“Innumeracy,” although an unfamiliar term, describes a familiar condition. Millions of Americans, although competent in arithmetic, cannot deal meaningfully with algebra, fractions, and other forms and manipulations of numbers. They are uncomfortable with quantitative comparisons, think scientific notation is a foreign language, and cannot put large numbers in the proper perspective. Many of these sufferers, however, admit to no shame and have little recognition of the impact which innumeracy has had on their everyday life. Indeed, otherwise highly educated Americans who are disdainful of those ignorant of proper grammar or unable to comprehend poetry often proudly proclaim their own inability to balance a checkbook, let alone understand geometry, trigonometry, statistics, or probability theory. Yet the consequences of not understanding mathematics, as John Allen Paulos points out, are not trivial. They include irrational decisions, wasted resources, even death from disease.
Paulos’ goal is not to ensure that all Americans can do basic arithmetic. That is a worthy objective, but beyond the scope of this book. He is trying to reach out to the otherwise educated, literate individual who perceives himself or herself functioning well in society despite innumeracy. Paulos wants such individuals to recognize that their innumeracy places limitations on the texture and richness of their lives; then, he wants them to do something about it. Paulos notes that the level of numerical comprehension of most Americans is pitifully low- quantitative data are used without context or comparison; probabilities and statistics are misunderstood or ignored. Mathematics can be a powerful tool in decision-making, whether personal or political. Paulos explains how to use that tool correctly.
To make his point, Paulos focuses on a number of consequences of faulty understanding of mathematics. One is the vulnerability to coincidences of those suffering from innumeracy. Not understanding what the probability would be of a certain event, these individuals are often greatly impressed by a coincidence which is mathematically highly probable. He places a number of illustrations of this under the classification of pseudoscience. Innumerates can easily be manipulated by charlatans or innocently misled by other innumerates. Parapsychology is one example of this. Failing to understand the nature of probability, innumerates do not realize that the predictions of psychics, dream interpreters, and astrologers can be explained without recourse to the claims of pseudoscience. More seriously, innumerates are frequently victims of medical fraud. They focus only on a practitioner’s
successes, ignoring the rate of success. The important question is whether the number of cures exceeds the number expected if nothing at all were done and nature allowed to take its course. Innumerates do not ask this question, because they are unaware of its significance; even if they were, they could not understand the numbers. Paulos also discusses the issue of mandatory drug testing. He asks legislators to consider the reliability of such tests, pointing out that a test with a 98 percent accuracy rate is still horribly inaccurate if the number of users is assumed to be relatively small. Under certain conditions innocent people would have the majority of the positive tests. For any given individual, the positive test would simply be a coincidence, not an indication of drug use.
Many individual and societal decisions involve deciding among trade-offs, such as the quality of a manufactured item versus its price....
(The entire section is 1472 words.)