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What ‘urban physics’ could tell us about how cities work

Boston as amorphous liquid, and other insights from an engineer

Boston’s layout is disordered, like the molecules of a liquid.

What does a city look like ? If you’re walking down the street, perhaps it looks like people and storefronts. Viewed from higher up, patterns begin to emerge: A three-dimensional grid of buildings divided by alleys, streets, and sidewalks, nearly flat in some places and scraping the sky in others. Pull back far enough, and the city starts to look like something else entirely: a cluster of molecules.

At least, that's what it looks like to Franz-Josef Ulm, an engineering professor at the Massachusetts Institute of Technology. Ulm has built a career as an expert on the properties, patterns, and environmental potential of concrete. Taking a coffee break at MIT's Stata Center late one afternoon, he and a colleague were looking at a large aerial photograph of a city when they had a "eureka" moment: "Hey, doesn't that look like a molecular structure?"

With colleagues, Ulm began analyzing cities the way you'd analyze a material, looking at factors such as the arrangement of buildings, each building's center of mass, and how they're ordered around each other. They concluded that cities could be grouped into categories: Boston's structure, for example, looks a lot like an "amorphous liquid." Seattle is another liquid, and so is Los Angeles. Chicago, which was designed on a grid, looks like glass, he says; New York resembles a highly ordered crystal.

So far Ulm and his fellow researchers have presented their work at conferences, but it has not yet been published in a scientific journal. If the analogy does hold up, Ulm hopes it will give planners a new tool to understand a city's structure, its energy use, and possibly even its resilience to climate change.


Ulm calls his new work "urban physics," and it places him among a number of scientists now using the tools of physics to analyze the practically infinite amount of data that cities produce in the 21st century, from population density to the number of patents produced to energy bill charges. Physicist Marta González, Ulm's colleague at MIT, recently used cellphone data to analyze traffic patterns in Boston with unprecedented complexity, for example. In 2012, a theoretical physicist was named founding director of New York University's Center for Urban Science and Progress, whose research is devoted to "urban informatics"; one of its first projects is helping to create the country's first "quantified community" on the West Side of Manhattan.


New York’s building layout is ordered much like a crystal structure, says MIT’s Franz-Josef Ulm.handout

In Ulm's case, he and his colleagues have used freely available data, including street layouts and building coordinates, to plot the structures of 12 cities and analogize them to existing complex materials. In physics, an "order parameter" is a number between 0 and 1 that describes how atoms are arranged in relationship to other atoms nearby; Ulm applies this idea to city layouts. Boston, he says, has an "order parameter" of .52, equivalent to that of a liquid like water. This means its structure is notably disordered, which may have something to do with how it developed. "Boston has grown organically," he said. "The city, in the way its buildings are organized today, carries that information from its historical evolution."

The fact that Boston is "disordered" may not be surprising to anyone who has tried to drive from Jamaica Plain to Charlestown, but the notion that it more closely resembles Los Angeles than New York is counterintuitive: Why don't the two older, East Coast cities resemble each other more? "City texture matters," Ulm wrote in an e-mail. Buildings in downtown Boston have roughly the same number and arrangement of neighbors as do buildings in downtown LA; New York is denser than both. And it's not just about simple average density, but about how that density forces building, blocks, and neighborhoods into varying arrangements.


So far, Ulm says, the work has two potential applications. First, it could help predict and mitigate urban heat island effects, the fact that cities tend to be several degrees warmer than their surrounding areas—a phenomenon that has a major impact on energy use. (His research on how this relates to structure is currently undergoing peer review.) Second, he says that cities' molecular order (or disorder) may also affect their vulnerability to the kinds of catastrophic weather events that are becoming more frequent thanks to climate change.

Are materials and metropolises really comparable? And if so, is the comparison useful as more than a metaphor? The urban planning community, which has its roots in the design world, has historically been wary of science's attempts to capture the incredible complexity of the urban environment. (In her classic 1961 book "The Death and Life of American Cities," Jane Jacobs lambasted modern urban planning itself as a "pseudoscience," in which "years of learning and a plethora of subtle and complicated dogma have arisen on a foundation of nonsense.")

But it is warming to these efforts. Today scientists are some of the leading investigators of urban design issues. "There have been ideas about cities since Aristotle and Plato," said Luis Bettencourt, professor of complex systems at the Santa Fe Institute. "But the ways we can measure cities, test ideas, and compare cities across time and place and size has become so much more possible, that we can now test those ideas." Bettencourt, who was trained as a theoretical physicist, published a paper in Science last summer proposing a new quantitative framework for understanding cities: They are a unique complex system, he argues, with predictable social, spatial, and infrastructure properties.


Michael Mehaffy, a planner and urban designer in Portland, Ore., who published an essay last month on the potential of this new "science of cities," calls Ulm's work "fascinating and potentially very important." But he also offers a cautionary note about the rush to reduce cities to elemental forms. "We can't just see cities as giant crystals any more than we can see cities as giant organisms or giant anything else," he said. "A city is a unique kind of structure."

To Ulm, comparing an urban layout to a liquid or a crystal isn't a way to ignore the city's inherent intricacy, but a new way to understand it. "We need to deal with the complexity of cities," he said. "The aim of this is to have tools to make predictions without reproducing the whole complexity."

Ruth Graham, a writer in New Hampshire, is a regular contributor to Ideas.