Dynamics in Cognitive Science

Since the early 1990s, some people have gotten very excited about the idea that dynamical systems theory can be used to model cognitive processes. As somebody trained in nonlinear dynamics, I applaud this development, since, if successful, it will enhance my material and academic prospects. Sadly, when they do things like purporting to explain decision-making with a low (8) dimensional model with no noise, I grow deeply suspicious. Worse, many of these same people believe that dynamics gives them an account of cognition which is incompatible with traditional models, whether of the (Newell-Simon) symbol-processing or connectionist sort, and in fact one which is fundamentally non-computational. As somebody trained in the symbolic aspects of nonlinear dynamics, and who uses that math to study the intrinsic computation carried out by dynamical systems, I have to wonder what they're talking about.

To do: Find something interesting to say about this by December, when abstracts are due for the Potsdam workshop on Dynamical Systems Approaches to Language and Symbol Grounding. Update, December 2005: Well, I don't know if what I found to say was interesting, but you can read the abstract here.

James P. Crutchfield, "Dynamical Embodiments of Computation in Cognitive Processes", Behavioral and Brain Sciences 21 (1998): 635--637 [Online]
Chris Eliasmith, "Attractive and In-discrete: A Critique of Two Putative Virtues of the Dynamicist Theory of Mind", Minds and Machines 11 (2001): 417--426 [Journal link, HTML preprint]
Clark Glymour, "Goethe to van Gelder: Comments on 'Dynamical Systems' Models of Cognition" [Abstract: "The 'dynamical systems' model of cognitive processing is not an alternative computational model. The proposals about 'computation' that accompany it are either vacuous or do not distinguish it from a variety of standard computational models. I conclude that the real motivation for van Gelder's version of the account is not technical or computational, but is rather in the spirit of natur-philosophie." Available as a (boo, his) RTF document, PHIL-SCI 139]
Melanie Mitchell
- "A complex-systems perspective on the 'computation vs. dynamics' debate in cognitive science", in M. A. Gernsbacher and S. J. Derry (eds.), Proceedings of the 20th Annual Conference of the Cognitive Science Society (Cogsci98), pp. 710--715 [PDF]
- "Theories of structure vs. theories of change", Behavioral and Brain Sciences 21 (1998): 645--646 [PDF]

Marco Giunti, Computation, Dynamics and Cognition [Actually, there's a lot of good stuff in this book, but I think it's quite unhelpful on this topic. For instance, while he correctly points out that all computational systems are dynamical systems, he takes a ridiculously restrictive view of computation, especially of analog computation. By his definition, y=sin(x) is an uncomputable function, and I think even y=x, the identity function, is uncomputable.]
T. van Gelder, "The dynamical hypothesis in cognitive science", Behavioral and Brain Sciences 21 (1998): 615--665 [On which the papers by Crutchfield and Mitchell in the same volume of BBS are commentary. Frankly the rest of van Gelder's work, e.g. the book he edited with R. Port called Mind as Motion, is no more impressive to me.]

Peter beim Graben, "Incompatible implementations of physical symbol systems", Mind and Matter 2 (2004): 29--51 [PDF via Dr. beim Graben]
Istavan S. N. Berkeley, "What the #$*%! is a Subsymbol?", Minds and Machines 10 (2000): 1--13
Rick Dale and Michael J. Spivey, "From apples and oranges to symbolic dynamics: a framework for conciliating notions of cognitive representation", Journal of Experimental & Theoretical Artificial Intelligence 17 (2005): 317--342
Herbert Jaeger, "From Continuous Dynamics to Symbols", in W. Tschacher and J.-P. Dauwalder (eds.), Dynamics, Synergetics, Autonomous Agents (Singapore: World Scientific, 1999) pp. 29--48 [PDF]
Teed Rockwell, "Attractor Spaces as Modules: A Semi-Eliminative Reduction of Symbolic AI to Dynamic Systems Theory", Minds and Machines 15 (2005): 23--55
Whit Schonbein, "Cognition and the Power of Continuous Dynamical Systems", Minds and Machines 15 (2005): 57--71

Notebooks

Dynamics in Cognitive Science