How will our cities grow?

Urban scaling shows that as cities expand, the trajectories of measures such as wages, crime and carbon dioxide emissions are somewhat surprising.

Hyejin Youn is a postdoctoral fellow working with the Santa Fe Institute’s Cities and Urbanization team, which includes Luis Bettencourt and Geoffrey West. Her expertise is in human behavior and statistical analysis on population distribution. She said the best way to create sustainable growth in our cities is to understand the mathematics behind their growth. Excerpts of our recent conversation are below.

Why is it important to study urban areas?

More than half of all people now live in urban areas, which
increased up to 80 percent in about 40 years, as reported by the United Nations. The rapid urbanization implies that understanding urban dynamics is a key to our sustainability.

Studying cities reveals the advantages and disadvantages of urban
life. We know cities usually have more educated, wealthy people but also have more crime. However we only recently started looking quantitatively at by how much the cities are educated and dangerous.

In the past we haven't been able to compare cities' performances over time because data were not available across cities. Rather, data were gathered over time for a particular city or groups of cities and this data was inconsistent with the data gathered for other cities. Cross-sectional data for many cities allows us to compare many cities, systematically and consistently, to get a better idea of trends and patterns. This allows us to create a generic baseline for cities for, say, carbon dioxide emissions. From that we can then see the significant or unique features of a particular city, what urban scaling reveals. We can also think in a more macroscopic way than those conventional studies have allowed.

The relationship from these cross-sectional data analyses we now know as urban scaling -- a power-law that describes how quantities increase with city size. My colleagues Luis Bettencourt and Geoffrey West of Santa Fe Institute are pioneers of these beautiful urban scaling forms. The power-law is the simplest yet most powerful, as the name indicates, mathematical form. This power-law fascinates lots of researchers because it reveals mathematical relationships at many scales of cities.

How are you using urban scaling in your work?

According to urban scaling, cities whose population doubles in size will have 15 percent more than twice socio-economic quantities such as wages, GDP, number of patents produced and number of educational and research institutions. The significance of this work comes from this systematic increase. The growth of cities also have negative aspects like more crime and more epidemic disease.

In America you have 366 metropolitan areas, so you collect 366 numbers for things like crime, number of patents, income, population, and then you plot them. You can reduce these trends into a mathematical function that’s called scaling. If you take a population of 1 million and double it, [the total population] becomes 15 percent richer, 15 percent more susceptible to crime, you’ll see 15 percent increase in wages, etc. Each person in a sense is more efficient and faster at these quantities—whether we’re getting more efficient at being better or worse.

What was most surprising about the data?

We know cities are richer, denser and wealthier and more creative, but the surprising part to me is those trends coincide with each other and the trend is consistent. They all change in unison. We want to see the reason behind why all these trends are the same.

The surprising thing is that the relations of city size with this negative aspects are the same mathematical form as those with positive aspects of cities. All of these expected socio-quantities can be used as a baseline of policy-making.

How can city planners use this information?

These trends will help us understand what will happen. So if you expect the city to double in a certain time, you can expect crime will be 15 percent more when the population doubles, and you can prepare for that. If you know what’s coming in the future, you can budget for infrastructure. Also if you know the expected quantity, you can see how your city performs and figure out how to improve your performance.

It’s not really about doubling the size of cities, but that makes it easier to think about. It’s the extrapolation of this trend. It’s not yet applied to any practical policy, but we expect it will be in the future.

What are you working on now?

As a statistical physicist, I studied human behaviors in transportation networks and the structural features of distribution of human population when I was a graduate student. Currently we are looking at carbon dioxide emissions of cities and found these quantities also have systematic trend in accordance with urban scaling.

What are you finding in terms of carbon dioxide emissions?

We find that you save energy by having a larger city. CO2 emissions, especially of transportation sectors, are saved by approximately 10 percent by doubling the city size. Larger cities usually have better transportation infrastructure and more people use public transportation than private cars. Everything is concentrated in a small area so people can walk. We even find that if you measure how fast the people walk in the city, you see the increase when you double the size. In a larger city, people walk faster than people in smaller cities.

This post was originally published on Smartplanet.com