinking. Creating a mathematical joke requires an understanding of mathematics, and appreciating the joke requires a similar level of understanding. Hence, mathematical jokes test your mathematical knowledge.

  With this in mind, I have gathered the world’s best mathematical jokes, classified them according to their degree of difficulty, and divided them into five examination papers distributed through the course of this book. As you continue exploring the mathematical humor that appears in The Simpsons, you will encounter these increasingly difficult test papers. Your task is to read through the jokes and see how many make you laugh (or groan), which will help you assess how your mathematical knowledge and sense of humor are developing.

  You may turn over your first exam paper . . . now!

  Good luck.

  Arithmetickle and Geometeeheehee

  Examamination

  A FIVE-PART TEST OF HUMOR AND MATHEMATICS

  The examination is divided into five separate sections.

  The first section is an elementary examination, consisting of eight simple jokes.7

  Subsequent sections are increasingly difficult.

  Score yourself according to the number of laughs/groans you experience.

  If you laugh/groan enough to score more than 50 percent, then you will have passed that particular section of the exam.

  Examination I

  ELEMENTARY PAPER

  Joke 1

  Q: What did the number 0 say to the number 8?

  2 points

  A: Nice belt!

  Joke 2

  Q: Why did 5 eat 6?

  2 points

  A: Because 7 8 9.

  Joke 3

  Knock, knock.

  3 points

  Who’s there?

  Convex.

  Convex who?

  Convex go to prison!

  Joke 4

  Knock, knock.

  3 points

  Who’s there?

  Prism.

  Prism who?

  Prism is where convex go!

  Joke 5

  Teacher: “What is seven Q plus three Q?”

  2 points

  Student: “Ten Q.”

  Teacher: “You’re welcome.”

  Joke 6

  A Cherokee chief had three wives, each of whom was pregnant. The first squaw gave birth to a boy, and the chief was so elated that he built her a teepee made of buffalo hide. A few days later, the second squaw gave birth, and also had a boy. The chief was extremely happy; he built her a teepee made of antelope hide. The third squaw gave birth a few days later, but the chief kept the birth details a secret.

  4 points

  He built the third wife a teepee out of hippopotamus hide and challenged the people in the tribe to guess the details of the birth. Whoever in the tribe could guess correctly would receive a fine prize. Several people tried, but they were unsuccessful in their guesses. Finally, a young brave came forth and declared that the third wife had delivered twin boys. “Correct!” cried the chief. “But how did you know?”

  “It’s simple,” replied the warrior. “The value of the squaw of the hippopotamus is equal to the sons of the squaws of the other two hides.”

  Other versions of Joke 6 have different punch lines. There are bonus points if either of these punch lines make you smile:

  Joke 7

  “The share of the hypertense muse equals the sum of the shares of the other two brides.”

  2 points

  Joke 8

  “The squire of the high pot and noose is equal to the sum of the squires of the other two sides.”

  2 points

  TOTAL – 20 POINTS

  CHAPTER 5

  Six Degrees of Separation

  While visiting Los Angeles in October 2012, I was lucky enough to attend a table-read of an upcoming episode of The Simpsons titled “Four Regrettings and a Funeral.” This involved the cast reading through the entire episode in order to iron out any problems before the script was finalized in preparation for animation. It was bizarre to see and hear a fully grown Yeardley Smith delivering lines with little Lisa’s voice. Similarly, I experienced extreme cognitive dissonance when I heard the voices of Homer, Marge, and Moe Szyslak, whose tones and diction are so familiar from years of watching The Simpsons, emerge from the all-too-human forms of Dan Castellaneta, Julie Kavner, and Hank Azaria.

  Although there is much else to appreciate in “Four Regrettings and a Funeral,” it is sadly lacking in mathematical references. However, that same day I was given a preliminary script for another upcoming episode, “The Saga of Carl,” which contained an entire scene dedicated to the mathematics of probability.

  “The Saga of Carl” opens with Marge dragging her family away from the television and taking them on an educational trip to the Hall of Probability at Springfield’s Science Museum. There, they watch a video introduced by an actor playing the role of Blaise Pascal (1623–62), the father of probability theory, and they also see an experimental demonstration of probability theory known as the Galton board. This involves marbles rolling down a slope and ricocheting off a series of pins. At each pin, the marbles bounce randomly to the left or right, only to hit the next row of pins and be met by the same random opportunity. The marbles are finally collected in a series of slots and form a humped distribution.

  The Galton board was named after its English inventor, the polymath Francis Galton (1822–1911). The balls enter at the top, bounce off the pins, and fall to the bottom, where they form
a so-called binomial distribution. A version of this classic probability experiment appears in “The Saga of Carl.”

  Having only read the script, it was impossible for me to know how the Galton board would appear on screen. The only thing I could be sure of was that the humped distribution would be mathematically accurate, because one of the writers explained that the exact nature of the marble distribution had dominated one of the script redrafting sessions. According to Jeff Westbrook, he and a couple of other mathematicians on the writing team argued about which probability equation correctly describes the marble distribution, while the other writers stared in silence. “We were arguing about whether it should be Gaussian or Poisson,” recalled Westbrook. “In the end, I decided it all depends on how you model it, but essentially it’s the binomial distribution. Everyone else was kind of looking bored and rolling their eyes.”

  Westbrook majored in physics at Harvard, and then completed a highly mathematical PhD in computer science at Princeton University. His supervisor was Robert Tarjan, a world-famous computer scientist, who in 1986 won the Turing Award, known as the Nobel Prize of computing. After finishing his PhD, Westbrook spent five years as an associate professor at Yale University and then joined AT&T Bell Laboratories. However, Westbrook loved slapstick and punnery as much as statistics and geometry, so he eventually left research and headed west to Los Angeles.