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Quantum Correlations: A Science of Scaling in Cities: A City as a Social Reactor

  By Alaina G. Levine It was less than a year ago that I sat in the back of a conference room at the storied Santa Fe Institute (SFI) listening to lectures on garbage, slums and cell phones. I was the only reporter invited to a workshop that converged scholars from realms as diverse as...

Image Credit: Gabriel Garcia


By Alaina G. Levine

It was less than a year ago that I sat in the back of a conference room at the storied Santa Fe Institute (SFI) listening to lectures on garbage, slums and cell phones.

I was the only reporter invited to a workshop that converged scholars from realms as diverse as physics, sociology, statistics, biology and urban planning to discuss an arguably lofty topic: can there be a science of cities? Can there be an equation, or series of equations, that describes what the heck a city actually is and does, and what it means to be a member of a city?

The scientists debated the subject for only a few days on top of the hill where this Institute dedicated to complex studies is located, but many of them had been working on this for years. One scientist had been analyzing patterns of refuse to better understand city residents’ behavior, while another had begun utilizing cell phone data to establish a better comprehension of human movements. One of the workshop leaders, Luis Bettencourt, is a physicist whose previous work related to the early Universe, and associated mathematical techniques of statistical physics, field theory and non-linear dynamics. Now a Professor at SFI, Bettencourt has been researching issues pertaining to city dynamics and function for a decade. And inspired by new perspectives and ideas that stemmed from this meeting of metropolis-focused minds, Bettencourt has now produced a science of scaling of cities, which he published in a cover paper in Science on 22 June 2013.

The fascinating paper takes a new look at how a city, any city in fact, evolves according to only a few principles, and how the social, spatial and infrastructural properties of cities can be described by scaling relationships.

But most perhaps importantly, the paper argues that a city is a new type of system in nature, something that is a cross between a star and a social network. In fact, Bettencourt says that “a city is not a place in space and time. It is a place to maintain and sustain social networks.” He refers to the holistic enterprise as a social reactor.

“About a year ago, I realized how it could all come together, which was the beginning of this paper,” he says. “The insight was a shift in perspective from what a city look likes, from how they work, and what is it that they are doing, and so vaguely speaking, it’s about the idea of social reactors: thinking about formalizing the idea of having a very large social network imbedded in space and time and how does its connectivity scale and what are the costs of maintaining that connectivity, and basically by answering those questions, you can write this paper.”

Others have suggested that cities look and operate like biological organisms, but that is not the case, says Bettencourt. “A city is a bunch of people, but more importantly, it’s a bunch of people interacting, so hence the social network,” he explains. “What’s important are the properties of this social network: the scaling was giving us clues. But then when you think of this superlinearity, which means the socioeconomic outputs are the result of those interactions, are expressed as growing superlinear functions of populations, the only system that I could think of in nature is a star. A star does have this property – it’s essentially a nuclear reactor sustained by gravity and shines brighter (has greater luminosity) the larger its mass. So there’s a sense that this behavior that is sustained by and created by attractive interactions and whose output is proportional to rate of interactions, is what a city is and a star is, and so in that sense they are analogous.”

Scaling of various relationships within a city is central. “There are these old models that balance the extent of a city in space with the cost of transportation,” he says. “If you live at the edge of the city, you pay almost no rent but pay a lot in transportation costs. I always thought these models were too simple. So [this paper] elaborated on those.” But this was not enough, he clarifies, because of the role of infrastructure and how it scales across cities: “There was large literature mostly from sociology and social psychology that say that cities impose all these burdens on these people and this is why they are not sustainable…Not so much that they impose a large transportation cost, but in fact they impose a large psychological burden. So I had to figure out a way of creating a system that had the properties of infrastructure that people could measure.”

The result is this “special social reactor” that adheres to four main assumptions about city dynamics and scaling:
1) There are “mixing populations”: basically, cities have attractive interactions and social outputs are the results of those, which leads to more social interactions.

2) There is “incremental network growth”: notably, the networks themselves and the supporting infrastructure develop gradually as the city grows. The infrastructure is decentralized as are the networks themselves. This is very different from an organism, says Bettencourt, whose internal “infrastructure” (analogous to a vascular system for example) develops basically all at once and has a centralized node.

