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.”

West illustrates the same concept by describing the Santa Fe Institute, an interdisciplinary research organization, where he and Bettencourt work. The institute itself is a sprawl of common areas, old couches and tiny offices; the coffee room is always the most crowded place. “S.F.I. is all about the chance encounters,” West says. “There are few planned meetings, just lots of unplanned conversations. It’s like a little city that way.” The previous evening, West and I ran into the novelist Cormac McCarthy at the institute, where McCarthy often works. The physicist and the novelist ended up talking about Antarctic icefish, the editing process and convergent evolution for 45 minutes.
Of course, these interpersonal collisions — the human friction of a crowded space — can also feel unpleasant. We don’t always want to talk with strangers on the subway or jostle with people on the sidewalk. West admits that all successful cities are a little uncomfortable. He describes the purpose of urban planning as finding a way to minimize our distress while maximizing our interactions. The residents of Hudson Street, after all, didn’t seem to mind mingling with one another on the sidewalk. As Jacobs pointed out, the layout of her Manhattan neighborhood — the short blocks, the mixed-use zoning, the density of brownstones — made it easier to cope with the strain of the metropolis. It’s fitting that it’s called the Village.

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.

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.”

- Jonah Lehrer, A Physicist Turns the City Into an Equation

(via underpaidgenius)