For those who are familiar with anthropology, the themes of chaos and complexity might seem intuitively related to the field. Immersion in unfamiliar cultures is understood to produce disorientation, confusion, and perceptions of the foreign culture as “chaotic.” Consequently, the relevance of chaos theory and complexity theory to anthropology might not require a detailed justification. Here, we make those connections explicit and suggest ways in which chaos theory and complexity theory might be useful in anthropological inquiry.
Chaos Theory
Both chaos and complexity theories have their roots in the development of systems theory, which emerged in the period during and after World War I. In particular, open systems were defined as “open” because they exchanged resources with their environment and “systems” since they were composed of a variety of interconnected and interacting components. The movement to systems theory might be thought of as the “holistic turn,” which marked a departure from the reductionist or atomistic approach that sought to break things down into smaller and smaller pieces in an effort to uncover their essence. In contrast, systems thinking can be characterized as the recognition that the whole is more than the sum of its parts. The parts can, in a sense, be understood as holographic representations of the whole, which, when combined create through their interaction a new and unique entity.
The development of chaos theory began in the 1970s with the work of Edward Lorenz, a meteorologist whose interest in modeling weather patterns led to the discovery that miniscule differences in initial conditions can have tremendous effects on outcomes. The observation became known as the “butterfly effect,” described here by Ian Stewart (1989):
The flapping of a single butterfly’s wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month’s time, a tornado that would have devastated the Indonesian coast doesn’t happen. Or maybe one that wasn’t going to happen, does. (p. 141)
While positivistic science would typically dismiss small differences as bothersome detail or noise, in chaos theory, these small differences became the subject of intense interest. Over time, this phenomenon became known as “sensitive dependence on initial conditions.” What this meant for Lorenz and his interest in weather modeling at the time of his initial experiments was that accurate prediction of the weather was impossible.
A second important observation by Lorenz came through his search for a simplified version of his original experiment. The resulting phenomenon illustrates again that slight differences in initial conditions bring about vastly different outcomes. However, this time, there was something new: What initially appeared to be random behavior turned out not to be random at all. James Glieck, who introduced chaos theory to the general public in 1987, describes the Lorenzian water wheel:
At the top, water drips steadily into containers hanging on the wheel’s rim. Each container drips steadily from a small hole. If the stream of water is slow, the top containers never fill fast enough to overcome friction, but if the stream is faster, the weight starts to turn the wheel. The rotation might become continuous. Or if the stream is so fast that the heavy containers swing all the way around the bottom and up the other side, the wheel might then slow, stop, and reverse its rotation, turning first one way and then the other. (p. 29)
Anyone can observe the workings of a simple water wheel. What Lorenz showed was that the seemingly chaotic behavior of this simple device was actually ordered. Until this time, scientists recognized two types of order: steady state and periodic order. Steady state order describes behavior in which the variables never change, resulting in a repetitive pattern. Periodic order describes a pattern of a single loop that repeats itself indefinitely. Yet when the results of Lorenz’s experiment were graphed, a third type of order emerged.
The results of the equations in Lorenz’s experiment were also ordered, but neither steady state nor periodic. Never settling on a single point, the patterns did not repeat themselves. What appeared at first to be chaotic was in fact ordered, a phenomenon that became known as the “Lorenz attractor.” Within the Lorenz attractor, the butterfly wings image shows both chaos and order: chaos in that the pattern is never repeated twice, and order in that the patterns fall within parameters.
The results of Lorenz’s experiments were published in 1963. However, since his work appeared in a meteorological journal, his findings didn’t reach a wide audience. It was years before those outside meteorology would hear about his work. Over time, individuals from fields including mathematics and biology reported similar phenomena in experiments with the flipping of a coin, the growth of populations, fluctuations in cotton prices, and coastline measurement. What these experiments brought to light were hidden and surprising aspects of behavior that were to become important concepts in chaos theory.
