Eliasmith, C. (in press). Dynamical models and van Gelder's dynamicism: Two different things. Commentary on T. van Gelder. Behavioral and Brain Sciences.

Dynamical models and van Gelder's dynamicism: Two different things

Chris Eliasmith ' Department of Philosophy ' Campus Box 1073 ' Washington University in St. Louis ' One Brookings Drive ' St. Louis, MO 63130 USA ' chris@twinearth.wustl.edu ' http://www.artsci.wustl.edu/~celiasmi/


Van Gelder has presented a position which he ties closely to a broad class of models known as dynamical models. While supporting many of his broader claims about the importance of this class (as has been argued by connectionists for quite some time), I note that there are a number of unique characteristics of his brand of dynamicism. I suggest that these characteristics engender difficulties for his view.

I find van Gelder's article commendable in many respects. However, my enthusiasm for certain aspects of his position is tempered by serious concern. A number of the central claims van Gelder presents are compelling: of course we should consider cognitive systems to be dynamical; of course time is central to a good understanding of such systems; and of course we should use the tools of dynamical systems theory to help construct and understand our models. Do these ideas present a new direction that cognitive science has yet to embrace? Of course not. Many connectionists have embraced them for well over ten years. But, there is more to the vision that van Gelder presents. I argue that that "more" is precisely the problem with van Gelder's dynamicism.

First, I'd like to be more explicit about why this article is compelling and, in many ways, right. Contrary to his previous writing, van Gelder has seen fit to explicitly include connectionism in the class of (the right kind of) dynamical systems . As well, he rightly stresses the importance of modeling real time and of using our best mathematical tools to understand real time systems (section 3.3 points 2, 3; sections 4.2.2 and 4.2.3). In other words, I completely agree that cognitive systems are dynamical systems. Note that given the two previous points we can derive a strong argument in favor of dynamical connectionist models. Finally, there are careful improvements over some of the more problematic claims in his prior discussions of dynamicism. For example, his assertion that "the DH can embrace the idea that cognitive processes are computational" (section 6.3), seems far more supportable than his previous suggestion that cognition is "the behavior of some (noncomputational) dynamical system" . Again, this view allies van Gelder with connectionists who have been making this suggestion for years . Overall, this article presents van Gelder's most persuasive version of dynamicism .

However, the problems which remain are central and, in my view, debilitating. I will outline three; the first of which is a problem of emphasis, the second a problem of interpretation and the third, and most important, a problem in principle.

First, to place an emphasis on the discrete/continuous difference between classical computational systems and dynamical systems is somewhat deceptive in the context of real world cognition. There is strong evidence that the brain processes information in a manner that can be effectively captured by discrete descriptions. Bialek and Reike have estimated that individual spikes in neurons carry approximately 3 bits of information . This means that the timing of spike occurrences can be represented by a finitely precise set of values, which could easily be given a discrete representation. If we really needed continuous variables in our models, then that would imply that an infinite amount of information was transmitted with each spike. This is highly improbable given the uncertain and noisy environments of neurons and brains. Thus, for van Gelder to emphasize the continuous nature of dynamical systems as important is uninteresting, if not misleading (see sections 2, 3.2, 3.3).

Second, van Gelder's position admits serious difficulties regarding model interpretation. How, in other words, can we tell what a variable means? Barton discusses the difficulties of effectively using such models in psychology. He notes that such models are strictly metaphorical. Though the metaphor's source is mathematical, that does not supply the model itself with any technical rigor. In terms of van Gelder's article, when he states: "Dynamical theories of cognitive processes are deeply akin to dynamical accounts of other natural phenomena such as celestial motion" (section 6.6, paragraph 2), he is ignoring an important difference between such models: we can measure angular velocity, but we have no idea what "valence" is in the DFT model or how to measure it in the real system. This difficulty stems from van Gelder's insistence on high-level and low-dimensional dynamical models (section 4.1), an insistence strangely contrary to admitting connectionist models in to the class of the "right kind" of dynamical systems (section 1).

Third, and most importantly, van Gelder's version of dynamicism seems to sidestep a central issue in cognitive modeling; representation . The CH cannot be so easily dismissed, particularly when compared to the DH. The CH offers a built-in prowess for manipulation of symbolic representation. Of course, as van Gelder is quick to point out, this comes a cost. Classical models have difficulty with many of the sorts of behaviors that dynamical models handle very gracefully. However, people are both dynamical and competent symbol manipulators. It would not be in the best interest of cognitive science to simply trade one set of strengths for another. Rather, a set of principles which is able to capture both sorts of behavior should be sought. It seems, in other words, that van Gelder has neglected the really interesting, and difficult, question of how a dynamical system could give rise to representational behavior and thus human-style intelligence.

In sum, claiming cognitive systems are dynamical seems fundamentally right. But, it seems equally wrong to emphasize continuity, proclaim low-dimensional models superior, and all but dismiss the importance of representation to understanding human cognition. Dynamical models are clearly desirable. Van Gelder's dynamicism is another matter.