ASHGATE Christopher S. Beekman William W. Baden f I , Nonlinear Models for I Archaeology and Anthropology I I Continuing the Revolution I, 1 i t J ,!ｾ＠ ｾ＠ ｾＺ＠ f % ! Edited by ｃｈ｝ｕｓｔｏｐｅｒＮｂｾ＠ University of Colorado at Denver and Health Sciences Center, USA WILLIAM W. BADEN Indiana University - Purdue University Fort Wayne, USA ASHGATE © Christopher S. Beekman and William W. Baden 2005 All rights reserved. No part of this publication may bereproduced,stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recordingor otherwise without the prior permission of the'publisher. Christopher S. Beekman and William W. Baden have asserted their right under the Copyright, Designs and Patents Act, 1988, to be identified as the editors of this work. Published by Ashgate Publishing Limited Gower House Croft Road Aldershot Hampshire GUll 3HR England Ashgate Publishing Company Suite 420 10 1 Cherry Street Burlington, VT 05401-4405 USA Li Li Li P, A( 1 2 Ashgate website: http://www.ashgate.com British Library Cataloguing in Publication Data Nonlinear models for archaeology and anthropology : continuing the revolution 1. Social archaeology 2. Nonlinear systems 1. Beekman, Christopher Stockard II. Baden, William W. 930.1'01 3 Library of Congress Cataloging-in-Publication Data Nonlinear models for archaeology and anthropology: continuing the revolution / edited by Christopher S, Beekman and William W. Baden. p.cm. Includes bibliographical references and index. ISBN 0-7546-4319-0 1. Archaeology-Mathematical models. 2. Nonlinear systems. I. Beekman, Christopher Stockard. II. Baden, William W. 5 4 6 7 CC80.6.N66 2005 930.101'51--dc22 2005024902 ISBN 0 7546 4319 0 1 J Printed and bound by Athenaeum Press Ltd, ' Gateshead, Tyne & Wear. Chapter 1 Continuing the Revolution Christopher S. Beekman University of Colorado at Denver and Health Sciences Center William W. Baden Indiana University-Purdue University Fort Wayne Introduction This volume presents theoretical perspectives and case studies extending nonlinear systems theory (commonly called complexity, chaos theory, or dynamical systems) to archaeological studies of politics and economy. Nonlinear systems theory has taken the scientific world by storm in the past two decades with promises to sweep away reductionistic approaches while retaining a scientific and experimental perspective. This revolution has taken place even as the social sciences have struggled to rebuild after the devastating critiques of Post-Modernism. The two trends collided in the 1990s, resulting in a burst of publications in sociology, political science, and anthropology that explored the possibilities that the new science offered. Archaeological applications have developed more slowly, and have not explored as widely. We assembled the contributors for this volume because it appeared to us that nonlinear systems theory was being interpreted and applied in a very limited way by archaeologists. In the course of discussions with colleagues, we found different concepts of how analysis should proceed and significantly different characterizations of what nonlinear dynamics might mean for archaeology. Is it a ‘Post-Modern Science’ attacking science from without? Is it a revolution from within that redefines what science itself means? Does complexity constitute a consistent theoretical package, or is it better understood as a cluster of methods capable of being used by different theoretical schools? Nonlinear research encompasses a more polyglot range of concepts than usually appreciated, and it is very unclear whether we can truly make pronouncements beginning with ‘chaos theory states…’. Continued exploration of these concepts is necessary. This volume presents contributions by archaeologists from both sides of the Atlantic and with different theoretical backgrounds seeking to continue the revolution and extend nonlinear systems to new areas of archaeological inquiry, such as social and political organization, and subsistence and political economy. 2 Nonlinear Models for Archaeology and Anthropology Nonlinear Systems: A Brief History Unlike many theoretical approaches used in archaeology, nonlinear systems theory was not so much borrowed from other disciplines as it emerged more or less independently from research in both the physical and social sciences. Research in physics, chemistry, economics, meteorology, biology, and other fields led to a recognition that many types of systems could not be studied using the intentionally reductionistic approach that has been the guiding principle of science since Sir Isaac Newton. In order to better understand energy, motion, disease, and other familiar topics, traditional science has proceeded by breaking the problem down into increasingly smaller parts that could be studied in isolation from the whole. This allowed experimental manipulation of different variables so as to isolate the effects of each one. The successes of this approach have been numerous and need not be repeated