Part of a continuing series about complexity science by the Santa Fe Institute and The Christian Science Monitor, generously supported by Arizona State University.

If you are reading this, you are very likely living in a city. City dwellers are now more than half the world’s population, and this proportion is increasing in every nation, rich and poor, creating for the first time in history a planet of cities.

In light of the many problems of large cities — high costs, crime, pollution, disease, congestion — why are so many people choosing to live in them?

It could be the conveniences and amenities we enjoy only in cities: a library, a hospital, the pleasure of music on the streets, or a great cup of coffee served up by an expert barista.

But it turns out that these are only part of the city’s allure. Research is revealing that cities have a unique transformational power in terms of both individual fulfillment and collective development — by bringing us closer to each other, cities enhance the benefits of our species’ sociality.

The nature of cities

What’s really happening within each city is a massive exchange of information across social and economic networks of people and organizations, all taking place on a complex infrastructural landscape of buildings, roads, pipes, and wires. For the most part there is no maestro; the properties of cities emerge from countless interactions of millions of people, driven by their individual goals and motivations.

In this sense, cities are an outstanding example of complex adaptive systems: collections of individual constituents (people, in this case) that interact in myriad ways, usually mediated by some sort of network.

All complex adaptive systems involve learning and adaptation by individuals and collectives, and, as a result, these systems develop intricate and unique histories. This is why Mumbai is so different from Seattle. Each is the result of its particular geography, its culture, its mixture of peoples, its politics, its accidents of history.

From this, you might assume that cities are all idiosyncratic agglomerations of humanity, and that the common essence of “cityness” can never be found. Not so. When we quantitatively compare the properties of Mumbai and Seattle, or New York City and Santa Fe, we find that all cities, from the tiniest hamlets to the largest megalopolises, share certain general spatial and socioeconomic features.

To study this underlying order, we and other researchers analyze lots of data to compare many different properties of thousands of cities around the world. Analysis on this vast scale is necessary to transcend the specificities of each place, though only now is it becoming possible to do this systematically as data on human societies become easier to collect and share.

We analyze just about anything that can be measured. A city’s total area, the extent of its roads and highways, its lights at night, its gross domestic product (GDP), the wages and professions of its workers, its crime rate, and much more.

Then, we organize all of these diverse quantities, typically studied separately by researchers in different academic disciplines, under a unifying complex systems framework. We do this by thinking of social and economic activity as a gigantic network of people and their interactions embedded into the physical built spaces of cities, which comprise places (buildings, public areas) and access networks (streets, pipes, electrical and telephone cables, internet hubs).

In these terms, all cities share a general shape (a “topology”), despite individual differences in the geometry of streets and city blocks. The general characteristics of these spaces allow us to estimate how often people meet, and thus the rate at which they can produce socioeconomic outputs ranging from ideas and wealth to crime and disease.

A scaling theory of cities

And here’s where it gets interesting: As cities grow and their networks evolve, the area or volume of the networks needed to keep them functionally connected tends to become smaller on a per capita basis. For example, in larger cities more people can share the same bus or segment of road or sewer pipe.

This introduces two important concepts: first, the idea of scaling, which refers to how measurable properties of a system change with its size; second, the concept of economies of scale.

The latter means that, as cities grow, they need less of something per person: roads, sewers, or gas stations, for example. What’s more, such economies of scale in infrastructure are, mathematically speaking, regular and predictable given a city’s size: If you double the size of a city, you only need 80-90 percent more street surfaces, gas stations, sewer lines, etc. This holds true, within a few percentage points, for cities of all sizes and across all nations.

This increase is nevertheless faster than the increase in the overall land area the city occupies. This is why roads, cables, and pipes become so ubiquitous in larger cities and eventually must be buried underground, especially in a city’s densest parts. This is also why roads in larger cities are more congested and often under construction: they are used much more intensely than in smaller towns.

The converse of economies of scale — increasing returns to scale — gets us closer to why cities exist. The size of a city’s economy (measured as its GDP), for example, is typically larger per capita in a bigger city. This is why New York City is so expensive, but it is also why New Yorkers make more money on average than people living in a city half its size (Los Angeles), and by a predictable amount (10-20 percent more).

