Math in the City

Well-written piece from Smithsonian magazine:

The systematic study of cities dates back at least to the Greek historian Herodotus. In the early 20th century, scientific disciplines emerged around specific aspects of urban development: zoning theory, public health and sanitation, transit and traffic engineering. By the 1960s, the urban-planning writers Jane Jacobs and William H. Whyte used New York as their laboratory to study the street life of neighborhoods, the walking patterns of Midtown pedestrians, the way people gathered and sat in open spaces. But their judgments were generally aesthetic and intuitive (although Whyte, photographing the plaza of the Seagram Building, derived the seat-of-the-pants formula for bench space in public spaces: one linear foot per 30 square feet of open area). “They had fascinating ideas,” says Luís Bettencourt, a researcher at the Santa Fe Institute, a think tank better known for its contributions to theoretical physics, “but where is the science? What is the empirical basis for deciding what kind of cities we want?” Bettencourt, a physicist, practices a discipline that shares a deep affinity with quantitative urbanism. Both require understanding complex interactions among large numbers of entities: the 20 million people in the New York metropolitan area, or the countless subatomic particles in a nuclear reaction.

The birth of this new field can be dated to 2003, when researchers at SFI convened a workshop on ways to “model”—in the scientific sense of reducing to equations—aspects of human society. One of the leaders was Geoffrey West, who sports a neatly trimmed gray beard and retains a trace of the accent of his native Somerset. He was also a theoretical physicist, but had strayed into biology, exploring how the properties of organisms relate to their mass. An elephant is not just a bigger version of a mouse, but many of its measurable characteristics, such as metabolism and life span, are governed by mathematical laws that apply all up and down the scale of sizes. The bigger the animal, the longer but the slower it lives: A mouse heart rate is around 500 beats per minute; an elephant’s pulse is 28. If you plotted those points on a logarithmic graph, comparing size with pulse, every mammal would fall on or near the same line. West suggested that the same principles might be at work in human institutions. From the back of the room, Bettencourt (then at Los Alamos National Laboratory) and José Lobo, an economist at Arizona State University (who majored in physics as an undergraduate), chimed in with the motto of physicists since Galileo: “Why don’t we get the data to test it?”

You know you want to read the whole thing!