PENGUIN BOOKS

INNUMERACY

John Allen Paulos is Professor of Mathematics and Presidential Scholar at Temple University in Philadelphia. He is the author, in addition to Innumeracy, of Beyond Numeracy: Ruminations of a Number Man, A Mathematician Reads the Newspaper and Once Upon a Number, all of which are published by Penguin. He has also published many scholarly papers on logic, probability and the philosophy of science. Paulos has appeared on many television and radio shows, frequently contributes articles to publications such as Nature, The Nation, Newsweek and The New York Times and is a monthly columnist for ABCNEWS.com. His Discover magazine article, ‘Dyscalculia’, won the 1994 Folio Ovation award.

To Sheila, Leah, and Daniel for numberless reasons

Introduction

‘Math was always my worst subject.’

‘A million dollars, a billion, a trillion, whatever. It doesn’t matter as long as we do something about the problem.’

‘Jerry and I aren’t going to Europe, what with all the terrorists.’

Innumeracy, an inability to deal comfortably with the fundamental notions of number and chance, plagues far too many otherwise knowledgeable citizens. The same people who cringe when words such as ‘imply’ and ‘infer’ are confused react without a trace of embarrassment to even the most egregious of numerical solecisms. I remember once listening to someone at a party drone on about the difference between ‘continually’ and ‘continuously.’ Later that evening we were watching the news, and the TV weathercaster announced that there was a 50 percent chance of rain for Saturday and a 50 percent chance for Sunday, and concluded that there was therefore a 100 percent chance of rain that weekend. The remark went right by the self-styled grammarian, and even after I explained the mistake to him, he wasn’t nearly as indignant as he would have been had the weathercaster left a dangling participle. In fact, unlike other failings which are hidden, mathematical illiteracy is often flaunted: ‘I can’t even balance my checkbook.’ ‘I’m a people person, not a numbers person.’ Or ‘I always hated math.’

Part of the reason for this perverse pride in mathematical ignorance is that its consequences are not usually as obvious as are those of other weaknesses. Because of this, and because I firmly believe that people respond better to illustrative particulars than they do to general exposition, this book will examine many real-world examples of innumeracy – stock scams, choice of a spouse, newspaper psychics, diet and medical claims, the risk of terrorism, astrology, sports records, elections, sex discrimination, UFOs, insurance and law, psychoanalysis, parapsychology, lotteries, and drug testing among them.

I’ve tried not to pontificate excessively or to make too many sweeping generalizations about popular culture or our educational system (à la Allan Bloom), but I have made a number of general remarks and observations that I hope are supported by the examples. In my opinion, some of the blocks to dealing comfortably with numbers and probabilities are due to quite natural psychological responses to uncertainty, to coincidence, or to how a problem is framed. Others can be attributed to anxiety, or to romantic misconceptions about the nature and importance of mathematics.

One rarely discussed consequence of innumeracy is its link with belief in pseudoscience, and the interrelationship between the two is here explored. In a society where genetic engineering, laser technology, and microchip circuits are daily adding to our understanding of the world, it’s especially sad that a significant portion of our adult population still believes in Tarot cards, channeling mediums, and crystal power.

Even more ominous is the gap between scientists’ assessments of various risks and the popular perceptions of those risks, a gap that threatens eventually to lead either to unfounded and crippling anxieties or to impossible and economically paralyzing demands for risk-free guarantees. Politicians are seldom a help in this regard since they deal with public opinion and are therefore loath to clarify the likely hazards and trade-offs associated with almost any policy.

Because the book is largely concerned with various inadequacies – a lack of numerical perspective, an exaggerated appreciation for meaningless coincidence, a credulous acceptance of pseudosciences, an inability to recognize social trade-offs, and so on – much of the writing has a debunking flavor to it. Nevertheless, I hope I’ve avoided the overly earnest and scolding tone common to many such endeavors.

The approach throughout is gently mathematical, using some elementary ideas from probability and statistics which, though deep in a sense, will require nothing more than common sense and arithmetic. Some of the notions presented are rarely discussed in terms accessible to a wide audience and are the kind of thing that my students, for example, often enjoy but usually respond to with: ‘Will we need to know that for the quiz?’ There won’t be a quiz, so they can be enjoyed freely, and the occasional difficult passage can be ignored with impunity.

One contention of the book is that innumerate people characteristically have a strong tendency to personalize – to be misled by their own experiences, or by the media’s focus on individuals and drama. From this it doesn’t necessarily follow that mathematicians are impersonal or formal. I’m not, and the book isn’t either. My goal in writing it has been to appeal to the educated but innumerate – at least to those whose fear of mathematics is not so great that (num) (ber) is automatically read as (numb) (er). The book will have been well worth the effort if it can begin to clarify just how much innumeracy pervades both our private and our public lives.