Geoffrey West doesn’t eat lunch. His doctor says he has a mild allergy to food; meals make him sleepy and nauseated. When West is working — when he’s staring at some scribbled equations on scratch paper or gazing out his office window at the high desert in New Mexico — he subsists on black tea and nuts. His gray hair is tousled, and his beard has the longish look of neglect. It’s clear that West regards the mundane needs of everyday life — trimming the whiskers, say — as little more than a set of annoying distractions, drawing him away from a much more interesting set of problems. Sometimes West can seem jealous of his computer, this silent machine with no hungers or moods. All it needs is a power cord. …. And so West set out to solve the City. As he points out, this is an intellectual problem with immense practical implications. Urban population growth is the great theme of modern life, one that’s unfolding all across the world, from the factory boomtowns of Southern China to the sprawling favelas of Rio de Janeiro. As a result, for the first time in history, the majority of human beings live in urban areas. (The numbers of city dwellers are far higher in developed countries — the United States, for instance, is 82 percent urbanized.) Furthermore, the pace of urbanization is accelerating as people all over the world flee the countryside and flock to the crowded street. … The mathematical equations that West and his colleagues devised were inspired by the earlier findings of Max Kleiber. In the early 1930s, when Kleiber was a biologist working in the animal-husbandry department at the University of California, Davis, he noticed that the sprawlingly diverse animal kingdom could be characterized by a simple mathematical relationship, in which the metabolic rate of a creature is equal to its mass taken to the three-fourths power. This ubiquitous principle had some significant implications, because it showed that larger species need less energy per pound of flesh than smaller ones. For instance, while an elephant is 10,000 times the size of a guinea pig, it needs only 1,000 times as much energy. Other scientists soon found more than 70 such related laws, defined by what are known as “sublinear” equations. It doesn’t matter what the animal looks like or where it lives or how it evolved — the math almost always works. … Consider the data: When Bettencourt and West analyzed the negative variables of urban life, like crime and disease, they discovered that the exact same mathematical equation applied. After a city doubles in size, it also experiences a 15 percent per capita increase in violent crimes, traffic and AIDS cases. (Of course, these trends are only true in general. Some cities can bend the equations with additional cops or strict pollution regulations.) “What this tells you is that you can’t get the economic growth without a parallel growth in the spread of things we don’t want,” Bettencourt says. “When you double the population, everything that’s related to the social network goes up by the same percentage.” …A Physicist Solves the City