Cities as complex systems – with scientific research to show it

False-color satellite image of China's Pearl River Delta. Top image is from 1973, bottom image from 2003. CC images from NASA.

False-color satellite image of China’s Pearl River Delta. Top image is from 1973, bottom image from 2003. CC images from NASA.

Building off of previous research working towards a universal theory of cities, Luis Bettencourt is back in the news with a new paper (working paper version here) that argues cities are a new kind of network not easily captured by analogies to natural systems. Rather, cities are “part social reactor, part network.”

Based on this theory, Bettencourt identifies the basic patterns of how cities grow. From that observation, Bettencourt builds his theory, allowing for the determination if cities are under or over-performing.

From the Santa Fe Institute’s article on the paper, this theory of cities is described as follows:

o what is a city? Bettencourt thinks the only metaphor that comes close to capturing a city’s function is from stellar physics: “A city is first and foremost a social reactor,” Bettencourt explains. “It works like a star, attracting people and accelerating social interaction and social outputs in a way that is analogous to how stars compress matter and burn brighter and faster the bigger they are.”

This, too, is an analogy though, because the math of cities is very different from that of stars, he says.

Cities are also massive social networks, made not so much of people but more precisely of their contacts and interactions. These social interactions happen, in turn, inside other networks – social, spatial, and infrastructural – which together allow people, things, and information to meet across urban space.

Ultimately, cities achieve something very special as they grow. 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.

The argument that cities can be partially explained with natural analogies sounds similar to the use of the constructal law to explain cities, but Bettencourt is arguing that there is a similar, but different relationship here.

Emily Badger summarizes and explains Bettencourt’s research at Atlantic Cities:

But Bettencourt is basically describing interconnected relationships between the population growth of a city; the incremental expansion of the infrastructure networks that more people require; the socioeconomic outputs that come from our social interaction; and the density that necessarily develops over time so that we can still benefit from ever-more social connections without spending ever-more energy to reach each other.

As cities grow, Bettencourt says, the city comes to you. This is a high-minded way of talking about infill development. If cities continued to grow but only grew outward, you would never get any benefits out of knowing or working with new people, since you’d have to sit in traffic for two hours to reach them. Density, however, allows us to reap the benefits of more social connections without adding too many costs in congestion and energy (like gas). All of this enables the amazing growth and benefits of cities to be open-ended.

Per Square Mile offers a summary as well:

Bettencourt believes there are four sparks that cause cities to form—the mixing of populations, the incremental growth of networks, the bounds of human effort, and the relationship between socioeconomic output and personal interaction. According to these assumptions, cities are founded and grow primarily so that people can interact frequently and on a personal level. As demand for face time swells, cities expand, incrementally adding to the existing network. Eventually, those networks reach a limit, bounded by the amount of effort we are willing to expend to expand and maintain them. The greater the benefit of living in a city, the more effort we’re willing to expend to sustain it. Bettencourt’s final assumption may be his most astute—that cities aren’t just agglomerations of people, but also concentrations of social interactions.

The formulas Bettencourt derived could prove powerful. His most muscular equation, that which models city growth, identifies cities that punch above and below their weights. Others show how substandard transportation can hold a city back, or how transportation networks tend to grow incrementally (perhaps that’s why automobile sprawl seems so intractable). But his formulas also highlight some perils, like how energy loss in transportation increases superlinearly—the more you move, the more energy it takes to move something. In sum, they appear to build a solid theoretical framework by which further questions can be asked and hopefully answered.

Questions immediately come to mind about matching our policies to this theory; what the trade-offs between growth and the benefit of living in cities look like in the real world beyond the theoretical framework. Conversely, how might such a theory influence policy? Could an understanding like this help with proposed policy frameworks such as the zoning budget? What about the qualitative elements of a place and the influence they have on these dense, social networks?

1 thought on “Cities as complex systems – with scientific research to show it

  1. Kenny

    After seeing those summaries on other sites, I read the actual article, and was a bit surprised at how much the conclusion emphasized in those other points (that various metaphors for cities lead to errors) seemed to be a minor point. The major point seemed to be the fact that one can actually derive power laws with exponents like 2/3 or 5/6 from relatively simple assumptions about the economic values of interactions, the costs of transportation, and the like. It made me start to consider whether there could be “phase transitions” in the growth of cities if changes in technology change any of those assumptions – for instance, if communications networks are primarily radial wireless technologies, rather than wired networks, then the costs of communication would scale like the radius of the city, rather than like the number of people in it, which would change some exponents.

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