My problem with books on mathematics is never remembering the formulas, even from one chapter to the next. OK, and being bored with them is a factor too. Kit Yates solved these problems by not using any formulas, or even much math in his delightful (when not frightening) The Math of Life and Death. His secret is really simple: he tells stories. The result is always engaging, often infuriating and sometimes horrifying. We defy the math at our peril.
Using examples from the news, such as epidemics or murder investigations, Yates shows what underlies the events – the basic numbers that anyone can see do or do not add up.
The whole strength of The Math of Life and Death is the power of true events. Yates recognizes their value, and provides the background facts that fit with numbers that prove a point. In the hot new service of gene sequencing, he shows clearly how our assumption about identifying people by DNA samples can go wrong – badly – enough to incarcerate the wrong person. In his own case, 23andMe gave him a death sentence through a wrong interpretation of his genes. He proved it (to his great relief) with other such services and went back to show just how the numbers can lead analysis astray. Sloppy math is hard to prove, but can ruin lives.
He shows that something as unmathematical as algae needs an understanding of math. An algal bloom doubles in size every day, until it covers a lake - in 30 days. If you see the lake is half covered, how long do you think it will take for it to be covered completely? Most would calculate numerous days, based on when the algae first appeared and had reached the halfway point, but the correct answer is one more day. Mistakes like this lead planes to crash, which Yates also shows in painful detail.
Doctors are forever misinterpreting test results, giving patients false death sentences or false reassurances. Yates gives the example of breast cancer tests, by which doctors seem to predict nine out of every two cases of breast cancer in women. The numbers are pretty stark. With false positives from tests, 981 women out of a random 10,000 will be told that they have breast cancer. But of those, only 90 will actually have it. Ninety out of ten thousand (ie. nine per thousand) is not the pandemic plague that should cause panicked fear in women, but that’s how doctors present it when they are surveyed. Given multiple choice questions, doctors fare far worse than if they had chosen random answers. They are prejudiced in the false direction. They have the facts and the numbers wrong. The result is needless surgery, needless chemotherapy, and much pointless suffering.
There is a horrifying chapter on legal ignorance as well. So-called expert witnesses bamboozle judges, juries and opposing lawyers with mumbo-jumbo that no one challenges, because they don’t understand what was said. They just pick out a major conclusion from what they heard, and accept it as true and significant. The result is wrongful convictions. In the major case cited, a young mother went to prison for murdering her first two children, because an expert incorrectly claimed the chances of two children from the same family dying from Sudden Infant Death Syndrome (SIDS) was one in 73 million. (He made up the number himself.) That’s all the jury needed to know. It didn’t matter that the expert was wrong about the odds, or even that the children didn’t really die of SIDS. The number was so overwhelming, the decision was easy to make: she had to be guilty as charged. In upholding the conviction, the appeals court said no one would be fooled by such a wild claim.
This is the same principle that guides media claims, and why so few trust the media any more. Shopping for statistics and angles, reporters hone in on some startling number, and taking it out of context, draw conclusions that it doesn’t merit, or maybe worse, just leaving it there to fester in the imagination of people with no other facts to weigh. Absent those facts, the population divides into believers and non-believers, ever more extreme in their positions. It is no wonder that a Boris Johnson can lie about the massive amounts of cash sent to the European Union, and even when the lie is pointed out, it continues to be the foundation for leaving the union. The result has been utter chaos in a farcical government. So while it’s critical to have the numbers behind the claims, few do. Worse, fewer can master them, and a select group will manipulate them to their own advantage.
Yates also tackles algorithms, epidemics, and antivaxxers. The antivaxxers rely on a single, tiny, invalid and misinterpreted study by a (since) defrocked doctor, where he claimed to show that vaccinations cause autism. They don’t, as Yates relates clearly and concisely. Nonetheless, the news traveled from Britain the USA, where it has become gospel to millions who have no need of the facts. They accept the headline as all they need to know. The result is a resurgence of diseases long thought banished, with thousands suffering needlessly. Perversely, parents even mail licked lollipops to each other, so more children can be infected. They believe the false headline, and are ignorant of the death and disfiguration rates from these so-called rites of passage diseases. It is craziness squared, because the numbers were cooked and won out over the facts.
The Math of Life and Death is an endlessly diverting, pleasing, engaging and horrifying look at how lives are affected by the math. It is math in very human terms, and Yates excels at making it plain. And you don’t even have to do the math to see it.
Editor's note: This review has been published with the permission of David Wineberg. Like what you read? Subscribe to the SFRB's free daily email notice so you can be up-to-date on our latest articles. Scroll up this page to the sign-up field on your right.