A Mathematical Guide to the World s Most Livable Cities

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

By Sophie Guterl

Image: 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.

Source: http://www.scientificamerican.com/article.cfm?id=a-mathematical-guide-to-cities

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