The Simpsons and Their Mathematical Secrets

by Simon Singh

  His mother, who had always supported his ambition to become a researcher, initially labeled his move into comedy writing an “absolute crime.” Westbrook thinks his father, a mathematician, had similar reservations, but was too polite to voice them. His research colleagues were equally unsupportive. Westbrook still remembers his boss’s final words to him when he left AT&T Bell Labs: “Well, I understand why you’re doing it. I hope you fail because I would like you to come back here and work.”

  After hearing about his academic background, I wondered if Westbrook was the most mathematically qualified of all the writers on The Simpsons. He had certainly climbed highest up the academic ladder, but perhaps others had written more research papers or collaborated with a wider range of mathematicians. In search of a metric for mathematical magnificence, it struck me that one way to obtain a rating would be to apply a technique based on the notion of six degrees of separation.

  This is the idea that everyone in the world is connected to everyone else by a maximum of just six relationships. For example, I probably know someone, who knows someone, who knows someone, who knows someone, who knows someone, who knows you. This is the most general and best-known version of six degrees of separation, but the technique can be adapted to specific communities, such as mathematicians. Hence, six degrees of separation can be used to identify who is well connected in the world of mathematics, and who, therefore, might have the best mathematical credentials. It is not a perfect measurement, but it can offer some interesting insights.

  The mathematical version of six degrees of separation is called six degrees of Paul Erdős, named after the mathematician Paul Erdős (1913–96). The goal is to find a connection between any given mathematician and Erdős, and mathematicians with closer connections are then ranked higher than those with more tenuous connections. But why is Erdős considered to be at the center of the mathematical universe?

  Erdős holds this position because he was the most prolific mathematician of the twentieth century. He published 1,525 research papers, which he wrote with 511 co-authors. This incredible achievement was made possible by Erdős’s eccentric lifestyle, which involved traveling from one campus to another, setting up shop with a different mathematician every few weeks, and writing research papers with each of them. Throughout his life, he was able to fit all his belongings into a single suitcase, which was very convenient for a nomadic mathematician constantly on the road in search of the most interesting problems and the most fruitful collaborations. He fueled his brain with coffee and amphetamines in order to maximize his mathematical output, and he often repeated a notion first posited by his colleague Alfréd Rényi: “A mathematician is a machine for turning coffee into theorems.”

  In six degrees of Paul Erdős, connections are made via co-authored articles, typically mathematical research papers. Anybody who has co-authored a paper directly with Erdős is said to have an Erdős number of 1. Similarly, mathematicians who have co-authored a paper with someone who has co-authored a paper with Erdős are said to have an Erdős number of 2, and so on. Via one chain or another, Erdős can be connected to almost any mathematician in the world, regardless of their field of research.

  Take Grace Hopper (1906–92) for example. She built the first compiler for a computer programming language, inspired the development of the programming language COBOL, and popularized the term bug to describe a defect in a computer after finding a moth trapped in the Mark II computer at Harvard University. Hopper did much of her mathematics in industry or as a member of the United States Navy. Indeed, “Amazing” Grace Hopper was eventually promoted to rear admiral, and there is now a destroyer named the USS Hopper. In short, Hopper’s hardheaded, applied, technology-driven, industrial, military mode of mathematics was utterly different from Erdős’s purist devotion to numbers, yet Hopper has an Erdős number of just 4. This is because she published papers with her doctoral supervisor Øystein Ore, whose other students included the eminent group theorist Marshall Hall, who co-authored a paper with the distinguished British mathematician Harold R. Davenport, who had published with Erdős.

  So, how does Jeff Westbrook rank in terms of his Erdős number? He started publishing research papers while working on his PhD in computer science at Princeton University. As well as writing his 1989 thesis, titled “Algorithms and Data Structures for Dynamic Graph Algorithms,” he co-authored papers with his supervisor Robert Tarjan. In turn, Tarjan has published with Maria Klawe, who collaborated with Paul Erdős. This gives Westbrook a very respectable Erdős number of just 3.

