It's Called Civilization

Human culture seems to have undergone some sort of major phase transition when we started living in cities. Progressive citification has only intensified in the last century or so as technology has permitted a smaller and smaller number of farmers to feed the rest of us. So what's so special about cities? Are they more than just a convenient way to stack a lot of people in a small amount of room?

It may not have taken a physicist to intuit the answer, says Jonah Lehrer, writing in the New York Times Magazine, but if you want the insight codified in some equations, a physicist, namely Geoffrey West, is the man.

West used to think about physics, but the cancellation of the Super Collider in 1993 caused him to look for new worlds to think about. His first big score was in biology,

West has been drawn to different fields before. In 1997, less than five years after he transitioned away from high-energy physics, he published one of the most contentious and influential papers in modern biology. (The research, which appeared in Science, has been cited more than 1,500 times.) The last line of the paper summarizes the sweep of its ambition, as West and his co-authors assert that they have just solved “the single most pervasive theme underlying all biological diversity,” showing how the most vital facts about animals — heart rate, size, caloric needs — are interrelated in unexpected ways.

The mathematical equations that West and his colleagues devised were inspired by the earlier findings of Max Kleiber. In the early 1930s, when Kleiber was a biologist working in the animal-husbandry department at the University of California, Davis, he noticed that the sprawlingly diverse animal kingdom could be characterized by a simple mathematical relationship, in which the metabolic rate of a creature is equal to its mass taken to the three-fourths power. This ubiquitous principle had some significant implications, because it showed that larger species need less energy per pound of flesh than smaller ones. For instance, while an elephant is 10,000 times the size of a guinea pig, it needs only 1,000 times as much energy. Other scientists soon found more than 70 such related laws, defined by what are known as “sublinear” equations. It doesn’t matter what the animal looks like or where it lives or how it evolved — the math almost always works.

The key to the biological problem turns out to be limitations of infrastructure. Crudely speaking, the volume that can be carried by a pipe (or blood vessel) scales like the square of the linear size, while the volume to be served scales like the cube. Similar consideration doubtless affect cities, but Lehrer doesn't really share those details.

The most interesting detail that he does share is that people in cities are more productive than those who aren't. There is a scaling law for that too:

The challenge for [co-author Luis] Bettencourt and West was finding a way to quantify urban interactions. As usual, they began with reams of statistics. The first data set they analyzed was on the economic productivity of American cities, and it quickly became clear that their working hypothesis — like elephants, cities become more efficient as they get bigger — was profoundly incomplete. According to the data, whenever a city doubles in size, every measure of economic activity, from construction spending to the amount of bank deposits, increases by approximately 15 percent per capita. It doesn’t matter how big the city is; the law remains the same. “This remarkable equation is why people move to the big city,” West says. “Because you can take the same person, and if you just move them to a city that’s twice as big, then all of a sudden they’ll do 15 percent more of everything that we can measure.”This implied that the real purpose of cities, and the reason cities keep on growing, is their ability to create massive economies of scale, just as big animals do. . .

After analyzing the first sets of city data — the physicists began with infrastructure and consumption statistics — they concluded that cities looked a lot like elephants. In city after city, the indicators of urban “metabolism,” like the number of gas stations or the total surface area of roads, showed that when a city doubles in size, it requires an increase in resources of only 85 percent.

The whole article is recommended for all, especially those interested in economics and its implications for the future of the species.