FOUR WAYS OF THINKING

A mathematician explains how to deal with the world.

Sumpter, a professor of applied mathematics and the author of Ten Equations That Rule the World, writes that our thinking as we navigate life can be classified as either statistical (or stable), periodic, chaotic, or complex. Making his approach as simple as possible, the author divides the book into four sections, one for each category of thought. The first section may seem like the easiest, but statistics can be misleading or even meaningless. In his discussion of periodic thinking, one of his anecdotes involves Adam Smith. A professor explained to him that Smith “had been wrong, because his stable thinking had convinced him that the market would reach and stay at equilibrium. But Smith’s thinking was, Parker said, reductionist. Accounting for our interactions, the way we also behaved like animal herds, showed that human society was anything but stable.” Perhaps the most startling category, chaos as a mathematical and scientific entity is a 20th-century discovery. (For more on the science of chaos, turn to Peter Gleick’s groundbreaking 1987 book, Chaos.) As Sumpter demonstrates, chaos is not the same as total confusion, but rather a specific natural phenomenon in which tiny changes in initial conditions lead to enormous unpredictable effects. This is why, no matter how much information computers can gather about weather conditions today, predictions beyond a week are unreliable. Unlike the previous three, complex thinking is less about solutions than “finding the stories which help us to better understand ourselves, as well as those around us.” Despite the upbeat conclusion, Sumpter has not written a self-improvement guide or another how-to-lie-with-statistics knockoff. Rather, he offers a fairly clearheaded popular mathematics survey that will appeal to readers of Daniel Kahneman’s Thinking, Fast and Slow and similar books.

The mathematics of problem-solving—always ingenious and often helpful.