Copyright © 2013 by Simon Singh All rights reserved. No part of this book may be used or reproduced in any manner whatsoever without written permission from the publisher except in the case of brief quotations embodied in critical articles or reviews. For information address Bloomsbury USA, 1385 Broadway, New York, NY 10018. This book has not been approved, licensed, or sponsored by any entity or person involved in creating or producing The Simpsons™, the film, or the TV series. The Simpsons ® is a registered trade- mark of Twentieth Century Fox Film Corporation, © 2013 Twentieth Century Fox Film Corporation. All Rights Reserved. Nor has this book been approved, licensed, or sponsored by any entity or person involved in creating or producing Futurama™, the TV series. Futurama ® is a registered trademark of Twentieth Century Fox Film Corporation, © 2013 Twentieth Century Fox Film Corporation. All Rights Reserved. Published by Bloomsbury USA, New York All papers used by Bloomsbury USA are natural, recyclable products made from wood grown in well-managed forests. The manufacturing processes conform to the environmental regulations of the country of origin. library of congress cataloging-in-publication data Singh, Simon. The Simpsons and their mathematical secrets / Simon Singh.—First U.S. Edition. pages cm Includes bibliographical references and index. ISBN 978-1-62040-277-1 (hardback) 1. Mathematics—Miscellanea. 2. Simpsons (Television program)—Miscellanea. I. Title. QA99.S48 2013 510—dc23 2013020884 First U.S. Edition 2013 1 3 5 7 9 10 8 6 4 2 Printed and bound in the U.S.A. by Thomson-Shore Inc., Dexter, Michigan Sing_5p_all_r2.indd 4 8/16/13 7:45 PM CHAPTER 4 The Puzzle of Mathematical Humor s might be expected, many of the mathematical writers of The ASimpsons have a passion for puzzles. Naturally, this love of puz- zles has found its way into various episodes. For example, the world’s most famous puzzle, the Rubik’s Cube, crops up in “Homer Defined” (1991). The episode features a flash- back to 1980, the year the cube was first exported from Hungary, when a younger Homer attends a nuclear safety training session. In- stead of paying attention to the instructor’s advice on what to do in the event of a meltdown, he is focused on his brand-new cube and cycling through some of the 43,252,003,274,489,856,000 permuta- tions in order to find the solution. Rubik’s Cubes have also appeared in the episodes “Hurricane Neddy” (1996) and “HOM ” (2001), and the Rubik’s Cube was in- voked as a threat by Moe Szyslak in “Donnie Fatso” (2010). As pro- prietor and bartender of Moe’s Tavern, Moe regularly receives prank calls from Bart asking to speak with particular people with fictitious and embarrassing names. This prompts Moe to call out to everyone in the bar with lines such as “Has anyone seen Maya Normousbutt?” and “Amanda Hugginkiss? Hey, I’m looking for Amanda Hug- ginkiss.” The “Donnie Fatso” episode is notable because Moe receives a phone call that is not a prank and not from Bart. Instead, Marion Anthony D’Amico, head of Springfield’s notorious D’Amico crime family, is calling. Fat Tony, as he is known to his friends (and ene- mies), simply wants Moe to find out if his Russian friend Yuri Nator is in the bar. Assuming that this is another prank by Bart, Moe makes 38 Sing_5p_all_r2.indd 38 8/16/13 7:45 PM the puzzle of mathematical humor · 39 the mistake of threatening the caller: “I’m gonna chop you into little pieces and make you into a Rubik’s Cube which I will never solve!” A more ancient puzzle appears in “Gone Maggie Gone” (2009), an episode that is partly a parody of Dan Brown’s novel The Da Vinci Code. The storyline begins with a total solar eclipse, ends with the discovery of the jewel of St. Teresa of Avila, and revolves around the false belief that Maggie is the new messiah. From a puzzle lover’s point of view, the episode’s most interesting scene concerns Homer, who finds himself trapped on one side of a river with his baby (Mag- gie), his dog (Santa’s Little Helper), and a large bottle of poison cap- sules. Homer is desperate to cross the river. There is a boat, but it is flimsy and can only carry Homer and one other item at a time. Of course, he cannot leave Maggie with the poison because the baby might swallow a capsule, and he cannot leave Santa’s Little Helper with Maggie in case the dog bites the baby. Hence, Homer’s challenge is to work out a sequence of crossings that will allow him to ferry everybody and everything safely to the other side. As Homer begins to think about this predicament, the animation