Tuesday, August 9, 2016

My journey in settlement scaling

I am posting today from beautiful Santa Fe, NM. I am here to attend a meeting of our working group on settlement scaling in the ancient world. Our article on scaling at Inka sites was accepted by the Journal of Archaeological Science, and it was posted online yesterday (Ortman et al. 2016):
Mantaro region, Peru

This paper is a particularly important step in our long-term objective of exploring the application of settlement scaling theory in the ancient world. To explain why, let me step back to 2013, when I first got involved with this project. I was invited to the Santa Fe Institute in summer 2013 to explore the notion that urban scaling theory should be applicable to ancient cities. Luis Bettencourt and Jose Lobo had been working on scaling in contemporary cities for some time, and Scott Ortman had begun to explore an application to the pre-Spanish Basin of Mexico. They were interested in how an expert in ancient cities would react to this research. I knew nothing of scaling when first invited, so I tried to read up on the topic before my visit to Santa Fe.

It was fascinating to me that the quantitative expression of many urban attributes could be predicted by city size in groups or systems of cities in the modern world. Many key economic features are amplified in urban settings, to a greater extent in larger than smaller cities. In economic geography, these changes associated with large cities are called "agglomeration effects." My reading of economic geography and urban economics in 2013 led me to think that agglomeration effects and quantitative regularities in contemporary city systems were due to processes in the contemporary economy. That is, these regularities were produced by the globalized capitalist economy.

I went up to the Santa Fe Institute ("SFI") in 2013 ready to argue that these scaling regularities should NOT apply to ancient cities. Ancient economies were not capitalist: wage labor was limited or non-existent, land was not a commodity, and the whole structure and functioning of the economy in ancient state societies was radically different from the contemporary situation (the advanced economy of imperial Rome may be a partial exception, though). "You guys are barking up the wrong tree" was the essence of my message for the scaling folks at SFI.

Within a couple of hours of my arrival at SFI, however, Luis, Jose and Scott had convinced me that the scaling regularities were NOT dependent upon the capitalist economy. Luis had just published his paper in Science (Bettencourt 2013). This paper presents a quantitative model that predicts, rather precisely, the scaling regularities observed in city systems today. But the model is not based on wage labor, firms, private property, industrial production, or other attributes of the modern capitalist economy. Instead, it is based on the way individuals move and interact within the confines of the urban built environment. Networks of individuals, interacting socially and exchanging information, were the foundation of Luis's model.

If Luis is correct (and I have since come to accept that he is), then there is no logical reason why premodern cities should not exhibit the same regularities found in modern city systems. I found this possibility quite exciting, and immediately set out to explore it further. This first meeting was on a Monday, and I was scheduled to give a public lecture at SFI on Tuesday. The theme of that lecture was the way ancient cities differed form modern cities, and how that implied urban scaling should not work in the ancient world! I had to scramble to revise my slides and lecture. That talk was later turned into a paper, coauthored with Jose, about the similarities and differences between ancient and modern cities (Smith and Lobo n.d.).

Anyway, logic suggested that the processes underlying Luis's 2013 model should also have operated in cities before capitalism. Furthermore, there was no reason why these processes should not apply to smaller, non-urban settlements. That is, village systems should exhibit the same scaling regularities. I started working in two directions to explore the possibility that scaling would apply to ancient and nonurban systems of settlement. First, I had to convince myself that this was indeed the case. The scaling framework implies (but evidently does not require) that in any urban system, people were able to move around easily, from the countryside into cities, and between cities. Yet many people in anthropology and history believed that peasants were typically tied to their fields and did not move as much as people do today. So I looked into the extent of geographical mobility in the ancient world, and found that movement was more prevalent and extensive than many had thought. This was published in World Archaeology (Smith 2014).

A central concept in the scaling model is the notion that interactions among individuals, and the exchange of information that takes place, is one of the driving forces of social and economic change. This idea came out of economics. But if such interaction is so crucial, then why hadn't I heard about this in anthropology and sociology? After all, these fields are devoted to the study of how individuals interact and exchange information. Again, I had to convince myself that this concept made sense in terms of how anthropologists and sociologists understand society. I had to make sure this wasn't another case of economists making up silly things about individuals and their behavior in order to preserve the purity of their models. Lo and behold, this concept of the generative role of social interactions is in fact quite common in the other social sciences. Perhaps it was my own ignorance that had prevented me from seeing this, or perhaps issues are simply not framed this way in anthropology and sociology. So I wrote a paper on this, which is now in press in an edited volume (Smith n.d.). I focused on architectural historian Spiro Kostof's concept of "energized crowding" in cities as a good label for the basic processes involved.

So, I have now convinced myself that the scaling framework fits with what we know of societies and cities in both ancient times and in the nonwestern world. They say that converts make the biggest fanatics, so maybe that explains my excitement about scaling. But my enthusiasm is based to a major extent on the second direction of my work scaling: the empirical study of quantitative patterns in ancient settlement systems. This work is truly a group effort. Our new paper on Andean scaling is a good example.

