In This Issue
Winter Issue of The Bridge on Complex Unifiable Systems
December 15, 2020 Volume 50 Issue 4
The articles in this issue are a first step toward exploring the notion of unifiability, not merely as an engineering ethos but also as a broader cultural responsibility.

The Simplicity and Complexity of Cities

Thursday, December 17, 2020

Author: Christopher P. Kempes and Geoffrey B. West

One of the most striking phenomena that has dominated the planet over the last 2 centuries is the extraordinary rate of urbanization. Averaging to the mid-21st century, this is now equivalent to adding a metropolitan New York City every few months or a country the size of Germany every year.[1]

Cities have evolved as marvelous machines for facilitating social interactions to create wealth, produce knowledge and ideas, innovate, and thereby increase standards and quality of life. This has come at a huge cost dictated by the second law of thermodynamics: the inevitable production of social entropy in the guise of increases in crime, disease, pollution, and climate change, as well as systemic inequality in both wealth and power.

Clearly, the future of the planet and its long-term sustainability are inextricably linked to cities. Consequently, there is an increasing urgency to develop a deeper understanding of their dynamics and organization to help mitigate and minimize this plethora of problems.

Cities as Complex Adaptive Systems

From almost any perspective, cities are quintessential complex adaptive systems that have much in common with ecosystems and organisms. Like them, energy and resources are distributed through networks to sustain their multitudinous constituents, whether individuals, organs, or cells. Evolutionary pressures typically result in all of these systems manifesting an economy of scale; indeed, optimizing these networks leads mathematically to explicit scaling laws for the ways almost all physiological and life history characteristics of organisms change with size.

For example, within a taxonomic group, the energy required to support a unit mass of tissue decreases systematically as the quarter power of body mass. More generally, such scaling laws are typically sub-inear power laws whose exponents are simple multiples of one quarter. This remarkable regularity is a reflection of the generic constraints that are embodied in the mathe-matics and physics of the multiple networks that support life and that typically manifest self-similar fractal-like properties.

Given these results it is perhaps not surprising that the physical infrastructure of cities also satisfies similar sublinear scaling laws originating in the dynamics and geometry of the various transport and resource networks that sustain them. Metrics such as the number of gas stations, the length of the roads and electrical lines, the volume of buildings, all scale in a similarly “universal” fashion in different urban systems across the globe.

Simply put, the degree of infrastructure per capita, whatever it is, systematically decreases with city size with an exponent of about 0.15 (rather than 0.25 as in biology). On average, therefore, predictably fewer gas stations, roads, or electrical lines are needed to support an individual citizen the bigger the city.

But cities are much more than their buildings, roads, and electrical lines. Infrastructure provides the physical framework for facilitating social and other interactions where information is exchanged and socioeconomic activity stimulated.

Social Networks and Scaling Effects

Social networks have a very different character from the physical networks that dominate biology and the infrastructure of cities: their dynamics embody positive feedback mechanisms that underlie the creation and exchange of wealth, knowledge, and ideas. This is engendered in formal institutional and business settings such as universities, convention halls, and company boardrooms—and, equally importantly, in informal settings such as parks, sports arenas, and concert halls.

The increased connectivity of social interactions and its multiplicative enhancement are the very essence of a city, leading to superlinear scaling of socio-economic activities and an increasing pace of life. It is this  dynamic that sets cities apart from biology and makes them more than just “superorganisms.” As size -increases so do per capita metrics: wages, patent production, and GDP—but also crime, disease, and inequality, all happening at a predictably faster rate. As noted above, all of these very different metrics scale with city population size with a similar exponent, around 1.15, in urban systems around the world.

Naïvely, the existence of universal scaling laws in evolving self-organized complex systems is very surprising given that history, geography, contingency, and their associated huge space of possibilities would seem to make it impossible to understand particularities of a single species or city. Can the structure of Paris really be understood without considering Napoléon III or Los Angeles without regard to its benign California climate?

History and geography certainly matter. Yet the amazing fact is that almost all critical features of both organisms and cities obey systematic, quantitative scaling relationships. This suggests that the coarse-grained behavior of their dominant degrees of freedom is determined by a small set of constraints and that the continuous feedback implicit in evolution by natural selection over long periods of time—the survival of the fittest—tends to drive the resulting system and its sub-components toward an optimization that becomes manifested in scaling relationships.

Like organisms, cities and social organizations operate in competitive markets, though over significantly smaller time scales, resulting in greater variance around the predicted idealized scaling laws. It is this variance that reflects the history, geography, and individuality of a city; its dominant behavior is determined by the universal dynamics of the infrastructural (physical) and social (informational) networks common to all cities.

A Framework for Urban Interdependence

Understanding in detail the fundamental mechanisms, including the structure and dynamics of the underlying networks, is critical for mitigating the problems and minimizing the unintended consequences that have traditionally plagued urban development, whether in existing cities or in the design of new ones. Of particular importance is the recognition that all of the multiple characteristics of a city are strongly coupled and interdependent—the very essence of a complex adaptive system. Treating each problem, such as traffic gridlock in one local area or housing development in another, as if it were disconnected from everything else can be a recipe for long-term dysfunctionality.

Having a framework that is quantitative, systemic, and principled and that, at the same time, naturally incorporates this fundamental interdependence is crucial for dealing with the multiple challenges and trade-offs facing 21st century urban systems.

For instance, knowing that overperformance in total wealth production or wages in a city (relative to expectations from scaling curves) is correlated with increased inequality or crime provides a quantifiable metric for making an informed scientific judgment regarding trade-offs and policy decisions. Similarly, knowing that different broad organizational strategies lead to different scaling relationships, as is the case for categories of higher education institutions, indicates which constraints are universal and which are malleable.

Another timely example is the recent observation that the covid-19 spreading rate systematically scales with city size following an exponent of approximately 0.15. This result has huge implications for how cities respond to pandemics because, for example, a city of a million people will double the number of cases in approximately half the time of a city of 10,000. This fundamental difference in cities of varying size should be built into every pandemic plan of action at both the local and national levels.

All of these examples highlight that the ideal framework should serve as a complement to the traditional but necessary methods focusing on specific issues in specific cities.

This work is still at an incipient stage, but the very existence of systematic laws across cities offers hope for understanding mechanisms sufficiently well to know how to optimize cities for a variety of important outcomes, including not only their long-term sustainability but that of the entire planet.


[1]  Metropolitan NYC comprises the Bronx, Brooklyn, Manhattan, Queens, Staten Island; Elizabeth, Jersey City, Newark, the Oranges, Paterson, and adjoining communities in New Jersey; and Nassau and Westchester counties—some 18.35 million people. Germany’s population is about 83 million.

About the Author:Christopher Kempes is a professor and Geoffrey West is the Shannan Distinguished Professor and president emeritus at the Santa Fe Institute.