The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse Read online

  Table of Contents

  Title Page

  Copyright Page

  Dedication

  Acknowledgements

  Chapter 1 - To Infinity and Beyond

  Chapter 2 - Drive Me Crazy

  Chapter 3 - Casino Royale

  Chapter 4 - The Devil’s Playground

  Chapter 5 - Show Me the Money

  Chapter 6 - A Pox upon It

  Chapter 7 - Body Heat

  Chapter 8 - The Catenary Tales

  Chapter 9 - Surfin’ Safari

  EPILOGUE

  APPENDIX 1 - Doing the Math

  APPENDIX 2 - Calculus of the Living Dead

  BIBLIOGRAPHY

  INDEX

  THE CALCULUS DIARIES

  Jennifer Ouellette is the author of The Physics of the Buffyverse (2007) and Black Bodies and Quantum Cats: Tales from the Annals of Physics (2006). Her work has appeared in the Washington Post, Discover, Salon, Nature, New Scientist, Physics Today, Symmetry, and Physics World, among other venues. She maintains a general science-and-culture group blog called Cocktail Party Physics, and blogs for Discovery News. In November 2008, Ouellette became director of the Science and Entertainment Exchange, a program of the National Academy of Sciences aimed at fostering creative collaborations between scientists and entertainment industry professionals. In spring 2008, she was Journalist in Residence at the Kavli Institute of Theoretical Physics in Santa Barbara. Ouellette holds a black belt in jujitsu, and lives in Los Angeles with her husband, Caltech physicist Sean M. Carroll.

  On the Web:

  www.jenniferouellette-writes.com

  www.cocktailpartyphysics.com

  Praise for The Calculus Diaries

  “In this wonderful and compulsively readable book, Jennifer Ouellette finds the signature of mathematics—and especially calculus, of course—in the most unexpected places, the gorgeously lunatic architecture of Spain’s Antoni Gaudi, the shimmering arc of waves on a beach. Just following her on the journey is half the fun. But the other half is learning about the natural beauty and elegance of calculations. Ouellette’s ever clear and always stimulating voice is a perfect match to the subject—and The Calculus Diaries is a tour de force.”

  —Deborah Blum, author of The Poisoner’s Handbook: Murder and the Birth of Forensic Medicine in Jazz Age New York

  “A charming, gentle introduction to important mathematical concepts and their relevance to everyday life.”

  —Leonard Mlodinow, author of The Drunkard’s Walk: How Randomness Rules Our Lives

  “Jennifer Ouellette’s calculus confessional is a delight, and an example of the finest kind of science writing. Her book reveals to its readers the gritty inner workings of the most important idea humans have ever thought. (Yes, calculus is that big: it’s all about understanding how things change in space and time, and there just isn’t much that’s more important than that.) Ouellette’s wit, her elegant wielding of metaphor, and her passion for both math and funky culture produce this crucial insight: every equation tells a story, she says, and she’s right, and the tales she tells here will captivate even the most math-phobic.”

  —Tom Levenson, author of Newton and the Counterfeiter

  “Back in the day, when I was close to flunking out of calculus class because I couldn’t understand why it was worth my valuable time to actually understand it, I needed someone like Jennifer Ouellette to gently explain how I wrong I was. She’s like every English major’s dream math teacher: funny, smart, infected with communicable enthusiasm, and she can rock a ‘Buffy’ reference. In this book, she hastens the day when more people are familiar with an integral function than with Justin Bieber.”

  —Peter Sagal, host of NPR’s Wait Wait . . . Don’t Tell Me! and author of The Book of Vice

  “As amusing as it is enlightening, The Calculus Diaries is no dry survey of abstractions. It’s a guide to everyday life—to car trips and roller-coaster rides, diet and exercise, mortgages and the housing bubble, even social networking. As Ouellette modestly recounts her own learning curve, she and her husband become characters alongside eccentrics such as Newton and Gaudi and William the Conqueror. Like a great dance teacher, Ouellette steers us so gently we think we’re gliding along on our own.”

  —Michael Sims, author of Adam’s Navel: A Natural and Cultural History of the Human Form

  “Zombies? Surfing? Gambling? Nobody told me calculus could be like this. To my twelfth-grade math teacher: I demand a do-over!”

  —Carl Zimmer, author of Parasite Rex and The Tangled Bank: An Introduction to Evolution

  “Like the movies Batman Begins, Spider-Man, or Superman, The Calculus Diaries is the story of how an insightful, creative, and hard-working young person acquires superpowers and uses them for the benefit of society. Only this tale is true: Jennifer Ouellette can’t fly or spin a web, but she can spin a yarn. The Calculus Diaries documents the author’s seduction by mathematics and her conquering of it—Eureka!—to see the world with sharper vision. For too many people, math—calculus in particular—is an albatross. But Ouellette reveals math for what it is: a powerful tool for solving problems and the exquisite language we use to describe nature. Reading this book will make you smarter. And more powerful.”