One of the key developments that emerged from continuing studies of chaos was the concept of the fractal, a graphic representation that embodies the attribute of self-similarity. The term fractal comes from fractional. Examples of fractals include bifurcation diagrams of Mandelbrot’s population equation, the Lorenz attractor, and the Koch curve. Each of these figures exhibits some paradoxical feature that reveals the hidden order within apparently chaotic systems. For example, the Koch curve illustrates how each time new triangles are added to the outside of a triangle, the length of the perimeter line gets longer. Yet the inner area of the Koch curve remains less than the area of a circle drawn around the original triangle. Essentially, it is a line of infinite length surrounding a finite area. Benoit Mandelbrot, a mathematician studying self-similarity, used this concept to explore anomalies in measuring the length of coastlines.
Developments in chaos theory were aided by advances in computation and measurement technologies. The introduction of high-speed computing had an effect similar to the impact made by the electron microscope. Both allowed scientists to see deeper into the nature of things that had previously been obscured because of the limitations of human vision and capacity to perform massive calculations. And while they allowed us to look deeper inside, they also expanded the scope of our vision: The bigger picture revealed obscure aspects of behavior that challenged long-held assumptions about the universe and the nature of life itself.
The implications of chaos theory would be taken up by researchers from a wide range of disciplines, who continued to evolve new theories. The following section introduces complexity theory and explains its relationship to chaos and other theories that emerged from the intellectual ferment of the early 20th century.
Complexity Theory
There is a close relationship between chaos theory and complexity theory. As previously noted, both grew out of the interest in holism and gestalt theories, followed after World War II by cybernetics and systems theory. What these intellectual movements had in common was the desire to replace reductionism with an appreciation for modeling interactions instead of simplifying them away. Described as strikingly similar to systems theory regarding environmental interaction and awareness, the three states defined by systems theory—organized simplicity, organized complexity, and chaos—are mirrored in the typologies of complexity theorists Stephen Wolfram and Chris Langdon: stability, Edge of Chaos, and Chaos.
Chaos theory, cybernetics, catastrophe theory, and general systems theory share a common interest in deterministic dynamic systems in which a set of equations predicts how a system moves through states from one point in time to another. What distinguishes complexity theory from the others is that it provides an alternative method for exploring regularities that emerge from the interactions of individual components within systems. In combination, these components form what is referred to in complexity theory as complex adaptive systems (CAS). One of the key contributors to the development of complexity theory, Murray Gell-Mann, identified four elements common to CAS: agents with schemata, self-organizing networks, coevolution to the Edge of Chaos, and recombination and systems evolution. As the examples of their application in the next section will attempt to demonstrate, each of these characteristics can be related to research topics in anthropology and the social sciences.
According to Robert Axelrod, known for his work on competition and collaboration involving Prisoner’s Dilemma (a type of game in which two people engage in a scenario in which the successful strategy is one of cooperation based on reciprocity), complexity theory is the study of many actors and their interactions. Actors or agents might be people, organizations, nations, fish, populations, atoms, or simulated creatures, and their interactions can include any activity from warfare, alliance building, and new product development to mating.
This wide range of application has been cited as evidence to argue that there is no consensus on a definition of complexity science. Moreover, some argue that we cannot refer to complexity as a science or theory at all but should, instead, think of it as a paradigm or discourse, similar to Martin and Frost’s characterization of postmodernism. Yet despite this debate, the application of constructs and concepts from complexity theory continues. The growing volume of related literature suggests that complexity is more than a theme. And, as with any new science, defining its parameters requires ongoing scholarly discourse.
A recognizable set of core concepts and principles has emerged to give form and substance to complexity theory. Many of these have worked their way into main-stream academic and practitioner literature. Examples include the Edge of Chaos, emergence, fitness landscapes, phase transitions, adaptive self-organization, and nonlinear feedback loops with mutual causality. The concepts of adaptive self-organization, coevolution, and agents have particular applicability to anthropology and are covered in some detail throughout this section. When applied to anthropological problems, each of these concepts provides new insight to the nonlinear dynamics of complex adaptive systems and the environments from which they emerge, develop, mature, and pass out of existence.
For anthropology, this means the opening of potential channels to investigate complex social systems, which are characteristically dynamic in nonlinear ways.
