(Note: This is a draft of the paper I gave today in Tübingen at CAA 2018, in a session organized by Iza Romanowska, Tom Brughmans, Benjamin Davies)

I will discuss some of the main lessons that emerge from complexity theory and chaos, and how they apply to the study of the past. These ideas are not new (Bentley and Maschner 2001). Some have been with us in their modern form since at least the 1950s, and they have been with us in one form or another for much longer. Some of them have been discussed explicitly in archaeology since at least the 1970s (Cooke and Renfrew 1979). You may recognize many of them from your own work.

However, I see some value in going over them once in a while and reflecting on how they should affect the way we think about the past, and the way we interpret archaeological evidence.

Complex patterns do not require complicated processes

Early computer simulation and modeling in archaeology tended to produce models that were complicated rather than complex. They sought to replicate the human social experience, which to us appears complicated. In order to get buy-in from the archaeological and wider scholarly community, they had to produce artificial societies that were convincingly human in their unpredictability and their incomprehensibility.

It wasn’t until the late 1980s that awareness grew that at least some human social phenomena are not complicated. They are simply complex. Complex patterns can be, and often are, the result of repeated simple interactions rather than of complicated, impenetrable machinery.

What looks complicated and inexplicable from the limited point of view of the participant or the agent, is revealed to the outside observer as the outcome of a limited number of simple interactions between a limited number of objects, using a limited set of simple rules.

That is, after all, how much of nature works. But much of archaeology, anthropology, and social science in general, are not quite ready to admit that human societies are part of nature. To the post-processual or post-modern reaction that nature is a social construct, the complexity informed modeler’s response must be that society is possibly a natural construct.

Contrary to the human exceptionalist’s firm belief that the tools used to study nature are inadequate for the study of humans, we must venture that, based on the lessons of complexity and chaos, we are at least willing  to try to understand our own confusing societies  and their bewildering histories  as the outcome  of repeated, simple interactions, just as if they were simply part of nature.

Unusual changes don’t require unusual causes

In the classic sand pile model of a complex system (Bak, Tang, and Wiesenfeld 1987), there is only one type of object: a grain of sand. There is only one type of event: a grain of sand is added to the pile. There is only one kind of interaction: a grain of sand exerts force on another. The consequences  of that single type of event, which exists in a world  where there is one type of thing  and one possible relationship,  range in magnitude  from a simple local nudging of a few grains, to a complete reorganization  of the entire pile, in the form of a system-wide avalanche. The barely perceptible local change and the system-wide avalanche share one important thing: they have the same proximal cause.

The normal, that is the most frequent impact of the event, is very local. Only occasionally and under very specific circumstances do we see a global impact. A power law function describes the relationship between the frequency of the most local events and the most global. The most local events are overwhelmingly the most frequent and would appear to the casual observer as normal. The most global events are very rare and might appear, depending on the time scale of observation, as extraordinary.

This is an important point for archaeologists. An observer  with a restricted view of the sand pile, both in space and time, is likely to find  that avalanches are so extraordinary  that they defy all explanation. An observer with a perspective that is spatially global  but very limited in time  might find an avalanche equally puzzling. An observer who has a global spatial perspective  and a long view of the pile has a much better chance  of discovering that avalanches  are not arbitrary phenomena  beyond all explanation.

The central point is that there is no difference between the cause of a very local disturbance and the cause of a global transformation. In other words, catastrophes don’t differ from routine events in their observable causes. Events which are apparently extraordinary do not necessarily require  extraordinary causes.

The renewed importance of context

What differentiates avalanches from local disturbances is not the cause, or the type of event, but rather the context in which the event occurs. Whether the change is local and hardly noticeable, or whether it consists of a catastrophic avalanche, the cause is the addition of a grain of sand.

The difference is the organization of the sand pile. As the grains are added, most system states will generate a local disturbance. Once in a while, the sand pile will be organized so that the addition of a grain will cause an avalanche. The context of the event is what matters. If the system is critically self-organized, the same old routine event that normally goes unnoticed will have massive and system-wide consequences.

The idea of context has always been central in archaeology. But we normally look at the spatial and relational context of the objects we find. What is the spatial relationship between that flint axe and that bit of charcoal? Are they in association? What is the context of that settlement area? Is it associated with that paleo-shoreline?

Complexity theory encourages us to radically expand our notion of context. Instead of thinking about the context of the objects we find, we have to think about the context of the events that generated those objects and their locations. In what context did the events take place? Was it a critically self-organized context?

Since an avalanche is an unfolding process rather than a static find or object, we must consider context over time. How far-reaching in time and space were the consequences of the event that produced the objects we found? Was it a local disturbance, or a system-wide reorganization? Are the object and its location the result of such a complete reorganization? These are the questions – we should be asking.

