Simplifying complexity: a review of complexity theory Steven M. Manson Graduate School of Geography, Clark University, 950 Main Street, Worcester, MA 01610-1477, USA Received 5 August 1999; in revised form 7 September 2000 Abstract Complexity theory has captured the attention of the scienti®c community to the extent where its proponents tout it as a dominant scienti®c trend. Geographers, and environmental, human, and regional planners have applied complexity theory to topics ranging from cultural transmission and economic growth to the braiding of rivers. While such a wide array of applications is heartening because it speaks to the utility of complexity theory, it is necessary to move beyond the hyperbole and critically examine the nature of complexity research. The author therefore provides an overview of the evolution of complexity research, establishes a preliminary typology of complexity approaches with their advantages and drawbacks, and identi®es areas of further research. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Complexity theory; Chaos; Self-organization; Emergence 1. Introduction ``Complexity theory is destined to be the dominant scienti®c trend of the 1990's ... This revolutionary technique can explain any kind of complex system ± multinational corporations, or mass extinctions, or ecosystems such as rainforests, or human consciousness. All are built on the same few rules.'' Lewin, 1992: back cover). Whether over-exuberance or merely aggressive advertising copy, this bold pronouncement has yet to be ful®lled. Growing acceptance of complexity is evidenced by a recent section on complex systems in the journal Science 1999) and the increasing amount of complexity research. This interest is countered by concern that complexity is an over-hyped fad Sarder and Ravetz, 1994). Does complexity merit the title of a ``dominant scienti®c trend'' or are ill-advised scientists rushing to capitalize on its cachet? What value does complexity theory hold for geographic research? Advocates of complexity theory see it as a means of simplifying seemingly complex systems. The actual practice of complexity theory, however, is anything but simple in that there is no one identi®able complexity theory. Instead, a number of theories concerned with complex systems gather under the general banner of complexity research. The exact nature of complexity research is hard to discover due to the large degree to which complexity ideas are traded across disciplinary boundaries. Thrift 1999), for instance, examines what complexity theory means to, and traces interactions among, managerial science, the social and natural sciences, and new age philosophy. There is also a propensity for disciplines to borrow techniques from other disciplines or to speculate naively on subjects typically seen as outside their purview Horgan, 1995; Lo Presti, 1996). In either case, exciting academic cross-fertilization occurs at the expense of potentially false leads. In sum, any de®nition of complexity is beholden to the perspective brought to bear upon it. While it is possible, therefore, to examine complexity on a discipline-by-dis- cipline basis, breaking complexity research into three major divisions aords a more coherent understanding of complexity theory. ``Algorithmic complexity'', in the form of mathematical complexity theory and information theory, contends that the complexity of a system lies in the diculty faced in describing system characteristics. ``Deterministic complexity'' deals with chaos theory and catastrophe theory, which posit that the interaction of two or three key variables can create largely stable sys- tems prone to sudden discontinuities. ``Aggregate com- plexity'' concerns how individual elements work in concert to create systems with complex behavior. Why have these three divisions if there is an identi- ®able body of complexity theory? The simplest answer is Geoforum 32 2001) 405±414 www.elsevier.com/locate/geoforum E-mail address: smanson@clarku.edu S.M. Manson). 0016-7185/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII:S0016-718500)00035-X