Complex Systems and Archaeology Timothy A. Kohler A complex system, according to Mitchell, presents “large networks of components with no central control and simple rules of operation giv[ing] rise to complex collective behavior, sophisticated information processing, and adaptation via learning or evolution” (2009:13). Such systems exhibit emergent and self‐organizing behaviors. They commonly exhibit “frustration”— a condition in which it is impossible to satisfy all competing interests within the constraints imposed (Sherrington 2010). They frequently exist in far‐from‐equilibrium conditions. They are not merely complicated—meaning that they have many “moving parts”—but they also exhibit non‐linear interactions involving structural contingencies or positive feedbacks. In this chapter I survey the implications for archaeology of the not‐fully‐formed theories of such systems, and the attempts by archaeologists to employ aspects of complexity theory, and its methods, in the study of prehistory. Before beginning, though, I need to demarcate the territory. Many archaeologists immediately connect the term complexity with the cultural‐evolutionary literature of the 1950s and 1960s, and the large literature in archaeology dealing with how “more complex” societies (meaning societies exhibiting inegalitarian social relations and political hierarchies) evolved from more egalitarian, smaller‐scale societies. This is an interest of complexity theory—since it involves the emergence of new political actors, levels of organization, and social relations—but the scope of complexity theory is much broader, and encompasses even the smallest‐scale human societies (and, for that matter, societies of ants, and networks of neurons inside an ant’s brain). Unlike many of the approaches outlined in this book, complexity theory is not first of all for and by archaeologists. It is therefore legitimate to wonder whether it has anything useful to offer us. As we explore the territory covered by complexity theory we shall see that its borders are unguarded and its inhabitants diverse. Archaeologists—especially those with an evolutionary orientation—wander freely about, either selecting particular concepts or just drifting. Physicists, biologists, and economists are quite common. While abundant, mathematicians and computer scientists tend to be crepuscular because they are in such demand. Historians, political scientists, and ecologists likewise make important contributions to this community. The web of interests connecting these diverse actors consists of— • A real interest in theory seeking commonalities across levels of organization within a system, and across abiotic and biotic systems of various sorts; • A special attraction to systems composed of many moving parts—dynamic systems—and the patterns that emerge from the interactions of these components through time; • A quantitative orientation and a commitment to computation; • Dissatisfaction with traditional, reductive practices as embodied by the positivistic, hypothesis‐testing, highly analytic approach to science most of us learned in high school—especially since such approaches cope poorly with highly connected complex systems;