  However, this does not make him a clear winner among the writers on The Simpsons. David S. Cohen has published a paper with Manuel Blum, another Turing Award winner, who in turn has published a paper with Noga Alon at Tel Aviv University, who in turn published several papers with Erdős. Hence, Cohen can also claim an Erdős number of 3.

  In order to break the tie between Cohen and Westbrook, I decided to explore another facet of being a successful writer on The Simpsons, namely being well connected to the heart of the Hollywood entertainment industry. One approach to measuring where a person sits in the Hollywood hierarchy is to employ another version of six degrees of separation, which is known as six degrees of Kevin Bacon. The challenge is to find an individual’s so-called Bacon number by linking him or her to Kevin Bacon through films. For example, Sylvester Stallone has a Bacon number of 2, because he appeared in Your Studio and You (1995) with Demi Moore, and she was in A Few Good Men (1992) with Kevin Bacon.

  So, which member of The Simpsons writing team has the lowest Bacon number, and therefore the best Hollywood credentials? That honor belongs to the remarkable Jeff Westbrook. He got his break as an actor in the naval adventure Master and Commander: The Far Side of the World (2003). While the film was in production, the director advertised for experienced seamen of Anglo-Irish extraction to man the ships, and Westbrook volunteered because he was a keen sailor who fit the ethnic bill. As a result, he was given a minor role in the film alongside leading actor Russell Crowe. Crowe is important, because he was in The Quick and the Dead (1995) with Gary Sinise, who co-starred with Bacon in Apollo 13 (1995). Hence, Westbrook has a Bacon number of 3, which puts him just behind Stallone. In short, he has impressive Hollywood credentials.

  Thus, Westbrook has both a Bacon number of 3 and an Erdős number of 3. It is possible to combine these numbers into a so-called Erdős-Bacon number of 6, which gives an indication of Westbrook’s overall connectivity in the worlds of both Hollywood and mathematics. Although we have not yet discussed the Erdős-Bacon numbers for the rest of the writing team behind The Simpsons, I can confirm that none of them can beat Westbrook’s score. In other words, out of the entire gang of Tinseltown nerds, Westbrook is overall the tinseliest and the nerdiest.8

  I first became aware of Erdős-Bacon numbers thanks to Dave Bayer, a mathematician at Colombia University. He was a consultant on the film A Beautiful Mind, based on Sylvia Nasar’s acclaimed biography of the mathematician John Nash, who had won the Nobel Prize in Economic Sciences in 1994. Bayer’s responsibilities included checking the equations that appeared on screen and acting as Russell Crowe’s hand double in the blackboard scenes. Bayer was also given a minor role toward the end of the film, when the Princeton mathematics professors offer their pens to Nash to acknowledge his great discoveries. Bayer proudly explained: “In my scene, known as the Pen Ceremony, I say, ‘A privilege, professor.’ I’m the third professor to lay down a pen before Russell Crowe.” So, Bayer was in a Beautiful Mind, acting alongside Rance Howard. In turn, Rance Howard was in Apollo 13 with Kevin Bacon, which means that Bayer has a Bacon number of 2.

  As a highly respected mathematician, it is no surprise that Bayer has an Erdős number of 2, which gives him a combined Erdős-Bacon number of just 4. When A Beautiful Mind was released in 2001, Bayer claimed to have the world’s lowest Erdős-Bacon number.

  More recently, Bruce Reznick, a mathematician at the University of Illinois, has claimed an even lower Erdős
-Bacon number. He co-authored a paper with Erdős, titled “The Asymptotic Behavior of a Family of Sequences,” which gives him an Erdős number of 1. Equally impressive is the fact that he had a very minor role in Pretty Maids All in a Row, a 1971 film written and produced by Gene Roddenberry, legendary creator of Star Trek. This teen slasher movie, which tells the story of a serial killer who hunts down his victims at Oceanfront High School, has a cast that includes Roddy McDowall, who was in The Big Picture (1989) with Kevin Bacon. This gives Reznick a Bacon number of 2, which means that he has an incredibly low Erdős-Bacon number of 3.

