How do big cities differ from small cities (in the ancient past and today)?

Are big cities different from smaller cities mainly in their size? Or do they differ in other ways that go beyond simple population size? Recent research on urban scaling has answered this question definitively for contemporary cities. Large cities ARE different from smaller cities in ways that transcend their size. They aren't simply larger. Yet many of the changes that come with size turn out to be linked systematically to population size.

For example, large cities of course have more miles of roads and and electrical cables than smaller cities. But when we look at roads or cable per person (miles per capita), the quantities are smaller for the biggest cities. This makes sense: if you have twice as many people in a city, you don't need twice as many roads, since some of the new people can use existing roads. While this much is obvious, quantitative research in urban scaling reveals a surprising finding: the way that the miles of roads per person changes with city size is extremely regular. The same quantitative relationship holds if you are studying cities in the U.S., in Europe, or other parts of the world. There is a basic underlying regularity to the quantities of urban infrastructures that get built and used, in cities all over the world.

Other types of regularities have been found by the urban scaling researchers. First, big cities have denser populations than smaller cities. One way to view this is that the areal extent of cities grows more slowly than does the population. The result is an increasing population density in larger cities. But again, this patterns is extremely regular and predictable mathematically. Second, the most remarkable regularity identified by urban scaling has to do with socioeconomic outputs. Whether you measure income, wealth, innovation, crime, poverty, or the number of rock bands, these features all increase more rapidly than does the population size. Big cities not only have more rock bands than smaller cities, but they have more rock bands PER PERSON than smaller cities. Furthermore, the mathematics are predictable. The rates of rock bands--or poverty, or patents--per person follow a very regular quantitative pattern.

Why is this? The basic idea is that as city population grows, so too does the number of social interactions among the residents and visitors to the city. But the number of potential  social interactions can increase at an exponential rate. And these interactions generate information and change. One basic metaphor is to say that cities are social reactors. They magnify the benefits (and negative consequences) of social interactions.

So far, I have been describing urban scaling research on modern cities. See the works of Luis Bettencourt and his colleagues listed below for more information, or see my earlier post on this research. But what about cities and settlements before the modern era? A new paper, published today, provides new evidence that similar predictable quantitative patterns are found in ancient cities. That is, Precolumbian settlements in central Mexico exhibit the same quantitative regularities in population density and social outputs as modern cities. Of course the society, the economy, and the nature of cities were very different back then. But still, the same quantitative patterns are present. To me, this is a remarkable finding.  The paper is:

Ortman, Scott G., Andrew H.F. Cabaniss, Jennie O. Sturm, and Luís M. A. Bettencourt   2015    Settlement Scaling and Increasing Returns in an Ancient Society. Science Advances 1(1).

This is an update and extension of their prior paper:

Ortman, Scott G., Andrew H.F. Cabaniss, Jennie O. Sturm, and Luís M. A. Bettencourt   2014   The Pre-History of Urban Scaling. PLOS-one 9 (2): e87902.

The authors analyze settlement size and other data from the Basin of Mexico Archaeological Survey Project  (Sanders et al, 1979), and find that the quantitative patterns match those predicted by models of urban scaling that were first worked out for contemporary cities (Bettencourt 2013). I find this line of research fascinating, to the extent that I have been measuring cities and the sizes of their central plazas to investigate the quantitative pattern. It turns out that the size of the central plaza relates to the overall city size in a quite regular pattern, but the form of the equation does not match any of the quantities measured for modern cities. Hmmmmmmmm. I'll write more on this later.

For now, the new paper by Ortman et al is important for several reasons:

1. It provides new data on quantitative patterns in the ancient cities and settlements of the Basin of Mexico.
2. The results compare rather precisely to the predictions of the models and to the data on modern cities.
3. This work shows the value of archaeological data for answering interesting questions about cities and urbanism in the past and the present. This only works when the original fieldwork was done well, and when the data are published and made available to other scholars.

Here are some publicity and news items about today's new paper:

An article by Emily Conover in Science Online

An article by Megan Gannon in LiveScience. 

Press release from the Santa Fe Institute

Bettencourt, Luís M. A.
2013    The Origins of Scaling in Cities. Science 340: 1438-1441.

Bettencourt, Luís M. A., José Lobo, Dirk Helbing, Christian Kühnert, and Geoffrey B. West
2007    Growth, Innovation, Scaling, and the Pace of Life in Cities. Proceedings of the National Academy of Sciences 104: 7301-7306.

Bettencourt, Luís M. A., José Lobo, Deborah Strumsky, and Geoffrey B. West
2010    Urban Scaling and its Deviations: Revealing the Structure of Wealth, Innovation and Crime Across Cities. PLoS One 5 (11): 1-9.

Sanders, William T., Jeffrey R. Parsons, and Robert S. Santley
1979    The Basin of Mexico: Ecological Processes in the Evolution of a Civilization. Academic Press, New York.