“I think that quantifying things that don’t have units is rarely fruitful” wrote on Twitter @UnlearningEcon (this was in the context of our discussion of Dani Rodrik’s Economics Rules). The following exchange went like this:
@Peter_Turchin: “But where do units come from? It’s not a linear process.”
@UnlearningEcon “I’m not following you. I like my variables to be measurable, is all”
Twitter is not a good platform for thoughtful discussion, so I will follow up in this blog.
We take measurement units for granted, but where do they come from? The short answer is that you need theory to be able to measure things. But you also need to be able to measure things to test theories. It’s not a Catch-22, because theories and units evolve (are developed) together. This is what I meant by saying that “it’s not a linear process.” We start with a vague idea of how the world works, formulate hypotheses, test them empirically, improve hypotheses, test them again, and so on. After multiple rounds we hopefully end up with a “mature theory”; one that is both internally (logically) cohesive and empirically adequate.
By the time theory has matured, we also converge on a way to measure its critical variables. There is a saying, “If you can’t measure something, you don’t really understand it.” But the opposite is also true: “If you don’t understand something (don’t have a good theory of it), you can’t measure it.”
Measurement depends on having a good theory.
In some cases, theory is fairly simple, and a good-enough theory can be developed empirically, simply by practitioners fulfilling some need. Take measuring weight. People have been using standard weights for thousands of years.
Mesopotamian weights made from haematite. The largest weighs 1 mina and the smallest 3 shekels. Source: Wikimedia Commons
But there is still a theory underlying it. First, the more fundamental quantity is not weight, but mass. The same thing will weigh less on the Moon. Second, when weighing things we actually rely on the Law of Conservation of Mass, which was discovered only in 1756 (by Mikhail Lomonosov). Of course, for most practical applications these complexities are not important, because merchants operate on this Earth, and typically don’t worry about chemical reactions changing their goods.
But let’s take a bit more involved example from physics. When I travel in Europe I have to pay attention to the fact that electric outlets have a different voltage from the American ones—220 versus 110 volts. Now, volts, amperes, and watts that we use so glibly today were not developed by practitioners using the method of trial and error. These units came from several meetings of the International Conference of Electricians in the late 19th century, and were based on the mature theory of electromagnetism (1873, James Clerk Maxwell, following a century of previous advances by multiple scientists).
Michael Faraday delivering a Christmas Lecture at the Royal Institution in 1856 (Wikimedia Commons)
Quantities don’t come with units ready-made; we have to develop ways to measure variables by building logically cohesive, empirically adequate theories.
Now let’s go beyond safe historical examples, and consider a hard-to-measure variable for which we don’t have a mature theory, and which we cannot, therefore, measure. How about social complexity of historical polities (states, empires, chiefdoms, politically independent villages, etc.). Quite a challenge!
Photograph by the author
But I expect that within a couple of years we will actually have a decent theory for the evolution of social complexity. Not mature yet—it will take time—but decent enough to allow measuring social complexity. The critical development is having a wealth of data for historical societies that addresses the many dimensions of social complexity. In the Seshat project we are currently analyzing data on many different aspects of complexity, such as social scale (e.g., what is the population size of the polity or its largest settlement?), the vertical dimension (e.g., how many hierarchical levels in administration are there?), sophistication of the money economy and informational infrastructure. Here’s a slide from my recent talk, in which I discussed our approach to quantifying complexity of historical societies, listing the variables on which our current analyses are based:
What analysis shows is that there is a single principal component that explains more than three-quarters of variation in our world-wide sample that includes many hundreds of historical polities across thousands of years. In other words, as societies become more complex, they increase in complexity along all dimensions, roughly in step. There is such a thing as generalized social complexity!
Why this happens is a very interesting question. We will know once we have developed a mature theory of the evolution of social complexity. But the observation that there is a generalized measure of social complexity is very interesting in its own right. Of course, all the societies in our sample are different, and there are also many variations in how they evolved (as well as devolved) in the multi-dimensional space defined by the specific components of social complexity. There are also other principal components than the first one, although they explain much less variance.
But having a single quantitative measure of generalized social complexity means that we should soon start discussing the units in which it should be measured.
One important decision is how we are going to name these units. Who of the past theorists have contributed the most to our understanding of social complexity? Who is the equivalent of Ampère and Watt? Make suggestions in the comments!