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New Math: Quantitative Urbanism

Can mathematics be used to understand cities? It is the focus of an article in this month's issue of The Smithsonian.

Jerry Adler's "Life in the City Is Essentially One Giant Math Problem" introduces the term “quantitative urbanism” to denote the "effort to reduce to mathematical formulas the chaotic, exuberant, extravagant nature of one of humanity’s oldest and most important inventions, the city." But, what does this mean?

It is strongly related to the idea of mathematical scaling. Biologists use math to study properties of organisms in terms of their mass. Theoretical physicist Geoffrey West offers this example: "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."

Are scaling principles valid for cities? Quantitative urbanism creates equations that represent relationships between various parameters (e.g. employment, GDP, new AIDS cases, crime numbers) and city populations.

In some cases the relationships are linear, and in others they are exponential (given the new term "superlinear scaling"). Dependant on the parameter, the exponent will be greater than, less than, or equal to 1.

West claims: "Give me the size of a city in the United States and I can tell you how many police it has, how many patents, how many AIDS cases, just as you can calculate the life span of a mammal from its body mass.”

Taking a somewhat different direction, Glen Whitney, Director of the new Mathematics Museum in New York City, has investigated the the height of skyscrapers. Noting that big cities tend to have more tall buildings than small cities, one wonders if this is related to a city's population? After sampling 46 metropolitan areas around the world, Whitney derived this equation as a model: H=134 + 0.5(G), where H is the height of the tallest building in meters and G is the Gross Regional Product (in billions of dollars).

Given my home town's population, perhaps G can be negative?

Try to find a copy of the article to read, as it offers some fascinating new insights about quantitative urbanism. A copy may still be available on-line...or you will need to search out a hard copy.

Source: The Smithsonian, May 2013