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Numbers in the City, Part 1

June 7, 2013


You’ve probably heard the expression, “I’m tired of being treated like a number.” In the past, “being treated like a number” has been a bad thing. That may change if experts in the emerging field of quantitative urbanism have their way. They “believe that many aspects of modern cities can be reduced to mathematical formulas” and want to use those formulas to make urban life richer and more efficient. [“Life in the City Is Essentially One Giant Math Problem,” by Jerry Adler, Smithsonian, May 2013] Ben Hecht argues that, thanks to big data analytics, being treated like a number will make things more, not less, personal in the future. [“Big Data Gets Personal in U.S. Cities,” Huffington Post TED Weekends, 8 February 2013] He writes:

“Much has already been said about how big data is dramatically changing the way that organizations make decisions. Today, more data is being created from more places than ever before. Blogs, Facebook, YouTube videos, retailer loyalty cards, mobile phones, and sensors on buildings are producing tons of data daily. Private sector companies, in their real-time data warehouses, are storing, analyzing, and harnessing it to help them to better understand their customers, dynamically alter pricing based on real-time demand, and even change their business models. And, increasingly government is putting the wealth of data that it generates to work to increase efficiency, save dollars, and create more proactive policy. But, as Deb Roy highlights in his TEDTalk, the true promise is where the numbers and patterns from this data connect and become personal — enabling us to understand and to respond to humanity and the world in ways previously unimaginable.”

Deb Roy’s TEDTalk begins with the story of how big data analyzed his son’s journey to an “adult” vocabulary and ends with how big data can be used to demonstrate important connections in society. If nothing else, the visualizations Roy uses in his presentation are stunning. Hecht asserts, “Already, in U.S. cities, we are seeing many promising signs of the transformative personal application of Big Data.” Adler calls mathematical principles “the highest product of the human intellect.” And even though he believes that “many aspects of modern cities can be reduced to mathematical formulas,” he doesn’t believe that means that all cities are alike. “Cities are particular,” he writes. “You would never mistake a favela in Rio de Janeiro for downtown Los Angeles.” Having made that point, he nevertheless asserts:

“Cities are also, at a deep level, universal: the products of social, economic and physical principles that transcend space and time. A new science — so new it doesn’t have its own journal, or even an agreed-upon name — is exploring these laws. We will call it ‘quantitative urbanism.’ It’s an effort to reduce to mathematical formulas the chaotic, exuberant, extravagant nature of one of humanity’s oldest and most important inventions, the city.”

What makes cities chaotic, exuberant, and extravagant, are not the structures, the climate, or the location as much as the people. That’s why big data analytics are so important in ensuring that our cities get smarter in the decades ahead. Big data analytics help us get personal. Adler explains:

“The systematic study of cities dates back at least to the Greek historian Herodotus. In the early 20th century, scientific disciplines emerged around specific aspects of urban development: zoning theory, public health and sanitation, transit and traffic engineering. By the 1960s, the urban-planning writers Jane Jacobs and William H. Whyte used New York as their laboratory to study the street life of neighborhoods, the walking patterns of Midtown pedestrians, the way people gathered and sat in open spaces. But their judgments were generally aesthetic and intuitive (although Whyte, photographing the plaza of the Seagram Building, derived the seat-of-the-pants formula for bench space in public spaces: one linear foot per 30 square feet of open area). ‘They had fascinating ideas,’ says Luís Bettencourt, a researcher at the Santa Fe Institute, a think tank better known for its contributions to theoretical physics, ‘but where is the science? What is the empirical basis for deciding what kind of cities we want?’ Bettencourt, a physicist, practices a discipline that shares a deep affinity with quantitative urbanism. Both require understanding complex interactions among large numbers of entities: the 20 million people in the New York metropolitan area, or the countless subatomic particles in a nuclear reaction.”

Adler reports that “the birth of this new field can be dated to 2003, when researchers at SFI convened a workshop on ways to ‘model’ — in the scientific sense of reducing to equations — aspects of human society.” The John D. and Catherine T. MacArthur Foundation believe this new field is so important that it provided a half-million grant to the Computation Institute (CI), a joint initiative between the University of Chicago and Argonne National Laboratory, in order to fund “a new Chicago-based research center using advanced computational methods to understand the rapid growth of cities. … The funds help launch the Urban Center for Computation and Data (UrbanCCD), an initiative … dedicated to data-driven urban research, planning and design.” [“MacArthur Foundation grant supports Urban Center for Computation and Data,” Green Car Congress, 20 January 2013] The MacArthur grant complements a $600,000-grant previously provided by the National Science Foundation.


Adler reports that Geoffrey West, a theoretical physicist, along with Bettencourt and José Lobo, an economist at Arizona State University, were the trio that founded the quantitative urbanism movement. They “produced the seminal paper in the field: ‘Growth, Innovation, Scaling, and the Pace of Life in Cities.'” The abstract of that paper reads:

“Humanity has just crossed a major landmark in its history with the majority of people now living in cities. Cities have long been known to be society’s predominant engine of innovation and wealth creation, yet they are also its main source of crime, pollution, and disease. The inexorable trend toward urbanization world- wide presents an urgent challenge for developing a predictive, quantitative theory of urban organization and sustainable development.”

Lobo told Adler, “What people do in cities — create wealth, or murder each other — shows a relationship to the size of the city, one that isn’t tied just to one era or nation.” Adler goes on to explain some of the math described in the paper:

“The relationship is captured by an equation in which a given parameter — employment, say — varies exponentially with population. In some cases, the exponent is 1, meaning whatever is being measured increases linearly, at the same rate as population. Household water or electrical use, for example, shows this pattern; as a city grows bigger its residents don’t use their appliances more. Some exponents are greater than 1, a relationship described as ‘superlinear scaling.’ Most measures of economic activity fall into this category; among the highest exponents the scholars found were for ‘private [research and development] employment,’ 1.34; ‘new patents,’ 1.27; and gross domestic product, in a range of 1.13 to 1.26. If the population of a city doubles over time, or comparing one big city with two cities each half the size, gross domestic product more than doubles. Each individual becomes, on average, 15 percent more productive. Bettencourt describes the effect as ‘slightly magical,’ although he and his colleagues are beginning to understand the synergies that make it possible.”

Adler reports that not only positive effects scale superlinearly. Some diseases, like AIDS, and serious crime also demonstrate superlinearity. On the other hand, he reports, “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.” The important point about these calculations is that “this phenomenon applies to cities all over the world, of different sizes, regardless of their particular history, culture or geography.” Adler continues:

“One implication is that … ‘big cities are not just bigger small cities,’ says Michael Batty, who runs the Centre for Advanced Spatial Analysis at University College London. ‘If you think of cities in terms of potential interactions [among individuals], as they get bigger you get more opportunities for that, which amounts to a qualitative change.’ … There is a point, Whitney says, at which a system — a market, or a city — undergoes a phase shift and reorganizes itself in a more efficient and productive way.”

That is exactly what the smart cities movement is trying to do as more of the world becomes urbanized. Adler goes on to discuss how mathematics can help people move through lines more quickly and how communications networks can be made more efficient using “a branch of mathematics called queuing theory.” He discusses how mathematics can help people save money or logisticians run a transit system. In the final installment of this series, I’ll continue the discussion of how quantitative urbanism can help make cities more efficient and livable.

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