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Numbers in the City, Part 2

June 14, 2013


In Part 1 of this series, I discussed an emerging movement called quantitative urbanism and how mathematics can be used to better understand life in city. The goal of the movement is to use this knowledge to make life better for people living in urban environments. The article from which many of the observations were drawn was written by Jerry Adler. [“Life in the City Is Essentially One Giant Math Problem,” Smithsonian, May 2013] According to Adler, the movement can trace its origin to a collaboration between Geoffrey West, Luís Bettencourt, and José Lobo. West and Bettencourt head up the “Cities, Scaling, and Sustainability” initiative at the Santa Fe Institute. This “research effort is creating an interdisciplinary approach and quantitative synthesis of organizational and dynamical aspects of human social organizations, with an emphasis on cities. … A particularly important focus of this research area is to develop theoretical insights about cities that can inform quantitative analyses of their long-term sustainability in terms of the interplay between innovation, resource appropriation, and consumption and the make up of their social and economic activity.” The movement is catching on and they have been joined by others. Adler reports:

“If Bettencourt and West are building a theoretical science of urbanism, then Steven Koonin, the first director of New York University’s newly created Center for Urban Science and Progress, intends to be in the forefront of applying it to real-world problems. Koonin, as it happens, is also a physicist, a former Cal Tech professor and assistant secretary of the Department of Energy. He describes his ideal student, when CUSP begins its first academic year this fall, as ‘someone who helped find the Higgs boson and now wants to do something with her life that will make society better.’ Koonin is a believer in what is sometimes called Big Data, the bigger the better. Only in the past decade has the ability to collect and analyze information about the movement of people begun to catch up to the size and complexity of the modern metropolis itself.”

Bettencourt writes, “A science of cities, recognizable across the full spectrum of urban disciplines, from physics and biology to social psychology and sociology is starting to emerge.” [“The Kind of Problem a City Is,” Santa Fe Institute Working Paper, 2013-03-008] He concludes his Working Paper this way:

“Cities reveal at once the best and the worst aspects of humanity, in terms of our creativity and imagination but also in our tendencies for violence or discrimination. Because of this enormous potential for human development cities should not be seen as systems to be controlled or resisted, but encouraged to evolve spontaneously in the direction of achieving the best open-ended expressions of our collective nature. That then is our challenge. We are living the last few decades of the great urban transition and finally fulfilling our potential as the most social of all species to create something altogether new in Earth’s history. We have within sight age-old human aspirations, such as to eliminate extreme poverty, to end most injustice, to gain access to good health for all, and to do all that in balance with the Earth’s biosphere. All this will have to happen in cities and it can now happen very quickly. Bigger data and a more scientific approach to cities will certainly help. But the ultimate challenge for all of us involved in influencing and practicing urban planning is to translate, apply and further develop these new ideas to promote urban environments that can encourage and nurture the full potential of our social creativity, targeted at sustainable and open-ended human development.”

Koonin agrees with Bettencourt. He told Adler, “We have acquired the technology to know virtually anything that goes on in an urban society, so the question is, how can we leverage that to do good? [How can we] make the city run better, enhance security and safety and promote the private sector?” Driving all of this potential is big data analytics. As we now know, the data comes from all sorts of sources: mobile phones, CCTV systems, the Internet, and so forth. Increasingly, data will come from machine-to-machine networks that help our systems run more efficiently and effectively.


Adler goes on to point out how mathematics can help us understand other things about how a city grows. For example, Glen Whitney, who founded the Museum of Mathematics in New York City, has a theory about the height of skyscrapers in cities (i.e., the better the Gross Regional Product the taller the buildings). Whitney admits that “building heights are constrained by engineering , while there’s no limit to how big a pile you can make out of money, so there are two very rich cities whose tallest towers are lower than the formula would predict. They are New York and Tokyo. Also, his equation has no term for ‘national pride,’ so there are a few outliers in the other direction, cities whose reach toward the sky exceeds their grasp of GDP: Dubai, Kuala Lumpur.” Adler notes, “Deep mathematical principles underlie even such seemingly random and historically contingent facts as the distribution of the sizes of cities within a country. There is, typically, one largest city, whose population is twice that of the second-largest, and three times the third-largest, and increasing numbers of smaller cities whose sizes also fall into a predictable pattern. This principle is known as Zipf’s law, which applies across a wide range of phenomena.” He concludes:

“As West and his colleagues are well aware, this research takes place against the background of a huge demographic shift, the predicted movement of literally billions of people to cities in the developing world over the next half century. Many of them are going to end up in slums — a word that describes, without judgment, informal settlements on the outskirts of cities, generally inhabited by squatters with limited or no government services. ‘No one has done a serious scientific study of these communities,’ West says. ‘How many people live in how many structures of how many square feet? What is their economy? The data we do have, from governments, is often worthless. In the first set we got from China, they reported no murders. So you throw that out, but what are you left with?”

The challenge, of course, is the fact that slums are generally considered to be places that are “off the grid.” The ubiquity of mobile phones is making this less true every day; nevertheless, getting data about slums remains difficult. Adler reports that “the Santa Fe Institute, with backing from the Gates Foundation, has begun a partnership with Slum Dwellers International, a network of community organizations based in Cape Town, South Africa,” to address challenges associated with off the grid communities. “The plan is to analyze the data gathered from 7,000 settlements in cities such as Mumbai, Nairobi and Bangalore, and begin the work of developing a mathematical model for these places, and a path toward integrating them into the modern economy.” Lobo told Adler, “For a long time, policy makers have assumed it’s a bad thing for cities to keep getting larger. You hear things like, ‘Mexico City has grown like a cancer.’ A lot of money and effort has been devoted to stemming this, and by and large it has failed miserably. Mexico City is bigger than it was ten years ago. So we think policy makers should worry instead about making those cities more livable. Without glorifying the conditions in these places, we think they’re here to stay and we think they hold opportunities for the people who live there.” To read a little more about slums, see my post entitled: Will Cities Save Us?


Adler writes that he hopes Lobo is correct because Michael Batty, who runs the Centre for Advanced Spatial Analysis at University College London, predicts “that by the end of the century, practically the entire population of the world will live in what amounts to ‘a completely global entity … in which it will be impossible to consider any individual city separately from its neighbors … indeed perhaps from any other city.'” Although I doubt that prediction will come completely true, I certainly believe that urbanization is going to continue unabated. Bettencourt told Adler that we are seeing “the last big wave of urbanization that we will experience on Earth.” Adler believes that it will be the math men, like West, Koonin, Batty and their colleagues, that will unlock the formulae that will point us down the road to a better urban future.

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