Self-organized criticality, the spontaneous development of systems to a critical state, is the first general theory of complex systems with a firm mathematical basis. This theory describes how many seemingly desperate aspects of the world, from stock market crashes to mass extinctions, avalanches to solar flares, all share a set of simple, easily described properties. "...a'must read'...Bak writes with such ease and lucidity, and his ideas are so intriguing...essential reading for those interested in complex systems...it will reward a sufficiently skeptical (...) reader." -NATURE "...presents the theory in a form easily absorbed by the non-mathematically inclined reader." -BOSTON BOOK REVIEW "I picture Bak as a kind of scientific musketeer; flamboyant, touchy, full of swagger and ready to join every fray... His book is written with panache. The style is brisk, the content stimulating. I recommend it as a bracing experience." -NEW SCIENTIST. (shrink)

Residual fluctuations produced in typical experimental methodologies are examined as correlated noises. The effective range of the correlations was assessed by determining whether the decay over look‐back time is better described as a power law or exponential. Both of these decay laws contain free parameters and it is argued that it is not possible to distinguish their models on the basis of simple measures of goodness‐of‐fit. Global analyses that evaluate models on the basis of how well they generalize are conducted. (...) The models are examined in terms of three constructs that all bear on generalization: cross‐validity, flexibility, and representativeness. Quantitative assessment of a large ensemble of data suggests that the correlations decay over time as a power law. The conclusion is that human residual fluctuation is a correlated fractal. (shrink)

In some areas of cognitive science we are confronted with ultrafast cognition, exquisite context sensitivity, and scale-free variation in measured cognitive activities. To move forward, we suggest a need to embrace this complexity, equipping cognitive science with tools and concepts used in the study of complex dynamical systems. The science of movement coordination has benefited already from this change, successfully circumventing analogous paradoxes by treating human activities as phenomena of self-organization. Therein, action and cognition are seen to be emergent in (...) ultrafast symmetry breaking across the brain and body; exquisitely constituted of the otherwise trivial details of history, context, and environment; and exhibiting the characteristic scale-free signature of self-organization. (shrink)

Self-organized criticality (SOC) is based upon the idea that complex behavior can develop spontaneously in certain multi-body systems whose dynamics vary abruptly. This book is a clear and concise introduction to the field of self-organized criticality, and contains an overview of the main research results. The author begins with an examination of what is meant by SOC, and the systems in which it can occur. He then presents and analyzes computer models to describe a number of systems, and he explains (...) the different mathematical formalisms developed to understand SOC. The final chapter assesses the impact of this field of study, and highlights some key areas of new research. The author assumes no previous knowledge of the field, and the book contains several exercises. It will be ideal as a textbook for graduate students taking physics, engineering, or mathematical biology courses in nonlinear science or complexity. (shrink)

How do people decide what to say in context? Many theories of pragmatics assume that people have specialized knowledge that drives them to utter certain words in different situations. But these theories are mostly unable to explain both the regularity and variability in people’s speech behaviors. Our purpose in this article is to advance a view of pragmatics based on complexity theory, which specifically explains the pragmatic choices speakers make in conversations. The concept of self-organized criticality sheds light on how (...) a history of utterances and subtle details of a situation surrounding a conversation may directly specify language behavior. Under this view, pragmatic choice in discourse does not reflect the output of any dedicated pragmatic module but arises from a complex coordination or coupling between speakers and their varying communicative tasks. (shrink)

The complex systems approach to cognitive science invites a new understanding of extended cognitive systems. According to this understanding, extended cognitive systems are heterogenous, composed of brain, body, and niche, non-linearly coupled to one another. This view of cognitive systems, as non-linearly coupled brain–body–niche systems, promises conceptual and methodological advances. In this article we focus on two of these. First, the fundamental interdependence among brain, body, and niche makes it possible to explain extended cognition without invoking representations or computation. Second, (...) cognition and conscious experience can be understood as a single phenomenon, eliminating fruitless philosophical discussion of qualia and the so-called hard problem of consciousness. What we call “extended phenomenological-cognitive systems” are relational and dynamical entities, with interactions among heterogeneous parts at multiple spatial and temporal scales. (shrink)

Abstract While agreeing that dynamical models play a major role in cognitive science, we reject Stepp, Chemero, and Turvey's contention that they constitute an alternative to mechanistic explanations. We review several problems dynamical models face as putative explanations when they are not grounded in mechanisms. Further, we argue that the opposition of dynamical models and mechanisms is a false one and that those dynamical models that characterize the operations of mechanisms overcome these problems. By briefly considering examples involving the generation (...) of action potentials and circadian rhythms, we show how decomposing a mechanism and modeling its dynamics are complementary endeavors. (shrink)

Most models of response time (RT) in elementary cognitive tasks implicitly assume that the speed-accuracy trade-off is continuous: When payoffs or instructions gradually increase the level of speed stress, people are assumed to gradually sacrifice response accuracy in exchange for gradual increases in response speed. This trade-off presumably operates over the entire range from accurate but slow responding to fast but chance-level responding (i.e., guessing). In this article, we challenge the assumption of continuity and propose a phase transition model for (...) RTs and accuracy. Analogous to the fast guess model (Ollman, 1966), our model postulates two modes of processing: a guess mode and a stimulus-controlled mode. From catastrophe theory, we derive two important predictions that allow us to test our model against the fast guess model and against the popular class of sequential sampling models. The first prediction—hysteresis in the transitions between guessing and stimulus-controlled behavior—was confirmed in an experiment that gradually changed the reward for speed versus accuracy. The second prediction—bimodal RT distributions—was confirmed in an experiment that required participants to respond in a way that is intermediate between guessing and accurate responding. (shrink)

The complex-systems approach to cognitive science seeks to move beyond the formalism of information exchange and to situate cognition within the broader formalism of energy flow. Changes in cognitive performance exhibit a fractal (i.e., power-law) relationship between size and time scale. These fractal fluctuations reflect the flow of energy at all scales governing cognition. Information transfer, as traditionally understood in the cognitive sciences, may be a subset of this multiscale energy flow. The cognitive system exhibits not just a single power-law (...) relationship between fluctuation size and time scale but actually exhibits many power-law relationships, whether over time or space. This change in fractal scaling, that is, multifractality, provides new insights into changes in energy flow through the cognitive system. We survey recent findings demonstrating the role of multifractality in (a) understanding atypical developmental outcomes, and (b) predicting cognitive change. We propose that multifractality provides insights into energy flows driving the emergence of cognitive structure. (shrink)