The risk inherent in applying constructs from complexity theory is that of allowing these concepts to degenerate into descriptive language or metaphor. Referred to as “soft complexity science,” the use of complexity concepts and language helps to visualize or “see” the complexity inherent in social systems and sociotechnical organizations. Some complexity theorists refer to the lack of rigor in the use of complexity thought and language as “pseudoscience,” which is thought to describe much of the work in complexity theory. While the value of metaphor is indisputable, there is much more that can be done in the way of applying complexity theory to the investigation of complex adaptive systems.
The maturation of new sciences (complexity science) involves the development of research tools and techniques. Rather than simply applying the concepts of complexity theory as a metaphorical lens, more rigorous approaches in the form of agent-based modeling and simulation are producing valuable insights across many scientific domains, including anthropology. Simulation allows researchers to model and demonstrate how the seemingly simple behavior of interacting agents can generate large-scale effects or “emergent properties” as they adapt to changing conditions in their environment.
It is important to stress that the objective of agent-based modeling and computer simulation is not to reproduce realistic models of empirical data. The goal instead is to bring to light the emergent recurring patterns of behavior that bring about a reordering of a complex system. It is important to have a deeper understanding of the dynamics of interaction that reappear across a wide range of diverse circumstances. So, rather than characterizing complexity theory by what is studied (i.e., societies, organizations, economies), Stephan Phelan argues that the focus should be on new methods for studying regularities or patterns such as those revealed by Axelrod’s work with agent-based models of competition and collaboration.
Where traditional science has focused on simple cause-effect relationships, complexity science seeks to detect simple “generative” rules that cause complex effects. Generative rules are few and simple; they have been used to demonstrate how a group of artificial agents, such as cellular automata in the “Game of Life” or computer-generated flocking patterns (“boids”), will behave over time in a virtual environment.
In Phelan’s words, “Complexity science posits simple causes for complex effects.” In CAS, this behavior is referred to as autogenesis, or self-organizing behavior, which is generated by a set of relatively simple rules that govern the interactions between agents over time (“time t influences conditions at time t + 1”). These rules, in turn, create structure. According to Philip Anderson, “Rules generate structure because the state that is the output of one application of rules becomes the input for the next round.” Structure evolves from ongoing interaction between agents within the unit itself, between the unit and other units with which it interacts, and within the larger systems to which it is related. Complexity theorists refer to as coevolution, a dynamic process through which components of a system known as “agents” not only adapt to their environments, but shape them over time. The conceptual overlap with cultural ecology and systems theory is clear.
It must be emphasized that models of adaptive behavior are significantly different from so-called rational choice models. The optimizing strategies that support rational choice models, such as those used in classic economics, are based on assumptions of rationality from which the consequences of specific choices can be deduced. In contrast, advocates of agent-based modeling and computer simulation argue it provides a more realistic representation of reality. Multiple agents following a few simple rules will often produce surprising effects, since anticipating the full consequence of even simple interactions is impossible. Although interaction is determined by the set of rules that generate the behaviors of individual agents, Anderson notes that agents need not be prisoners of a fixed set of rules. This notion of infinite variability and surprise is a common characteristic of complexity theory in computer and physical sciences, as well as in the application of complexity theory to social phenomena. In the domain of social phenomena, we can equate this to the capacity of human actors for choice, what Giddens refers to as “agency.”
Understanding the central role and functions of the agent in agent-based models is essential to appreciating how complexity can be applied as a theoretical framework in anthropological research. Depending on the level of analysis, agents can be defined as individuals, groups, families, units, firms, or any other entity distinguished by their differentiation from some “other.” The key characteristic of agents is their ability to interact with other agents. The response of each agent is based on the responses of other agents, and their interaction results in the phenomenon of “coevolution.” The “adaptive landscape,” the field in which they interact, is constantly shifting. This connectivity is what gives CAS their dynamic nature.
Chaos, Complexity, and Anthropology
With its primary interest being the study of human societies and cultures, anthropology undoubtedly qualifies as a science interested in complex systems. The conceptualization of culture from the systems view can be discerned in the work of many of anthropology’s key contributors to anthropological theory, notably Malinowski and Radcliff-Brown (functional-ism), Steward and White (cultural ecology), and Lévi-Strauss (structuralism). More recent versions of cultural ecology have expanded on this systems view.