here. But as researchers have tackled more and more difficult problems, the reductionistic model has become less useful. There has been a growing realization that studies of closed systems are often unrealistic, and that assumptions of system equilibrium must be left behind if we are to study more complex systems where the interaction of many components leads to quite unexpected emergent properties. Science as a whole has, in a sense, caught up with the kinds of systems that social scientists have had to deal with for years - open, fluctuating, unpredictable, yet patterned - and has begun to develop conceptual tools for understanding them. The research that comes under the heading of nonlinear systems is diverse. Related research findings in meteorology, mathematics, and geometry (e.g., Lorenz 1963; Mandelbrot 1977; May 1976) were baptized with the term Chaos theory in the 1960s, encompassing deterministic systems (i.e., based on equations that behave predictably over short periods of time) that nonetheless eventually become unpredictable due to the equations’ sensitive dependence upon initial conditions. In other words the relationships between parts are understood, but prediction fails at the level of the entire system due to the complexity of all the interrelationships and our inability to observe the initial conditions with sufficient precision. The canonical example is Lorenz’s experiment with weather prediction. Lorenz discovered that an extraordinarily small, seemingly insignificant, variation in the initial input of one parameter (from 0.506127 to 0.506) into his computer program resulted in an eventual divergence between two predictions that were expected to be exactly identical (Gleick 1987:16). This variation related to the arbitrary precision of his model’s input, i.e., what he could measure coupled with the accuracy of his observations and the computer’s ability to maintain that precision. From a statistical perspective these precision issues produce what appear to be random fluctuations in the model’s trajectory. The mechanisms for the weather are highly quantifiable and relatively well-known, but their sensitivity to our ability to accurately measure or observe them means that predictions can only be made a short distance into the future (up to the prediction horizon), after which the Nonlinear Models for Archaeology & Anthropology: Continuing the Revolution 3 potential variations become too great. Despite the impossibility of ever adequately measuring initial conditions (Heisenberg 1927; Nicolis 1995:58-61) or making medium or long term predictions, recurring trends around topological attractors allow retrodictive analysis and explanation. We can typically explain the weather in hindsight, even if we are unable to effectively predict it. Another significant element of classical chaos theory is the concept of bifurcations. Analysis may well identify points in time when change is almost certain to occur, but it is often impossible to determine which of the possible new trajectories will predominate due to apparent elements of randomness. Historical pathways and contingency are therefore deeply rooted elements of chaos theory, despite the presence of the often misinterpreted term ‘deterministic’ which reminds us that even the most irregular trajectory is defined by causal forces. Another related field of inquiry that developed in mathematics is Catastrophe theory (Poston and Stewart 1979; Thom 1975), largely a creation of the 1970s. This is closely related to chaos, and largely focuses on how even systems with very few variables can show surprising transformations and nonlinear trajectories depending upon their interaction. Its abstract mathematical and topological nature tended to prohibit its use in real world situations, where it became extremely difficult to quantify any system in terms of just a few variables. Complexity or Complex systems theory (Pines 1987; Cowan, et al. 1994) emerged in the 1980s and shares many elements with the previous approaches, but has de-emphasized deterministic chaos and instead focuses on how the mutual interaction of many agents or variables can lead to unexpected emergent properties within the broader system. Complex systems theorists therefore explicitly reject the intentionally reductionistic perspective associated with the Newtonian approach to science and have instead tried to develop methods to study entire systems. A major element here has therefore been the imprecise but nonetheless powerful concept of emergence, colloquially described as ‘the whole is more than the sum of its parts’. That is, systems cannot be described through the aggregation of their components, but require an entirely new description at the level of the system. In a terminological shift, complexity researchers have appropriated the term Chaos to contrast unpatterned systems (not strictly true in the earlier definitions of chaos theory) as an opposing pole to Order – a situation of low