It Must be Beautiful edited by Graham Farmelo, Granta, 拢20, ISBN 1862074798
A MATHEMATICAL friend declared: 鈥淚 don鈥檛 believe in great theorems, only in great theories.鈥� A theorem can be great only if it leads somewhere. I was reminded of this bit of wisdom when I picked up It Must Be Beautiful, because the style and content of this volume speak eloquently and entertainingly to this point. But instead of great theorems we have great equations, the lifeblood of great theories in science.
Graham Farmelo has done a magnificent job both of choosing a representative sample of great equations from across the spectrum of science and of assembling a superstar cast of authors to tell us about them. Who could resist reading Roger Penrose describing the story of Albert Einstein鈥檚 equations of general relativity, or Robert May regaling us with the central role of the logistic equation in the development of the theory of chaos? Then there are John Maynard Smith鈥檚 account of the game-theory equations underlying modern evolutionary theory, Igor Aleksander鈥檚 account of Claude Shannon鈥檚 equations measuring information, and Steven Weinberg鈥檚 beautiful concluding essay on the fundamental equations of modern physics.
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Each chapter is by itself justification for buying, savouring and rereading this outstanding work. While about half the book is devoted to famous equations in physics, I found those outside physics to be more intriguing. Perhaps this is because they are of more recent vintage, and hence less well known.
Let me give a flavour of the character of this book by focusing on a couple of the equations themselves. May鈥檚 piece on the logistic equation and its role as a kind of touchstone for the 鈥渃haotic revolution鈥� of the 1970s is certainly the best and most compact account yet of this pivotal development in our understanding of natural phenomena. The logistic equation itself is deceptively simple: xn+1 =axn(1鈭抶n)), where xn is, say, the level of a population of animals at a particular time and xn+1 is the population level at the next moment, a being a growth parameter. May shows how, as a changes from 1 to 4, the population levels move from cyclic rise and fall into completely unpredictable chaotic fluctuations.
With great verve and enthusiasm, May recounts the story of the revolution in dynamical system theory brought on by the (re)discovery of chaos. He then discusses the subsequent efforts of meteorologist Ed Lorenz (the 鈥渂utterfly effect鈥�), Steven Smale, James Yorke and others who developed our understanding of chaotic processes in nature and in mathematics.
Certainly the strangest equation in the book is the one dreamed up by astronomer Frank Drake in 1961. It gives an estimate of the number of extraterrestrial intelligences 鈥渙ut there鈥� in our Galaxy. It鈥檚 odd because it describes something that might not exist. Nevertheless, it has served for decades as an encapsulation of all the factors entering into the emergence of a technical civilisation: the right kind of star, the right physical environment, the development of life forms, the emergence of intelligence, the ability to communicate, the creation of a culture and technological civilisation. Oliver Morton gives a beautiful exposition of the Drake equation, tackling not only the equation, but also the entire SETI research programme.
Bertrand Russell once said: 鈥淢athematics possesses not only truth but supreme beauty.鈥� It Must Be Beautiful is as fine a confirmation of this epigram as you鈥檙e ever likely to see.