Do the Math!: On Growth, Greed, and Strategic Thinking


John K. White

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  • Dedication

    For Belén


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    In Do the Math!

    • How do pyramid scams work?
    • When did the real downturn in the economy occur?
    • Do inflation measures work in fast-changing times?
    • Are reality television shows fair?
    • Can one win game shows using simple probabilities?
    • Which state was really responsible for George W. Bush's 2000 win?
    • Why do disagreements persist in Northern Ireland?
    • How can you avoid paying interest?
    • Is the economy expanding or contracting at any given moment?
    • Can we calculate the cause of reduced crime?
    • Why are North American sports leagues better than those in Europe?
    • How do stock pickers win at the market?
    • Why is the average person not the most likely person?
    • Do birth dates indicate success in life?
    • Where did the concept of lucky numbers originate?
    • How does Arnold Schwarzenegger send secret messages?
    • Is debt destroying the world?
    • Who is profiting from your debt?
    • Can No. 1 chart toppers explain increasing world poverty?
    • How much do advertisers add to the cost of goods?
    • Why are sports so uncompetitive?
    • Who really broke the bank in 2009?


    I am indebted to many people who helped and advised me during the writing of Do The Math!, especially to those who provided essential background, read parts or all of the manuscript, and prepared the manuscript for publication. Writing Do The Math! has been an immensely rewarding journey, one where I have looked under many mathematical stones to see the teaming world of numbers at our fingers. Happily, I was ably helped throughout.

    In particular, I would like to thank Doug Alderman for his creative comments and for keeping me on my toes, Vicki Knight for her constant guidance and careful shepherding from draft to book, Tom and Pat Lawson for inspiring me to think creatively about issues, Tom McCormack for our many discussions about the intersection of physics and economics, Owen Priestly for reminding me that economics is about common sense, and David Thomas who helped make the theoretical real.

    I would especially like to thank the academic reviewers for the thoroughness of their remarks and many excellent comments, in particular, John Bohte of University of Wisconsin Milwaukee, James I. Bowie of Northern Arizona University, Steve B. Lem of Kutztown University, Stephen N. Kitzis of Fort Hays State University, Liza L. Kuecker of Western New Mexico University, Terry F. Pettijohn II of Coastal Carolina University, Nancy Sonleitner of University of Tennessee at Martin, and Guillermo Wated of Barry University. The final result is all the more rigorous for their attention. I would also like to thank Danny Heffernan, Kirk Junker, Belén Roza, and Gerry O'Sullivan for their invaluable comments, as well as Maurice Coyle, David Lockey, Rosa Monleon, Emma Sherry, Laurie Snell, Avelino Valle, and Peter Whitney for their kind assistance along the way.

    I am also indebted to my many colleagues at the School of Physics, University College Dublin, for their help and support. Many kernels of ideas began at UCD and were first sounded there. In particular, I would like to thank Ann Breslin, Peter Duffy, Padraig Dunne, David Fegan, Andrew Fitzpatrick, Bairbre Fox, Alison Hackett, Lorraine Hanlon, Colm Harte, Brian McBreen, Tom McCormack, Alex Montwell, Fergal O'Reilly, and Gerry O'Sullivan. I would also like to thank everyone at Sage, in particular Vicki Knight. Thanks to Vicki I was able to enjoy the whole process as we shared many ideas about writing and learning. I would also like to thank Kalie Koscielak and Brittany Bauhaus for their generous help and careful attention, and Megan Granger for her expert editing. I am indebted to Megan for her thorough attention to detail as well as her many helpful suggestions. I would also like to thank Gail Buschman, Nicole Elliott, Lauren Habib, Adele Hutchinson, Kelley McAllister, and Dory Schrader for their help.

    This book would not be possible without Belén Roza, who kick started the process and offered many thoughts and inspirations along the way. She is my partner and my constant guide. Thank you for sharing your beautiful spirit. Daisy White has been a constant source of inspiration to me, from her indomitable joie de vivre to her always positive approach to life, and I would like to thank her for her unwavering support.

    It has been a joy to be involved in the writing of Do The Math!, and I thank everyone involved for their encouragement and invaluable contributions. I hope I have advanced the discussion about how to live in a fairer world, and I thank you all for helping.

