The Simpsons and Their Mathematical Secrets

by Simon Singh

  Although the episode ends with Lisa and Bart reconciled, the siblings clearly have two entirely different philosophies. According to Lisa, baseball demands to be analyzed and understood, whereas Bart believes the sport is all about instinct and emotion. These views mirror a bigger argument about the role of mathematics and science. Does analysis destroy the intrinsic beauty of the world around us, one might ask, or does it make the world even more beautiful? In many ways, Bart’s attitude encapsulates the views expressed by the English Romantic poet John Keats:

  Do not all charms fly

  At the mere touch of cold philosophy?

  There was an awful rainbow once in heaven:

  We know her woof, her texture; she is given

  In the dull catalogue of common things.

  Philosophy will clip an Angel’s wings,

  Conquer all mysteries by rule and line,

  Empty the haunted air, and gnomed mine—

  Unweave a rainbow, as it erewhile made

  The tender-person’d Lamia melt into a shade.

  These lines are from a poem titled “Lamia,” the name of a child-eating demon from Greek mythology. In the context of the nineteenth century, Keats’s use of the word philosophy included the concepts of mathematics and science. He is arguing that mathematics and science dissect and unpick the elegance of the natural world. Keats believes that rational analysis will “unweave a rainbow,” thereby destroying its inherent beauty.

  By contrast, Lisa Simpson would argue that such analysis turns the sight of a rainbow into an even more exhilarating experience. Perhaps Lisa’s worldview was best articulated by the physicist and Nobel laureate Richard Feynman:

  I have a friend who’s an artist and he’s sometimes taken a view which I don’t agree with very well. He’ll hold up a flower and say, “Look how beautiful it is,” and I’ll agree, I think. And he says—“you see, I as an artist can see how beautiful this is, but you as a scientist, oh, take this all apart and it becomes a dull thing.” And I think that he’s kind of nutty. First of all, the beauty that he sees is available to other people and to me, too, I believe, although I may not be quite as refined aesthetically as he is . . . I can appreciate the beauty of a flower. At the same time I see much more about the flower than he sees. I could imagine the cells in there, the complicated actions inside which also have a beauty. I mean it’s not just beauty at this dimension of one centimeter; there is also beauty at a smaller dimension, the inner structure. Also the processes, the fact that the colors in the flower evolved in order to attract insects to pollinate it is interesting—it means that insects can see the color. It adds a question: Does this aesthetic sense also exist in the lower forms? Why is it aesthetic? All kinds of interesting questions, which shows that a science knowledge only adds to the excitement and mystery and the awe of a flower. It only adds; I don’t understand how it subtracts.

  CHAPTER 7

  Galgebra and Galgorithms

  In “They Saved Lisa’s Brain” (1999), Lisa’s mathematical talents and general brilliance earn her an invitation to join the local chapter of Mensa, the society for people with high IQ. Her membership coincides with Mensa members taking control of Springfield after Mayor Quimby flees to avoid accusations of corruption. It seems like a great opportunity for Springfield to grow and prosper under the guidance of the community’s smartest men, women, and child.

  Unfortunately, a high IQ does not automatically equate to wise leadership. For example, one of the more absurd decisions of Springfield’s new leaders is to adopt a metric time system, something akin to the French model that was tried in 1793. The French thought it was mathematically appealing to have a day with ten hours, each hour containing one hundred minutes, and each minute containing one hundred seconds. Although the French abandoned the system in 1805, Principal Skinner proudly boasts in this episode: “Not only are the trains now running on time, they’re running on metric time. Remember this moment, people: 80 past 2 on April 47th.”