Agency and intentionality  are related  but different

One of the inescapable consequences of complexity theory for archaeology is that while intentional actions are important drivers of change, intentions are ultimately irrelevant to the outcomes of human actions. Just as the addition  of a grain of sand  to a pile  can have a local  or a global effect,  depending on the context  in which it takes place,  common intentional human actions, like selecting certain kinds of seeds  over others, killing a brother-in-law, or adding a line to a pottery design,  can result  either in a local disturbance  or in a complete  and wide-ranging re-organization  of society. The local disturbances will be frequent and the social reorganizations will be rare, but they will not differ in their proximal causes.

In the end, the system does not care about our intentions. It only cares about its own state, to which we are completely blind.

This not to say that intentional behaviour is not important. Without intentional behaviour, there is no human system, and there is no change. There are no disturbances, large or small, local or system-wide. Human agents must have intentions. However, the content of their intentions is unrelated to the behaviour of the system. All agents try to do things. The system never does what any agent tries to do.

Simulation is our only salvation

Complex systems can surprise us. We can picture their simple interactions, but we can’t mentally, or even mathematically, extrapolate their global behaviour. Human societies are likely made of multiple interacting systems of simple interactions, iterated over long periods. Imagining the behaviour of one of these systems of simple interactions over the long term is likely impossible. Imagining the behaviour of many such interacting systems of simple interactions is certainly impossible.

In the face of this complexity, the only thing we can do is simulate. We must experiment. We must imagine, as far as we can, systems of simple interactions that could generate the kinds of behaviours in which we are interested, and then we must watch them unfold. Hopefully, our simulations produce something which helps us think about our archaeological problems.

In our collective imagination, archaeology often starts with finds. We find objects in the ground. We assemble them into contexts and extract data from them: morphometrics, isotopic composition, decoration patterns. From this information we try to infer events, and from the events we try to reconstruct process. From process, we imagine past societies.

The inferred events play a key role in this kind of archaeology. But complexity theory tells us that the events themselves are largely irrelevant. It tells us that the causes of change, even major change, are unremarkable. We can probably understand how sets of simple interactions, sequences of unremarkable events, produce patterns and then modify them, sometimes radically and rapidly. But we probably can’t explain why particular events take place. What should interest us is not the event itself, or even what caused it. Rather, we should be interested in the extent of the disturbance it generates, and of the restructuring  to which it leads.

To what extent can we use complexity theory in archaeology?

Complexity theory holds many insights that are useful for archaeologists. It teaches us that extraordinary or infrequent events and radical transformations don’t force us to search for extraordinary or infrequent causes. It teaches us that we must expand our concept of archaeological context. It teaches us to carefully separate agency and intentionality in social processes.

But beyond giving us general principles for thinking about the past, can it help us build actual archaeological interpretations of processes of change?

In order for complexity theory to be more than a simple heuristic that helps us think about the past,  we must be able  to determine whether an archaeological find  was generated by an event  which took place in a system that was in a state of critical self-organization.

It is easy to wonder whether we would ever have enough information about an archaeological context  to measure  its level of self-organized criticality. Most reasonable individuals, at this point I suppose, would think not.

As with everything else in archaeology, the answer is probably in the indirect observation of a phenomenon. For example, there is some limited evidence that various modern behavioural traits first appeared in fits and starts in Southern Africa (Wurz 2013:S313-14). If it is the case that they appeared locally for short periods of time here and there before they really took off and spread, it may be that their initial short lived appearances were the result of events in a nearly  critically self-organized system. Their final spread may then have occurred when the system reached full self-organized criticality.

Closer to us, we might wonder why the 1905 Russian revolution did not spread, when the 1917 one did. Or why the LBK disturbance did not reach the Baltic coast for 1000 years.

Finding self-organized criticality in archaeology may not involve looking at the state of a system, but at its behaviour as it is represented in the archaeological record. Any sudden global change, such as the rapid spread of agriculture in a region, or the sudden replacement of one decoration style with another is a candidate. Any very local change that fails to spread out may signal a system far from criticality.

We have to start thinking more often in terms of disturbances, local and global,  rather than in terms of people  doing things in the past.


Bak P, C Tang, K Wiesenfeld 1987. Self-organized criticality: an explanation of 1/f noise, Physical Review Letters 59:381-384.

Bentley RA, HDG Maschner 2001. Stylistic change as a self-organized critical phenomenon: An archaeological study in complexity, Journal of Archaeological Method and Theory 8:35-66.

Renfrew C, KL Cooke 1979. Transformations: Mathematical approaches to culture change, Academic Press, New York.

Wurz S 2013. Technological trends in the Middle Stone Age of South Africa between MIS 7 and MIS 3, Current Anthropology 54:S305-319.

4 thoughts on “Thoughts on archaeology and complexity

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