Complexity Theory

by

John T. Murphy

• LAST REVIEWED: 17 October 2022
• LAST MODIFIED: 28 February 2017
• DOI: 10.1093/obo/9780199830060-0169

Introduction

Complexity theory is a collection of theories and approaches that began to grow to prominence in the 1990s, that attempt to address the behavior of systems not readily understood using traditional approaches, and that do so in a way that finds common ground across a wide array of such systems, regardless of domain. Complexity theory addresses highly nonlinear systems and systems that exhibit emergent, self-organized, and adaptive behavior. Domains include virtually every field of study, from economics, to cosmology, to genetic evolution, to cognition and artificial intelligence. Its appeal is that it proposes that common principles guide the dynamics and evolution of systems across all of these domains, and that these principles reflect a deeper order that profoundly structures the physical and social world in which we live. The theory includes rich mathematical approaches and a heavy emphasis on models and modeling, and it is closely associated with advances in computational techniques and computing power. Complexity theory remains a field on its own, in part due to the existence of several prominent centers that take complexity as their central organizing principle and bring researchers from multiple disciplines to work together within a complexity framework; the most notable of these is the independent Santa Fe Institute, but many others exist. Because of its wide range, complexity theory can be approached in a number of ways, but the position taken here is that it should be discussed in part as a body of theory, and in part as a collection of applications in various fields. The main line of complexity theory can be abstracted away from any specific domain, but doing this would hide some of the richness that is found in the specific domain applications. (Additionally, as pointed out by Ladyman, et al. 2013 (cited under Defining and Measuring Complexity), the question of whether there is a “true” definition of a complex system that crosses domains is still open.) A true representation of Complexity Theory demands, and deserves, both. Hence, we begin with General Overviews, then turn to Defining and Measuring Complexity. After this we briefly discuss two theories that are related to complexity theory: Chaos Theory and General System Theory. The discussion then explores themes from complex systems perspectives, including Computation within Complex Systems, Dynamical Systems Theory, self-organization, Emergence, and Complex Adaptive Systems. Subsequently, extensions of complexity theory are presented, including a computational view of systems, considerations of system scaling, and the study of networks; these draw from and contribute to the main body of complexity theory. Next are examples of applications, first to biological and ecological sciences, then to social sciences. Last, we examine complexity theory via philosophy of science, and consider its current manifestation and application to real-world problems.

General Overviews

A number of general overviews of complexity theory are available. Nicolis and Prigogine 1989 provides one of the earliest, grounded in the scientific vocabulary of physics and chemistry. Waldrop 1993, Gell-Mann 1994, and Mitchell 2009 provide overviews for a popular audience. Cowan, et al. 1999 provides a kind of overview in the form of a recapitulation of one of the early workshops among the leaders in developing complexity theory. Other general resources include the journal Complexity and the collection of working papers generated by the Santa Fe Institute Working Papers.

• Complexity.

  The flagship journal for research in complexity science, this journal publishes articles representing the full spectrum of the domains to which complexity theory has been applied.

• Cowan, G. A., David Pines, and David Meltzer, eds. 1999. Complexity: Metaphors, models, and reality. Cambridge, MA: Perseus.

  This extensive volume is a record of one of the formative workshops held at the Santa Fe Institute, and thus an excellent review of a wide array of applications and approaches within complexity theory; it contains papers presented at the workshop (some also published elsewhere), as well as transcripts of the discussions that followed these presentations.

• Gell-Mann, Murray. 1994. The quark and the jaguar: Adventures in the simple and the complex. New York: Owl Books.

  Gell-Mann attempts to bridge the “simplicity” of the fundamental principles of physics, including chance, with the complexity observable in the natural and social worlds. Gell-Mann’s view of science shapes his definition of complexity (see Defining and Measuring Complexity for comments on Gell-Mann’s definition of complexity). The focus is heavily on quantum processes; the extensions to biological and social worlds are intriguing but less well developed and are by now somewhat superseded.

• Mitchell, Melanie. 2009. Complexity: A guided tour. New York: Oxford Univ. Press.

  Mitchell presents a very accessible tour through both the basic mathematics of complexity and some of its applications. She focuses primarily on computational approaches (especially Cellular Automata), and only in the later part of her narrative does she turn to other components, such as network theory. However, like Waldrop, Mitchell presents an additional view on the social history of complexity theory, especially among those who focus on computational approaches and artificial life.

• Nicolis, G., and I. Prigogine. 1989. Exploring complexity: An introduction. New York: Freeman.

  This book presents an early exploration of complex systems science. Its inclination is somewhat different from later works, but its grounding in physics, chemistry, and thermodynamics, as well as its connection to chaos theory (see citations under Chaos Theory) make it an excellent reference that will appeal to those in the physical sciences.

• Santa Fe Institute Working Papers.

  These constitute an excellent record of original research in developing complexity theory and applying it to a wide array of domains.

• Waldrop, Mitchell M. 1993. Complexity: The emerging science at the edge of order and chaos. New York: Simon & Schuster.

  This is an overview for a popular audience of the foundations of complexity as a science, and, especially, of the personal stories surrounding the founding of the Santa Fe Institute. Waldrop provides an overview of the topics and research questions that pushed the initial work in complexity forward, while also opening a revealing window into the social history of the discipline.