    About the Author

    John K. White received his B.Sc. in Applied Physics from the University of Waterloo, Canada, and a Ph.D. from University College Dublin, Ireland. He has worked around the world as a physicist, lecturer, project manager, and computational analyst over a 25-year career. He has worked as a project manager and technical writer for Sun Microsystems, The Netherlands Organization, and Berminghammer Foundation Equipment, a consultant for Interactive Image Technologies, ScotiaBank, and the Ontario Government, and as a lecturer and research fellow at University College Dublin. He is also active in promoting physics and numeracy in schools, and has published widely in academic journals, contributed chapters to edited volumes, and authored numerous technical publications. A series of Do The Math!-related downloads, exercises, and links are available on his website at


    When I was growing up in the ’60s and ’70s, my parents often reminded me and my siblings of leaner times after World War II, when supplies were scarce and food was rationed. Although we wanted for little, our lifestyle was nonetheless economical, as we were taught to measure our wants and not to expect too much. We could always ask for more, even for an occasional luxury item such as a new bike or the latest toy, but we were taught that the primary goal of acquiring and using was need and not want; in so doing, we learned the value of our material world.

    The ongoing economic troubles in the world's financial centers, however, suggest that something is not quite right, from the questionable ethics of trusted institutions to a poor understanding of numbers and systems—although the mathematics of collateralized debt obligations, credit default swaps, and derivatives would baffle many a PhD mathematician. Complicated financial instruments and creative accounting have now become the norm, contrary to the well-taught ethics of the past, such as hard work, fairness, and public good, as most of us understand them. In the process, our world, which we call egalitarian, meritocratic, and religious, has been usurped by those in the financial know—aided by government inadequacy—creating a culture defined more and more by money and less and less by the common good.

    One wonders if the age in which we live—one of scientific mastery over resources that produces newer technological gadgets by the day—has created such a world, where our wants are manufactured as needs. We do seem to be in a hurry to have it all as we marvel at the lifestyles of the materially well-endowed. Growth is the buzzword, apparently at any cost, and greed is its motive. But to what end? Constant economic uncertainty? A permanently stressed-out workforce? Everyday stories of government and corporate corruption and abuse? What's more, are we falling behind in the race to get ahead as we deplete the earth's finite and dwindling resources?

    Limping from one crisis to another upsets and destroys the fabric of our lives and that of our communities, as witnessed by dramatic increases in unemployment and mortgage defaults during the now-regular economic downturns. There are better ways to proceed, but we need stronger knowledge of basic systems to understand our world and to analyze the more complicated problems of our times.

    One place to start is with counting and mathematics, perhaps our oldest mental constructs, on which numerous systems have been created—from ancient calendars, weights and measures, and games of chance to today's world of finance, banking, and statistics. Our modern way of living, from household bills to the details of modern economics, would be scarcely possible without the age-old language of counting. And yet many of us recoil from even the simplest math, seemingly afraid to grasp the basics, believing the sums too hard or better left to others—no matter that it is impossible to communicate in today's world without a proper mathematical grounding.

    Perhaps the first battle is to overcome our fear and cast away the notion that some can and some can't. Mathematics is easier than we think. As with any skill, one must practice. We train our bodies and souls in regular sessions, so why not train our minds to acquire better understanding? Problem solving need not be left to uninformed trial and error, where old-world ideas and new-age logic trump informed thought.

    Without an understanding of mathematics, we simply can't make the right decisions. Fuzzy thinking keeps us in the dark about consumer costs, enslaves us to lending institutions, leads to poor choices, and confuses wisdom with jargon. But, more important, by shying away from the numbers, we can't make important decisions about essential issues such as government bailouts, oil supplies, or global warming. Our inability to analyze numerical information keeps us from understanding issues that are incumbent on our being and have exceedingly important ethical implications for our future.

    To be sure, lustful gurus abound, telling us how to interpret our fast-changing technological landscape, and many of us are unsure to whom we should listen or which data to trust. Life is full of “asymmetrical information,” we are told, where those in the know pass on insider info via hidden networks, leading many to believe that real knowledge is unattainable. But that belief is false. Any person on the street can communicate about today's number-filled world without an advanced degree in business or statistics. All it takes is the right data, the right tools, and some straightforward techniques to analyze the numbers.

