The Living City

From the Archive / by Jonah Lehrer /

In some ways, cities are like elephants: they get more economical with size. But as scientists apply metabolism to the metropolis, they are uncovering the surprising paradoxes of urban growth.

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A few years ago, West started to wonder if social organizations, like cities, could also be described with a set of simple equations. Did cities behave like living things? What were the constants of urban life? Or was each city its own city, an eminently local construction? The first problem was finding the data. Modeling a metropolis requires a vast amount of information. “It wasn’t easy to locate this stuff,” says Luis Bettencourt, a physicist at Los Alamos and a lead researcher on the project. “We ended up looking at all sorts of crazy statistics. I never thought I’d know so much about the electrical consumption of German cities.”

The researchers began by analyzing the data on urban infrastructure. They wanted to know if big cities were more “metabolically” efficient than smaller cities. Living things utilize economies of scale. But what about urban areas? Does efficiency scale with population?

After analyzing the statistics, the answer was clear: Cities are like elephants. They get more economical with size. It doesn’t matter whether the city is located in China, Europe, or the American Midwest; every city is simply a scaled version of the same city. In metropolis after metropolis, the indicators of urban “metabolism”—like the per-capita consumption of gasoline or the surface area of roads or the total length of electrical cables—scaled to an exponent of (population)0.8, which is very similar to the biological equivalent of (mass)0.75. This means that a city can double its population without doubling its resource consumption. “One of the basic principles of cities is that it’s more efficient to bring people together,” West says. “You need a little bit less of everything per person. It’s the exact same way in biology. As animals get bigger, they require less energy to support each unit of tissue.”

This simple observation has some unexpected consequences. When most of us think about environmentally friendly places, we imagine rural landscapes and bucolic open spaces, a terrain untouched by concrete. Cities, in contrast, seem like ecological nightmares. They are polluted, artificial environments where nature consists of cockroaches, pigeons, and florist shops. But according to Bettencourt and West, the conventional wisdom is exactly backward. Cities are bastions of environmentalism. People who live in densely populated places lead environmentally friendly lives. They consume fewer resources per person and take up less space. (On average, city dwellers use about half as much electricity as people living outside the city limits.) And because efficiency scales with the size of the population, big cities are always more efficient than small cities. An environmentally friendly place is simply one with lots and lots of people. While rural towns might look green—all those lawns and trees are reassuring—their per-capita rates of consumption and pollution are significantly higher. The secret to creating a more environmentally sustainable society is making our big cities bigger. We need more metropolises.

Of course, cities are not simply a mass of efficient infrastructure. An urban area benefits from economies of scale, but we don’t cram into cities just to save money on the electric bill. The real reason cities exist is because they further human interaction. Every metropolis represents an unprecedented density of social activity. Only ants live closer together, and ants don’t have brains.

When the scientists began to analyze social phenomena in cities, the Platonic metaphor of the city-as-body broke down. They could no longer model metropolises as massive biological organisms. Instead, the team needed to come up with an entirely new set of equations.

The easiest way to grasp the difference between a city and a living thing is to observe a city street. Look at the pedestrians. They are walking fast, scurrying along the sidewalk. Everyone seems to be rushing somewhere. The data backs up the cliché: In bigger cities, people literally move faster. In biological systems, the opposite trend occurs. As creatures get bigger, their bodies slow down. Pulse rates decelerate. A brake is applied to the heart. This is why elephants live longer than mice: Their bodies operate at a more leisurely setting.

The fast pace of the metropolis isn’t reflected only in the speed of pedestrians. When the researchers examined quantitative data that results from social interaction—these include measurements like GDP, patent filings, and wages—they discovered that, as cities got bigger, each individual got more productive. A doubling of population led to a more than doubling of creative and economic output. (The scaled equations for these social variables had exponents greater than 1.) The end result is a positive feedback loop: A bigger population means more economic activity for each person, which encourages more people to move to the city, which results in more economic activity, and so on. Imagine an elephant that never stops growing, and whose growth just encourages more growth. That’s what a city is like. “For biological systems, growth is straightforward,” West says. “They eventually stop growing. Economies of scale can take you only so far. But when you have these superlinear exponents [exponents greater than 1], the growth equation is completely changed. These cities can go on growing forever.” All this potential growth has a dark side. At a certain point, every city runs out of resources. Their superlinear exponents, tilted toward infinity, collide with the practical demands of reality. The positive feedback loop exhausts itself.

How do cities deal with this dismal limitation? They innovate. “The only way to avoid stagnation from a shortage of resources,” West says, “is to change something. You have to reset the clock, reset the initial parameters of growth. We call this an innovation cycle, and they are clearly apparent throughout history. There’s the invention of the steam engine, the car, the digital revolution. What these advances all have in common is that they allowed cities to continue growing.” West quotes a Bob Dylan lyric to make his point: “He not busy being born is busy dying.” A city that isn’t innovating is on the verge of collapse.

There’s a disturbing wrinkle buried in this theory of growth and innovation. As the population of a city expands, each innovation has a smaller relative return. It’s harder to redesign a metropolis than a small town. The end result is that the bigger a city is, the quicker it must innovate in order to continue its patterns of growth. It needs to undergo increasingly frequent periods of wrenching social change just to survive. The mathematical equations describe this acceleration—the positive exponents ensure that everything speeds up.

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