Tag Archives: universal theory

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?

Different types of urban science

CC image from futureatlas.com

CC image from futureatlas.com

Jeff Wood’s handy mailing list on behalf of Re-connecting America pointed me towards this article from Urban Omnibus, disputing the broad conclusions from Geoffrey West’s work towards discovering a universal theory of cities.  Eric Peterson, the author, does not like the implications of West’s quantitative work and the implications of physical laws that might apply to cities:

Despite proposing to have radically reinvented the field in which architects and urbanists work, the article appears to have garnered little attention among commentators and blogs from within architecture and urbanism. Perhaps the article’s lack of substance explains professionals’ reluctance to engage with the implications of West’s work. Nonetheless, it is crucial for those of us interested in the serious study of urbanism to look closely at the article, if only because many of the assumptions it advances strike me as undermining an understanding of cities as complex and important things.

The charge that West’s work is somehow lacking in substance struck me as harsh and misguided.  The notion that there can be only one true understanding of how cities work misses the obvious difference between  West’s work and the more conventional urban studies that Peterson seems to prefer.  The difference appears to be a simple one, based on a misunderstanding of the kinds of universal rules West seeks to understand, as well as the fundamental difference between qualitative and quantitative observation.

Remembering that West is a physicist, Peterson’s charge that a universal theory of urbanism misses out on all of the complexity of a city represents a fundamental misunderstanding of what such a universal theory really means.  Just look at West’s field – physics – and you can easily see exceedingly complex movements that can all be understood by the basic laws of Newtonian mechanics.  A full understanding of motion, as we know it, is an exceedingly complex undertaking, yet Newton essentially boiled that complexity down to three basic laws of motion, which can easily be translated into simple maxims.  Bodies at rest tend to stay at rest; bodies in motion tend to stay in motion; for each and every action there is an equal and opposite reaction; etc.

These laws have limits to their validity, of course, but that does not discount the fact that complex systems can be understood via the basis of simple laws. This reduction isn’t something to be feared.

Peterson also seems to gloss over the mutually beneficial relationship between both qualitative and quantitative analysis.  He frames urbanism in a qualitative way and then implies that the quantification of urbanism not only has little to offer, but is indeed dangerous to our understanding of urban places:

Further, such an approach should be read as dangerous to all of us who see cities as phenomena formed at the collision of dynamic economic, historical, social, political and ecological forces.

This fear seems so misguided that I don’t even know where to begin.

Instead of recognizing cities as the products of these complex forces, the object of West’s study is purposefully contextless and unspecified. Describing how he applies his scientific principles to a specific city he’s studying, he says, “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.” West goes on to qualify this assertion by saying that, essentially, the differences between cities that we so often discuss are merely superficial, material ones, related to how a city functions rather than to each city’s unique history.

Even in areas of knowledge where we have a strong quantitative understanding of how things work, this knowledge has never derailed our searches for qualitative understanding as well – for context, for history, for social interactions.

Some of this confusion between the respective role for quantification and qualification stems from language.  Peterson notes early in his piece his disdain for West’s characterization of cities as “problems” to be solved.  Here, the word problem would have completely a different meaning to a mathematician and a physicist as compared to a ethnographer or an architect.  To the mathematician, a problem is not necessarily a social ill but a riddle to be solved, a question to be answered.

In the end, both approaches are crucial to our understanding of the places we live in.