    Do the Math! is not a mathematics refresher, nor does it shy away from the numbers. Instead, many creative examples are given to explain our number-filled world, such as pyramid scams and economic growth (Chapter 2); the stock market and auto racing (Chapter 3); cost-benefit analysis and reality television shows (Chapter 4); the Electoral College and inflation (Chapter 5); Shakespeare's plays, the death penalty, and sports competitiveness (Chapter 6); Monopoly, blackjack, and roulette (Chapter 7); astrology, codes, and lottery odds (Chapter 8); looking under the hood of modern financial practices (Chapter 9); consumer rip-offs (Chapter 10); and cooperative thinking (Chapter 11). Along the way, we look to mathematics to explain geometric series, small-world phenomena, power laws, continuous variables, derivatives, error, statistical methods, correlation, computing, probability, game theory, and more. Just as Lynne Truss stresses the importance of grammar for better literacy in her book Eats, Shoots & Leaves, numbers and analytical methods are stressed here for better numeracy. Indeed, being innumerate is no more acceptable than being illiterate.

    Aesop's well-known fable “The Tortoise and the Hare” can be used to explain sophisticated theories such as inflation and derivatives. Other fables show how exponential growth left unchecked leads to disastrous results, and help us better understand the pyramid scams of Enron, Bernie Madoff, and Allen Stanford, or how Bear Stearns, Lehman Brothers, and Ameriquest played their parts in a near global economic meltdown.

    Other stories help us question past methods, such as the tale of the woman who cut off the sides of the family roast before putting it in the oven as her mother had done, not knowing that her mother did so only because her roasting pan was too small. Or the story of the woman who put all her money—a farthing—in the collection plate, thus giving less and yet more than all the others.

    Here, a simple calculation shows how one-size-fits-all justice contradicts the notion of a shared society—which we have been taught to believe exists—where the relative difference can be more than the absolute difference and a flat rate is not the same for everyone. Indeed, a $500 fine is nothing to a millionaire, and were a fine charged in like proportion to someone earning $25,000 a year, it would be only $12.50—hardly a credible deterrent. For a fine to have the same weight to the millionaire as the $500 fine does to the person earning $25,000 (2%), it would need to be $20,000—an amount perhaps not as easily scoffed at by today's typically undeterred rich. Similarly, are thousand-dollar fines for cutting corners any better? For example, is such a fine sufficient for an oil spill, where cleanup costs can amount to tens of billions of dollars, or for a bank disaster that requires public money to ensure private liquidity, where costs are socialized but benefits are privatized? What about uneven tax codes, accounting loopholes, or preferential trading practices, which subsequently disadvantage others? Mathematics can quantify the disparities.

    Obviously, we don't have everything right if half the world lives on so little (Europe, the United States, China, and Japan account for 60% of the world's estimated $73 trillion GDP1), a small percentage controls most of the world's wealth (in the United States, one estimate states that 1% owns one third of the country's wealth, whereas in the United Kingdom 1% owns more than two thirds), and the debt load of the world's poorest countries is so great they can never repay it. Nor can it be right that the divide is getting worse (relative GDP of the bottom countries has decreased sixteenfold), that average consumer debt is greater than average income (in 2011, American personal debt was more than $16 trillion, or $50,000 per person), or that failed financial institutions have destroyed people's savings and cost jobs by the millions. Perhaps the so-called trickle-down wealth system said to benefit everyone actually polarizes society. But for whom does the world exist—for you and me, or for the financial elite?

    Numbers always have a moral side, hidden behind a society that increasingly rips people off. What is a 50% sale when the markup is 100%? Why do we pay twice as much for goods before Christmas as after Christmas? Airlines tack on so many extras that the final price bears no resemblance to the advertised price (one such $0 out and $0 return was more than $100). Our culture has become one of hard-to-read numbers, hidden logic, and dubious claims, where in the absence of proper regulation, one must doubt every claim and question every transaction, vigilantly acting as one's own regulator. In such an unfair world, it seems that more than a cursory understanding of numbers is needed to identify the traps, the red queens, the wicked witches, and even our own gluttony.

    By looking at the numbers, we expose the myths, the half-truths, and the out-and-out lies routinely trotted out by suspect sources wielding made-up facts and figures. Banks affect our well-being. How does a bank calculate compound interest? How much are you actually spending on those “no money down, no interest” loans? Can we understand a banking system that loaned 100 times its capital to speculate on mortgages, which dramatically impacted the lives of millions when it failed and resulted in a trillion-dollar banking bailout?