potential for change (Langton 1990). Complex systems (or Anti-Chaos in the most recent parlance – Shermer 1995; Lansing 2003) lie in the boundary zone between these extremes, within which there are forms of temporary stability that emerge through the interaction of internal components. The complex systems approach has been closely linked to the extensive use of computer simulation due to the amount of data and number of variables being analyzed, and the field is significantly related to issues of adaptive learning and artificial intelligence. The best known of these simulations are the agent based models or artificial societies, in which simulators have attempted to model phenomena ‘from the bottom up’, concentrating on simple rules that nonetheless produce complex behaviour and emergent properties at the level of the group (Langton 1988, 1994; Langton, et al. 1992; Epstein and Axtell 1996). 4 Nonlinear Models for Archaeology and Anthropology Much of the impetus for the coalescence of research into complex systems theory came from the influential research of Ilya Prigogine into dissipative structures and self-organization over the prior few decades (e.g., Glansdorff and Prigogine 1971; Nicolis and Prigogine 1977, 1989; Prigogine, et al. 1972a, 1972b). Briefly, his research recognized that pivotal physical laws such as the second law of thermodynamics (the pessimistic law referring to the unavoidable loss of energy) only worked in a closed system, and failed to accurately describe behaviour in an open system in which energy could be introduced from the outside. The introduction of energy produced perturbations to the system and caused it to self-organize into complex patterns far from equilibrium. Common examples of these dissipative systems from the physical world include fluid dynamics and other phase transitions. But the perceptive Prigogine quickly saw the application to biological evolution (particularly the emergence of animate forms from inert matter) and even social change (popularized in Prigogine and Stengers 1984). Prigogine’s own inconsistent use of the terms Chaos, Complexity, and Stability theory to refer to his work reflects the rather loose approach to this material that most practitioners have taken. For this reason, in this volume we prefer the one aspect that all these approaches hold in common – their focus on nonlinear systems. Less catchy perhaps, but more accurate and inclusive. By nonlinear systems we mean those systemic environments in which the number of variables or the relationships between them are so structured as to lead to quite unpredicted and emergent properties. Analysis tends to be oriented towards retrodictive explanation, not prediction, and the simplistic theoretical dichotomies that archaeologists are so attracted to, such as materialism vs. idealism, functionalism vs. conflict, agency vs. structure, or intention vs. adaptation, become difficult to maintain. As opposed to the systems theory of decades past, nonlinear systems are open and subject to varying degrees of stability. Rather like the much touted landscape archaeology of recent years, nonlinear systems invite parallel analysis at multiple scales (see McGlade 2003). Many prominent social scientists have weighed in on the importance of nonlinear studies for human societies (e.g., Adams 1988; Luhmann 1986, 1995; Maturana and Varela 1980; Wallerstein 1997). Textbooks specifically for use in the social sciences have appeared (Brown 1995; Byrne 1998; Guastello 1995; Marion 1999), numerous collections of applications have been assembled (Albert 1995; Arthur and Arrow 1994; Bertuglia, et al. 1998; Bütz 1997; Ellis and Newton 2000; Eve, et al. 1997; Kiel and Elliott 1996; Leydesdorff and van den Besselaar 1994; Milanovic 1997, 2002; Prietula, et al. 1998; Richards 2000; Schieve and Allen 1982), and a listing of individual studies would probably fill this introduction, although we might single out a few (Allen 1997a; Artigiani 1989; Gilbert 1995; Harvey and Reed 1994, 1996; Lansing 1991; Lansing and Kremer 1993; Leydesdorff 2001; Reed and Harvey 1992; Shermer 1995) as fruitfully exploring the links between existing social theory and nonlinear approaches. But the dynamism in nonlinear systems theory may perhaps have most to offer archaeology, as the social science most deeply involved in the issue of social change over time. Nonlinear Models for Archaeology & Anthropology: Continuing the Revolution 5 Archaeology and Nonlinear Systems The earliest interest in nonlinear modelling for archaeology was primarily amongst those European and American researchers who had drifted away from the ecological functionalism, or Processualism, of the 1960s and 1970s to explore the utility of General Systems Theory (Maruyama 1963; von Bertalanffy 1951; Wiener 1948). Concepts broader than adaptation were considered, such as the role of information in social change, and archaeologists such as David Clarke, Colin Renfrew, Sander van der Leeuw, and