Increasing returns characterize most outputs of human social interaction in a city, manifesting itself in predictably higher wages, faster technological innovation, more congested streets, and more incidents of violent crime per person in larger urban areas.

The integration of all these urban quantities suggests that these two effects — economies of scale and increasing returns to scale — are not independent but rather mirror images of each other. In this way, the geometry of our social lives is, in a very formal sense, interdependent of the spaces we build in cities.

Cities as social reactors

Another, more intuitive way to understand urban scaling is the speed of life in cities. Life in larger cities is generally faster, meaning one can do more, both good and bad, by having more social exchanges over the same amount of time. This speed of social life is intimately connected to the spatial density of many activities, creating spaces and times when a lot can happen quickly.

This reveals the ultimate function of cities: Cities are social reactors, places where interactions among many different strangers can be realized and sustained. Ultimately, it is this accelerating dynamic that creates the buzz of a great city.

As economists have known for a long time, this continuous feedback between peoples’ productive activities and new ideas is the driver of economic growth. As we become networked on ever-larger scales, we can exploit the division of knowledge and labor to create organizations that are more efficient and that, collectively, contain and process more knowledge. Cities are a general-purpose way to build such networks and to rev up the engines of growth and change in human societies.

But here’s the rub: This magical power of cities does not always work well or apply equally to everybody. All the quantities for which we find scaling relationships are merely averages — quantitative snapshots of entire metropolitan areas. Being able to predict the average per capita income in New York City (about $60,000 per year) is obviously important for understanding the dynamics of cities, but equally important is to understand why it has the same income inequality as Port-au-Prince, Haiti, which of course is much poorer.

The challenge of cities

It’s clear that the increased social opportunity of larger cities affects different people in different ways, young and old, rich and poor. This results in very large inequalities and heterogeneities across any large city, a phenomenon still poorly understood and often mismanaged.

In our own cities, and certainly in developing cities throughout the world, it is common for poverty and exclusion to coexist side by side with wealth and opportunity. Even as cities continue to grow, many people in developing countries lack access to even the most basic services such as clean water, modern sanitation, or basic justice. The imperative of meeting basic necessities on a daily basis leaves little time for educational pursuits, and much less for sophisticated entrepreneurship.

This is the greatest obstacle to human development for some 1 billion people on our planet today, a number that could triple by 2050 if no practical policy solutions are devised to tackle these issues systematically.

To deal with these challenges, representatives from all 193 countries of the United Nations General Assembly signed a remarkable blueprint for the future in September that commits us to worldwide Sustainable Development Goals to be met over the next 15 years. These goals set quantitative local targets to eliminate extreme poverty, provide universal access to basic services, institute higher standards of justice and government, and achieve urban growth that is environmentally sustainable.

Achieving these goals may well represent the only way to save ourselves and the planet from major environmental and humanitarian crises and thereby set the course for a world of open-ended creativity and urbanized human development.

The complexity and urgency of these challenges are colossal, far outweighing the Apollo Program or Manhattan Project. Fifteen years is not a lot of time. But the key to their solution is to understand the systemic nature of these problems defined by the lives and economic activities of people, and by the environments and services that we build in cities. To continue to seize the transformative power of cities, and to do it fast, we need to match extraordinary action with holistic and exacting knowledge that captures the nature of cities as complex adaptive systems.

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Luís M. A. Bettencourt is a theoretical physicist and professor of complex systems at the Santa Fe Institute. He seeks to describe cities in quantitative and predictive ways, informed by the growing availability of empirical data worldwide, to suggest transformative policy solutions and help cities achieve their human development potential.

Geoffrey West is s a theoretical physicist, a senior fellow at Los Alamos National Laboratory, and a distinguished professor and past president of the Santa Fe Institute. His primary current research interest is in universal scaling laws that pervade biology and human social organizations, such as cities and corporations, and their implications for sustainability.