Depending on which source of pop-rationality you consult, there are three, five, six or more ways of thinking that need to be mastered before the psychology-entertainment complex will consider you “smart”. So is there a good argument for four? And is making good arguments one of them?
Well, here one will not learn about syllogisms or the perils of affirming the consequent. The author, a professor of applied mathematics, has instead adapted a classification of natural systems once proposed by the whiz-kid Stephen Wolfram to describe in turn four ways of understanding the world: statistical, interactive, chaotic and complex.
Statistics can help uncover broad truths across populations, such as, for example, the basic truths of healthy eating, but headline-grabbing claims can be statistically underpowered and so unreliable, as Sumpter lucidly demonstrates with claims such as that psychological “grit” is a hugely important factor in success. (“Although grit explains around 4% of the variation between individuals,” he notes mildly, “this leaves a further 96% unexplained.”)
Statistics are also of limited value when thinking about dynamic situations when parts affect one another. Then it is time to move to “interactive” thinking, which is at the heart of how we can study changing populations of foxes and rabbits in a field but also social epidemics, such as how dog breeds go in and out of fashion. Refreshingly in our data-worshipping age, Sumpter insists that mere facts are not everything; successful interactive thinking instead is “bottom-up” and relies on careful logical inferences.
Some systems, however, spiral rapidly out of predictability, which brings us to thinking about chaos. This is pictured most famously as the flap of a butterfly’s wing (actually a gull’s, in Edward Lorenz’s original formulation) that causes a storm on the other side of the world. Unpredictability is also a central concept of information theory, in which the “entropy” of a message is a measure of how unpredictable it is. Chaos is not random, but in a deep sense, the author happily reveals, “randomness is information”.
Complexity is what is left after the first three approaches have all failed, when we arrive at some irreducible phenomenon. According to an early theorist, “a pattern is as complex as the length of the shortest description that can be used to produce it”. In Sumpter’s intriguing analysis, complexity is therefore a function of our own (lack of) understanding, rather than an objective feature of the world, which leads him to the lovely thought that science itself is simply “the process of finding progressively shorter explanations for the phenomena around us”.
All the foregoing is very interesting, though it overpromises as a therapeutic manual. (Books in the “smart thinking” category are industrially obliged also to pose as self-help books, but the trivial carrots of “a new way to convince your friends to go jogging with you” or “a new way of controlling chocolate-cake addiction”, as here, reflect publishing’s institutional underestimation of readers’ intellectual appetites.) More cheering is its originality of literary approach: many subjects are introduced by fragments of memoir from the author’s time studying at the Santa Fe institute in the 1990s; while a made-up group of London thirtysomethings is used to illustrate different ways of approaching problems.
Most successful is Sumpter’s practice of introducing complex ideas with affectionate pen portraits of the people who first grappled with them. Thus we become warmly acquainted with Ronald Fisher, who established the “maximum likelihood estimate” in statistics (but then got into eugenics and spent decades denying the link between smoking and lung cancer), and Claude Shannon, who described the mathematical theory of information and spent happy evenings with his girlfriend trying to measure the entropy of the English language.
The true hero of this book, though, is Andrej Kolmogorov, a pioneer of probability and complexity theory and a star of Soviet mathematics. We follow him from his days as a brilliant youth, through his passionate intellectual friendships and love of cross-country skiing, to his twilight years, when, hiking with his beloved students, he suddenly stops and announces: “I am proud that I lived a worthy life.” It is salutary to be reminded, at the end of this eccentrically fascinating and enjoyable book, that no data set or algorithm can help with that.
• Four Ways of Thinking: Statistical, Interactive, Chaotic and Complex by David Sumpter is published by Allen Lane (£18.99). To support the Guardian and Observer, order your copy at guardianbookshop.com. Delivery charges may apply.
