In a TED talk this month, physicist Geoffrey West explained his application of universal mathematical laws that define the growth of organisms—from multi-cellular ones to the ecosystem—to the growth of cities. “Cities are the crucible of civilization,” he said to introduce his talk.

When he pursued a scientific theory for the prediction of urbanization, West was on a quest to create quantifiable and generic principles that could estimate urbanization in a given amount of time. So he turned to the biology of organisms, a topic familiar to him, in order to describe the phenomenon of city growth.

According to West, the pace of life decreases as you get bigger. “Heart rates are slower, you live longer, diffusion of oxygen and resources across membranes are slower, etc.,” he explains. “The question is,” however, “is any of this true for cities?”

What applies to cities is the aspect of scalability, “the economy of scale,” as West describes it. Despite cities having evolved independently of one another, there is something universal happening. Unlike the application of the theory for organisms, where the pace of life decreases as you get bigger, an opposite scale is true for cities.

“Doubling the size of a city systematically increases income, wealth, number of patents, number of colleges, number of creative people, number of police, crime rate, number of AIDS and Flu cases and amount of waste by approximately 15 percent, regardless of the city,” West explains.  There is a universal phenomenon happening in cities.

When organisms grow they follow a sigmoidal graph, where they grow quickly but eventually stop. The same path would be detrimental for cities and certainly detrimental for their economies. But the same theory that yields the sigmoidal behavior of organisms shows an exponentially growing and unbounded graph for the growth of cities. The catch of such a behavior, West explains, is that this system is destined to collapse.

Many reasons contribute to such a collapse, including running out of resources. The next important question for West to answer is how to avoid such a future. “As we approach the collapse, a major innovation takes place and we start all over again,” West explains. This becomes a continuous cycle of innovation that is necessary to sustain growth and avoid collapse. But there is a catch to this theory, too. In order to maintain this cycle, you have to innovate faster and faster.

Here is an excerpt from a 2010 New York Times article explaining West and his colleague, Luis Bettencourt, a theoretical physicist’s findings.

“West and Bettencourt discovered that all of these urban variables could be described by a few exquisitely simple equations. For example, if they know the population of a metropolitan area in a given country, they can estimate, with approximately 85 percent accuracy, its average income and the dimensions of its sewer system. These are the laws, they say, that automatically emerge whenever people ‘agglomerate,’ cramming themselves into apartment buildings and subway cars. It doesn’t matter if the place is Manhattan or Manhattan, Kan.: the urban patterns remain the same. West isn’t shy about describing the magnitude of this accomplishment. ‘What we found are the constants that describe every city,’ he says. ‘I can take these laws and make precise predictions about the number of violent crimes and the surface area of roads in a city in Japan with 200,000 people. I don’t know anything about this city or even where it is or its history, but I can tell you all about it. And the reason I can do that is because every city is really the same.’ After a pause, as if reflecting on his hyperbole, West adds: ‘Look, we all know that every city is unique. That’s all we talk about when we talk about cities, those things that make New York different from L.A., or Tokyo different from Albuquerque. But focusing on those differences misses the point. Sure, there are differences, but different from what? We’ve found the what.’”

 

What do you think about West’s application of the mathematical formulas that describe biological growth to urbanization?