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Sim City in Real Life: The Insights of Quantitatitive Urbanism

By Wesley Fenlon

A growing field of mathematics models cities all over the world and discovers that, regardless of culture or location, they develop very similarly.

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.

Photo credit: Flickr user photochiel via Creative Commons.

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."

Photo credit: Flickr user thomashawk via Creative Commons.

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:

"The most striking feature of the data is perhaps the many urban indicators that scale superlinearly...Wages, income, growth domestic product, bank deposits, as well as rates of invention, measured by new patents and employment in creative sectors all scale superlinearly with city size, over different years and nations with exponents that, although differing in detail, are statistically consistent. Costs, such as housing, similarly scale superlinearly, approximately mirroring increases in average wealth."

Private R&D jobs increase by a scale of 1.34, for example, while GDP increase by up to 1.26. If a city doubles in size, its population becomes, on average, 15% more productive. This can potentially be explained by physical proximity, which promotes collaboration.

If a city doubles in size, its population becomes, on average, 15% more productive.

But there are also negative city traits that increase superlinearly. "new AIDS cases also scale superlinearly, at 1.23, as does serious crime, 1.16," writes Smithsonian. "Lastly, some measures show an exponent of less than 1, meaning they increase more slowly than population. These are typically measures of infrastructure, characterized by economies of scale that result from increasing size and density. New York doesn’t need four times as many gas stations as Houston, for instance; gas stations scale at 0.77; total surface area of roads, 0.83; and total length of wiring in the electrical grid, 0.87."

The data works with cities all over the world, despite differences in culture or geography. There are always unique exceptions, of course--for example, the study includes a formula for how tall the largest skyscraper in a city will be, based on that city's wealth. But New York and Tokyo's tallest buildings don't measure up to their extreme wealth, while Dubai's Burj Khalifa exceeds the formula.

Smithsonian's feature goes on to consider how this mathematical approach to cities could be used to affect them, not just study them. Transit, particularly, will become more efficient as we gather more data from cellphones. It's possible that, through the smart application of data, some of those negatives increasing superlinearly could be reigned in, making cities safer and more efficient.