  So far, the record low Erdős-Bacon numbers have been posted by mathematicians venturing into acting, but some actors have dabbled in research and have thereby achieved respectable Erdős-Bacon numbers. One of the most famous examples is Colin Firth, whose path to Erdős began when he was guest editor for BBC Radio 4’s Today program. For an item on the program, Firth asked neuroscientists Geraint Rees and Ryota Kanai to conduct an experiment to look at correlations between brain structure and political views. This led to further research, and in due course the neuroscientists invited Firth to join them as co-author on a paper titled “Political Orientations Are Correlated with Brain Structure in Young Adults.” Although Rees is a neuroscientist, he has an Erdős number of 5, because of convoluted collaborations that ultimately link him to the world of mathematics. Having published with Rees, Firth can claim an Erdős number of 6. He also has a Bacon number of just 1, because he worked with Bacon on Where the Truth Lies (2005). This gives Firth an Erdős-Bacon number of 7—impressive, but a long way from Reznick’s record.

  Similarly, Natalie Portman is notable for having an Erdős-Bacon number. She conducted research while she was a student at Harvard University, which led to her becoming a co-author on a paper titled “Frontal Lobe Activation During Object Permanence: Data from Near-Infrared Spectroscopy.” However, she is not identified as Natalie Portman on any research databases, as she published under her birth name, Natalie Hershlag. One of the other co-authors was Abigail A. Baird, who has a link into mathematical research, which results in her having an Erdős number of 4. This means Portman has an Erdős number of 5. Her Bacon number relies on a directorial credit for one of the segments in the anthology film New York, I Love You (2009). Some versions of the film contain a segment starring Kevin Bacon, so technically Portman has a Bacon number of 1. This gives Portman an Erdős-Bacon number of 6, which is low enough to beat Firth, but too high to offer any hope of a serious challenge to Reznick’s record.

  What about Paul Erdős? Surprisingly, he has a Bacon number of 4, because he appeared in N Is a Number (1993), a documentary about his life, which also featured Tomasz Luczak, who was in The Mill and the Cross (2011) with Rutger Hauer, who was in Wedlock (1991) with Preston Maybank, who was in Novocaine (2001) with Kevin Bacon. His Erdős number, for obvious reasons, is 0, so Erdős has a combined Erdős-Bacon number of 4—not quite enough to match Reznick.

  And, finally, what about Kevin Bacon’s Erdős-Bacon number? Bacon, being Bacon, has a Bacon number of 0. As yet, he does not have an Erdős number. In theory, he might develop a passion for number theory and collaborate on a research paper with someone who already has an Erdős number of 1. This would give him an unbeatably low Erdős-Bacon number of 2.

  CHAPTER 6

  Lisa Simpson, Queen of Stats and Bats

  When the Simpsons made their television debut as part of The Tracey Ullman Show, their individual personalities were not quite as developed as they are today. Indeed, when Nancy Cartwright, the voice of Bart Simpson, wrote a memoir titled My Life as a Ten-Year-Old Boy, she highlighted a major character flaw in Lisa: “She was just an animated eight-year-old kid who had no personality.”

  The description is harsh but fair. If Lisa had any personality in those early appearances, then it was merely as a watered-down female version of Bart; slightly less mischievous and just as bored with books. Nerdvana was the last thing on Lisa’s mind.

  However, as the launch of The Simpsons stand-alone series approached, Matt Groening and his team of writers made a concerted effort to give Lisa a distinct identity. Her brain was reconfigured and she was reincarnated as an intellectual powerhouse, blessed with additional reserves of compassion and social responsibility. Cartwright neatly summarized the personality of her revamped fictional sister: “Lisa Simpson is the kind of child we not only want our children to be, but also the kind of child we want all children to be.”

  Although Lisa is a multitalented renaissance student, Principal Skinner acknowledges her special talent for mathematics in “Treehouse of Horror X” (1999). After a large of stack of bench seats falls on Lisa, he cries out: “She’s been crushed! . . . And so have the hopes of our mathletics team.”

