In praise of reductionism

Suppose I have a business making clothing. I want to know how many items of what size to manufacture. If I can know the distribution of men's and women's adult heights in the U.S., I can plan how many shirts or pants to make of each size. Assume that the height data are not readily available. So I draw a sample of people, measure their heights, and calculate means, standard deviations, quartiles, and probably other measures of the distribution. I think that an anthropologist down at the U might be interested in my height data, so I head downtown.

The first anthropologist I run into is a cultural anthropologist. When I show him my data, he chides me for being simplistic. How can I possibly think I have described my population of people when I have only looked at their height? We want to know so much more about people, she says. My little study is ridiculously limited and it can't help him understand people at all. It is reductionist, It is useless. Why did I bother.

Then I run into an evolutionary anthropologist. She likes the data I gathered. She can compare these results with her own measurements of height in Lower Slobovia, and learn something about human height variation. To her, these are interesting and important data.

For my own purposes, and for the evolutionary anthropologist, my little study of height provides important data. It helps each of us answer a question of importance about height. Is this study rigorous and useful? Yes.It is reductionist? Yes, again. Is that bad? Only for the cultural anthropologists who wants more information and more nuance.

You can probably see where I am going here. Over the past couple of years, I have encountered considerable opposition to our work in settlement scaling from archaeologists, historians, and others.

(On the scaling work, see this post from 2014,  or a bunch of posts in Wide Urban World; this is the latest post there.)

These people  complain that this research is reductionist. How can we possibly understand ancient settlements by just comparing the population to one other variable using a graph and an equation? Cities and settlements are far too complex to be explained by two variables. But we have never claimed to explain ancient cities or settlements on the basis of a scaling regression. Instead, we claim to produce a better understanding of a particular limited domain of ancient settlements. If you want a comprehensive analysis of individual ancient cities, then be my guest. I have done that kind of thing (Smith 2008), and it is a useful approach. But now, when I am addressing a limited domain using a few variables, please don't accuse me of reductionism, as if that charge invalidates the research.

This is not just me feeling oppressed by clueless reviewers, colleagues, audience members, and such. The roster of the reductionism naysayers I have encountered includes some good, smart scholars. In fact, even very well-known and respected scholars fall victim to this malady of poo-pooing single indices or variables for not explaining everything one might want to know about a phenomenon. For example, here is what Thomas Piketty, in Capital in the Twenty-First Century, says about the Gini index:  "Indeed, it is impossible to summarize a multidimensional reality with a unidimensional index without unduly simplifying matters and mixing up things that should not be treated together" (Piketty 2014:266). As pointed out by Branko Milanovic (2014), Piketty dismisses the Gini index as an "aseptic" measure of inequality. But who has claimed that the Gini index will tell us everything we want to know about inequality? It tells us one kind of thing, and it allows us to compare separate contexts.

The Gini index, and my hypothetical measure of height, are intentionally reductionist. Their goal is NOT to document or explain everything about some domain. Rather, their goal is to abstract a key dimension from a complex reality, to reduce the messy details to a single measure so that comparisons can be made among domains. Comparative analysis is impossible without simplification, without ignoring a lot of details. If  you want to say, "I'd rather do a detailed comprehensive analysis of one case," that is fine. If you want to say "I don't like statistical studies or regression analysis," that is fine (well, maybe its not really fine, but it is not too uncommon). But please do not say "Because I happen to like details, then your reductionist measure is worthless."

I gave a talk in Europe recently promoting comparative approaches to past urbanism. I made the point that in order to compare cities, one had to abstract some key aspects and ignore many details. This allows one to generate useful and interesting conclusions. When I was done, the first question (from an urban historian) was,"Isn't all this quite reductionistic?" My answer was "Yes! And that is precisely why I do it!"

Take a look at my post from last year , "Against nuance," for some related ideas.

Milanovic, Branko
2014    The Return of 'Patrimonial Capitalism': A Review of Thomas Piketty's Capital in the Twenty-First Century. Journal of Economic Literature 52 (2): 519-534.

Piketty, Thomas
2014    Capital in the Twenti-first Century. Belknap Press, Cambridge, MA.

Smith, Michael E.
2008    Aztec City-State Capitals. University Press of Florida, Gainesville.

Urban scaling arrives in archaeology

Urban population dynamics

The first application of the methods of urban scaling to archaeological data was published last week (Ortman et al. 2014). This should be the first of a series of archaeological applications of urban scaling research, a trend that has the potential to revolutionize scholarly understanding of the basic processes of urbanization. While some of the discussion is pretty technical, the basic results and their implications are clear. The population sizes and areas of a large sample of ancient settlements conform to the expectations of urban scaling power laws as identified for contemporary cities. Yes, I said settlements. Not just cities, but smaller settlements as well, all conform to the scaling model. I discussed the scaling research on modern cities in Wide Urban World last fall, based mainly on Bettencourt (2013).
in PLOS-one (

Superlinear scaling (Bettencourt 2013)

To summarize briefly, the relationships between the sizes of contemporary cities, and various social, economic, and spatial phenomena, conform two two basic power law patterns called superlinear scaling and sublinear scaling. Superlinear scaling has been found for diverse social outputs, from economic productivity to crime. It means that as the population of cities increases, the level or frequency of these traits (per capita) increases faster than the rate of increase of the population. Sublinear scaling means that the level or frequency of other traits increases more slowly than the population does. This has been found for two types of urban phemonema: infrastructure, and the area or footprint of the city. The infrastructure pattern is pretty obvious: if you have twice as many people, you don't need twice the length of roads or cables (per capita). As for area, the pattern indicates that larger cities have a higher density than smaller cities. What is fascinating and important about these patterns is that the rates of increase (measured by the slope when plotted on a log-log graph) conform to a narrow range of values. In other words, these processes follow trajectories with similar quantitative parameters.

