Superlinear Cities

A Summary by Stewart Brand

“It’s hard to kill a city,” West began, “but easy to kill a company.” The mean life of companies is 10 years. Cities routinely survive even nuclear bombs. And “cities are the crucible of civilization.” They are the major source of innovation and wealth creation. Currently they are growing exponentially. “Every week from now until 2050, one million new people are being added to our cities.”

“We need,” West said, “a grand unified theory of sustainability— a coarse-grained quantitative, predictive theory of cities.”

Such a theory already exists in biology, and you can build on that. Working with macroecologist James Brown and others, West explored the fact that living systems such as individual organisms show a shocking consistency of scalability. (The theory they elucidated has long been known in biology as Kleiber’s Law.) Animals, for example, range in size over ten orders of magnitude from a shrew to a blue whale. If you plot their metabolic rate against their mass on a log-log graph, you get an absolutely straight line. From mouse to human to elephant, each increase in size requires a proportional increase in energy to maintain it.

But the proportion is not linear. Quadrupling in size does not require a quadrupling in energy use. Only a tripling in energy use is needed. It’s sublinear; the ratio is 3/4 instead of 4/4. Humans enjoy an economy of scale over mice, as elephants do over us.

With each increase in animal size there is a slowing of the pace of life. A shrew’s heart beats 1,000 times a minute, a human’s 70 times, and an elephant heart beats only 28 times a minute. The lifespans are proportional; shrew life is intense but brief, elephant life long and contemplative. Each animal, independent of size, gets about a billion heartbeats per life. (West added that human bodies run on 100 watts—2,000 calories of food a day. But our civilizational energy use adds up 11,000 watts per person. We’re like blue whales walking around.)

Does such scalability apply to cities? If you plot, say, the number of gas stations against the size of population of metropolitan areas on a log-log scale, it turns out you get another straight line. Ditto with the length of electrical lines, carbon footprint, etc. Per capita, big city dwellers use less energy than small town dwellers. As with animals, there is greater efficiency with size, this time at a 9/10 ratio. Energy use is sublinear.

But unlike animals, cities do not slow down as they get bigger. They speed up with size! The bigger the city, the faster people walk and the faster they innovate. All the productivity-related numbers increase with size—wages, patents, colleges, crimes, AIDS cases—and their ratio is superlinear. It’s 1.15/1. With each increase in size, cities get a value-added of 15 percent. Agglomerating people, evidently, increases their efficiency and productivity.

Does that go on forever? Cities create problems as they grow, but they create solutions to those problems even faster, so their growth and potential lifespan is in theory unbounded.

(West pointed out that there is a bit of variability between cities worth noticing. On the plot of crimes/population, Tokyo has slightly fewer crimes for its size, and Osaka has slightly more. In the U.S., the most patents per capita come from Corvalis, Oregon, and the least from Abiline, Texas. Such variations tend to remain constant over decades, despite everyone’s efforts to adjust them. “Exciting cities stay exciting, and boring cities stay boring.”)

Are corporations more like animals or more like cities? They want to be like cities, with ever increasing productivity as they grow and potentially unbounded lifespans. Unfortunately, West et al.’s research on 22,000 companies shows that as they increase in size from 100 to 1,000,000 employees, their net income and assets (and 23 other metrics) per person increase only at a 4/5 ratio. Like animals and cities they do grow more efficient with size, but unlike cities, their innovation cannot keep pace as their systems gradually decay, requiring ever more costly repair until a fluctuation sinks them. Like animals, companies are sublinear and doomed to die.

What is the actual mechanism of difference? Research on that continues. “Cities tolerate crazy people,” West observed, “Companies don’t.”