Do the Math!: On Growth, Greed, and Strategic Thinking, by John K White, SAGE Publications, 392 pp, £15.99, ISBN: 978-1412999595
Literacy and numeracy open up different worlds. Literacy accesses other people’s thoughts – rich with nuance, colour, texture. Numeracy, on the other hand, never seems to get out of Mr Gradgrind’s classroom full of dull repetition: “wrong, again! Do the Math!”
This book, despite its title, was not written by Mr Gradgrind. It was written by someone who knows that mathematical thinking is not really about numbers but about processes. So, from the first chapter, we find ourselves out in the world with an engaging guide whisking us from Bernie Madoff’s recent pyramid scam, to population growth, to Moore’s Law in electronics, to economic growth and the emergence of the BRICs (Brazil, Russia, India, and China) to overtake the G7 in the next two decades, state pension systems, global warming, and commodity shortages. All these are examples of the same process – exponential growth – and, in a finite world, must end in the same way. The question he playfully poses is when each will have its Minsky moment. All that is breezily covered in just the first chapter without straining the understanding of the general reader.
There are twelve chapters in all. Each can be read independently, as each covers a different topic. The topics covered will surprise all but those who studied mathematics at university. Chapter 4, for instance, treats fairness. Errors, of course, will happen but sometimes errors are unfair – over time systematically favouring one party over another. The Chance cards in Monopoly are not random – two out of three cards favour the player, and the Community Chest cards are even better with 76 per cent making the player better off (87 per cent if weighted by their monetary value). Real banks, White notes, tend to make more errors that go against customers than in their favour. From such simple examples he shows how such biases are commonplace – from political elections to Google’s search engine results, to decisions to ground aircraft, to how wealthy sports clubs can buy sporting success, to how students are graded. The tone is not one of simplistic moral outrage, but questioning how much bias is acceptable and what are its implications. As one is pondering how much fairness is fair enough, one is learning about many forces influential in forming our brave new world.
The essence of mathematics is not, as school kids are taught, to get the right answer: it is to ask the right questions. A theme running through the entire book is whether our society’s increasing emphasis on the economy – a competitive, want-driven, money-measured game – is now reducing individuals’ welfare. White treats this, refreshingly, not as an ideological argument but as an empirical one. He marshals the numbers – and modern states are awash with statistics – and puts things in a new light. Wealth disparities, now at the their highest since the late nineteenth century, are now so extreme that it means pretty much everyone is losing this game – the top 1 per cent now owns more than two-thirds of the country’s wealth in the United Kingdom. Against such concentrations of wealth and power, individual citizens must not be afraid to use their numeracy to see the nuances, colour and texture in our economies and not rely on others to tell them what to see. What is the best way to act when everyone is not trustworthy? Turn the other cheek? An eye for an eye? No, in his fascinating penultimate, chapter he demonstrates the overall best strategy is: “Fool me once, shame on you; fool me twice, shame on me.”
The author’s motivation in writing this book is entirely different from that behind other popularising maths or science books. He does not start with a modern theory in mathematics and try to find clever applications in the real world – starting with the answer and trying to find a question, as most do. He begins with the real world and its pressing problems and tries to make sense of them through mathematical reasoning. He knows he does not have the full answer but maybe he is asking some of the right questions. There are no abstract monologues or equations. So, this is manifestly not written by a Dr Sheldon Cooper or his like, full of ego and self-conscious cleverness. Many of the examples and illustrations are drawn from popular culture and, while most are North American in origin, there are still enough European, and even one or two Irish examples, to say that this was written for a citizen of the world.
So who would get great pleasure from this book? Any geek like me. I wish, though, that Dr White had written it thirty-five years ago. If you know of a teenager, possibly in transition year, who is getting good grades in mathematics, and maybe likes science or science fiction or The Big Bang Theory, then this book could help her to make sense of her world.
Dr Shane Whelan, an actuary, lectures at the School of Mathematical Sciences at University College Dublin.