Skyscrapers are not built of steel and glass, but from statistics. They are bar graphs, their height and size representing population and wealth and other statistics of the urban landscape. At least, that's what mathematicians in the field of quantitative urbanism see when they gaze up at the buildings towering above. While the general idea of studying how cities form and operate dates back as far as cities have existed, the specific practice of quantitative urbanism is much newer.
Smithsonian recently published a lengthy feature about the mathematicians in the field, what they're studying, and how it formed. "The birth of this new field can be dated to 2003, when researchers at [Santa Fe Institute] convened a workshop on ways to 'model'—in the scientific sense of reducing to equations—aspects of human society," writes Smithsonian's Jerry Adler. This new form of studying cities through detialed mathematics actually resembles how biologists study mammals. Adler continues:
"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....the same principles might be at work in human institutions."
This idea prompted research, and a paper titles "Growth, innovation, scaling, and the pace of life in cities." Here's a basic explanation: aspects of a city, such as crime or employment or population growth, are charted based on the size of that city. Some of these factors increase linearly--Smithsonian gives the example "Household water or electrical use...shows this pattern; as a city grows bigger its residents don’t use their appliances more."
Other elements of the city scale super-linearly or sub-linearly, meaning they increase more or less as the size of a city increases. The study itself offers an interesting perspective on these relationships: