Where Do (Measurement) Units Come from?



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“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:

complexityWhat 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!

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Lee Wang

I hope this will finally lay to rest anti-‘Whiggish’ linear evolution crowd. Of course it won’t.


Ibn Khaldun and his concept of asabiyya which is of social cohesion and is non-linear.


Interesting post. We do take measures for granted. And the epistemological questions behind how we come to have units are fascinating both from a historical and philosophical point of view. One of my favorite books in history and philosophy of science is precisely on the topic : Inventing Temperature by Hasok Chang. How can one measure temperature ? By using a thermometer. But how did it come to be ? In order to build a thermometer you need to be able to measure temperature, but in order to do that you need a thermometer. Chang’s book shows how that was done, and even though we’re talking hard sciences, it was a fairly complicated process. I’m pretty sure, that you’ll enjoy it Peter.

Ross Hartshorn

It reminds me somewhat of the debate in biological circles on whether there is such a thing as different levels of complexity between species, and whether it has been evolving towards greater complexity over time. In recent years the Human Genome Project and other research gave the surprising result that the size of our genetic code does not seem to be a good measure of the complexity of the organism (e.g. humans and quite simple worms can have similar sized genetic codes). So, the debate on whether there has been a general trend towards greater complexity has been confused by the problem of how one measures the complexity of an organism.

Given your background in biology, I wonder if there are lessons there (positive or negative) that could be applied?


Let’s call it the Turchin. It’s distinctive enough and you well deserve it.
Although you’ll probably want to be humble and call it the Khaldun.

Martha Dunham

May I suggest Mead or Bateson. Not that you don’t merit the distinction.


There are really two issues here. The first is that as we attempt to reduce complex, changeable social phenomena to measurable units, we typically lose something. Without knowing much about your specific example, this is evident from what you say: your social complexity measure “explains more than three-quarters of variation in our world-wide sample”. While somewhat impressive, this is clearly much less accurate than Newton’s laws, which can predict things to however many decimal places. And I expect that unlike many physical theories, this one does not predict its own shortcomings. In other words, it is right until it isn’t, something that is common in the social sciences (hello macroeconomics). It’s possible the measure itself is hiding important non-linearities and perhaps things fundamentally not amenable to maths/measurement (I could be wrong here).

More importantly, however, you and I are talking at cross purposes. I do not completely object to attempts to measure the social, economics and psychological worlds. My objection is to models in economics which have variables that are poorly defined (often only by their name), with no attempt given to define how they might be measured, what they can predict and so forth. An earlier draft of my Rodrik review actually used the example of ‘effort’, common in the contract literature. Workers exert more effort and this increases the chance they will produce a higher output. Yet no effort (!) seems to have been put into exploring what this ‘effort’ actually means, estimating it, and so forth. It is a variable defined only in terms of itself. And all you have is a mathematical model whose conclusions are implied almost directly by its assumptions, but is completely up in the air as far as reality is concerned. This is a problem.

Derek McDaniel

The problem with the economic treatment of units is quite simple, economists do not adequately recognize the social and cultural construction of the units they use.

Looking for correlations between GDP and well being is like looking for correlations between heads collected in headhunter societies and well being.

Keynesian principles use aggregates like GDP, employment figures, inflation, (and more questionably “interest rates”). But the context in which these figures are valid is very specific: “Should the government spend more or tax more?” If we try to use these figures empirically outside of this context, results will be garbage and not reproducible.

The purpose of tax is to force participation in governmental fiscal programs, implement regulatory programs, and encourage private enterprise to operate in a manner supportive of the overall political program of the nation.

The political and social construction of governmental entities and business entities could not be more different. Thus, it is complete nonsense to claim they are subject to the same financial constraints. Banks and other entities are subject to solvency constraints BECAUSE OF the political program of the U.S. government(or other sovereign country) wherein it imposes accounting rules and taxes.

Economists spend all their time tweaking random inputs and outputs, unwilling to evaluate, debug, or disrupt the internals of this social and political machine. They adopt our social cultural units, but fail to examine their meaning and context (others do this to a degree, for example, David Graeber).