Ezra Zubrow were of central importance, both in the work they did and the work they inspired in their students (e.g., Clarke 1972, 1978; Renfrew and Cooke 1979; Van der Leeuw 1981a; Van der Leeuw and McGlade 1997a; Van der Leeuw and Torrence 1989; Zubrow 1985). A genuine problem remained in that the rare applications of nonlinear approaches at this time were very simplistic and abstract (Renfrew’s application of catastrophe theory to the Maya collapse used 3 variables), and it remained quite difficult to determine exactly how to measure or even identify the important variables in a human system. Hence variants such as catastrophe theory enjoyed an extremely brief period of popularity (e.g., Renfrew 1978, 1979). Ilya Prigogine was a distinct source from which the interest in nonlinear systems spread to archaeology. Surely encouraged by his own wide range of interests (see Prigogine 1998 to see what we mean), colleagues of his began to apply dissipative structures to the social sciences (e.g., Schieve and Allen 1982; Adams 1988). Eventually, the intellectual descendents of this line carried the approach further to archaeology (e.g., McGlade 1990, 1999). Besides his work out of Brussels, Prigogine also spent time at the University of Texas at Austin, and Americans became introduced to his work more directly (perhaps first mentioned by Blanton and Kowalewski 1982:15). This southern focus, European in origin, independently influenced the early work of some of the contributors to this volume (Baden 1987, 1995; Stone 1999). Nonlinear systems approaches had an unclear relationship to other theoretical schools in archaeology. It was the eclectic Jonathan Friedman (1982) who would make reference to Prigogine’s work in the context of punctuated equilibrium and other rapid transformational models from the physical and biological sciences as part of a larger argument - that Processual archaeologists, in their desire to put their discipline on a scientific footing, had chosen idealized and discredited equilibriumbased theories as their model of science. Nonlinear systems research thus went from being an approach parallel to Processualism to an independent source of critique. But interest in these approaches may have failed to catch on more widely because most of these applications focused on the analysis of entire systems (see particularly the contributions in Van der Leeuw and McGlade 1997a), even as archaeology as a discipline was turning away from macro-scale analysis. Regardless of whether it caught on immediately or not, Prigogine’s work spawned 6 Nonlinear Models for Archaeology and Anthropology some of the earliest direct archaeological applications of nonlinear systems since Renfrew and Zubrow (Baden 1987; McGlade 1990). It is also members of this loosely defined ‘Prigoginian’ line that will make attempts to confront the PostProcessual critique, by addressing issues of power and top-down political control (McGlade 1997). Significant changes occurred in the field in the late 1980s and 1990s, due to two major related trends. The first was the rapid growth in computing power, allowing the development of considerably more complex simulations, particularly agent based modelling. The second was the development of institutional infrastructure in the form of the Santa Fe Institute (SFI) and other research organizations within or parallel to university settings. We suspect that agent based modelling created a fascination for archaeologists that earlier system-wide analyses of complexity could not, and it brought the scale of modelling down to the level of individuals just as other theoretical approaches in archaeology were doing the same. But we must also consider the training in technical methods that the new infrastructure made possible. Few archaeologists leave graduate school with a mathematical background beyond that required to carry out multivariate statistical analyses, and interdisciplinary institutions such as SFI provide an entirely new training opportunity. The simulations of Anasazi culture change by Timothy Kohler, Jeffrey Dean, George Gumerman, and their colleagues are the best known examples of archaeological collaborations to come out of SFI (Dean, et al. 2000; Kohler and Van West 1996; Kohler, et al. 2000). But this highly prominent organization (positively treated in Waldrop 1992 and less so in Helmreich 1998) served as host to a series of other archaeologists over the 1990s and 2000s such as Robert Hommon, Mark Lehner, Suzanne Spencer-Wood, Tony Wilkinson, and Henry Wright (see also the contributions in Kohler and Gumerman 2000). Some have worked on computer simulation while others have chosen to apply complex systems more metaphorically, and examples of their work appears in this volume. Certain prominent themes run through much of the research at SFI whether practiced by archaeologists or by representatives of other disciplines. Human societies, flocks of birds, the economy, sand piles, the brain, immune