Springing from my recent post distinguishing types of inter-disciplinary research, I now will go into more detail on a related topic: the difference between studying particular systems that happen to be complex, and studying complexity itself. The main point is that complexity theory includes several commitments related to levels of organization and to there being shared principles/mechanisms underpinning the dynamics of disparate systems. Studying complexity is the overt researching of these commitments and underpinnings. However, most scientists that describe themselves as doing complexity research are not doing that. Instead they are studying particular complex systems and typically ignore the commitments and underpinnings that define complexity science.

As my first example, imagine a generic agent-based model of some social system (you can think of Schelling's segregation model as an example, or your favorite if you have one). Because the agents act autonomously via a set of neighbor-contingent rules, the resulting model is some kind of complex system (see later posts for types of complex systems). And the real-world phenomena it models is also a complex system; in the Schelling case it's people moving in and out of neighborhoods. Using this ABM of a complex system we want to better understand an aggregate property of the system; in the Schelling case that's the resulting segregation patterns. When you are using a ABM like that to study an aggregate property like segregation then you are using a complex system to study a domain specific phenomena, and that is a different project than using the complex system to understand how patterned macro-level phenomena are generated by micro-level agent behaviors.

The above is a case of people studying a complex system (society) with a complex system (an agent-based model). Not all complexity research does even that. In many cases a complex system is modeled as a set of equations, a static network, or a set of descriptive statistics. All of these approaches can be useful for revealing new insights into the modeled phenomena, and as such they can all be used to better understand complexity itself as well. An example would be discovering the number of disparate systems that produce power-law distributions for some property. Of course, there are a dozen different methodological explanations for seeing a power-law distribution, and the substantive explanation will be unique to each domain in which it was discovered. The point is that if you are studying why city sizes follow a power law distribution by investigating the growth dynamics of cities then you are (possibly) studying a complex system, but you are not studying the complexity of that system. If you are instead investigating why cities and war causalities and asteroids all have power-law size distributions then you are possibly studying complexity itself. I say "possibly" because most of the purported explanations I've heard for the observed similarities across systems also do not address any of the commitments or underpinnings of complexity science either.

To help clarify my point, I came up with the following list of projects for a recent presentation on the foundations of complexity science. I asked the audience (and now you) to vote on which is a project for studying complex systems vs studying complexity.

  • Build a model with rule-based interacting agents and measure the aggregate properties resulting from their behavior.

  • Model the relationships among objects/places/people and how those relationships affect aggregate properties across that system.

  • Capture the nonlinear dynamical behavior of a system's properties and measure the sensitivity of detected patterns.

  • Demonstrate how endogenous niche creation by evolving agents switches from favoring generalists to specialists.

  • Determine how system behavior differs when captured as a dyadic bipartite graph versus a hypergraph.


Of course it's a trick. The last one is a methodological question: it is not about complexity or a complex system, it's about how to best capture the system of interest. For the first four it depends on whether you are applying the model to a particular situation/environment/problem or to a general class of related phenomena (possibly across disciplines). That is, it depends on whether you are applying/harnessing the complexity of the situation to help answer your specific domain-related question or you are trying to answer a theoretical question about the complexity of the studied systems. It is not the model that makes the difference -- it's the questions being asked.

Some researchers believe that the best (or only) way to study complexity (or other general, abstract, unifying principles) is through copious examples. So, these people claim, by studying specific complex systems they are studying complexity itself, albeit indirectly. And that by seeing lots of specific complex systems they can generalize the commonalities and gain insight into those general principles. I do not disagree with this claim as a path to understanding complexity in a loose way, but it is not a way to research complexity as a scientific principle. To do the latter requires asking a different set of questions; questions that are not about the specific phenomena being modeled or the problem it was designed to address. Some such questions are the following:

  • Are there coherent behaviors at the macro-level (that are generated from the micro-level) that can be captured in its own set of behavior rules for the revealed macro-phenomena; i.e., can you transform this macro-level into the micro-level for a model of higher-level phenomena?

  • Can you change the interpretation of the model (without changing the model's construction) to make it about a different system? Or, how much do you have to change?

  • Can you provide equivalent explanations of the observed micro and macro behaviors at both the micro and macro levels? Are the inter-level translations lossy or lossless?

  • What aspects of the macro-level are insensitive to what details of the micro-level?

  • Can a different set of micro-objects and/or micro-behaviors also generate the same observed macro-phenomena?


The key area of inquiry for these questions is the micro-macro relationships. Another common (though less informative) way of phrasing these questions is to ask about emergent phenomena: What are they, how do they arise, and when do they appear? I avoid this terminology because people talk loosely about "emergence", and what I am proposing is to establish formally described relationships among the levels of a system's phenomena. Also implicit in the partial list of questions above is a special concern regarding the relationship between micro and macro behaviors. For example, in the Schelling model the macro-phenomena of interest is the observed segregation of agent types. That can be measured in various ways, but neighborhoods in that model don't "do" anything. Contrast that to the "glider" configuration in the game of life; it clearly moves diagonally across the screen via the on/off behaviors of the micro-level. Whether we call both phenomena "emergent" is not at issue; regardless they are clearly different kinds of phenomena.

That last statement has severe import: it means that Schelling's segregation model is a complex system, but it is not useful for studying complexity because all the behavior of the system is at one level (the caveat being that if you expand the scale enough, then with some parameter settings and rule combinations it looks like the neighborhoods grow, and so that growth behavior could be codified as macro-behavior). However, there are benefits to approaching a specific problem with complexity in mind (including modeling it as a complex system) even when the resulting model is not useful for studying complexity itself. Here are some questions you should ask when modeling a complex system if you are interested in harnessing the complexity of that system:

  • What objects/phenomena/behaviors to choose for the micro and macro levels?

  • Do you need more than two levels?

  • Which micro-level phenomena generate which macro-level phenomena?

  • How do the micro-level phenomena generate the macro-level phenomena?

  • How do you identify and measure the macro-level phenomena?

  • Is the relationship between the micro and macro levels underdetermined or overdetermined?


I think many people who are self-described complexity enthusiasts are often addressing these questions (although typically in a very basic way), and they take that to be doing research on complexity. What I am claiming is that they are instead doing research within complexity, but not studying complexity itself. And my observation is that more and more models, and the questions the models are built to answer, are of this variety. Good for addressing questions about a particular complex system, and perhaps abstract enough to apply to multiple systems in a non-trivial way, but not rich enough for direct research into the system's complexity. And even when a model could support such inquiries, those inquiries are not made. This may just be part of the general trend in science of pushing away from basic research. It may also be a symptom of the conceptual mess that complexity science is still stagnating in. However it does neither the field nor the particular researchers justice to call all this research by the same name. Asking questions about the theory of complexity and asking questions using the current (messy) theory of complexity is as different as theoretical physics and engineering.

Yet, despite the rise in complex systems thinking and of complexity models, there has been little progress on understanding complexity itself. And, I claim, this leads to an insufficient ability to harness complexity and use a system's complexity to improve our understanding of the complex systems models we build. We have tantalizing hints of the promise of complexity to unify our thinking across many disciplines, but it remains merely a promise as long as we fail to engage the necessary theoretical research. And the first step to making this theoretical progress is to recognize the differences outlined above; ask different questions and build richer models.