Despite obvious correlations, the systems view has been criticized by social science researchers for its mechanistic, deterministic overtones, which did not reflect the often messy reality of social systems. Its unpopularity can also be linked to the influence of postmodernism and distrust of theories of culture that hint at a unified theme. However, more recent iterations of systems thinking, such as chaos theory, have revealed dimensions within the randomness (or messiness) of apparently disordered systems that are found upon closer examination to be ordered, what Glieck calls the stable chaos of self-organizing systems. Complex systems such as social systems can give rise to both turbulence and coherence at the same time. Emergent order within apparent chaos is at the core of both chaos and complexity thinking. Modeling and simulation are the tools that have been developed by complexity scientists to explore this phenomenon.
In applying agent-based modeling to the investigation of complex social systems, it is important to establish the distinction between human responses to routine, known situations and those that address uncertain, complex, and unknown situations. This distinction highlights the critical difference between a closed system, in which equilibrium is maintained through routine responses without regard to external influences, and an open system that must respond to an unpredictable and constantly changing environment.
Although it can be argued that the closed-system model might have been appropriate for traditional anthropological studies of single, small-scale, and relatively isolated populations, it is clearly not adequate for the highly integrated, globalizing world that faces contemporary anthropologists. Chaos and complexity science provide not only a theoretical framework but also unique methods and tools useful in investigating how discrete parts of complex social systems, such as indigenous populations within developing countries or divisions of a multinational firm, relate to and are integrated within the larger environment as a whole. The interest in part-whole relationships is also a primary concern of anthropologists working in the social-cultural ecology framework.
The theme of interaction is consistent within systems and ecological approaches that share a common concern with the dialectic interplay between sociocultural systems, their environments, and reciprocity, or feedback causality, in which both the sociocultural system and environment influence each other. Environment has an active, selective role in shaping the evolution of culture; culture, in turn, influences the characteristics of its environment. This understanding of the relationship between environment and culture relates directly to the notion of coevolution, a key concept from complexity theory.
From the systems perspective, culture is conceptualized as a system of socially transmitted behavior patterns that serve as mechanisms that “adjust” human communities to their environments. Closely aligned to the concept of coevolution described in the previous section, manifestations of this perspective as sociotechnical or sociocultural systems tend to revolve around the notion of reciprocity and feedback. These concepts were also noted in earlier references to Axelrod’s work with patterns of competition and cooperation.
The blending of variations of the systems view, chaos theory, and complexity science with anthropological theory provides new avenues for research. Within contemporary anthropology, the complexity of cultural multiplicity has become a prominent theme. Notions of negotiated cultures and nested cultural layers have developed through ongoing dialogue since postmodernism first challenged the assumptions of traditional anthropological thought. Hamada and Jordan explain that the classical concept of nature that explains differences between small, relatively homogeneous societies is challenged by social groups without boundaries and whose memberships in these groups may overlap, causing shifting allegiances depending on the situation.
While complexity is a hallmark of contemporary social systems, as Hamada and Jordan suggest, the application of complexity theory is not limited to anthropological research on contemporary topics such as the effects of globalization on indigenous communities. Because of its capacity to bring to light emergent patterns within complex and seemingly chaotic systems, complexity theory has the potential to provide the theoretical framework and analytical tools required to accommodate research on complex social systems, regardless of their historic timestamp.
The village simulation model developed by Tim Kohler to study of the collapse of complex social systems and Robert Reynolds’s work with cultural algorithms serve as examples. Developed using data collected from sedimentation and other archeological findings from the Mesa Verde region, the village simulation model was initially designed as an approach to understanding the behavior of pre-Hispanic inhabitants. It was hoped that the model would bring to light possible explanations for their disappearance, evidence of which is based on archeological studies of the region. The simulation produced evidence that suggested that more than environmental factors were involved in shaping the social history of the region.
Using Kohler’s agent-based model of the Mesa Verde pre-Hispanic Pueblo region, Reynolds employed a framework for modeling cultural evolution. With the addition of cultural factors, Reynolds applied cultural algorithms to explore the emergent properties’ impact. If the social system was brittle, it was hypothesized that any factor that induced stress could cause its collapse. By investigating the impact of environmental variability on the formation of social networks, Reynolds and coresearcher Ziad Kobti looked at how the spatial distribution of agricultural land and the temporal distribution of rainfall affected the structure of the social system.
