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The Math of Cities

Geoffrey West is a physicist who searches for fundamental laws, and he likes finding them in areas which haven't already been picked over.
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.”

However, low-density cities don't work as well.
In recent decades, though, many of the fastest-growing cities in America, like Phoenix and Riverside, Calif., have given us a very different urban model. These places have traded away public spaces for affordable single-family homes, attracting working-class families who want their own white picket fences. West and Bettencourt point out, however, that cheap suburban comforts are associated with poor performance on a variety of urban metrics. Phoenix, for instance, has been characterized by below-average levels of income and innovation (as measured by the production of patents) for the last 40 years. “When you look at some of these fast-growing cities, they look like tumors on the landscape,” West says, with typical bombast. “They have these extreme levels of growth, but it’s not sustainable growth.” According to the physicists, the trade-off is inevitable. The same sidewalks that lead to “knowledge trading” also lead to cockroaches.

I wonder whether the web is a sort of loose urbanization.

Some caveats:
While listening to West talk about cities, it’s easy to forget that his confident pronouncements are mere correlations, and that his statistics can only hint at possible explanations. Not surprisingly, many urban theorists disagree with West’s conclusions. Some resent the implication that future urban research should revolve around a few abstract mathematical laws. Other theorists, like Joel Kotkin, a fellow in urban futures at Chapman University, in Orange, Calif., argue that the working model of Bettencourt and West is already obsolete and fails to explain recent trends. “In the last decade, suburbs have produced six times as many jobs,” Kotkin says. And these aren’t just unskilled service jobs. Kotkin says the centers of American innovation are now low-density metropolitan areas like Silicon Valley and Raleigh-­Durham, N.C. “For a supposedly complete theory” of cities, Kotkin says, “this work fails to explain a lot of what’s happening right now.”

The sting in its tail:
But it turns out that cities and companies differ in a very fundamental regard: cities almost never die, while companies are extremely ephemeral. As West notes, Hurricane Katrina couldn’t wipe out New Orleans, and a nuclear bomb did not erase Hiroshima from the map. In contrast, where are Pan Am and Enron today? The modern corporation has an average life span of 40 to 50 years.

This raises the obvious question: Why are corporations so fleeting? After buying data on more than 23,000 publicly traded companies, Bettencourt and West discovered that corporate productivity, unlike urban productivity, was entirely sublinear. As the number of employees grows, the amount of profit per employee shrinks. West gets giddy when he shows me the linear regression charts. “Look at this bloody plot,” he says. “It’s ridiculous how well the points line up.” The graph reflects the bleak reality of corporate growth, in which efficiencies of scale are almost always outweighed by the burdens of bureaucracy. “When a company starts out, it’s all about the new idea,” West says. “And then, if the company gets lucky, the idea takes off. Everybody is happy and rich. But then management starts worrying about the bottom line, and so all these people are hired to keep track of the paper clips. This is the beginning of the end.”

The danger, West says, is that the inevitable decline in profit per employee makes large companies increasingly vulnerable to market volatility. Since the company now has to support an expensive staff — overhead costs increase with size — even a minor disturbance can lead to significant losses. As West puts it, “Companies are killed by their need to keep on getting bigger.”

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.”


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