The Urban Equation

As cities continue to grow, scientists are trying to define the “Urban Equation” – a mathematical expression that defines not just a group of buildings, but a complex network of physical and social interactions.  Why?  Because our cities control previously elusive aspects of human evolution.  To understand our cities is to understand us.  In this episode, Luis Bettencourt and Tyler Nordgren discuss various elements of the urban equation.  We see how complex networks give rise to creativity; how to break an urban metropolis down into a series of mathematical symbols; and how our cities are dramatically affecting a cultural connection reaching back nearly 400 years.

Download Episode  (Right-click and select Save Link As…)

This episode was produced by Leslie Chang, Mike Osborne, and Miles Traer.
Additional music by Kevin Macleod (Tracks used: Finding Movement and Perspectives.  License available here)


As of 2008, more than half of the world’s population lives in cities.  Urban populations grow at the astonishing rate of one million people per week.  And more and more of us can’t escape the mobile networks, the busy streets, or the orange sodium glow of streetlamps.  Cities today, and throughout history, serve as the epicenters of social networks and as the hubs of economic growth.  To understand our urban centers is to understand what we value, and understand where we might go in the future.

Today’s cities also provide the backdrop for scientific research.  Luis Bettencourt, a professor of complex systems at the Santa Fe Institute, has chosen a peculiar approach to learning more about our urban centers – he has spent years developing a grand mathematical equation that describes all cities throughout history and across the world.  His “urban equation” provides the theoretical framework for describing a city as a unit of measurement, and creates predictive power for anticipating how cities will grow.

What drives Bettencourt’s urban equation are connections, both physical – roads, power lines, buildings – and social.

“Shop clerks, car mechanics, scientists.  All of that speaks to a sort of social economic activity.  For me, the interesting part of that is how people are connected; how they interact with each other; what they do with each other when they interact,” said Bettencourt.  “You should think of a city as a means to an end.  The connectivity – the telecommunications technology, transportation – these are all means to get to this dynamic.  That’s the nature of the problem that cities solve.”

After years of research, Bettencourt believes that these human connections are what will ultimately drive the resilient cities of the future.  As he explains, cities were not built with long-term resilience in mind.  But imagine what could happen if we decided to focus our energy (pun intended) on creating resilient cities.

As Bettencourt puts it, “The way I think we’re really starting to understand cities is that they’re really networks where our individual agency, imagination, and ability to change things in directions we like can be empowered and amplified.”

Yet, as our cities continue to grow, one term in the urban equation is challenging a connection that affects us in more ways than scientists have previously realized – a connection to darkness.  Tyler Nordgren, a professor of physics and astronomy at the University of Redlands in southern California has worked for years trying to identify how darkness secretly controls many surprising aspects of human life.

Until 200 years ago, when gas lighting was invented, star and moonlight was the only light we had when the sun went down.  Darkness controlled our sleep schedules, harvests, and navigation.  But in recent years, scientists have learned that it plays a remarkably important role in our health.

“There are studies that show that people who work at night, who no longer experience a period of true darkness, are at a higher risk of developing cancers,” Nordgren said.

What drives Nordgren is a lingering question between humans, the night, and evolution.  As he says, “We have evolved, just like other animals, to experience 12 hours of darkness each night.  And in the last 100 years, we are conducting an experiment on ourselves and the animals around us to remove that darkness.”

What happens as artificial lights continue to spill into our night skies?  “The history of science is the history of astronomy, the history of our understanding of where we are in this universe and what it means to be a citizen of the universe,” says Nordgren.

In this way, our connection to the night sky is what connects us to Galileo, Isaac Newton, and countless others who gazed upon the star-filled sky for centuries.  Losing that connection is troubling to Nordgren.  “We are drawing a curtain around our planet.  And that curiosity that has driven us is something that we are now tinkering with by turning off the stars.”

by Miles Traer