I can’t recall when first I picked up John Allen Paulos’ A Mathematician Reads the Newspaper, but it has remained one of my favorite non-fiction books for years. The basic premise is that Paulos takes a typical newspaper and comments on the mathematical aspects of the kinds of stories that appear. However, that’s a bit of a simplification. Many of the chapters have very little to do with math or statistics and instead have a lot more to do with psychology and sometimes are merely Paulos’ musings on the subject. Nevertheless, most of them offer some insight on how to interpret what appears in the newspaper and how to put newspaper stories in context.
The first section deals with stories that would appears on page 1. National stories. Important stories. Paulos covers a number of topics, but what I stick to most out of this is his chapter on availability error (and two particular forms of it: the halo effect, and the anchoring effect). It has little to do directly with mathematics and a lot more to do with economics and psychology. Availability error is the tendency for people to make judgments or evaluations in light of the first thing that comes to mind. For example, if read a list of names, half male names and half female names, people will judge the list to be mostly male of the male names include a few famous names and the female names do not. There are lots of applications of the availability error, but the large red warning sign is that we all have huge biases based on previous knowledge and experience, and that bias is often so predictable that we actually have a chance to counter it.
The second section considers local stories. I particularly liked Paulos discussion of conditional probability. It is particularly valuable when considering D.N.A. evidence and such. Consider a D.N.A. test that determines that only one in a million people will match the D.N.A. collected. In a city of 7 million like New York City that means that 7 people match. The conditional probably that someone is not guilty, given that their D.N.A. matched, is over 85%. In other words, the D.N.A. alone isn’t really enough to overcome reasonable doubt. In order to convict, there really needs to be other, corroborating evidence. Even something that is one in a billion will result in six people in the world matching. His other notes on conditional probably as applied to testing for diseases is very apropos as well. Consider a test that is 99% accurate, and 0.1% of the population has the condition for which the test was devised. The probability that you do not have the condition were you to test positive is actually more than 90%. Meaning less than 1 in 10 of the people who test positive actually have the disease. For a fairly accurate test. To see how this works, read this book.
Paulos continues with sections devoted to lifestyle, science, and entertainment news stories. My favorite of all of those is him showing that the number of perfect games in baseball actually is predicted pretty accurately by chance and statistics rather than skill.
In any case, this is a great complement to Freakonomics. Freakonomics attempts to use novel methods to explain unexplained but common phenomena. But the writers of that book take great pains to make the mathematics available to casual readers. And that’s what Paulos has in common, though his take in this book is to explain common things which are generally known to researchers in ways that us mortals can understand.