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.