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A Mathematical Guide to the World’s Most Livable Cities

Can quality of urban life be boiled down to a formula?
City, park



Flickr/tomdz

Most people might think of a city such as Paris or Tokyo as a unique entity, with a character that is distinct from other metropolises. But large cities, towns and even smaller villages also share common purpose: they strive to provide a good place to live. Urban planners are trying to find a way to bring mathematical rigor to analyzing how well a city accomplishes this universal goal.

Professor and theoretical physicist Luis Bettencourt teamed up with his colleagues at the Santa Fe Institute and recently published a theory that suggests cities, towns and villages are more similar than different. He observed statistical trends across urban areas worldwide—how size, geographic location, wealth and other measures vary—and identified universal components that are integral to a city’s success. Bettencourt has tried to synthesize these components into a mathematical formula, intended to quantify how successful a city or town really is. Scientific American asked Bettencourt about what makes cities successful and how a more formalized, mathematical approach to urbanization can be used to diagnose and improve struggling cities.

[An edited transcript of the interview follows.]

What was your approach in identifying universal patterns from one city to the next?

It took a long time. Our team here at Santa Fe Institute is generally interested in complex systems. I’ve always been interested in cities. I grew up in Lisbon and lived in London, and I just love trying to understand how the hell we create all these amazing things that we see in our society. Where does it go wrong, and how can we make it better? Essentially, we’ve been looking at every scrap of data that we can find in the last 10 years, not only in the West but also in Japan. Then we moved to China and Brazil.

What do your findings contribute to our current understanding of cities?

A lot of ways we’ve viewed cities in the past have been through analogies to other complex systems, such as organisms. What this paper tries to do is create a shift in perspective from what cities look like and describe and formalize a city’s function. Trying to shift this perspective creates a new view of cities and allows us to say what cities are. Our conclusion is that cities are a kind of social reactor; they exist to solve the problem of putting lots of socializing people together and coordinate them in space and time in an open-ended, sustainable way.

What makes a city successful?

You want a balance between interactivity and the cost of creating those interactions, and that’s what this formula is about. That balance is what defines a city that is working well and can be achieved for cities of any size. Although people sort of knew that, this paper allows us to formalize that and put all these things in the same equation for the first time.

Does more social interaction necessarily mean a city will be more successful? Or can social interaction sometimes be a bad thing?

Some interactions make you want to be in a city, like the exchange of innovative ideas. But others can deter people from cities. Social interactions have to give you an overall advantage in order for cities to exist. You have to take the advantageous social interactions, like measures of innovation and creativity, and subtract the negative interactions, like violence or crime. You also have to subtract the cost of these advantageous interactions, like transportation. When you subtract that cost, that gives the conditions for the city to exist in this balance between creating value through interactions and paying the price for that value.

What cities are doing it right at the moment, and which cities are less successful?

Most cities actually do pretty well, but some cities create more interactivity than others. For example, according to the formula, New York City and Chicago are both doing a little better than L.A., which is slightly more spread out and has a higher cost for interaction.

You also have cities that are very dense, like Mumbai, but very difficult to travel across due to poor infrastructure or traffic congestion. This makes it very hard to have interactions across the cities. Then you have dissolved cities. These cities become so diluted that it would cost a lot of energy to move around and promote interactions. Neither of these forms is good.

Can you give an example of how this formalized understanding of a city’s function can improve cities that lack advantageous social interaction?

Detroit is a city that fell apart as a contained social network and in some sense reconstituted itself in the suburbs. A lot of its decay happened because the city separated socially and spatially in the ’60s. The city of Detroit was a wonderfully rich and vibrant cultural center, but people started moving to the suburbs when cars became available. That left the city with less revenue, which led to a reduction of services, which led to more people leaving and therefore a vicious cycle of people leaving the center and services being removed. In some sense, they have too much space [in the suburbs]. It’s expensive for people to move around in Detroit and realize activity that leads to urban vitality.

Concentrating populations in certain parts of the city could promote social interactions and services at lower costs. Detroit represents a thinning of the social structure, a thinning of its density and space that somehow needs to be reconstituted in a different way socially and in a way that we can provide services very efficiently to commence social interactions.

You mention that your formula does not account for socioeconomic disparity within a city. Is this important to a city’s efficiency?

We’re now starting to look at neighborhoods within cities and see how they vary. City neighborhoods are extremely heterogeneous: there are rich and poor neighborhoods, neighborhoods that are more about shopping, others that are residential, others are more industrial. People organize themselves inside a city in ways that have to do with these and other things, like violence and segregation. A city that works well overcomes these obstacles to establish connectivity. The fact that you can have economic and civic relations with people that are very different from you is what makes a city work well.

Cities are heterogeneous by nature; they are about combining different natures and functions to create something more elaborate and interesting. To capture that mathematically and formally is still a challenge, but the data is getting there. Achieving an understanding and synthesis of it is still something that we’re working on and that we hope to do in the future, but it’s still a work in progress

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