Scaling laws for cities

Shorter Geoff West on cities (isn't math great?): resource consumption scales sub-linearly with population, whereas economic output scales super-linearly.

Uncompressed version follows below and at link ;-)

NYTimes: ... 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.”

There is something deeply strange about thinking of the metropolis in such abstract terms. [REALLY?!?] We usually describe cities, after all, as local entities defined by geography and history. New Orleans isn’t a generic place of 336,644 people. It’s the bayou and Katrina and Cajun cuisine. New York isn’t just another city. It’s a former Dutch fur-trading settlement, the center of the finance industry and home to the Yankees. And yet, West insists, those facts are mere details, interesting anecdotes that don’t explain very much. The only way to really understand the city, West says, is to understand its deep structure, its defining patterns, which will show us whether a metropolis will flourish or fall apart. We can’t make our cities work better until we know how they work. And, West says, he knows how they work.

West has been drawn to different fields before. In 1997, less than five years after he transitioned away from high-energy physics, he published one of the most contentious and influential papers in modern biology. (The research, which appeared in Science, has been cited more than 1,500 times.) The last line of the paper summarizes the sweep of its ambition, as West and his co-authors assert that they have just solved “the single most pervasive theme underlying all biological diversity,” showing how the most vital facts about animals — heart rate, size, caloric needs — are interrelated in unexpected ways.

... 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.

This straightforward observation has some surprising implications. It suggests, for instance, that modern cities are the real centers of sustainability. According to the data, people who live in densely populated places require less heat in the winter and need fewer miles of asphalt per capita. (A recent analysis by economists at Harvard and U.C.L.A. demonstrated that the average Manhattanite emits 14,127 fewer pounds of carbon dioxide annually than someone living in the New York suburbs.) Small communities might look green, but they consume a disproportionate amount of everything. As a result, West argues, creating a more sustainable society will require our big cities to get even bigger. We need more megalopolises.

But a city is not just a frugal elephant; biological equations can’t entirely explain the growth of urban areas. While the first settlements in Mesopotamia might have helped people conserve scarce resources — irrigation networks meant more water for everyone — the concept of the city spread for an entirely different reason. “In retrospect, I was quite stupid,” West says. He was so excited by the parallels between cities and living things that he “didn’t pay enough attention to the ways in which urban areas and organisms are completely different.”

What Bettencourt and West failed to appreciate, at least at first, was that the value of modern cities has little to do with energy efficiency. As West puts it, “Nobody moves to New York to save money on their gas bill.” Why, then, do we put up with the indignities of the city? Why do we accept the failing schools and overpriced apartments, the bedbugs and the traffic?

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.”

It’s when West switches the conversation from infrastructure to people that he brings up the work of Jane Jacobs, the urban activist and author of “The Death and Life of Great American Cities.” Jacobs was a fierce advocate for the preservation of small-scale neighborhoods, like Greenwich Village and the North End in Boston. The value of such urban areas, she said, is that they facilitate the free flow of information between city dwellers. To illustrate her point, Jacobs described her local stretch of Hudson Street in the Village. She compared the crowded sidewalk to a spontaneous “ballet,” filled with people from different walks of life. School kids on the stoops, gossiping homemakers, “business lunchers” on their way back to the office. While urban planners had long derided such neighborhoods for their inefficiencies — that’s why Robert Moses, the “master builder” of New York, wanted to build an eight-lane elevated highway through SoHo and the Village — Jacobs insisted that these casual exchanges were essential. She saw the city not as a mass of buildings but rather as a vessel of empty spaces, in which people interacted with other people. The city wasn’t a skyline — it was a dance.

If West’s basic idea was familiar, however, the evidence he provided for it was anything but. The challenge for Bettencourt and West was finding a way to quantify urban interactions. As usual, they began with reams of statistics. The first data set they analyzed was on the economic productivity of American cities, and it quickly became clear that their working hypothesis — like elephants, cities become more efficient as they get bigger — was profoundly incomplete. 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.” While Jacobs could only speculate on the value of our urban interactions, West insists that he has found a way to “scientifically confirm” her conjectures. “One of my favorite compliments is when people come up to me and say, ‘You have done what Jane Jacobs would have done, if only she could do mathematics,’ ” West says. “What the data clearly shows, and what she was clever enough to anticipate, is that when people come together, they become much more productive.” ...