Sublinear scaling (Bettencourt 2013)

The new paper focuses on this latter factor. The authors ask whether the area of Prehispanic settlements in the Basin of Mexico increase at the equivalent rate as in modern cities; do the data conform to the same power laws? The answer is yes. The authors analyzed a mass of settlement pattern data from the surveys of William Sanders, Jeffrey Parsons, and others. Not only do larger settlements have a higher density than smaller settlements, but the increase in density occurs at a predictable rate. Why is this so revolutionary? Because it suggests that not only do ancient cities follow the same quantitative laws of growth and change as modern cities, but non-urban settlements conform to these patterns as well.

As my students are probably tired of hearing, I think urban scaling is a really important topic of study for archaeology right now. I am in the process of measuring a bunch of Mesoamerican urban maps, and before long I'll be able to test whether they exhibit super-linear scaling. Actually, I should say that I have a talented undergraduate, Alexandra Norwood, measuring the maps! And I know Scott Ortman is working on other data, as are a few other colleagues.

I approach this topic as a convert, and they say that converts are the biggest fanatics. When physicists Geoffrey West and Luis Bettencourt announced that finding power laws of urban scaling meant that they had found "a unified theory of urban living (Bettencourt and West 2010), and could point for the first time to a "science of cities," I was highly skeptical. My skepticism came more from these grandiose claims than from the content of the scaling research (which I didn't understand at the time). If there is to be a science of cities, it will have to be considerably broader than finding a few power laws.

Then I was invited to spend a week at the Santa Fe Institute to discuss ancient cities: In what ways were they similar or different from contemporary cities? Can we expect scaling laws to work for ancient cities? How could archaeologists test these models? In preparation for my visit, I read a bunch of literature in economic geography and urban economics. It seemed clear the the processes of urban growth are at the heart of the scaling relationships, and urban growth is the major theme of these disciplines today. I found that the key processes identified for contemporary cities center on agglomeration effects. The spatial concentration of labor, firms, and information in cities is synergistic, and creates economies of scale and increasing returns, and many authors suggested that these are responsible for regularities like the scaling effects. But premodern cities did not have capitalist economies, and agglomeration effects either did not exist, or else existed at a much smaller scale than in contemporary cities. Urban growth in the past was a quite different phenomenon than urban growth today.

So when I arrived in Santa Fe I had two propositions in mind:

• IF agglomeration economies are the cause of scaling laws today, then ancient cities should not exhibit similar scaling patterns, because they lacked agglomeration economies.
• If ancient cities DO exhibit scaling laws like contemporary cities, then the causes must lie at a more fundamental level than agglomeration economies.

After only a day of discussion with Luis Bettencourt, Geoffrey West, José Lobo, and Scott Ortman, it became clear that the processes that generate scaling regularities in fact lie in the basic realm of social interactions among people within a delimited space. This is the basis of Luis's model of contemporary urban scaling (Bettencourt 2013), although I was too obtuse to pick up on it until I got to Santa Fe.

Urban dynamics ???

If it is indeed the case that social interaction generates scaling effects, this opens up new avenues of research. Scaling should work not only for premodern and ancient cities, but also for non-urban settlements as well. Processes of rural-to-urban migration, and settlement nucleation become central to these dynamics. I wrote a paper on these processes, now under review at World Archaeology. One of the conclusions is that in premodern societies, spatial movement (within and among regions) was quite common, including nucleation and urbanization. There were few barriers to people moving into settlements, and thus there were few barriers to settlement growth. One implication is that urbanization and nucleation dynamics in the past could generate interactions and growth comparable to the agglomeration economies of the modern world.

Jeff Parsons

I think research in urban scaling has the potential to illuminate basic human processes of social interaction and their effects on society. Those effects include urbanization, economic change, and a host of other social phenomena. Ancient cities were different from modern cities, and the specific urbanization processes were different, yet several kinds of end result (such as the amount of infrastructure, or the level of social outputs) were quite similar. This situation is nothing new to those who work with complexity theory, but it is something that the rest of us need to learn. And for me, the important implications lie not in the abstract realm of scaling parameters and network structure, but in the on-the-ground realm of human behavior and social processes. I wonder if Jeff Parsons ever thought his survey data would be analyzed and discussed by physicists.

When is the last time scholars from other disciplines came knocking on your door, saying they need archaeological data in order to answer fundamental scientific questions?

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

Bettencourt, Luís M. A. and Geoffrey B. West  (2010)  A Unified Theory of Urban Living. Nature 467:912-913.

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.