3) “Human effort is bounded”: as he writes in his paper, “The increasing mental and physical demand from their inhabitants has been a pervasive concern to social scientists. Thus this assumption is necessary to lift an important objection to any conceptualization of cities as scale-invariant systems.” In other words, “The costs imposed on people by living in the city do not scale up,” he says, because as the number of social interactions increase, one doesn’t have to necessarily travel more to get to these interactions. “The city comes to you as it becomes denser,” he notes.

4) “Socioeconomic outputs are proportional to local social interactions”: this gives us an interesting snapshot of exactly what a city is – not just a conglomeration of individuals, but rather a concentration of social interactions.

“Ultimately, cities achieve something very special as they grow,” notes the SFI press release about the paper. “They balance the creation of larger and denser social webs that encourage people to learn, specialize, and depend on each other in new and deeper ways, with an increase in the extent and quality of infrastructure. Remarkably they do this in such a way that the level of effort each person must make to interact within these growing networks does not need to grow. How these networks fit together, and the tensions and tradeoffs among them, often determines how productive or prosperous a city is, or whether it fissions into smaller ‘burbs, or if people want to live in them or don’t.”

This mathematical model is only a first step, says Bettencourt. It is not THE unified theory of cities. “Science is never once and for all,” he clarifies. “To me this is the unified theory of scaling – it explains how all these quantities scale with population size.”

He anticipates that with better data collecting methods and new analyses of city dynamics in developing nations, in particular slums, there will be “new opportunities to test the theory in places where understanding urbanization is most critical.”

“Rapid urbanization is the fastest, most intense social phenomenon that ever happened to humankind, perhaps to biology on Earth,” says Bettencourt. It is planet-wide, after all, and “reorganizes the way the biosphere and humanity interact with each other…I think we can now start to understand in new and better ways why this is happening everywhere and ultimately what it means for our species and for our planet.”

Alaina G. Levine is a freelance science writer, professional speaker, corporate comedian, and President of Quantum Success Solutions, a leadership and career consulting enterprise. Her new book on networking strategies for scientists and engineers will be published by Wiley in 2014. She can be contacted through her website at or on twitter @AlainaGLevine.

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Meet the Author

Alaina G. Levine is science journalist, professional speaker, corporate comedian, and science and engineering careers consultant. As President of Quantum Success Solutions, a career consulting enterprise with a focus on advancing the professional development expertise of scientists and engineers, she has been advising emerging and established scientists and engineers about their careers for over a decade, and has personally consulted with hundreds of early- and mid-career scientific professionals. The author of over 100 articles pertaining to science, science careers and business in such publications as Science, Nature, Scientific American Online, IEEE Spectrum, New Scientist, and Smithsonian, she was recently named a Contributor to National Geographic, where she writes articles and blogs for NatGeo News Watch. Levine also writes the Careers Column for The Euroscientist and the Profiles in Versatility career column for the American Physical Society's national publication, APS News. Previously, she directed a master's program in science and business and taught entrepreneurship to science graduate students at the University of Arizona. She has given over 450 workshops and seminars around the country and in Europe. Levine holds degrees in mathematics and anthropology from the University of Arizona, studied abroad at the American University in Cairo as a DoD National Security Education Program/Boren Fellow, and pursued grant-funded research in cosmology and mathematics history. Recently, she was honored with a travel fellowship to cover the 62nd Lindau (Physics) Nobel Laureates Meeting in Lindau, Germany (which she used to cover the meeting for National Geographic and APS News), during which she broke the Higgs news for NatGeo. She also has been honored as a Logan Science Journalism Fellow at the Marine Biological Laboratory, Robert Bosch Stiftung Science Journalism Fellow and an Institutes for Journalism & Natural Resources Fellow. In addition, Levine is an award-winning entrepreneur, winning more than 20 business and leadership awards in under a decade, including being named one of the youngest YWCA Women on the Move winners; the Tucson Leader of the Year, an honor previously bestowed upon former US Surgeon General Richard Carmona; and a Tucson 40 Under 40 Leader, an honor she shared with former US Congresswoman Gabrielle Giffords. Read her complete bio at