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Math Can Predict the Future of Cities and Urban Sprawl

The age of the “megacity” is upon us. Might as well welcome anything that can help us prepare for it with open arms.
The urban populations of the world, visualized by UNICEF

Urban growth isn't determined by millions of random decisions by individual citizens, but can be explained by regular correlations of time and space.

This according to a new study published on the arXiv preprint server by Cornell University. And researchers are confident they can predict the future of this rapid urbanization with simple math.

Demographers at a Swiss university analyzed a large set of urban data and were able to quantify the social patterns that have made cities ebb and flow over the last century.


After parsing data from the Spanish Government's Institute INE—one of the largest collection of city information, with records from 45 million people living in 8,100 cities from 1900 to 2011—researchers found city growth can be predicted based on two space-time correlations: the past growth, or inertia, of the city, and the growth of nearby cities.

Past growth patterns proved an accurate indicator of future growth for up to 15  years, and then the correlation weakened. So the researchers concluded the inertia of a city has a window of about 15 years. The growth correlation to other cities as was a strong indicator of future growth up to 50 miles, at which point influence dropped.

That what happened before and what's happening nearby can give clues about the growth of a city is not exactly a shocker. But what makes the study important is that the researchers developed a mathematical formula that can explain these patterns, and can apply the model to the future in order to make more accurate predictions about the evolution of global cities. Lead researcher Alberto Hernandez wrote that these space-time patterns are “an important step toward understanding collective, human dynamics at the macro scale.”

Note, the phrase “macro scale” is a key one. The data wasn’t analyzed at an in-depth level to study how local factors or socio-economic factors influence growth. Nuances and specifics—the rise and fall of the economy, new technology and transportation, etc.— of course have a crucial effect on what makes people move to or leave cities. But this study didn’t get into all that; it took a big picture look at the numbers and found reoccurring patterns.

Empirical space-time correlations of population growth, from the paper.  Figure A shows "time-correlations versus town-sizes for yearly relative growths (red curve and red dots)," fig. B shows "time correlation for the relative growth of towns populated by more that 10,000 inhabitants," fig. C is a "comparison of widths: bivariate-normal vs. empirical correlations-distribution," and fig. D shows "spatial correlation of Spain’s municipalities’ relative growth for populations larger than 10,000 inhabitants."

So why care? Because cities are growing like gangbusters around the world, and as they reach full capacity, the result is urban sprawl. The consequences of urban sprawl are pretty grave.

Here’s a snapshot of urban sprawl today: The population of New York grew from 3.4 million in 1900 to 8 million today—plus another 18 million in the larger New York urban area. San Francisco has less than 800,000 residents, but more than three million people live in the Bay area. Buenos Aires is almost four times as big as the city proper. And then there’s Los Angeles.

These rising metropolises have troubling implications for global economics and the planet. As open space becomes developed, pollution rises, plant and animal species' risk extinction, farmland is destroyed, water and air quality decline, traffic goes up and happiness suffers, experts predict.

If city planners were able to better predict growth and sprawl, they could minimize its negative effects, and maximize quality of life—anticipate needs for infrastructure, services, buildings, schools, and so on. To this end, an entire “smart growth” movement has sprung up to encourage cheaper, more efficient development that make more livable urban areas.

The age of the “megacity” is upon us. Might as well welcome anything that can help us prepare for it with open arms.