200% of Nothing

A.K.Dewdney

Introduction

Mathematics lies at the very heart of our scientific and technical civilization. The ability to make and use mathematics is the single, common, indispensable ingredient to all the sciences and every branch of technology. I am hardly the first mathematician to point out how strange it is that such an important subject gets so little support in a part of the world that stresses science and technology.

It is easy to understand why people don’t rush out to buy mathematical journals, poring over the latest results in the cohomology of fiber bundles. After all, mathematics does get pretty abstract and seemingly far removed from life. But it is difficult to understand why so many people must struggle with concepts that are actually simpler than most of the ideas they deal with every day. It is far easier to calculate a percentage than it is to drive a car. The notion of probability is child's play compared to the concept of a bridal shower.

Thanks to authors like Douglas Hofstadter and John Allen Paulos (among many others), innumeracy is now widely accepted as the mathematical parallel of illiteracy. Innumeracy, the inability or unwillingness to understand basic mathematical ideas involving numbers or logic as they apply in everyday life, imposes a grave handicap on its victims. In some ways, the handicap is far graver than illiteracy.

Innumeracy has become a major problem in North American society. As our educational system continues its steady decline, as our population slides slowly into the 'unthink' of pop culture and instant gratification, people are losing on every front. Their innumeracy is costing money, property, and freedom of choice. Even lives sometimes hang in the balance.

Out there, in the streets that we travel, in the offices where we work, and in the newspapers we read and the television programs we watch await forces that would mislead and misinform us, exploiting the enormous public confusion over subjects like percentages, averages, fractions, compounding, and other basic mathematical ideas. This situation has no parallel in illiteracy. Literacy, after all, concerns a translation skill-learning to move easily between written and spoken speech. Numeracy concerns thought itself. You might exploit people's innumeracy through an advertisement, for example, making a claim that seems to be valid but isn't. But how would you exploit their illiteracy through an ad they can't even read?

Individuals, companies, special-interest groups, the media, and even governments abuse mathematics to sell products and propositions. Math abuse, as I call it, exploits innumeracy by twisting logic and distorting numbers. As this book will demonstrate, it isn't always clear whether abusers of mathematics really understand what they're up to. If they did, we would have a right to be angry. But, sometimes despair seems the more appropriate reaction.

It will take two chapters just to lay out the major forms of math abuse in today's world. Chapter 1, for example, explores how numbers, counting, percentages, and other simple mathematical ideas are twisted to suit private agendas. The most abused branch of mathematics, statistics, needs a chapter all to itself-Chapter 2. Chapters 3 through 9 focus on various areas of abuse such as advertising, lotteries and gambling, finance, business, government, health care, and the media.

Two final chapters attempt to remedy the abuses by laying out a brief course in self-defense for readers who would like to be mathematically streetwise. There are logical meditations and numerical kung fu.

The book's title, 200% of Nothing, barely hints at the range of abuses. It's time now to buckle your mental seat belt in preparation for a sometimes shocking, sometimes amusing ride through the streets of math abuse. Here are nothings dressed up as somethings, somethings dressed up as nothings, and everything in between.

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