The dynamical approach to cognition is a confederation of research efforts bound together by the idea that natural cognition is a dynamical phenomenon and best understood in dynamical terms. This contrasts with the "law of qualitative structure" (Newell and Simon 1976) governing orthodox or "classical" cognitive science, which holds that cognition is a form of digital COMPUTATION.

The idea of mind as dynamical can be traced as far back as David HUME, and it permeates the work of psychologists such as Lewin and Tolman. The contemporary dynamical approach, however, is conveniently dated from the early cy-bernetics era (e.g., Ashby 1952). In subsequent decades dynamical work was carried out within programs as diverse as ECOLOGICAL PSYCHOLOGY, synergetics, morphodynamics, and neural net research. In the 1980s, three factors -- growing dissatisfaction with the classical approach, developments in the pure mathematics of nonlinear dynamics, and increasing availability of computer hardware and software for simulation -- contributed to a flowering of dynamical research, particularly in connectionist form (Smolensky 1988). By the 1990s, it was apparent that the dynamical ap-proach has sufficient power, scope, and cohesion to count as a research paradigm in its own right (Port and van Gelder 1995).

In the prototypical case, the dynamicist focuses on some particular aspect of cognition and proposes an abstract dy-namical system as a model of the processes involved. The behavior of the model is investigated using dynamical systems theory, often aided by simulation on digital computers. A close match between the behavior of the model and em-pirical data on the target phenomenon confirms the hypothesis that the target is itself dynamical in nature, and that it can be understood in the same dynamical terms.

Consider, for example, how we make decisions. One possibility is that in our heads there are symbols representing various options and the probabilities and values of their outcomes; our brains then crank through an ALGORITHM for determining a choice (see RATIONAL DECISION-MAKING). But this classical approach has difficulty accounting for the empirical data, partly because it cannot accommodate temporal issues and other relevant factors such as affect and context. Dynamical models treat the process of DECISION-MAKING as one in which numerical variables evolve interactively over time. Such models, it is claimed, can explain a wider range of data and do so more accurately (see, e.g., Busemeyer and Townsend 1993; Leven and Levine 1996).

A better understanding of dynamical work can be gained by highlighting some of its many differences with classical cognitive science. Most obviously, dynamicists take cognitive agents to be dynamical systems as opposed to digital conputers. A dynamical system for current purposes is a set of quantitative variables changing continually, concurrently, and interdependently over quantitative time in accordance with dynamical laws described by some set of equations. Hand in hand with this first commitment goes the belief that dynamics provides the right tools for understanding cognitive processes. Dynamics in this sense includes the traditional practice of dynamical modeling, in which scientists attempt to understand natural phenomena via abstract dy-namical models; such modeling makes heavy use of calculus and differential or difference equations. It also includes dynamical systems theory, a set of concepts, proofs, and methods for understanding the behavior of systems in general and dynamical systems in particular. A central insight of dynamical systems theory is that behavior can be understood geometrically, that is, as a matter of position and change of position in a space of possible overall states of the system. The behavior can then be described in terms of attractors, transients, stability, coupling, bifurcations, chaos, and so forth -- features largely invisible from a classical perspective.

Dynamicists and classicists also
diverge over the general nature of cognition and cognitive agents.
The pivotal issue here is probably the role of time. Although all
cognitive scientists understand cognition as something that happens *over* time,
dynamicists see cognition as being *in* time, that is, as an
essentially temporal phenomenon. This is manifested in many ways.
The time variable in dynamical models is not a mere discrete order,
but a quantitative, sometimes continuous approximation to the real
time of natural events. Details of timing (durations, rates, synchronies,
etc.) are taken to be essential to cognition itself rather than
incidental details. Cognition is seen not as having a sequential
cyclic (sense-think-act) structure, but rather as a matter of continuous
and continual coevolution. The subtlety and complexity of cognition
is found not *at* a time in elaborate static structures, but
rather *in* time in the flux of change itself.

Dynamicists also emphasize SITUATEDNESS/EMBEDDEDNESS. Natural cognition is always environmentally embedded, corporeally embodied, and neurally "embrained." Clas-sicists typically set such considerations aside (Clark 1997). Dynamicists, by contrast, tend to see cognitive processes as collective achievements of brains in bodies in contexts. Their language -- dynamics -- can be used to describe change in the environment, bodily movements, and neurobiological processes (e.g., Bingham 1995; Wright and Liley 1996). This enables them to offer integrated accounts of cognition as a dynamical phenomenon in a dynamical world.

In classical cognitive science, symbolic representations and their algorithmic manipulations are the basic building blocks. Dynamical models usually also incorporate representations, but reconceive them as dynamical entities (e.g., system states, or trajectories shaped by attractor landscapes). Representations tend to be seen as transient, context dependent stabilities in the midst of change, rather than as static, context-free, permanent units. Interestingly, some dynamicists claim to have developed wholly representation-free models, and they conjecture that representation will turn out to play much less of a role in cognition than has traditionally been supposed (e.g., Skarda 1986; Wheeler forthcoming).

The differences between the dynamical
and classical approaches should not be exaggerated. The dynamical approach
stands opposed to what John Haugeland has called "Good
Old Fashioned AI" (Haugeland 1985). However, dynamical
systems may well be performing computation in some other sense (e.g.,
analog computation or "real" computation; Blum, Shub,
and Smale 1989; Siegelmann and Sontag 1994). Also, dynamical systems
are generally effectively computable. (Note that something can be *computable* without
being a digital *computer.*) Thus, there is considerable
middle ground between pure GOFAI and an equally extreme dynamicism
(van Gelder 1998).

How does the dynamical approach relate to connectionism? In a word, they overlap. Connectionist networks are generally dynamical systems, and much of the best dynamical research is connectionist in form (e.g., Beer 1995). However, the way many connectionists structure and interpret their systems is dominated by broadly computational preconceptions (e.g., Rosenberg and Sejnowski 1987). Conversely, many dynamical models of cognition are not connectionist networks. Connectionism is best seen as straddling a more fundamental opposition between dynamical and classical cognitive science.

Chaotic systems are a special sort of dynamical system, and chaos theory is just one branch of dynamics. So far, only a small proportion of work in dynamical cognitive science has made any serious use of chaos theory. Therefore the dynamical approach should not be identified with the use of chaos theory or related notions such as fractals. Still, chaotic dynamics surely represents a frontier of fascinating possibilities for cognitive science (Garson 1996).

The dynamical approach stands or falls on its ability to deliver the best models of particular aspects of cognition. In any given case its ability to do this is a matter for debate among the relevant specialists. Currently, many aspects of cognition -- e.g., story comprehension -- are well beyond the reach of dynamical treatment. Nevertheless, a provisional consensus seems to be emerging that some significant range of cognitive phenomena will turn out to be dynamical, and that a dynamical perspective enriches our understanding of cognition more generally.

- COGNITIVE MODELING, CONNECTIONIST
- COMPUTATION AND THE BRAIN
- COMPUTATIONAL THEORY OF MIND
- CONNECTIONIST APPROACHES TO LANGUAGE
- NEURAL NETWORKS
- RULES AND REPRESENTATIONS

- The Dynamical Hypothesis in CognitiveScience
- The Third Contender: A Critical Examination of the Dynamicist Theory of Cognition

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