A Physicist Solves the City

http://www.nytimes.com/2010/12/19/magazine/19Urban_West-t.html

After two years of analysis, West and Bettencourt discovered that all of these urban variables could be described by a few exquisitely simple equations. For example, if they know the population of a metropolitan area in a given country, they can estimate, with approximately 85 percent accuracy, its average income and the dimensions of its sewer system. These are the laws, they say, that automatically emerge whenever people “agglomerate,” cramming themselves into apartment buildings and subway cars. It doesn’t matter if the place is Manhattan or Manhattan, Kan.: the urban patterns remain the same. West isn’t shy about describing the magnitude of this accomplishment. “What we found are the constants that describe every city,” he says. “I can take these laws and make precise predictions about the number of violent crimes and the surface area of roads in a city in Japan with 200,000 people. I don’t know anything about this city or even where it is or its history, but I can tell you all about it. And the reason I can do that is because every city is really the same.” After a pause, as if reflecting on his hyperbole, West adds: “Look, we all know that every city is unique. That’s all we talk about when we talk about cities, those things that make New York different from L.A., or Tokyo different from Albuquerque. But focusing on those differences misses the point. Sure, there are differences, but different from what? We’ve found the what.”

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The correspondence was obvious to West: he saw the metropolis as a sprawling organism, similarly defined by its infrastructure. (The boulevard was like a blood vessel, the back alley a capillary.) This implied that the real purpose of cities, and the reason cities keep on growing, is their ability to create massive economies of scale, just as big animals do. After analyzing the first sets of city data — the physicists began with infrastructure and consumption statistics — they concluded that cities looked a lot like elephants. In city after city, the indicators of urban “metabolism,” like the number of gas stations or the total surface area of roads, showed that when a city doubles in size, it requires an increase in resources of only 85 percent.

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In essence, they arrive at the sensible conclusion that cities are valuable because they facilitate human interactions, as people crammed into a few square miles exchange ideas and start collaborations. “If you ask people why they move to the city, they always give the same reasons,” West says. “They’ve come to get a job or follow their friends or to be at the center of a scene. That’s why we pay the high rent. Cities are all about the people, not the infrastructure.”

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According to the data, whenever a city doubles in size, every measure of economic activity, from construction spending to the amount of bank deposits, increases by approximately 15 percent per capita. It doesn’t matter how big the city is; the law remains the same. “This remarkable equation is why people move to the big city,” West says. “Because you can take the same person, and if you just move them to a city that’s twice as big, then all of a sudden they’ll do 15 percent more of everything that we can measure.”

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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.”

West and Bettencourt refer to this phenomenon as “superlinear scaling,” which is a fancy way of describing the increased output of people living in big cities. When a superlinear equation is graphed, it looks like the start of a roller coaster, climbing into the sky. The steep slope emerges from the positive feedback loop of urban life — a growing city makes everyone in that city more productive, which encourages more people to move to the city, and so on. According to West, these superlinear patterns demonstrate why cities are one of the single most important inventions in human history. They are the idea, he says, that enabled our economic potential and unleashed our ingenuity. “When we started living in cities, we did something that had never happened before in the history of life,” West says. “We broke away from the equations of biology, all of which are sublinear. Every other creature gets slower as it gets bigger. That’s why the elephant plods along. But in cities, the opposite happens. As cities get bigger, everything starts accelerating. There is no equivalent for this in nature. It would be like finding an elephant that’s proportionally faster than a mouse.”

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Because our lifestyle has become so expensive to maintain, every new resource now becomes exhausted at a faster rate. This means that the cycle of innovations has to constantly accelerate, with each breakthrough providing a shorter reprieve. The end result is that cities aren’t just increasing the pace of life; they are also increasing the pace at which life changes. “It’s like being on a treadmill that keeps on getting faster,” West says. “We used to get a big revolution every few thousand years. And then it took us a century to go from the steam engine to the internal-­combustion engine. Now we’re down to about 15 years between big innovations. What this means is that, for the first time ever, people are living through multiple revolutions. And this all comes from cities. Once we started to urbanize, we put ourselves on this treadmill. We traded away stability for growth. And growth requires change.”

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For West, the impermanence of the corporation illuminates the real strength of the metropolis. Unlike companies, which are managed in a top-down fashion by a team of highly paid executives, cities are unruly places, largely immune to the desires of politicians and planners. “Think about how powerless a mayor is,” West says. “They can’t tell people where to live or what to do or who to talk to. Cities can’t be managed, and that’s what keeps them so vibrant. They’re just these insane masses of people, bumping into each other and maybe sharing an idea or two. It’s the freedom of the city that keeps it alive.”