  Comic Book Guy, a fan of Star Trek, makes the proposal to limit sex to only once every seven years. It is an attempt to mimic Pon farr, a phenomenon whereby Vulcans go into heat every seven years. Subsequent decrees, such as a broccoli juice program and a plan to build a shadow-puppet theater (both Balinese and Thai), eventually cause the decent citizens of Springfield to rebel against the intellectual elite. Indeed, as the episode reaches its finale, the revolting masses focus their anger on Lisa, who is only saved when none other than Professor Stephen Hawking arrives in the nick of time to rescue her. Although we associate Hawking with cosmology, he spent thirty years as the Lucasian Professor of Mathematics at the University of Cambridge, which makes him the most famous mathematician to have appeared on The Simpsons. However, not everyone recognizes Hawking when he arrives in his wheelchair. When Hawking points out that the Mensa members have been corrupted by power, Homer says: “Larry Flynt is right! You guys stink!”11

  The writers had been anxious to persuade Professor Hawking to make a guest appearance in this particular episode, because the plot required a character who was even smarter than all Springfield’s Mensa members put together. The professor, who had been a fan of the series for many years, was already planning to visit America, so immediately his schedule was rejigged to allow him to visit the studios and attend a voice-recording session. Everything seemed in place for Hawking to make his guest appearance on The Simpsons, until his wheelchair had a bout of stage fright and suffered a major breakdown forty-eight hours before he was supposed to fly from Monterey to Los Angeles. Hawking’s graduate assistant, Chris Burgoyne, fixed the glitch, but only after working for 36 hours through the night and into the next day.

  Once Hawking arrived at the recording studio, the writers waited patiently as every script line was keyed into his computer. The only remaining problem occurred when the voice synthesizer struggled to deliver the line that describes Hawking’s disappointment at the way Springfield was being governed: “I wanted to see your utopia, but now I see it is more of a Fruitopia.” The computer’s dictionary did not contain this American fruit-flavored drink, so Hawking and the team had to figure out how to construct Fruitopia phonetically. Commenting later on the episode, writer Matt Selman recalled: “It’s good to know that we were taking the most brilliant man in the world and using his time to record Fruitopia in individual syllables.”

  The most memorable aspect of Hawking’s appearance in “They Saved Lisa’s Brain” concerns the manner in which he rescues Lisa from the mob. His wheelchair deploys a helicopter rotor, and he whisks Lisa off to safety. Presumably he realizes that Lisa is capable of achieving great things in the future and he wants her to fulfill her academic potential. Indeed, we can be sure that Lisa will be successful at university, because we catch a glimpse of Lisa’s destiny in “Future-Drama” (2005). The storyline relies on a gadget invented by Professor Frink, which allows people to look into the future. Lisa sees that she will graduate two years early and win a scholarship to Yale. Frink’s gadget also reveals that women will dominate science and mathematics in the decades ahead, so much so that some subjects are given more appropriate names. We see Lisa deciding whether to study galgebra or femistry.

  The overt support for women in mathematics and science in “Future-Drama” was largely prompted by a news story that had broken while the script was being written. In January 2005, Lawrence Summers, president of Harvard University, made some controversial comments at a conference titled Diversifying the Science & Engineering Workforce. In particular, Summers theorized about why women were underrepresented in academia, stating that “in the special case of science and engineering, there are issues of intrinsic aptitude, and particularly of the variability of aptitude, and that those considerations are reinforced by what are in fact lesser factors involving socialization and continuing discrimination.”

  Summers was speculating that the spread of ability was broader among men compared to women, which would result in more men and fewer women being spectacularly
high achievers in science and engineering. Not surprisingly, his theory provoked an enormous backlash, partly because many felt that such comments from a high-profile figure in academia would discourage young women from pursuing careers in mathematics and science. The controversy contributed to Summers’s resignation the following year.

  The writers of The Simpsons were pleased that they could make a passing topical reference to the Summers incident in “Future-Drama,” but they were keen to more fully explore the question of women in mathematics and science, so they returned to the subject the following year and tackled it in an episode titled “Girls Just Want to Have Sums” (2006).

  The episode starts with a performance of Stab-A-Lot: The Itchy & Scratchy Musical12 After a series of inevitably macabre songs, there is a standing ovation and the director, Juliana Krellner, appears on stage to take a bow. Next to her is Principal Skinner, who proudly reveals that Krellner used to be a student of Springfield Elementary School:

  SKINNER:

  You know, Juliana, it’s no surprise you became such a success. You always got straight As in school.