systems, ecologies, ant colonies, and pre-organic molecular formations are all conceptualized as Complex Adaptive Systems (CAS) sharing many features in common (Lansing 2003). That is, much of the self-organization of these systems is described as occurring under adaptive pressures towards greater fitness. Modelling has often, though not exclusively, made use of computational mechanisms such as modelling strings of cultural attributes through genetic algorithms (Holland 1998), adaptive interaction through game theoretic exchanges (Axelrod 1984), the creation of fitness landscapes to represent optimal and sub-optimal solutions (Kauffman 1999), artificial life studies involving adaptive learning (Langton 1988, 1994; Langton, et al. 1992), and other tools with strong ties to some form of Darwinian selection. Even when religious concepts or symbols are given an equally important role in modelling behaviour or communication, they are often operationalized again through programming methods that follow a selectionist structure. Nonlinear Models for Archaeology & Anthropology: Continuing the Revolution 7 Thus CAS is a distinctive approach that does not represent the entire gamut of theories currently practiced in archaeology. That in turn suggests that there is only room here for certain theoretical approaches to society. SFI has been very inclusive in its efforts to cross traditional disciplinary boundaries. But research concentrating on the similarities between complex systems may fail to appreciate the differences between them, which can be just as significant for our understanding. Adaptivist theory is perfectly legitimate as a theoretical approach, but the rather exclusive focus on the concept suggests that perhaps other theoretical schools are not compatible with CAS. This is an implication to be considered as we look at other areas. Research on human societies and nonlinear systems in Europe traces distinct trajectories. Themes that run through social simulation work in western Europe by researchers like Nigel Gilbert and Jim Doran (Gilbert and Conte 1995; Gilbert and Troitzsch 1999; Gilbert and Doran 1994) include religion, belief systems, irrationality, and social action. Social theorists such as Anthony Giddens and Fernand Braudel are cited alongside Ilya Prigogine. This greater interest in the social leads to applications that look quite different from those recently appearing in the United States (e.g., Doran 2000; Doran, et al. 1994; various in Van der Leeuw and McGlade 1997a) and greater weight to the notion that social systems are qualitatively different from other complex systems. Archaeologists working within this intellectual milieu have often chosen to use nonlinear concepts as metaphors to frame a verbal analysis rather than develop computer simulations (e.g., Bintliff 1997, 1999a, 2003). The last five years have seen the range of practical applications of nonlinear systems theory to archaeology continue to expand. Fractal analysis has been applied to Maya and Central Plains settlement patterns (Blakeslee 2002; Brown and Witschey 2003; Brown, et al. 2005) and urbanism at Teotihuacan (Oleschko, et al. 2000), technological innovations have been examined through the metaphorical application of dynamical systems and emergence (Roux 2003), self-organized criticality has been used to analyze pottery style (Bentley and Maschner 2001), and nonlinearity has been applied to human organization (Crumley 2001). Nonlinear systems theory has been discussed (R. McC. Adams 2001) and applied (Yoffee 2005) in more metaphorical terms to Mesopotamian social evolution, and theoretical links between Feminist theory and complexity have been outlined (Spencer-Wood 2000). R. Alexander Bentley and Herbert Maschner have published a diverse collection of articles (Bentley and Maschner 2003) examining complex systems in archaeology and history. Their contributors examined settlement patterns, chronology, and social networks, and came much closer than previous volumes to what we wanted to assemble here. Despite (or because of) its growing profile, nonlinear systems theory has had its detractors. Helmreich (1998) examined the Santa Fe Institute from a deconstructionist perspective, pointing out that white male heterosexuals make up the majority of complex systems researchers and arguing that this has led to a narrower view of social modelling than might otherwise be the case (e.g., use of the metaphor of biological reproduction). Khalil (1995) argues that the work of 8 Nonlinear Models for Archaeology and Anthropology Prigogine and others is inappropriate for human societies, where intention distinguishes human organization from quasi-cyclical phenomena such as those modelled from the natural world. Offhand comments by prominent archaeologists such as Adam Smith (2003:104) and private communications with colleagues have alluded to what many perceive as the lack of complexity in ‘complex’ systems research. Much of this comes