A Mathematician Reads the Newspaper

The title of a 1995 book by John Allen Paulos, a followup to his book about numerical illiteracy, which was called "Innumeracy". The book consists of a number of short essays, divided into sections. In the essays, Paulos examines how innumeracy affects media coverage of politics, social issues, the environment and other issues. Paulos debunks and discusses numerical issues the media handles irresponsibly.

A typical essay is "Science, Medicine, and the Environment", in which he explains the problem with conditional probability and false positives in tests. Assume 100000 people are tested for disease D. On average, 0.1% of the population has this disease (i.e. 100 people), and 99% of the time the test will catch this (99 of those 100 will test positive for D). Of the 99900 healthy people, say around 1% test positive for D (erroneously, this is the false positive rate). That's about 999 people. That gives 1,098 people testing positive for D. The conditional probability that you have D, given that you test positive, is only around 9%!!! This startling calculation has obvious implications for seemingly straightforward public policy issues such as mandatory AIDS tests or drug tests.

While it is refreshing to read an interesting debunking of, say, the Laffer Curve, there is also a feeling that you are reading a series of rants from a grumpy mathematician who knows what's best for everyone, and is exasperated that the proles won't listen.

by John Allen Paulos, Basic Books, 1995

This book seeks to help readers of newspapers (and consumers of news in general) to have a better understanding of the ways that numbers are used and misused in the news media. Most of the actual math presented is simple arithmetic, though naturally higher-level topics such as statistics, probability, differentials and matrix operations are touched upon. The purpose here is not to teach new concepts but rather to remind people to use the math they already know in order to understand better. The structure of the book (see below) does not really lend itself to reading straight through, but is more suited to being browsed idly, say when one has to sit somewhere for a few minutes attending to some basic task. This would be a good gift for a bright high school Senior or college Freshman who is discovering the value of paying attention to the news beyond sports and celebrity scandals. There is much for the news junkie as well, and having a short attention span won't be a barrier. There is a bit of humor here and there, often a mildly amusing joke near the beginning of an article, in a style familiar to anyone who has ever sat in a math class. Most articles also have a point where a concrete example of a concept is given and the reader is asked to think of an extension or variation, with the answer in a footnote on the same page. These features and the book's structure serve to keep it light and well paced.

The book is fairly short, 200 pages in the Anchor Books paperback edition, and is arranged in a way meant to reflect a standard newspaper - first are articles covering numbers and math in national and international news about politics, economics, etc. The second section covers the types of stories that are closer to home - business, local government, and so on. Lifestyle, Science & Medicine, and finally Food & Culture follow in their respective sections. As might be expected the topics in the first sections are 'meatier' than those later in the book, and a few of the articles are a bit forced, since the format requires them, rather than Paulos having anything urgent to communicate about the specific topic covered. A few of the articles intimate Paulos' sociopolitical leanings, but it would be hard to say more than he's somewhat socially liberal with a Libertarian bent (maybe). The focus is kept squarely on the numbers and what they mean and don't mean, the underlying issues are left to themselves for the most part.

There are a couple of good pieces about how different ways of counting votes can lead to different results and how various ways of distributing votes to blocs can easily concentrate power while seeming to give all a say. The article about how context, association, and ordering of news stories affect perception is eye-opening. Attention is given to how economic forecasts either say essentially nothing - "Things will stay the same, until they change" - or they are purely speculative, since slight changes in initial conditions lead to huge differences in outcome. The usual crew of fallacies is covered (A flipped coin has come up heads 6 times in a row, what are the odds that the next throw will be heads?). Particularly satisfying is a quick piece about finding coincidences and linkage between news items, including a gentle debunking of the old Lincoln-Kennedy Connection list via pointing out links between Presidents McKinley and Garfield. Other topics covered include how comparing different populations tends to accentuate the differences at the extremes and downplay the large area of similarity, the S-curve of fads, our desire to see patterns even in the truly random, and the problem of aggregating averages.

Paulos concludes by emphasizing two main points. First, that "besides Who, What, Where, When, Why, and How we need to ask How many? How likely? What fraction?", assess statistical data qualitatively (not just quantitatively), and consider sources and motives. Second, we have to accept that we have 'complexity horizons' (defined in the text) beyond which more than superficial understanding is hopeless, There's an ever-growing flood of information washing over us, and at some point we have to decide and act despite imperfect knowledge. By seeking more than basic education and striving to understand concepts rather than simply latching onto figures floating by we can stand on firmer ground and see to horizons a bit further off.