People in big cities do just about everything faster: walk and talk, create and invent, earn and spend, steal and murder. These speed increases are proving surprisingly predictable. As a city’s population grows, its residents’ collective actions and behaviors accelerate in a common pattern that can be described by the same mathematical formula.

Scientists at Los Alamos National Laboratory and the Santa Fe Institute in New Mexico, who worked out the math, draw some counter-intuitive conclusions: none other than Corvallis stands out as the top city in the country for innovation — after you account for its size. New York is merely average. Portland is a bit above the mean but not outstanding.

The goal of the research is to give researchers and planners better ways to compare cities and pinpoint the factors that make some succeed where others fall short. It’s part of an expanding scientific field that approaches cities as if they were self-directed living things with a shared metabolism and a hidden genetic code waiting to be deciphered.

Typical city comparisons use per capita measures of income, crime and other indicators. But in per capita comparisons, larger cities persistently look better than smaller cities because of pronounced advantages that emerge with a bigger population.

“If you just divide by population to get a per capita measure you get a number that is biased by these accelerations,” says Luis Bettencourt, a physicist at Los Alamos National Laboratory and the Santa Fe Institute. “The way we see it, that’s not a property of New York or Dallas, that’s a property of a large city.” Bettencort, fellow Los Alamos physicist Geoffrey West, and colleagues at Arizona State University and the University of North Carolina described their way of analyzing cities in

in the journal PLoS ONE.

The physicists’ ranking method shows whether a city performs better or worse than expected given its size. In essence, they subtract the added boost that cities gain with increasing population. They say it more accurately represents a city’s successes or failures relative to other cities and allows more meaningful rankings.

Corvallis, then, outperforms Portland and Seattle on economic output, personal income and preventing violent crime. And Corvallis leads the nation in patented inventions, as it has for more than a decade, according to

.

The U.S. Patent Office issued more than 314 patents to inventors based in Corvallis last year. Among their ideas: an improved variety of bluegrass, a human-powered water purifying device using UV light, a clog detection and clearing method for ink jet printers, a drug that kills bacteria by targeting their genes, and a method for processing chicken manure for use in filtering heavy metal contamination.

Portland produces 30 percent more patents than similar-sized peers, and has a 22 percent lower rate of violent crime, the rankings show. But personal income in Stump Town is lower than expected and has been for years.

“Portland is a nice city, but it’s not an outstanding city,” says Bettencourt. “It’s not particularly wealthy, for example. I was surprised by that.” In the adjusted comparisons, Boulder, Colo. greatly exceeds Portland on personal income, economic output and inventions.

The scale-adjusted indicators highlight the persistent character of cities, good or bad. Most places that were rich and innovative in the 1960s remain so today, the researchers say. San Jose, Calif., for example, was a leader in wealth creation even before the birth of Silicon Valley. Rankings of disadvantaged cities have also persisted since the 1960s. In Phoenix, Ariz., lower than expected personal income has persisted for 40 years.

Critics such as

question the practical significance of the work.

“It’s fair to say that Corvallis is, relative to its size, the most inventive metro in the country,” Cortright says. But he says the explanation is obvious: Hewlett Packard Corp. moved its Advanced Products Division to Corvallis in 1975. HP researchers crank out inventions by the score and company lawyers zealously guard them with overlapping patents.

“So if there’s a policy lesson here, it appears to be if you are a relatively small metro area it really helps if a large company builds a big research and manufacturing center in your town,” he says.

Cortright, president of the Portland-based consulting firm Impresa, says it’s already known that education explains much of the difference in prosperity and inventiveness among cities. That it takes decades to change ingrained urban characteristics doesn’t surprise him. Cities reflect their people, Cortright says, and fewer than 3 percent of people move to a different metro area in a given year. Businesses and institutions are even more fixed.

Bettencourt acknowledges that his group’s research doesn’t yet explain what makes exceptional cities work better. But he believes the research will help lead people to the right places to search for answers.

Architect

, an assistant professor at the University of California Berkeley who has collaborated with Bettencourt and West, sees promise in the use of physics to explore the metabolism of cities. “We’ve always been dissatisfied with the messiness of cities, by our inability to control them,” de Monchaux says.

In the influential 1961 book “The Death and Life of Great American Cities”, writer Jane Jacobs was among the first to argue that the apparent messiness is essential to stir up ideas, social innovations and economic prosperity.

But the complexity of cities stands in the way of effective planning. A deeper understanding of the physics of cities, de Manchaux says, should help reveal the best ways to make them thrive and to balance the need for structure and orderliness with the need for messiness and creative upheaval.

Michael Batty, a professor of planning at University College London, sounded a similar theme in

in the journal Science. The new physics of cities, he says, underscores the limits of planning.

“It is likely to lead to a view that as we learn more about the functioning of such complex systems, we will interfere less but in more appropriate ways.”

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