from theoretical perspectives other than the selectionist approaches welcomed within prominent centres like SFI. But recently there have also been critiques from within. McGlade (2003) has expressed concern that nonlinear dynamics embraces a wider array of concepts, methods, and implications than appreciated by some practitioners. Among other things, he argues for the construction of multiple models of the same system from different perspectives, for more attention to differences across scales, and for a greater appreciation of the fact that we are constructing tools, not representations of reality. Mark Lake (2005) has recently argued that the utility of computer simulation of complex systems may be more limited than once thought. It may be most useful for sensitivity analysis and specific methodological questions, but it has produced far less in the area of theory. These critiques, especially from those in the thick of current research, point up the need for a more detailed examination of nonlinear systems’ applicability to the archaeological record, and a careful appraisal of current approaches. This Volume and the Contributors A brief exposition of nonlinear studies in Thomas Kuhn’s (1970) terms brings us to the central concern of this volume. Since at least Poincaré, studies in various disciplines have been producing what Kuhn called anomalies, or cases left unexplained by the dominant science paradigm emphasizing the isolation of individual variables in closed experiments. Complexity and chaos were born as self-referential entities when the commonalities among these anomalies were recognized, and Kuhn’s stage of ‘revolutionary science’ followed with the creative adoption of new approaches and the application of ideas to new disciplines. That was in the late 1980s and early 1990s, and is best exemplified by the formation of new institutes devoted to the study of nonlinear dynamics. Over the past 10 years, however, complexity has become more established and less avant-garde, and practitioners have focused more on Kuhn’s ‘normal science’, working out the methodological aspects of how to model this or that phenomenon. The revolution is evidently over. This book has its origins in our conviction that the revolutionary and exploratory period of nonlinear systems studies was too brief and incomplete, at least in the realm of the social sciences (see also Turner 1997). The CAS approach promulgated by SFI and other centres for complexity studies seems to imply a distinct theoretical package different from existing schools of thought in archaeology. The work by many in Europe on the other hand tends to suggest that various different theoretical orientations might profitably use nonlinear tools for Nonlinear Models for Archaeology & Anthropology: Continuing the Revolution 9 their own questions and topics of research interest. These are quite different interpretations. This volume is intended to present the ideas of a variety of researchers known for their contributions to other areas of archaeology, with the hope that it may be possible to clarify what nonlinear systems signify for the discipline. Is it a new paradigm that offers nothing to those archaeologists who prefer studies of agency, hermeneutics, and multivocality, or does it cross-cut old divisions in a manner that can potentially unify the scattered remnants of archaeological thought left in the early 21st century? It has recently become clear that practitioners sometimes have different ideas of what complexity is, and as a result adopt highly distinct forms of discourse. Some refer to it as a ‘Post-Modern’ science (Spencer-Wood 2000) because it eschews determinism and embraces contingency, while others see it as simply a development that unifies major trends within many of the sciences (see Price 1997). Some see nonlinear studies as a natural outgrowth of the computer revolution, allowing analysts to work with vastly increased volumes of data, while others see little need to adopt computer simulation to apply the theoretical principles involved. Our goal for this volume is to continue the revolution in the study of nonlinear systems by re-evaluating its theoretical bases and how they relate to paradigms already in place within the discipline. To this end we have assembled research from a broad variety of viewpoints as to what nonlinear dynamics might mean for archaeology. The articles in this volume are meant to bridge the gap between anthropological and archaeological theory and nonlinear concepts. In some chapters the authors have chosen to work with archaeological case studies to illustrate their points, but in others they have drawn upon ethnographic, historical, or contemporary societies where the characteristic ambiguities of archaeological data could be overcome. Regardless of the datasets used, the contributors are all concerned with the importance of nonlinear systems for archaeology. The ability of humans to incorporate, integrate, and use