Reynolds and Kobti were able to show how the distribution of agricultural resources was conducive to the development of so-called small-world networks, which depended on the existence of conduits or agents whose connectivity was sufficiently powerful to link the small worlds together. Without the conduits, the small-world network would be prone to collapse. Experiments suggest there was, in fact, a major decrease in these conduits, which would have had a negative impact on the resiliency of the small-world network.
Applicability of Chaos and Complexity Theories
What is particularly noteworthy about the development of both chaos theory and complexity theory is their widespread applicability to phenomena across diverse fields, ranging from computer science to the physical and social sciences. Both theories are inherently interdisciplinary with demonstrated relevance for investigating the workings of complex systems, meaning that the principles are applicable across a diverse spectrum of systems. For example, Joseph Sussman’s characterization in 2000 of a complex system describes transportation, but it could also be applied to an economy or a society:
A system is complex when it is composed of a group of related units (subsystems), for which the degree and nature of the relationships is imperfectly known. Its overall emergent behavior is difficult to predict, even when subsystem behavior is readily predictable. The time-scales of various subsystems may be very different… Behavior in the long-term and short-term may be markedly different and small changes in inputs and parameters may produce large changes in behavior.
The closed-system perspective is, at best, an inaccurate lens for investigating the complex interactions and nested systems that characterize contemporary societies. For similar reasons, theoretical and methodological boundaries that limit the capacity of anthropologists to embrace the scope and depth of their research topics should be transformed by new theoretical paradigms that have proven in other fields to provide valuable insight on a wide range of complex adaptive systems. The recent works in archeology by Koehler and Reynolds serve as examples of how concepts from chaos theory and the methods and tools of complexity science can be applied.
Chaos theory and complexity theory offer anthropologists new areas of exploration and cross-disciplinary collaboration, especially important as the signature concept of anthropology (culture) and core methodology (ethnography) are being appropriated by other disciplines. Anthropologists are remarkable in their ability to apply their unique skills, methods, and tools to other fields of research, for example, medicine, business, and engineering. However, we could be better at communicating and making explicit what Diana Forsythe called the “invisible” aspects of anthropological work.
Computer simulation has become a common research tool in applying complexity theory to the study of complex adaptive systems across a wide range of disciplines.
Engaging in interdisciplinary research, presenting at academic conferences outside anthropology, and coauthoring journal publications with colleagues from other fields all serve to enhance appreciation for the relevance of anthropology and value that anthropologists can bring to the study of crucial human problems and challenges confronting the world today.
The quote by Henry Miller that opens this entry suggests that order lies hidden beyond the state of con-fusion in which all appears chaotic. This encapsulates the basic premise of chaos theory and reflects an underlying approach to the investigation of phenomena that is compatible with the basic tenets of anthropology.
Exploring new research perspectives such as chaos and complexity theory provides opportunities for interdisciplinary discourse that both broaden anthropology’s research perspective and further a wider understanding of the philosophical and theoretical underpinnings that form the foundation of anthropological inquiry.
References:
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- Anderson, P. (1999). Complexity theory and organizational science. Organization Science, 10(3) 216-232.
- Axelrod, R. (1997). The complexity of cooperation. Princeton, NJ: Princeton University Press.
- Glieck, J. (1987). Chaos: Making of a new science. New York: Penquin Books.
- Hamada, T., & Jordan, A. (1990). Cross-cultural management and organizational culture. Studies in Third World Societies, 32.
- Martin, J., & Frost, P. (1999). The organizational culture war games: A struggle for intellectual dominance. In S. Clegg & C. Hardy (Eds.), Studying organization theory & method. London, Sage Publications.
- Phelan, S. E. (2001). What is complexity science, really? Emergence, 3(1), 120-36.
- Reynolds, R. G. (1979). An adaptive computer model of the evolution of agriculture for hunter-gatherers in the Valley of Oaxaca, Mexico. Ann Arbor: University of Michigan.
- Stewart, I. (1989). Does God play dice? The mathematics of Cambridge, MA: Blackwell.
- Sussman, D. (2000). Ideas on complexity in systems: Twenty views. Cambridge: MIT Engineering Systems Division.