  —Eric Roston, author of The Carbon Age

  PENGUIN BOOKS

  Published by the Penguin Group

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  First published in Penguin Books 2010

  Copyright © Jennifer Ouellette, 2010

  All rights reserved

  Illustrations by Jason Torchinsky. © 2009 Jason Torchinsky

  Figures in Appendix 1 by Sean Carroll

  eISBN : 978-1-101-45903-4

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  For Sean, the sine to my cosine.

  Neglect of mathematics works injury to all knowledge, since one who is ignorant of it cannot know the other sciences, or the things of this world. And what is worst, those who are thus ignorant are unable to perceive their own ignorance, and so do not seek a remedy.

  ACKNOWLEDGMENTS
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  This book grew out of my impulsive Internet purchase of a DVD lecture series, Calculus Made Clear, offered by the Teaching Company. The instructor, a math professor at the University of Texas-Austin, named Michael Starbird, combined the necessary rigor—in the form of simple diagrams and derivations—with an appealing (to me) conceptual approach, punctuated with colorful historical anecdotes. Nothing makes an English major happier than a compelling narrative. Tell us a good story and we’ll follow you anywhere, even into the minefield of scary calculus equations. Starbird’s lectures inspired me first to write a series of blog posts on Cocktail Party Physics about my adventures exploring calculus, and then to expand those into a full-length book.

  But Starbird had the advantage of working with fertile ground. I owe a great debt to Alan Chodos, a physicist who taught for years at Yale University before becoming associate executive officer of the American Physical Society. That gift for teaching never really left him. Alan not only encouraged me to write my first book, but carefully explained many basic physics concepts to me and insisted that I let him walk me through the relevant equations. We now live on opposite sides of the country, but Alan has had a lasting impact on my life, in the tradition of great teachers and mentors everywhere.

  I also benefited greatly from close readings of a handful of other works, most notably Charles Seife’s Zero: The Biography of a Dangerous Idea; Jason Bardi’s The Calculus Wars; David Berlinski’s A Tour of the Calculus; and Leonard Mlodinow’s The Drunkard’s Walk. All were instrumental in shaping my thinking about the concepts of calculus. When it came to putting those concepts into practice, I found W. Michael Kelley’s The Complete Idiot’s Guide to Calculus to be a helpful resource.

  Thanks are due to the many people (mathephiles and mathephobes alike) who generously shared their stories and insights over the two years I spent researching and writing this book, including (but not limited to) Bisi Agboola, Dave Bacon, Jason Bardi, Allyson Beatrice, Adam Boesel, Ben Carey, Deborah Castleman, Rob Chiappetta, Calla Cofield, K. C. Cole, Julianne Dalcanton, Geoffrey Edelstein, Adam Frank, Milton Garces, David Grae, David Gross, Lauren Gunderson, Kevin Hand, David Harris, Joanne Hewett, Karen Heyman, Daniel Holz, Alice Hung, Valerie Jamieson, George Johnson, Rich Kim, Lee Kottner, Tom Levenson, M. G. Lord, Gabrielle Lyon, Malcolm MacIver, Alex Morgan, Chad Orzel, Dennis Overbye, Phil Plait, Joe Polchinski, Lisa Randall, Abbas Raza, James Riordon, David Saltzberg, Robert Smith?, Tara Smith, Shari Steelsmith-Duffin, Ben Stein, Brian Switek, Carol Tavris, Kip Thorne, Mark Trodden, Jatila van der Veen, Robin Varghese, Rosie Walton, Gordon Watts, Margaret Wertheim, Risa Wechsler, Glen Whitman, Carolee Winstein, Mark Wise, and Tony Zee. Extra special thanks to Janet Blumberg, Diandra Leslie-Pelecky, and Eric Roston, who slogged through parts of the draft manuscript and offered helpful critiques.

  Jason Torchinsky did a fantastic job devising nifty illustrations of the abstract concepts throughout the book. Thanks are also due to Thomas Roberge, my editor at Penguin, and to my agent, Mildred Marmur, who offered her usual unstinting support and sage advice. And as always, I am deeply grateful to friends and family; miraculously, everyone still speaks to me after yet another lengthy disappearing act to write a book.

  I took great pains to ensure I understood the underlying concepts, not just the mechanical processes of calculus. Invariably, this means channeling one’s inner three-year-old and constantly asking “Why?” That can get pretty annoying. So I owe the greatest debt to my husband, Sean Carroll (aka the World’s Most Patient Man), who put up with my inner toddler for two years. I’m not sure I would have written this book without him. He helped me “find the calculus” in each chapter and allowed me to caricature him in the text for comic effect. He also proof-read the entire manuscript and deftly avoided the odd bit of metaphorical heaved crockery when I hit an obstacle (“integrate that!”), calmly guiding me toward the solution. I promise my next book will be about something simpler, like butterflies and rainbows. Or bunnies. Surely there’s no math in bunnies.

  PROLOGUE

  I Could Be Mathier

  Xander: Giles lived for school. He’s actually still bitter that there are only twelve grades.

