When I was growing up in the Sixties and Seventies, my parents would often remind my siblings and me of leaner times after World War II, when supplies were scarce and food was rationed. Although we wanted for little, our lifestyle was nonetheless one of economy 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, and in so doing we learned the value of our material world.

The ongoing economic troubles in the financial centers of the world, 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 (CDOs), credit default swaps (CDSs), 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-while in the process, our world, one we call egalitarian, meritocratic, and religious, has been usurped by those in the financial know, aided by government inadequacy, while creating a culture defined more and more by money and less and less by a common good.

One wonders if the age in which we live, one of scientific mastery over resources, and with newer technological gadgets by the day, has created such a world, where our wants have become manufactured as must-have 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, with greed 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?

There are better ways than limping from crisis to crisis that upset and destroy the fabric of our lives and those of our communities as witnessed by dramatic increases in unemployment and mortgage defaults during the now regular downturns in the economy, and a better knowledge of basic systems is needed 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, upon 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 would scarcely be possible without conversing in the age-old language of counting, from household bills to the details of modern economics. And yet many of us recoil from even the simplest math, afraid it would seem 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 to cast away the notion that some can and some can't. Mathematics is not as difficult as we think. As with any skill, one must practice. We train our bodies and our souls in regular sessions, why not 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 trumps informed thought.

Without an understanding of mathematics, we simply can't make the right decisions, where fuzzy thinking keeps us in the dark about consumer costs, enslaves us to lending institutions, and leads to poor choices, where wisdom is confused with jargon. But, more importantly, by shying away from the numbers, we can't make the 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 incumbent on our being that 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 to 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, leaving many to think that real knowledge is unattainable. But real knowledge is not unattainable, and the person in 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, but 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), as well as 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 the mathematics to explain geometric series, small-world phenomena, power laws, continuous variables, derivatives, error, statistical methods, correlation, computing, probability, game theory, and more. As in Lynne Truss's book Eat, Shoots & Leaves, where she stresses the importance of grammar for better literacy, numbers and analytical methods are stressed here for better numeracy. Indeed, it is no more acceptable to be innumerate than illiterate.

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

Other stories help us to question past methods such as the woman who cut off the sides of the family roast before putting it in the oven as her mother had done before her, not knowing that her mother had done 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 a one-size-fits-all justice is contrary to the notion of a shared society, one in which we have been taught to believe exists, where the relative difference can be more than the absolute difference, and that a flat rate is not the same for everyone. Indeed, a $500 fine is nothing to a millionaire, and were a fine given out in like proportion to someone earning $25,000, the fine would be $12.50, hardly a credible deterrent. For a fine to have the same weight to the millionaire as the $500 fine to a $25,000-earner (two percent), the fine would 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, such as an oil spill disaster, where cleanup costs can amount to tens of billions of dollars or a bank disaster paid for by 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 disparity.

Obviously, we haven't got everything right if half the world lives on so little (Europe, the United States, China, and Japan account for 60 percent of the world's estimated $73 trillion GDP), a small percentage control most of the world's wealth (in the United States, one estimate states that one percent owns one-third, whereas in the United Kingdom one percent owns more than two-thirds), and the debt load of the world's poorest countries is so great they can never repay. Nor can it be right that the divide is getting worse (relative GDP of the bottom countries has decreased 16-fold), that average consumer debt is greater than average income (in 2011, American personal debt was over $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 work to everyone's benefit in fact polarizes society, contrary to the stated goal of a better living for all. But for whom does the world exist-you and me or the financial elite?

There is always a moral side to numbers, hidden behind an increasingly more rip-off society. What is a 50-percent sale when the markup is 100 percent? Why do we pay twice the price for goods before Christmas than after Christmas? Airlines tack on so many extras that the final price bears no resemblance to the advertized price (one such $0 out and $0 return was more than $100). Our culture has become a culture 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 would seem 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 that are routinely trotted out by suspect sources with 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 lends out 100 times its capital to speculate on mortgages, which dramatically impacts the lives of millions by its failure and resultant 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, especially since 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 make money from other people's ignorance or 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, hell bent on 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, such that it becomes easier to challenge bad practice.

"The unexamined life is not worth living" said Socrates-wise words, which hopefully 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 which are as stern and autocratic as the tides, some which apply in certain conditions, and others which are as down-right whimsical as the weather. Of course, there are many competing ideas and conflicting ways suggesting the best ways forward, but how we 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 continually expand 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 post-war 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 an equal opportunity, then we must learn the systems and count the costs. We must do 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 have been 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 to better understand.

What qualifies me? Well, I am good at 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 multi-core parallel computing architectures. I have also delved into the world of sports scores, gaming, and financial trading, creating numerical models and statistical analysis, all to see how the numbers work.

Perhaps, more importantly, 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 upon-and not just the mathematics of our daily world, but how the numbers jibe with what we are told.

I also want to stand up 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.

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, consultant for Interactive Image Technologies, ScotiaBank, and the Ontario Government, and as a lecturer and research fellow at University College Dublin, and has analyzed game playing strategies, from professional sports teams to the stock market as well as many other thought provoking systems.

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. Born in Dublin, Ireland, he grew up in Toronto, Canada, and now lives and works in Dublin.

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

John K. White
Softcover, 350 pages, Sage Publications (2013)

Better numeracy, Do-it-yourself analysis, Social inclusiveness, Foster critical and strategic thinking, Uncomplicated mathematical discussion

Our world has become more complicated, and the notion of growth at any cost has led to constant economic uncertainty, a permanently stressed-out workforce, and everyday stories of government and corporate abuse. John K. White argues that a better knowledge of basic systems is needed to understand the world we live in, from pyramid scams to government bailouts, from sports leagues to stock markets, from the everyday to the seemingly complex.

Prologue