L.A. Math: Romance, Crime, and Mathematics in the City of Angels Read online

  L.A. MATH

  L.A. MATH

  Romance, Crime, and Mathematics in the City of Angels

  James D. Stein

  PRINCETON UNIVERSITY PRESS

  Princeton and Oxford

  Copyright © 2016 by James D. Stein

  Requests for permission to reproduce material from this work should be sent to Permissions, Princeton University Press

  Published by Princeton University Press,

  41 William Street, Princeton, New Jersey 08540

  In the United Kingdom: Princeton University Press,

  6 Oxford Street, Woodstock, Oxfordshire OX20 1TW

  press.princeton.edu

  Jacket art: Detective © Dm-Cherry/Shutterstock

  All Rights Reserved

  Library of Congress Cataloging-in-Publication Data

  Stein, James D., 1941–

  L.A. math : romance, crime, and mathematics in the City of Angels / James D. Stein.

  pages cm

  Includes index.

  ISBN 978-0-691-16828-9 (hardback)

  1. Criminal investigation—Fiction. 2. Mathematics—Fiction. 3. Mathematics—Miscellanea. 4. Los Angeles (Calif.)—Fiction. I. Title. II. Title: Los Angeles math. III. Title: Romance, crime, and mathematics in the City of Angels.

  PS3619.T45L3 2016

  813'.6—dc23 2015018419

  British Library Cataloging-in-Publication Data is available

  This book has been composed in Glypha LT Std & Sabon LT Std

  Printed on acid-free paper. ∞

  Printed in the United States of America

  10 9 8 7 6 5 4 3 2 1

  TO LINDA

  —with whom 1 + 1

  STILL equals 1

  CONTENTS

  PREFACE: L.A. Math

  ix

  MATHEMATICAL TOPICS BY CHAPTER

  xv

  CHAPTER 1. A Change of Scene

  1

  CHAPTER 2. The Case of the Vanishing Greenbacks

  11

  CHAPTER 3. A Matter of Time

  21

  CHAPTER 4. The Worst Forty Days since the Flood

  31

  CHAPTER 5. The Accidental Guest

  40

  CHAPTER 6. Message from a Corpse

  50

  CHAPTER 7. Animal Passions

  60

  CHAPTER 8. Nothing to Crow About

  69

  CHAPTER 9. The Winning Streak

  78

  CHAPTER 10. One Long Season

  88

  CHAPTER 11. The Great Basketball Fix

  97

  CHAPTER 12. It’s All in the Game

  106

  CHAPTER 13. Division of Labor

  115

  CHAPTER 14. The Quarterback Controversy

  123

  APPENDIXES: Continuing the Investigations

  1. Mathematical Logic in “A Change of Scene”

  137

  2. Percentages in “The Case of the Vanishing Greenbacks”

  143

  3. Averages and Rates in “A Matter of Time”

  148

  4. Sequences and Arithmetic Progressions in “The Worst Forty Days since the Flood”

  153

  5. Algebra, the Language of Quantitative Relationships, in “The Accidental Guest”

  161

  6. Mathematics of Finance in “Message from a Corpse”

  166

  7. Set Theory in “Animal Passions”

  175

  8. The Chinese Restaurant Principle: Combinatorics in “Nothing to Crow About”

  184

  9. Probability and Expectation in “The Winning Streak”

  189

  10. Conditional Probability in “One Long Season”

  198

  11. Statistics in “The Great Basketball Fix”

  202

  12. Game Theory in “It’s All in the Game”

  213

  13. Elections in “Division of Labor”

  219

  14. Algorithms, Efficiency, and Complexity in “The Quarterback Controversy”

  225

  An Introduction to Sports Betting

  231

  Notes

  235

  Index

  239

  PREFACE: L.A. MATH

  WHY L.A. MATH?

  You may be wondering why this is book is called L.A. Math. After all, just because math somehow takes place in Los Angeles doesn’t mean it’s different. 2 + 2 = 4 here (yes, I live in L.A.), just like everywhere else.

  There are actually three reasons. The first has to do with getting people to look at the book. Any time you put “L.A.” in the title of anything, you virtually guarantee that people will be interested—I hope, even if the next word is “Math.” L.A. Law was a successful TV series; L.A. Confidential was both a successful book and a successful movie. There’s still a mystique and a fascination to L.A. that Wichita, Kansas, and Peoria, Illinois, simply don’t have. Even New York, L.A.’s archrival in practically everything, doesn’t have it—at least, that’s what we in the City of Angels like to think.

  The second reason is that this really is a book about Los Angeles and math—although not quite the way you might suspect.

  And the third reason? Well, to find that out, you’ll have to read on.

  HOW THIS BOOK CAME TO BE

  I’ve always loved short stories. A good short story has plot, characters, dialogue—with the added bonus of not having to invest a lot of time reading it. Got fifteen minutes? You can read a short story.

