But why is it a problem? What does it matter if people get a little confused over numbers and probabilities? Well, just consider how many important decisions we are faced with, almost on a daily basis, that involve numbers and probabilities. Nearly all political discussions these days involve mention of millions, billions, or even trillions of dollars, so it would be prudent to have some familiarity with those concepts. Nearly all discussions of product safety and drug efficacy involve the results or studies, which require some understanding of probability and statistics. Yet another reason to get a grip on numerical reasoning, Paulos claims, is that innumeracy is linked with belief in pseudoscience and other outright nonsense. As Paulos points out, "...a significant portion of our adult population still believes in Tarot cards, channeling mediums, and crystal power." With a bit more quantitative savvy, these ruses would not hold sway.
Paulos writes in a very engaging style, although he admits at the outset that "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." Yet, Paulos's method of debunking is friendly and even comical. He typically uses social scenarios to make his points. For example, he relates the following story: "...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 of rain for Sunday, and concluded that there was therefore a 100 percent chance of rain that weekend." Paulos notes that he had to explain the error to others who were listening to the weathercaster; and even then, one of the listeners "wasn't nearly as indignant as he would have been had the weathercaster left a dangling participle." Given the generally sad state of literacy in this country, anecdotes like this should make one wonder just how deplorable the state of numeracy is.
If you are looking for a friendly and readable book that will help you to make sense of the ever-increasing use of numerical data and probabilistic thinking that is appearing in public discussions of all forms, I recommend this book very highly. If you are yourself a "numerate" person (perhaps even an instructor of mathematics), it behooves you to understand just how ill-prepared the majority of our population is to deal with such reasoning; you need to know what you are up against. It will shock you.
If you are feeling cowed about your math ability, take heart! Most of the concepts here you can handle. For example, can you multiply two numbers together? You can answer "yes" to my question if you can do so with a calculator. If so, you can appreciate almost all of the examples in the book.
Professor Paulos has a mind that works differently and more inquisitively from mine, but I enjoyed learning how his thoughts. He thinks about topics like how long it would take dump trucks to excavate Mount Fuji, how many times a deck of cards need to be shuffled to become random, and what the Earned Run Average is for a pitcher who lasts one-third inning and gives up 5 runs. I realized that if I thought about more things like this, I would develop new perspectives on the world.
He makes a helpful attempt to create solutions so that more people can appreciate the world in a quantitative sense. These include using exponents to indicate the size of numbers (such as the Richter Scale does for earthquake strength), refocusing secondary math education to practical applications rather than teaching calculus earlier and earlier, having talented mathematicians teach younger people, and disciplining those who communicate in public to check the mathematical accuracy of what they say.
What do we lose if we don't? Well, those who don't learn a little math will end up in careers that pay a lot less. Social resources will be misapplied to problems that are less serious (obscure diseases and terrorism get a lot more attention to reducing accidental deaths among young people, which is a greater danger). We will make bad resource decisions in our own lives (such as by playing the lottery without realizing that 50% of the money is not paid out to anyone buying a ticket).
I also appreciated how few people can use mathematics in creative ways, to solve problems. For instance, in our professional practice we developed a new way to forecast certain forms of investment behavior. Over 20 years of doing this work, I have never found anyone who could make a single useful suggestion for how to improve the mathematics of our approach, despite having had conversations with dozens of people with advanced math and statistics degrees who would get benefit from an improved approach. I suspect from this experience that there's a higher level of mathematical thinking that Professor Paulos did not explain in his book that we would all benefit from learning. Where do we start? I can hardly wait to learn!
It is entertaining and enlightening to those whom Paulos attempts to reach, but not as much so to those whom he probably does reach. I would recommend either Huff's _How to Lie With Statistics_ or Sagan's _The Demon Haunted World_ (or even _Billions and Billions_). Paulos' book does not live up to its hype or status as a bestseller.
Nonetheless, it is short and worth the read.