While the philosophical, mathematical, and scientific question “Where does measurement even come from?” is intriguing (what is a dimension? what is a physical phenomenon? What are numbers? etc), we really need to be asking “Where does this specific measurement come from?”

That last question always has a specific answer. Temperature, which you brought up in comments above, is the average kinetic energy of molecules(at least in an ideal gas, i believe). Economic variables all exist in a political context, and their measurement is primarily relevant to the dynamics of that polity and less so to other social groups and phenomenon.

If economists and other social scientists want to be useful, they need to come up with their own units that make sense for describing social structures and social phenomenon. Your “social complexity” idea, is a starting point, at least, in that direction. But already I see some problems with that measure, because it should also be valid in a completely general biological context AND computer science context, otherwise you are unnecessarily limiting your definition of social peers and society.

Derek McDaniel

If you want to measure complexity etc, I think information theory might have good tools for that kind of thing. But like you say, it’s very ambitious and not the most useful pursuit.

I think it’s more important to describe the social, cultural, and political aspects of the units we are already using, like the dollar. Like I was saying, I think these units are useful, but only if we keep them within the right context.

This context is about federalism and the political roles of parallel political entities: local, state, and federal governments. Federal imposes rules and standards on local and state governments. Problems arise when the actions and rules of federal government block local and state governments from resolving issues. This can happen because everyone needs the dollar to operate, but only the federal government controls the dollar. I’m saying that this relationship needs to change.

Dollars should be an important part of the operations of state and local governments, but if investment, taxation, spending, and saving all depend only on the dollar, it significantly ties the hands of all these entities, and puts pressure on federal government to perform a complex highly involved political role. Then what happens when federal government is blocked by political gridlock or over-leveraged politically and expected to solve all of our problems?

My current attitude is that federal should enforce standards (wage standards, safety, environmental, etc) but allow political and business entities to operate very autonomously, including by issuing their own currencies.

Most people don’t recognize that the units we use are critically important parts of this problem, which makes your article so timely.

Mike Riddell

Why don’t we measure ‘work producing social or environmental good’, rather than complexity?

After all, what get’s measured gets done, especially if the measurement facilitates investment into the work being done?

At some point in history, there must have been a social or trade-based need to regularise the weight of something. Perhaps in a market, say. The same for distance….

Nowadays, there’s a need for work to produce public good. A lot of people simply don’t know what good looks like.

Let’s define what good looks like, then measure it?


It seems network effectiveness is what we are interested in measuring rather than complexity. A simple switch can be more effective than a complex Rube Goldberg device ending in a switch.

That said, complex systems with extensive specialization and integration can work as more effective networks. They can solve more problems better on net for agents within the network. Thus the network can be more adaptive for the network in total and for the agents.

I suspect the unit of measure is net problems solved though, not complexity. The problem with net problems solved of course is the subjective nature of a solution.


In a very generalized form- I’ve found complexity tends to demonstrate “folding behavior”. Look at a city, it’s taken space and folded it over many ways to create more space, three dimensionally. Same with the human brain- it’s folds and wrinkles allow for denser packing and more interactions. Letters in the alphabet are folded lines, books folded strings of text. Social complexity may have parallels where it’s not levels of hierarchy but “folded” interrelationships that allow for denser packing… Love your work, all the best

Steve Heise

A Verhulst (or its inverse) as a unit of what level of population can be supported by the institutions of the society.


It’s a mouthful as a standard unit name, but Thucydides seems to have been among the first to recognize that some of the highland or islander peoples surrounding the classical Greeks represented an earlier stage of sociopolitical development, one that would have prevailed even in Greece until relatively recently. Book 1 (the Archaeology) proposes a process of escalating social organization in some (perhaps fanciful) detail.


If you want a theory of complexity, the first step is to define it. Without a definition, you can’t quantify. Ask two people what complexity means and you get two different answers (three or more if at least one of the persons you asked is a lawyer).

As you pointed out, there are several dimensions of social complexity. So overerall complexity is a volume in a multi-deminsional parameter space. So you need several definitions, one for each aspect. You have quite some work to do.

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