information is the focus of Robert Hommon’s investigation into the concepts behind CAS. Collective behaviour is presented as a result of ‘schema-driven behaviour of interacting agents’ where schema refers to internal, experience-based rules following GellMann’s use of the term (1992:10), but the definition could equally well have come from current authors in social theory. Hommon is interested in how human societies differ from other CAS by invoking processes of appropriatizing (encouraging conformity) and ecaptation (altering the environment), and the presence of stratified control hierarchies (unequal empowering of specific agents or groups of agents). Although primarily drawing upon examples from modern and recent human societies, he cites archaeological and historical evidence to demonstrate the influence of these three processes in Hawaiian culture prior to European contact. Carole Crumley is also interested in human organization, but particularly those forms that do not correspond to the stereotypical stepped hierarchy. Since the interaction of components is one of the central elements of any complex systems approach, she focuses her chapter on those interactions, in particular the concept of 10 Nonlinear Models for Archaeology and Anthropology heterarchy. A heterarchy is a meshwork of systems whose elements are either unranked or potentially ranked in a number of ways. The less rigid, more flexible structure of heterarchical systems is an adaptive tool that can more effectively combat ‘surprise’ within a society (e.g., environmental change, invasions, epidemics, etc.). Using examples of ‘disorganized organizations’ from recent times such as Al-Qaeda and the Anarchist movement, Crumley demonstrates that in uncertain times the sharing of information through flexible authority structures reduces risk by increasing available information to decision makers and multiplying solutions. The fact that the concept of agency, in varying degrees, runs through many of these contributions reinforces the notion that the role of the individual is an important element of nonlinear studies. Many aspects of the nonlinear approach concentrate on mapping the emergent outcomes of the actions of individual agents, whether those agents represent people, ducks, or water molecules. Christopher Beekman builds upon prior suggestions by Nigel Gilbert that the authors of agent based simulations of human societies need to pay greater attention to the social actor and current social theory on agency. Prominent social theorists like Anthony Giddens, Margaret Archer, Pierre Bourdieu, and others have all discussed agency in different ways that have significant implications for agent based modelling. Beekman argues that, far from pursuing an empirical, ‘bottom up’ agenda with agent based simulation, modellers have unknowingly espoused particular theories about how the individual relates to society and left others unconsidered. He also argues that the empirical ideal that crops up repeatedly in enthusiastic portrayals of complex systems may not be possible. While many authors have emphasized selfsimilarity across scales (drawn from fractal analysis) as a central element of nonlinear studies, Beekman instead points to the work by Prigogine and by social theorists arguing instead for phase transitions, thresholds, emergence, and distinct scales of analysis with different rules. He finishes with an example drawn from Late Formative-Classic period (200 B.C.-A.D. 550) western Mexico to illustrate some of the complexities of collective agency. Tammy Stone is also interested in the issue of quasi-group formation, or the appearance of highly unstable social groups in middle-range societies. Social institutions which aid in the flow and processing of information are argued to be self-organizing (Van der Leeuw 1981b; Stone 1999). Thus changes in information flow can have major repercussions on the structure of social groups which process information. As the intensity of flow among closely interacting groups increases, social complexity can differentially expand or collapse at spatially concentrated loci on the social landscape, forming information vortices (after Van der Leeuw 1981b). Stone applies these insights to quasi-group or faction formation as they occurred among the Hopi early in the 20th century. She contrasts the response at Orayvi against that of other Hopi communities that did not fission. Stone’s discussion is consistent with Prigogine’s argument that the current state of a system is one of many possible outcomes ultimately self determined by its initial conditions and by the response to subsequent disruptions in the flow of necessary resources (here, information). Nonlinear Models for Archaeology & Anthropology: Continuing the Revolution 11 William Baden examines the applicability of dissipative structures within archaeological models of agricultural systems. Baden provides an historical overview of anthropology’s adoption of thermodynamic