  Two of my favorite short story genres are science fiction and mystery. I’m not exactly sure why there seem to be fewer short stories published now than when I was growing up, when many of the greatest authors of science fiction and mystery wrote short stories. I was reminded of this a while back when I found myself in Culver City with a couple of hours to kill. Fortunately, I was near the library and so spent the time happily reading an anthology of the best science fiction stories of 1969. It was time rewardingly spent.

  Actually, very rewardingly spent, because it was one of the factors that led to my completing this book. I had originally started writing this book more than twenty years ago—using now-defunct word-processing software. I had approached a company that wanted to get into the textbook business with an idea for a different type of text for a Math for Liberal Arts (aka Math for Poets) course. I wanted to write a series of short stories introducing the basic idea for a number of topics that would constitute a Math for Liberal Arts course and then write accompanying textual material that would expand the idea. It would be the most student-friendly math text ever written.

  And that’s the third reason. L.A. Math is an abbreviation for Liberal Arts Mathematics.

  The company went for it, they sent me an advance, and I started work. A few months later, the company was taken over by a giant textbook publisher that decided to scrap the project, as it did not fit in with the type of textbook they produced. I had mixed feelings; I wanted the book to see the light of day, but I also wanted to write the book I wanted to write, not the book a panel of educators wanted me to write. I wanted to write a book that would appeal to readers. Whether a textbook appeals to readers is unimportant from the standpoint of textbook publishers; what matters to them is that it will be rejected (for whatever reason) by as few educators as possible.

  So I stopped writing the book. I had kept all the files, as well as numerous other files from this period, but I had been unable to convert them into Microsoft Word, which is by now the standard in word processing. I knew I coul
d take the files to a computer expert, pay some money, and have it done—but I’m both cheap and stubborn, and there was no urgency to updating the files, as I had no use for them.

  Flash-forward roughly two decades, and here I was, in the Culver City library, reading The Best from Fantasy and Science Fiction, 19th Series (Ferman 1971). The first story in the anthology I read was entitled “Gone Fishin’.” It was written during the height of the Cold War, so there were some slightly dated aspects, but to say that it was riveting is a giant understatement—it was easily the best short story I had read in a number of years. Memo to any film or TV producer who reads this (and I’m sure there will be lots, LOL)—get the rights, update the story, and make a movie or TV series out of it. I think it’s a guaranteed winner. Anyway, the story was written by a Robin Scott Wilson, of whom I had never heard. So, when I got back home, I decided to check him out.

  Robin Scott Wilson was a former president of California State University, Chico!

  You may not think that this deserves italics, but I did. I teach math at California State University, Long Beach—a much larger branch of the California State University system than the one at Chico, and also, if I may say so, one with more academic substance. In fact, while Wilson was president, CSU Chico was named the number one party school in the country! Wilson took umbrage at this and restored a measure of academic dignity to the campus.

  After discovering the not-so-secret life of science fiction author Robin Scott Wilson, I decided to buckle down and see how the stories that I had written for the abandoned math book measured up to “Gone Fishin’.” Granted, the genre was totally different, but I’ve been reading for so long that I can generally tell good writing from bad. You might think that I couldn’t be dispassionate about my own stories, but I’m generally my own worst critic. Also, it wouldn’t be like I was reading stuff that I had written—I would be reading stuff that somebody else wrote twenty years ago, a somebody else who previously tenanted the body that I now inhabit (regrettably not exactly the same body; the one I now inhabit is somewhat the worse for wear). I’m not the same person I was twenty years ago—who is?

  It took me two hours to figure out how to translate the files from the format in which they had been stored by the obsolete word processor. It was embarrassingly easy—but at least I had saved the fee I would have been charged. I started to read the stories. Although I knew the general theme, I had completely forgotten most of the stories—but I was pleasantly surprised, as, I hope, you will be when you read them. I admit that I’m somewhat prejudiced, but I feel that they’re all eminently readable, and a few are considerably more than that. IMHO, of course.

  MATH CAN ACTUALLY BE ENTERTAINING

  Mathematics has managed to infiltrate itself into science fiction. There is an extremely entertaining anthology of mathematically oriented science fiction stories entitled Fantasia Mathematica, edited by Clifton Fadiman. Two of my all-time favorite stories appear in it. “The Devil and Simon Flagg,” written by Arthur Porges, describes what happens when a mathematician summons Lucifer and bets his soul that the Devil can’t come up with a proof of Fermat’s Last Theorem in twenty-four hours. The story was written forty years before Andrew Wiles actually solved the problem, but the charm of the story will last as long as there are people to read it. “A Subway Named Moebius,” written by A. J. Deutsch at about the same time (the early 1950s), describes the unexpected consequences when the city of Boston constructs a subway system with bizarre topological properties.

  These stories, like most science fiction, are one-shot affairs; the characters never appear again in another story. There are science fiction books with recurring characters (think Star Trek), but for the most part they are soap operas set in a galaxy far, far away—it is the characters and their interactions that generate appeal, rather than the ingenuity of the stories. Mystery stories are different; it is a combination of the characters, their interactions, and the ingenuity of the stories that generates appeal (think Sherlock Holmes).