    How about the lottery, seemingly simple by comparison? Should we teach a work ethic to our children, yet devalue that same ethic by encouraging get-rich-quick, instant-freedom, one-in-a-million chances at amounts in excess of $100 million? No matter how altruistic the cause, lotteries are regressive taxes that disadvantage the less well-off, who use them most. Or what about a now-ubiquitous gambling culture spawned by our fascination with numbers and chance that exists solely to profit from other people's ignorance and failure? Should those of us in the know permit such practices, or do we keep a competitive advantage by allowing the less-informed to be so abused?

    Behind a number, a calculation, a story lie useful methods, and not only mathematicians and economists should understand them. Should our economies rumble on, stumbling from one spike to the next, hellbent on producing unsustainable growth? What is inflation and how is it measured? To whom do we owe such large national debts, given that economics is a closed system? We must become better informed, working with known facts and proven methods, so it becomes easier to challenge bad practice.

    Socrates said, “The unexamined life is not worth living”—wise words that I hope still apply in our fast-changing world of globalization and the Internet. Or are we stuck with an out-dated, superstitious, fad-ridden society that continually falls victim to the latest swindle and unsubstantiated claim? Can we expose garbled facts, wonky myths, and screwed-up tales that serve only to separate our money from our wallets? One hopes so, and that we can tackle the harder questions and put into practice better thinking and better strategies.

    In Do the Math!, we learn about such strategies, some as stern and autocratic as the tides, some that apply in certain conditions, and others as downright whimsical as the weather. Of course, many competing ideas and conflicting methods suggest the best road forward, but how we should progress to achieve the best ends and to whom the world belongs are questions we must ask and for which we must have the right information and tools to proceed. Using less by reevaluating our wants is one solution. Better cooperation using organized strategies is another and is essential in any working system, whether to reduce, reuse, and repair, or to expand continually at increasing peril. Indeed, the goal of committed citizens and their political institutions must be to apply strategies that work to create a better living for all as set out in the great parchments of our times.

    Our world has improved enormously since the uncertain and impecunious postwar times of my parents, but does it serve the needs of everyone or even a majority of its citizens? If we say we live in a fair, democratic, and enlightened world, where everyone has equal opportunity, then we must learn the systems and count the costs. We must work the numbers, lest we be sold a bill of goods.

    Do the Math! puts together various thoughts about numbers and noise, statistics and probability, and money and economics that are making the rounds as we begin to understand the limitations of our world and its many varied systems. The presentation is purposefully eclectic, allowing the mind to synthesize ideas from different areas. As such, I have borrowed liberally from the anecdotal and the academic, from literature and the newspaper, and from the stock market and the casino—all in the hopes of improving numeracy.

    What qualifies me for this task? Well, I am good with numbers and have spent a career as a computational physicist, analyzing many diverse systems, from nuclear reactors to rocket propulsion, using anything from a Commodore 64 (with its fantastically slow input cassette drive) to the latest multicore parallel computing architectures. I have also delved into the world of sports scores, gaming, and financial trading, creating numerical models and statistical analyses, all to see how the numbers work.

    Perhaps more important, I have worked in different areas, including academia, industry, and business, where I have seen firsthand how numbers are used and abused. I am also a generalist, constantly looking for the common in the seemingly disparate, what overlaps and can be agreed on—and not just the mathematics of our daily world, but how the numbers jibe with what we are told.

    I also want to stand and be counted, literally, as someone who is trying to assess the increasing discrepancy between fact and fiction at play in today's seemingly more complicated world. The intention is to look more closely at the perceived wisdom and to see the real mechanisms at work. I hope you enjoy the journey.


    1 Gross national product and gross domestic product: Gross national product (GNP) is the value of all goods and services produced annually by citizens of a country regardless of where they live. Gross domestic product (GDP) is the value of all goods and services produced annually within a country regardless of whether by citizens or foreign nationals. GNP numbers throughout are from the Central Intelligence Agency's World Factbook (2011). Barber (2007) cited a report that such measures overestimate the health of an economy, whereas the GPI (genuine progress indicator) measures the quality as well as quantity of an economy (p. 148).

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