The Geometry Of Urban Life

Even a roaming cartophile, looking through an airplane window at night, would be challenged to identify a city by its sodium-glow footprint. There are exceptions, like peninsular San Francisco or the archipelago of New York. But few cities can be said to have more famous footprints than skylines.

New York.

There’s a reason schoolchildren aren’t called on to memorise the outlines of cities. In the modern metropolis, settlement spins outward from the centre, hurtling through administrative boundaries, over hills and through swamps, claiming cheap land in all directions. Who can tell one blotch of light from the next?

The major exception to this pattern occurs when cities straddle, as they often do, major geographic obstacles. Rivers may blur to irrelevance at a metropolitan scale, but lakes, bays and mountains have thus far formed strong barriers to human settlement. Lakefront cities, like Toronto and Chicago, are rough semicircles; island cities like Hong Kong and Singapore have their own distinctive shapes.

A growing body of research indicates that this question of urban shape may be more than just trivia. A metropolitan pattern, at the regional level, may be associated with particular urban characteristics.

New evidence for this comes from Mariaflavia Harari’s paper “Cities in Bad Shape.” For her job market paper at the Massachusetts Institute of Technology, Harari analysed more than 450 Indian cities to elucidate what influence, if any, a city’s shape would have on indicators like rent, wages and commute time. (Measuring cities by their nighttime lights, Harari uses a neat proxy for developed land that ignores official boundaries.)

What she found is that “compactness” — in her paper, the nearer, basically, that a city’s shape is to a circle — is a kind of urban amenity, like a subway line or a movie theatre, that people will pay for. All else being equal, India’s compact cities have lower wages, higher rents and shorter commutes. “One standard deviation deterioration in city shape, corresponding to a 720 meter increase in the average within-city round-trip,” Harari writes, “entails a welfare loss equivalent to a 5 percent decrease in income.”

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An instructive comparison is between Kolkota (Calcutta) and Bengaluru (Bangalore). Among the country’s largest cities, these are on opposite ends of Harari’s measurement system: giraffe-like Kolkota has the “worst” geometry, squat Bengaluru the “best.” According to Harari, “if Kolkota had the same compact shape that Bengaluru has, the average trip to the center would be shorter by 4.5 kilometers and the average trip within the city would be shorter by 6.2 km.”

Just a couple of miles difference, right? But the average commute speed in India is 12 km per hour, and is forecast to fall to 9 km per hour within the decade. For the average person, on an average potential trip, compactness could save an hour a day.

When we spoke on the phone, Harari was reluctant to apply those conclusions to cities in other parts of the world. Indeed, there’s reason to think that the compact city, where the distance between points is minimized, would be particularly important in India. Relative to cities elsewhere in Asia (to say nothing of Europe and North America) modeshare in Indian cities is dominated by walking and biking. In Indian cities with fewer than 1 million people, about two-thirds of trips are taken on foot, on bike or by rickshaw. Human-powered travel is particularly sensitive to distance.

What Indian cities don’t have are booming subway networks like those recently constructed in China’s new metropolises. Only two Indian cities currently have more than one subway line. Heavy rail lines are not only well-suited for linear developments (hence the popularity of “finger plans” in transit-oriented development), but also render commuters less sensitive to distance. An extra three miles is a matter of mere minutes on a commuter train.

These distinctions don’t discount the idea of geometric determinism; on the contrary, they reinforce its importance as a field of study. But there are different ways to think about what constitutes “shape.”


Harari’s focus on isolating geometry is unusual. Previous work on the “compact city” has been primarily focused on residential density as the indicator of “compactness.” More recent studies have expanded to include 14 different characteristics of compactness, including employment density, social interaction, and transportation options. In this sense, the compact city is the opposite of urban sprawl — and surely, by the expanded definition, all of India’s cities would be considered compact.

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Other researchers think the most important shape distinction is between monocentric cities, like Chicago, and polycentric cities, like Houston. The former has the iconic Loop; the latter has seven “downtowns.” The World Bank planner Pedro Ortiz has proposed that in anticipating future urban growth, the radial, “dartboard” model — typical of geometrically compact cities — is inferior to the “chessboard” of nodes strung along linear transit corridors.

Mathematicians have been interested in the urban pattern in and of itself. One field that has shown particular promise is the study of the metropolis as a fractal — a shape that contains many smaller, self-similar copies of itself. Cities are “classic examples of fractals,” Michael Batty has written, because they contain a hierarchy of clusters across different scales.

Just as the central metropolitan business district is linked to sizable regional town centers, so each of those is connected to various suburbs, and each of those anchored by commercial districts, each of which can in turn be broken into component businesses. A city, in this sense, has much in common with a head of Romanesco broccoli.

Barcelona’s Eixample.
Barcelona’s Eixample.

When we talk about a city’s shape, we often refer to 19th century plans like Manhattan’s grid, Barcelona’s Eixample or Haussmann’s Parisian boulevards. These famous design schemes certainly exert their influence on urban life.

But cities have done a lot of growing since then. For clues about the metropolis of tomorrow, we should turn our heads toward the bigger pattern – the luminous expanse that you see from an airplane at night.


This article originally appeared on Salon.


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