concepts, positioning Prigogine’s nonlinear paradigm within anthropology’s on-going theoretical use of these principles. By applying Prigogine’s concept of systems far from equilibrium to prehistoric cultures, he updates and operationalizes Leslie White’s (and his followers’) original arguments linking the Second Law to cultural evolution. Using Mississippian examples from the southeast United States, Baden demonstrates how agriculture, as a dissipative structure, can be seen as an external source of negative entropy consistent with the theoretical suggestions of Schrödinger and Prigogine. Predictable disruptions in the flow of energy and their impact on social systems far from equilibrium are correlated with observed phase transitions in the archaeological record. Tony Wilkinson represents the MASS project and its work on settlement formation in northern Mesopotamia, and his paper discusses the impact of simulation upon traditional landscape archaeology. Clearly influenced by Kohler’s highly important simulations of the ancestral puebloans, the MASS project seeks to model an entire city of a complex, stratified society. This is a tall order, but is an excellent example of how agent based simulation is growing in ambition and capability. The subject has required increased attention to the spatial organization of subsistence and political economy. Wilkinson also clarifies how an agent based approach can improve upon traditional methods such as site catchment analysis. Instead of applying the fixed parameters of catchment analysis to a site, the MASS project models the activities of individual agents from below. While reading this article, one can easily envision future simulations that will model certain activities and predict the presence, volume, and diversity of material residue likely to result from those activities, providing a powerful tool for middle-range theory. Stephen Lansing and Robert Axtell generously agreed to review the articles in this collection and give us their thoughts on the application of complex systems theory to archaeology. Lansing and Axtell have been at the centre of the maelstrom for over 15 years, and they discuss the merits of the expanding perspective from their unique vantage points in complexity research and agent based modelling. Conclusion The editors and contributors to this book do not seek to appropriate nonlinear studies for a specific area within archaeology. The diverse backgrounds of our contributors – Heterarchy, Social Agency, Information Theory, Factionalism, Systems Ecology, Landscape studies – should make that point clearly. Each has ties to one or the other of the theoretical lineages discussed above, and each shows how nonlinear dynamics might be considered within their own field. There are differing positions amongst the two editors as well, creating a dynamic tension that we find stimulating and fruitful. The differences amongst all contributors suggest that nonlinear systems models have provoked a curious realignment of theoretical 12 Nonlinear Models for Archaeology and Anthropology traditions quite different from the outmoded Processualist vs. Post-Processualist divide. We hope that this volume will widen the field of debate over the utility of nonlinear systems for archaeology, and help other archaeologists evaluate the field differently than they might if they were only to consider the high profile work produced within some American institutions. Because, as Stone argues in her chapter, perception of the approach is as important as the approach itself. We end our introduction with an anecdote to bring this point home. The editors originally organized the session that slowly and painfully inspired this volume for the 2002 American Anthropological Association meetings in New Orleans. At the time, there was a vocal ‘pro-Science’ splinter group that was holding its own sessions down the street from the conference hotel, sessions that had not been accepted into the official AAA programme because (according to the dissidents) they were too scientific. The group circulated a list of AAA sessions that did meet their criteria for a scientific approach, and our session was included. This unsolicited testimonial was bestowed on the basis of no more information than the title of the session – ‘Nonlinear Systems Approaches in Archaeology’ – all that was available to the group when they made their pronouncement. Our session participants showed mixed reactions to the news, and happily our audience represented a gratifyingly diverse cross-section of our anthropological colleagues. In the polarized aftermath of the debates within archaeology in the 1980s and 1990s, some archaeologists are willing to declare an approach valid or not on the most superficial of evidence. We direct this book to those members of the field who are dedicated to the work, and are still open to potentially effective and innovative ways of analyzing human society, regardless of what one calls them.