  We see this gift for mathematics in action in “Dead Putting Society” (1990), an episode that revolves around Homer and Bart challenging Ned and Todd Flanders, their holier-than-thou neighbors, to a miniature golf tournament. In the buildup to the big match, Bart is struggling to develop his putting technique, so he turns to Lisa for advice. She should have suggested that Bart change his grip, because he is naturally left-handed, and throughout this episode he adopts a right-hander’s putting stance. Instead, Lisa focuses on geometry as the key to putting, because she can use this area of mathematics to calculate the ball’s ideal trajectory and guarantee Bart a hole in one every time. In a practice session, she successfully teaches Bart how to bounce the golf ball off five walls and into the hole, prompting Bart to say: “I can’t believe it. You’ve actually found a practical use for geometry!”

  It is a neat stunt, but the writers use Lisa’s character to explore deeper mathematical ideas in “MoneyBART” (2010). In the opening scene of this episode, the glamorous Dahlia Brinkley is welcomed back to Springfield Elementary as the only student to have gone on to attend an Ivy League college. Not surprisingly, Principal Skinner and Superintendent Chalmers try to ingratiate themselves with Ms. Brinkley, as do some of the students. This includes the usually philistine Nelson Muntz, who tries to impress Springfield’s most successful alumna by pretending to be Lisa’s friend. Feigning interest in Lisa’s mathematical aptitude, he encourages her to demonstrate her ability to Ms. Brinkley:

  NELSON:

  She can do the kind of math that has letters. Watch! What’s x, Lisa?

  LISA:

  Well, that depends.

  NELSON:

  Sorry. She did it yesterday.

  During this encounter, Dahlia explains to Lisa that exam results will not be enough to get into the best universities, and that her own success was partly built on a wide range of extracurricular activities while at Springfield Elementary. Lisa mentions that she is treasurer of the jazz club and started the school’s recycling society, but Dahlia is not impressed: “Two clubs. Well, that’s a bridge bid, not an Ivy League application.”

  Meanwhile, Bart’s Little League baseball team, the Isotots, has lost its coach, so Lisa seizes the opportunity to improve her Ivy League credentials by taking charge. Although she has gained a new extracurricular activity, she realizes that she does not know the first thing about baseball, so she heads to Moe’s Tavern to ask Homer for advice. Rather than pass on his own expertise, Homer’s response is to point his daughter toward an unlikely quartet of geeks sitting in the corner. To Lisa’s surprise, Benjamin, Doug, and Gary from Springfield University are having an intense discussion about the finer points of baseball with Professor Frink. When Lisa asks why they are discussing sport, Frink explains that “baseball is a game played by the dexterous, but only understood by the Poindexterous.”9

  In other words, Frink is stating that the only way to understand baseball is through deep mathematical analysis. He hands Lisa a stack of books to take away and study. As Lisa departs, Moe approaches the geeks and bemoans the fact that they are not drinking any beer: “Oh, why did I advertise my drink specials in Scientific American?”

  Lisa follows Frink’s advice. Indeed, a reporte
r spots her poring over piles of technical books immediately prior to her first game in charge of the Isotots. This extraordinary sight prompts him to remark: “I haven’t seen this many books in a dugout since Albert Einstein went canoeing.”

  Lisa’s books have titles such as eiπ + 1 = 0, F = MA, and Schrödinger’s Bat. Although these titles are fictional, the book tucked below Lisa’s laptop is The Bill James Historical Baseball Abstract, which is a real catalog of the most important statistics in baseball, compiled by one of baseball’s deepest thinkers.

  Bill James has come to be revered in the worlds of both baseball and statistics, but his research in these areas did not begin within the sports establishment or in the ivory towers of academia. Instead, his initial and greatest insights came to him during long and lonely nights as a night watchman at a pork and beans factory owned by Stokely–Van Camp, one of America’s venerable canning companies.

  Lisa surrounded by books, including The Bill James Historical Baseball Abstract.

  While protecting the nation’s supply of pork and beans, James sought out truths that had eluded previous generations of baseball aficionados. Gradually, he came to the conclusion that the statistics being used to assess the strength of individual baseball players were sometimes inappropriate, occasionally poorly understood, and, worst of all, often misleading. For example, the headline statistic for assessing the performance of a fielder was the number of errors made: the fewer the errors, the better the fielder. This seems obviously sensible, but James had doubts about the validity of the error statistic.