  Buffy: He probably sat in math class thinking, There should be more math. This could be mathier.

  —“THE DARK AGE,”

  Buffy the Vampire Slayer

  Archimedes of Syracuse was the quintessential math nerd. Granted, he invented many practical devices, including devastatingly effective engines of war that helped Syracuse beat back an attack by the Roman general Marcellus in the siege of 212 B.C.—at least temporarily. But his one true love was pure mathematics, especially geometry. The Roman historian Plutarch tells how Archimedes’ servants had to forcibly bathe their preoccupied master, who would sketch geometrical figures in chimney embers, and in the oils that anointed his naked body after bath time.

  That single-minded obsession proved to be his downfall. Eventually Marcellus overcame Archimedes’ ingenious defenses, and Roman soldiers swarmed through the city of Syracuse. Historical accounts report that Archimedes was so engrossed in studying a geometric figure he’d drawn in the dust that he barely noticed the chaos around him. A Roman soldier “in quest of loot” marched up to the scholar and demanded that Archimedes accompany him to Marcellus’s tent. Archimedes demurred, saying he wished to finish solving his geometrical problem first: “I beg you, don’t disturb this.” Incensed, the soldier summarily killed him, so that “with his blood he confused the lines of his art.”1

  This account of the death of Archimedes provided inspiration centuries later, when a young French girl named Sophie Germain read the story in the late eighteenth century. She concluded that if someone could be so consumed by a geometric problem, then geometry must be the most fascinating subject in the world. So Germain set out to learn it, defying her family’s strictures by studying math in secret under the bedclothes at night. Later she masqueraded as a male student at the École Polytechnique in Paris (girls were not admitted), and by the time she died of breast cancer in 1831, she was a highly accomplished mathematician.2

  The soldier who killed Archimedes wasn’t quite so inspired. Perhaps Archimedes reminded him uncomfortably of his high school math teacher, who may have ridiculed the soldier’s failure to grasp the fundamentals of geometric proofs in front of snickering classmates. All that pent-up resentment and frustration boiled over into an impulsive act of rage, making the Greek scholar an early casualty in the longstanding war between jocks and nerds.

  Pure conjecture, naturally, but many of us can relate—even more so when we learn that Archimedes came dangerously close to inventing calculus. Two thousand years later, traumatic memories of high school calculus evoke powerfully negative reactions among people of all ages, genders, and backgrounds. Most people would rather be strung up by their thumbs and systematically tortured with sharp, pointy objects than be forced ever again to find the antiderivative of a polynomial. Math in general, and calculus in particular, is something to be avoided like the plague once we leave high school. An episode of the TV series House opens with a group of students taking the AP calculus exam. A boy collapses and is rushed to the hospital. When House is told of the circumstances of the boy’s collapse, he quips, “That’s the way calculus presents.”

  So calculus has a formidable reputation. I have always been among those nonmathematical sorts who viewed it with trepidation and preferred to keep a safe distance. In fact, I avoided taking calculus altogether by cleverly skipping out on my senior year of high school for early admission to college. Since I am a science writer who specializes in physics topics, it surprises many people to learn that I have a lingering phobia about math. Chalk it up to my English-major roots, but the sight of even a simple algebraic equation still elicits an involuntary shudder, unless I consciously counteract it.

  I am not alone in my ambivalence. My friend Allyson, in particular, seems to be a kindred spirit to that long-ago Roman soldier. “My initial reaction to the word calcu
lus is not unlike a caveman throwing rocks at the moon in ignorance and fear resulting in blind rage,” she confessed when I asked about her aversion to all things math. “There is no such thing as ghosts creeping up behind me on the stairs, but there is such a thing as a polynomial monster, and it has hooked teeth and causes chronic yeast infections, I’m sure.”

  Our stubborn resistance to calculus is not entirely rational. Frankly, most of us don’t even know what calculus entails; its reputation for being difficult and unpleasant precedes it. Calculus is quite simple and straightforward in concept; the devil is in the details. Essentially it’s a way of measuring change, whether it be change in position, temperature, or what have you. Its power comes from its universality: The same basic concepts can be applied to systems as diverse as a car driving down a road, the stock market, the Black Death, or surfing. That’s why calculus textbooks are so thick.

  Calculus boils down to two fundamental ideas: (1) the derivative (differential calculus), which is a way of measuring instantaneous change, such as finding the speed of a car when you only know its position; and (2) the integral (integral calculus), which describes the accumulation of an infinite number of tiny pieces that add up to a whole and can be used, for instance, to determine the distance a car has traveled when only its speed is known. Everything else is just a variation on these two themes. The derivative and the integral are like the two ends of a hammerhead: One is for pulling out the nails, and the other is for pounding them in. The first is a process of subtraction and division; the second, a process of multiplication and addition. Each “undoes” the work of the other. And not every math problem requires a hammer; sometimes a screwdriver works best. So calculus is just one tool in a broad arsenal of mathematical instruments, applicable to specific kinds of problems.