style changes and the problem is summarized in the style of a medi- eval illuminated manuscript, accompanied by the words: “How does the fool cross the river with his burdens three?” This is a reference to a medieval Latin manuscript titled Propositiones ad Acuendos Juvenes (Problems to Sharpen the Young), which contains the earliest refer- ence to this sort of river-crossing problem. The manuscript is a mar- velous compilation of more than fifty mathematical puzzles written by Alcuin of York, regarded by many as the most learned man in eighth-century Europe. Alcuin poses an identical problem to Homer’s dilemma, except that he frames it in terms of a man transporting a wolf, a goat, and a cabbage, and he has to avoid the wolf eating the goat, and the goat eating the cabbage. The wolf is essentially equivalent to Santa’s Little Helper, the goat has the same role as Maggie, and the cabbage is in place of the poison. The solution to Homer’s problem, which he works out for himself, Sing_5p_all_r2.indd 39 8/16/13 7:45 PM 40 · simon singh is to start by taking Maggie across the river from the original bank to the destination bank. Then he would return to the original bank to collect the poison, and row back to the destination bank and deposit the poison. He cannot leave the poison with Maggie, so he would bring Maggie back to the original bank and leave her there, while he takes Santa’s Little Helper across to the destination bank to join the poison. He would then row back to the original bank to collect Mag- gie. Finally, he would row to the destination bank to complete the challenge with everyone and everything having safely crossed the river. Unfortunately, he is unable to fully implement his plan. For when Homer leaves Maggie on the destination bank, at the end of the first stage, she is promptly kidnapped by nuns. This is something that Alcuin failed to factor into his original framework for the problem. In an earlier episode, “Lisa the Simpson” (1998), a puzzle plays an even more important role by triggering the entire plotline. The story starts in the school cafeteria, where Lisa sits opposite Martin Prince, who is perhaps Springfield’s most gifted young mathematician. In- deed, Martin experiences life from an entirely mathematical perspec- tive, as demonstrated in “Bart Gets an F” (1990), in which Bart temporarily befriends Martin and offers him some advice: “From now on, you sit in the back row. And that’s not just on the bus. It goes for school and church, too . So no one can see what you’re doing.” Martin then reframes Bart’s advice in terms of mathematics: “The potential for mischief varies inversely to one’s proximity to the au- thority figure!” He even jots down the equation that encapsulates Bart’s wisdom, in which M represents the potential for mischief and PA is proximity to an authority figure: Sing_5p_all_r2.indd 40 8/16/13 7:45 PM the puzzle of mathematical humor · 41 In the cafeteria, Martin becomes interested in Lisa’s lunch, which is not the usual cafeteria food, but rather a vacuum-packed space- themed meal. When Lisa holds up the lunch and explains that it is “what John Glenn eats when he’s not in space,” Martin spots a puzzle on the back of the packet. The challenge is to find the next symbol in this sequence: Martin solves the puzzle in the blink of an eye, but Lisa remains perplexed. She gradually becomes more and more frustrated as stu- dents sitting nearby, including Bart, say that they can identify the next symbol in the sequence. It seems that everyone can work out the answer . except Lisa. Consequently, she spends the rest of the epi- sode questioning her intellectual ability and academic destiny. Fortu- nately, you will not have to suffer such emotional turmoil. I suggest you spend a minute thinking about the puzzle, and then take a look at the answer provided in the caption on the next page. The lunch puzzle is noteworthy because it helped to shore up the mathematical foundations of The Simpsons by playing a part in at- tracting a new mathematician to the writing team. J. Stewart Burns had studied mathematics at Harvard before embarking on a PhD at the University of California, Berkeley. His doctoral thesis would have involved algebraic number theory or topology, but he abandoned his research before making much progress, and he received a master’s degree instead of a PhD. The reason for his premature departure from Berkeley was a job offer from the producers of the sitcom Unhappily Ever After. Burns had always harbored ambitions to become a televi- sion comedy writer, and this was his big break.