Since our first session in 2013, we have been scouring archaeology and history for datasets that can be used for scaling. The data requirements are actually somewhat stringent for past urban systems. Even where we have decent population figures for an urban system, it is hard to measure economic productivity or the other variables we want to scale against population. We had a couple of working groups, with colleagues invited to Santa Fe.

Scott has taken the lead in most of the archaeological cases. Beyond his initial forays into the Basin of Mexico settlement pattern data (Ortman et al. 2014, 2015), Scott has found the scaling regularities in a couple of samples of North American village societies (Ortman and Coffey 2015). He and his students took the lead with the Andean data in our new paper; I mainly contributed some contextual and framing information. I made sure we emphasized that the Inca were one of the few large-scale ancient state societies that did not have markets, money, or commercial exchange. The fact that we find, again, the same scaling regularities in a society with a non-commercial economy is simply astounding; this is one of the major points of significance for the new paper.

My student Rudy Cesaretti was our RA on this project a year ago, and he took charge of a study of scaling in medieval European towns (Cesaretti et al. 2015). This is a great dataset with fantastic results. I wish PLOS-One would get off their duff and complete the review! Rudy is now working on a paper that uses data from Henry VIII's beard tax to show superlinear scaling! I want to be a co-author just so I can add "Henry VIII" and "beard tax" to my CV! I took the lead in applying the scaling methods to the question of plaza size at Mesoamerican settlements. We included a sample of Aztec-period sites (Smith 2005), and Alanna Ossa contributed data from her own research on plazas in the Mixtequilla area of Veracruz (Ossa 2014), and we found some published data on the Palenque region. When we scaled plaza size against population, we got statistically regular results, but they don't match any known scaling coefficient. Oops. What is going on? And now Scott's post-doc, Jack Hanson, has produced the first scaling paper on Roman cities (still in preparation, I think).

We now have a good conceptual foundation, and empirical results supportive of Luis's scaling model are piling up. We will have a symposium at the 2017 meeting of the Society for American Archaeology. Settlement scaling is expanding through the historical and archaeological records. Resistance is futile. I'll bet if we scaled the size and structure of ships like the Borg collective and the Enterprise against their population, we would not be surprised by the results.

I would guess that many people remain dubious about this enterprise. Personally I am baffled and amazed at our results. Wow, where does all this cross-cultural and cross-historical regularity come from? As my ASU colleague Charles Perreault has pointed out, there is nothing in our background in anthropology that would have predicted these results, or that can explain them. So, go read some of these works and see for yourself why a growing number of scholars are getting excited about settlement scaling.

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

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.

2015 Settlement Scaling and Increasing Returns in an Ancient Society. Science Advances 1 (1): e1400066.

Ossa, Alanna
2014 Plazas in Comparative Perspective in South-Central Veracruz from the Classic to the Postclassic period (A.D. 300-1350). In Mesoamerican Plazas: Arenas of Community and Power, edited by Kenchiro Tsukamoto and Takeshi Inomata, pp. 130-146. University of Arizona Press, Tucson.

Ossa, Alanna, Michael E. Smith, José Lobo, and Scott Ortman  (n.d.)  The Size of Plazas in Mesoamerican Cities: A Quantitative Analysis and Social Interpretation. (paper under review)

n.d.   The Generative Role of Settlement Aggregation and Urbanization. In Coming Together: Comparative Approaches to Population Aggregation and Early Urbanization, edited by Attila Gyucha. State University of New York Press, Albany.

Smith, Michael E. and José Lobo
n.d.   Cities through the Ages: One Thing or Many? (unpublished ms).


  1. Great post. However, I suggest you to read this recent paper about the scaling laws in Europe: http://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0159465

  2. @Marco - Thanks for this. Here are 2 of the conclusions(from the abstract):

    "The results suggest that the GMP/pop super-linear scaling represents a phase of economic growth rather than a steady, universal urban feature."
    --- The fact that we are finding superlinear scaling in a variety of premodern urban systems (15th C Britain; Inca period Andes; Late prehistoric North America) suggests that superlinear scaling is not just some transitional phemoneman for modern cities in a capitalist economy.

    "The results also suggest that relationships between cities are embedded in their political and economic context and cannot be neglected in explanations of cities, urbanization and urban economics."
    --- This isn't very useful - OF COURSE city relationships need to take into account the social, political, and economic context of urban systems. But what is remarkable to me is that the same scaling patterns are found in many diverse urban systems, despite their great differences in economics and politics.

    The scaling work for contemporary cities was critiqued by:

    Arcaute, Elsa, Erez Hatna, Peter Ferguson, Hyejin Youn, Anders Johansson and Michael Batty (2015) Constructing Cities, Deconstructing Scaling Laws. Journal of the Royal Society Interface 12(102).

    And this was countered by:

    Bettencourt, Luis M. A. and José Lobo (2016) Urban Scaling in Europe. Journal of the Royal Society Interface 13.

    But the math is above my pay grade!