Tag Archives: economies of scale

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?

A universal theory of cities

CC Image from lopolis

CC Image from lopolis

Last week, the New York Times Magazine featured a lengthy piece from Jonah Lehrer about two physicists who have formulated a sort of universal law for urban living.  The single biggest determinant of urban performance is size – increasingly large agglomerations offer economies of scale – people who live and work there are more productive, more creative, etc.  The physicists (Geoffrey West and Luis Bettencourt) summarize their main conclusions:

Three main characteristics vary systematically with population. One, the space required per capita shrinks, thanks to denser settlement and a more intense use of infrastructure. Two, the pace of all socioeconomic activity accelerates, leading to higher productivity. And three, economic and social activities diversify and become more interdependent, resulting in new forms of economic specialization and cultural expression.

We have recently shown that these general trends can be expressed as simple mathematical ‘laws’. For example, doubling the population of any city requires only about an 85% increase in infrastructure, whether that be total road surface, length of electrical cables, water pipes or number of petrol stations. This systematic 15% savings happens because, in general, creating and operating the same infrastructure at higher densities is more efficient, more economically viable, and often leads to higher-quality services and solutions that are impossible in smaller places.

These core economies of scale, positive feedback loops, and benefits of agglomeration are what lets cities be cities.  Now, we have some math behind it.

Some more quotes from the NYT Mag piece.

On urban systems:

There is something deeply strange about thinking of the metropolis in such abstract terms. We usually describe cities, after all, as local entities defined by geography and history. New Orleans isn’t a generic place of 336,644 people. It’s the bayou and Katrina and Cajun cuisine. New York isn’t just another city. It’s a former Dutch fur-trading settlement, the center of the finance industry and home to the Yankees. And yet, West insists, those facts are mere details, interesting anecdotes that don’t explain very much. The only way to really understand the city, West says, is to understand its deep structure, its defining patterns, which will show us whether a metropolis will flourish or fall apart. We can’t make our cities work better until we know how they work. And, West says, he knows how they work.

On similarities and dissimilarities to natural systems:

[T]he real purpose of cities, and the reason cities keep on growing, is their ability to create massive economies of scale, just as big animals do. After analyzing the first sets of city data — the physicists began with infrastructure and consumption statistics — they concluded that cities looked a lot like elephants. In city after city, the indicators of urban “metabolism,” like the number of gas stations or the total surface area of roads, showed that when a city doubles in size, it requires an increase in resources of only 85 percent.

…

What Bettencourt and West failed to appreciate, at least at first, was that the value of modern cities has little to do with energy efficiency. […] In essence, they arrive at the sensible conclusion that cities are valuable because they facilitate human interactions, as people crammed into a few square miles exchange ideas and start collaborations. “If you ask people why they move to the city, they always give the same reasons,” West says. “They’ve come to get a job or follow their friends or to be at the center of a scene. That’s why we pay the high rent. Cities are all about the people, not the infrastructure.”

On positive feedback loops:

West and Bettencourt refer to this phenomenon as “superlinear scaling,” which is a fancy way of describing the increased output of people living in big cities. When a superlinear equation is graphed, it looks like the start of a roller coaster, climbing into the sky. The steep slope emerges from the positive feedback loop of urban life — a growing city makes everyone in that city more productive, which encourages more people to move to the city, and so on. According to West, these superlinear patterns demonstrate why cities are one of the single most important inventions in human history. They are the idea, he says, that enabled our economic potential and unleashed our ingenuity. “When we started living in cities, we did something that had never happened before in the history of life,” West says. “We broke away from the equations of biology, all of which are sublinear. Every other creature gets slower as it gets bigger. That’s why the elephant plods along. But in cities, the opposite happens. As cities get bigger, everything starts accelerating. There is no equivalent for this in nature. It would be like finding an elephant that’s proportionally faster than a mouse.”

Scarcity is the check on this superlinear growth, and innovation is what breaks that check.

On counterpoints to these universal laws: Lehrer quotes suburbanist Joel Kotkin in his piece, with Kotkin arguing against this logic of density and economies of scale, citing Silicon Valley and the Research Triangle.  Kotkin is too focused on the traditional narrative of cities and suburbs, however.  Both of those examples are still agglomeration economies, just comprised in a different physical form. A ‘city’ here is also the total urban area, not the arbitrary political boundaries that Kotkin often hangs his hat on.

It’s also important to note that this kind of universal law sets the baseline for what’s to be expected of a city – certain places will under or over-perform.  That’s where the quality of a place comes in, in my estimation.

On qualitative measures: West and Bettencourt specifically avoid the qualitative, since they can’t measure it well with data.  It’s important to not set qualitative and quantitative measurements in opposition, however.  WNYC’s RadioLab delved into the qualitative aspects of what makes cities into cities back in October.  These different explanations of cities are not mutually exclusive.  Indeed, they are complimentary.

This discussion, both the qualitative and quantitative aspects of it, seem to further embrace the Three D’s of density, diversity, and design.  The question is then about how to assess each of those factors.  Given that each one of those factors can be defined expansively (diversity of people, of skills, of land use, of incomes, of languages, of cultures, etc) and not all of those varied elements can be effectively quantified, this only reinforces the co-dependence of both analytical methods.

On planning: Lehrer closes his piece with a note about the inherent messiness of cities – the “energized crowding”, to steal a phrase from Spiro Kostof.

Unlike companies, which are managed in a top-down fashion by a team of highly paid executives, cities are unruly places, largely immune to the desires of politicians and planners. “Think about how powerless a mayor is,” West says. “They can’t tell people where to live or what to do or who to talk to. Cities can’t be managed, and that’s what keeps them so vibrant. They’re just these insane masses of people, bumping into each other and maybe sharing an idea or two. It’s the freedom of the city that keeps it alive.”

One common misconception about planners and planning is that we seek to control everything.  Instead, I am more interested in this kind of messy interaction.  Planning is about facilitating those interactions, not about controlling them.  For that reason, I find this kind of research fascinating.

The entire piece is fantastic.  Read the whole thing.