  JULIANA:

  Well, I remember getting a B or two in math.

  SKINNER:

  Well, of course you did. You are a girl.

  [Audience gasps.]

  SKINNER:

  All I meant was, from what I’ve seen, boys are better at math, science, the real subjects.

  JULIANA:

  [To audience] Calm down, calm down. I’m sure Principal Skinner didn’t mean girls are inherently inferior.

  SKINNER:

  No, of course not. I don’t know why girls are worse.

  Principal Skinner then becomes the subject of a hate campaign and, despite his best efforts to make amends, he only stirs up further controversy. Eventually, Skinner is replaced by a radically progressive educationalist, Melanie Upfoot, who decides to protect Springfield’s girls against prejudice by placing them in a separate school. At first, Lisa relishes the idea of an educational system that will allow girls to flourish, but the reality is that Ms. Upfoot wants to indoctrinate her girls with a form of mathematics that is supposedly both feminine and feminist.

  According to Ms. Upfoot, girls should be taught mathematics in a much more emotional manner: “How do numbers make you feel? What does a plus sign smell like? Is the number 7 odd, or just different?” After becoming frustrated by her new teacher’s approach to numeracy, Lisa asks if the girls’ class is ever going to tackle any real mathematical problems. Ms. Upfoot replies: “Problems? That’s how men see math, something to be attacked—something to be figured out.”

  This division between feminine and masculine mathematics is only fictional, but it echoes a real trend in recent decades toward touchy-feely mathematics for both boys and girls. Many members of the older generation are concerned that today’s students are not being stretched in terms of tackling traditional problems, but instead are being spoon-fed a more trivial curriculum. This concern has given rise to a spoof history of mathematics education known as “The Evolution of a Mathematical Problem”:

  1960:

  A lumberjack sells a truckload of lumber for $100. His cost of production is 4/5 of this price. What is his profit?

  1970:

  A lumberjack sells a truckload of lumber for $100. His cost of production is 4/5 of this price, or in other words $80. What is his profit?

  1980:

  A lumberjack sells a truckload of wood for $100. His cost of production is $80, and his profit is $20. Your assignment: Underline the number 20.

  1990:

  By cutting down beautiful forest trees, a lumberperson makes $20. What do you think of his or her way of making a living? In your group, discuss how the forest birds and squirrels feel, and write an essay about it.

  Desperate for some real mathematics, Lisa sneaks out of her class and peers in through the window of the boys’ school, where she glimpses a traditional geometry problem on the blackboard. It is not long before she is caught spying and escorted back to the girls’ school, and once again she is fed a diet of diluted arithmetic gruel.

  It is the final straw. When she returns home that afternoon, Lisa asks her mother to help her disguise herself as a boy so that she can attend the boys’ school and participate in their lessons under the identity of Jake Boyman. The storyline mirrors the plot of Yentl, in which a young orthodox Jewish girl cuts her hair and dresses as a man in order to study the Talmud.

  Unfortunately, dressing as a boy is not enough. Lisa soon finds out that, in order to be accepted by her new classmates, she has to start behaving like a stereotypical boy. This flies in the face of everything she values. Ultimately, she is even willing to bully Ralph Wiggum, one of the most innocent pupils in her class, just to earn the approval of the notorious bully Nelson Muntz.

  Lisa resents having to behave like a boy to get a decent education, but continues with her plan in order to study mathematics and prove that girls are just as good as boys. Her determination pays off: Lisa not only excels academically, she also receives the award for Outstanding Achievement in the Field of Mathematics. The award is presented to her at a joint assembly for boys and girls, and Lisa uses this opportunity to reveal her true identity, and proclaims: “That’s right, everyone! The best math student in the whole school is a girl!”

  Dolph Starbeam, who usually hangs out with fellow school bullies Kearney Zzyzwicz, Jimbo Jones, and Nelson Muntz, shouts: “We’ve been Yentled!”