  To the best of my incomplete knowledge, nobody has ever tried to do what I started to do twenty years ago: write a collection of short stories, with a continuing set of characters, in which mathematics plays an important role—and a role that varies from story to story. Yes, there was the popular TV series Numb3rs; I’m pretty sure that if you liked that series you’ll like this book as well. However, the mathematics in the TV show was sort of a deus ex machina plot device; for the most part, the viewer simply accepted the idea without really “doing the math.”

  This is different. The stories in this book are unified not only by the presence of a continuing set of characters but also by the fact that the mathematical topics that play roles in the stories constitute a reasonably respectable Math for Liberal Arts course of the type offered by community colleges and universities. You can read the stories and painlessly absorb some interesting and useful mathematics en passant; but if you want, you can plunge a little more deeply into the mathematics by reading the appendix that accompanies each chapter. That portion is written somewhat like a math text—it presents the ideas and illustrative examples relevant to the story, but you’ll be happy to know that there isn’t a single problem that you’ll be asked to do. There is additional material available online at press.princeton.edu/titles/10559.html.

  Most first-semester courses in a subject like calculus cover the same material, no matter where you take the course, but Liberal Arts Mathematics is different; it varies a lot from place to place, and even from instructor to instructor at the same school. There are three broad categories of material—different takes on subjects such as algebra and geometry, finite mathematics such as probability and statistics, and relatively recent developments such as game theory and the mathematics of elections. This book includes material from all three categories, so there’s almost certainly going to be something in it that is covered in a Liberal Arts Mathematics course if you happen to be taking one.

  There are three people to whom this book owes a significant debt. The first is Jordan Ellenberg, who is not only a top-flight mathematician but the author of How Not To Be Wrong: The Power of Mathematical Thinking, an absolutely first-rate book about how mathematicians think and why mathematics is so powerful. I had an opportunity to interview Jordan, and in reading his book, I was impressed by how similar his sense of humor was to mine. I asked him to look at a chapter from this book and, if he felt comfortable doing so, to recommend an editor. He suggested the second of the three, Vickie Kearn, who turned out to be the perfect editor for this book. She smoothed out many of the rough edges and anachronisms that were present in the original manuscript during the editing and also helped with suggestions that made the characters more appealing, bringing a sensitivity to the manuscript that it originally lacked. The third is my wife Linda, who has faithfully supported my writing efforts over the years without ever reading a single book I have written—but who has promised to read this one. I’m going to hold her to it. I would also like to thank two people who read the manuscript for their contributions. George Zamba is a detective who brought firsthand knowledge of the detective business to help shore up my admittedly secondhand knowledge of it, and James Coyle came up with several suggestions for improving the stories, including one that put the icing on the cake.

  MATHEMATICAL TOPICS BY CHAPTER

  CHAPTER 1

  Propositions

  Logical operators

  Truth tables

  CHAPTER 2

  Percentage

  CHAPTER 3

  Averages

  Rates

  CHAPTER 4

  Sequences

  Arithmetic progressions

  CHAPTER 5

  Linear equations

  Systems of two linear equations

  CHAPTER 6

  Simple and compound interest

  Installment purchases

  Amortization

  CHAPTER 7

  Set theory

  Fundamental Counting Princ
iple

  CHAPTER 8

  Combinatorics

  Chinese Restaurant Principle

  CHAPTER 9

  Probability

  Expectation

  CHAPTER 10

  Conditional probability

  CHAPTER 11

  Frequency and probability distributions

  Mean and standard deviation

  Normal distribution

  Bernoulli trials

  CHAPTER 12

  2 × 2 games

  Pure and mixed strategies

  Saddlepoints

  CHAPTER 13

  Voting methods

  Arrow’s Impossibility Theorem

  CHAPTER 14

  Algorithms

  Traveling Salesman Problem

  Task complexity

  NP-complete problems

  CHAPTER 1

  A CHANGE OF SCENE

  Santa Monica is up against the ocean. Five miles or so to the east, you’ll find Westwood, and in Westwood you’ll find UCLA and a lot of movie houses. Between the two is Brentwood, where the rents are more reasonable than Westwood or Santa Monica. That was why I was looking for a place to rent in Brentwood, while I tried to adjust to the fact that, big as New York was, I kept bumping into Lisa when I was there. Really, really awkward. At our wedding, lots of people kidded us about a marriage between a freelance investigator (me) and an artist (Lisa) being an odd-couple type of arrangement. Maybe it was too odd, as we were now separated.

  I felt I could use a change of scene, and L.A. is a definite change of scene from New York. At this moment, I was eyeballing a little guesthouse just behind a typical California hacienda off San Vicente north of Wilshire. For those with long memories, that’s the general area where O.J. Simpson also had a guesthouse, but O.J. would have turned up his nose at this one—maybe not now, as he was doing a stretch in a Nevada jail, but back when he had money. A rather dilapidated sign declared that it (the guesthouse) was for rent. The sign was dilapidated, but the guesthouse looked okay.