  Bart also stands up and declares: “The only reason Lisa won is because she learned to think like a boy; I turned her into a burping, farting, bullying math machine.”

  As the episode reaches its climax, Lisa continues with her speech: “And I did get better at math, but it was only by abandoning everything I believed in. I guess the real reason we don’t see many women in math and science is . . .”

  And at that very moment, the school’s music teacher cuts her off midsentence in order to introduce Martin Prince playing the flute. In this way, the writers sneakily sidestepped having to confront this controversial issue.

  When I met writers Matt Selman and Jeff Westbrook, they both recalled that it was almost impossible to find a satisfactory ending to the episode, because there is no easy way to explain why women continue to be underrepresented in many areas of mathematics and science. They did not want to deliver a simplistic or glib conclusion. Neither did they want to find themselves in, as Selman described it, “Skinner-like trouble.”

  The storyline of “Girls Just Want to Have Sums” mirrors not only the plot of Yentl, but also the life of the famous French mathematician Sophie Germain. Incredibly, the facts of Germain’s battle against sexism are even stranger than the fictional narratives of Lisa and Yentl.

  Born in Paris in 1776, Germain’s obsession with mathematics began when she chanced upon Jean-Étienne Montucla’s Histoire des Mathématiques (History of Mathematics). In particular, she was struck by his essay on the extraordinary life and tragic death of Archimedes. Legend has it that Archimedes was busy drawing geometric figures in the sand when the Roman army invaded Syracuse in 212 B.C. Indeed, he was so obsessed with analyzing the mathematical properties of his shapes in the sand that he ignored an approaching Roman soldier who was demanding his attention. Offended by the apparent rudeness, the soldier raised his spear and stabbed Archimedes to death. Germain found the story inspiring; mathematics had to be the most fascinating subject if it could spellbind someone to such an extent that he might ignore threats to his own life.

  As a result, Germain began to study mathematics all day and even through the night. According to a family friend, her father confiscated her candles to discourage her from studying when she should have been sleeping. In due course, Sophie’s parents relented. Indeed, when they accepted that she would not marry, but instead would devote her life to mathematics and science, they introduced her to tutors and supported her financially.

  At the age of twenty-eight, Germain decided that she wanted to atte
nd the newly opened École Polytechnique in Paris. The stumbling block was that this prestigious institution would only admit male students. However, Germain found a way around this problem when she learned that the college made its lecture notes publicly available and even encouraged outsiders to submit observations on these notes. This generous gesture was intended for gentlemen, so Germain simply adopted a male pseudonym, Monsieur LeBlanc. In this way, she obtained the notes and began submitting insightful observations to one of the tutors.

  Just like Lisa Simpson, Germain had adopted a male identity in order to study mathematics. So when Dolph Starbeam shouts out, “We’ve been Yentled!” it would have been more germane had he exclaimed, “We’ve been Germained!”

  Germain was sending her observations to Joseph-Louis Lagrange, not only a member of the École Polytechnique but also one of the world’s most respected mathematicians. He was so astonished by the brilliance of Monsieur LeBlanc that he demanded to meet this extraordinary new student, which forced Germain to own up to her deception. Although she feared he would be angry with her, Lagrange was actually pleasantly surprised to discover that Monsieur LeBlanc was a mademoiselle, and he gave Germain his blessing to continue with her studies.

  She could now build a reputation in Paris as a female mathematician. Nonetheless, she occasionally relied on her male alter ego when writing to mathematicians whom she had not met and who might not otherwise take her seriously. Most notably, she became Monsieur LeBlanc in her correspondence with the brilliant German mathematician Carl Friedrich Gauss, author of Disquisitiones Arithmeticae (Arithmetical Investigations), arguably the most important and wide-ranging treatise on mathematics for more than one thousand years. Gauss acknowledged the talents of his new pen friend—“I am delighted that arithmetic has found in you so able a friend”—but he had no idea that Monsieur LeBlanc was actually a woman.