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Metascience Symposium on Mind as Motion Response to Commentators Tim van Gelder Robert Port Mind as Motion (Port & van Gelder, 1995) was produced with a number of goals in mind. One was to provide a general introduction to dynamical cognitive science. (To this end, the book provided an introductory overview of the dynamical approach, a tutorial introduction to dynamics, brief introductions to all chapters, guides to further reading, and a glossary.) A second goal was to parade the power and scope of dynamical research by gathering together in one place a representative sampling of quality contributions. A third (and perhaps most ambitious) goal was that of forging a coherent theoretical paradigm out of what had previously been related, but nevertheless scattered and diverse research projects. Critical reactions to the book, as illustrated by the contributions to this symposium, generally accept (implicitly, if not explicitly) that these goals have been achieved. In particular, whether enthusiastic or dismissive, they treat the dynamical approach as something to be reckoned with. Prior to Mind as Motion, there was a considerable amount of dynamical research in various branches of cognitive science. Since Mind as Motion, there has been something identifiable as "the dynamical approach to cognition." We count this as progress. The issue these days is not whether or not there is such a thing as "dynamicism" (an ugly term, but one we can live with). Rather, discussion is concerned with how best to characterize dynamicism, in what way it competes with computationalism, and how successful it is likely to be. On questions such as these, Mind as Motion took up a deliberately provocative stance. It laid out a particular interpretation of dynamicism, presenting it as fundamentally different from and superior to the mainstream computational approach. In Brendan Kitts' apt phrase, Mind as Motion "flung down the gauntlet." Modest positions are always more safe in science, but they are also less interesting and less likely to stimulate significant advances in the field. Mind as Motion boldly conjectured that dynamicism stands to inherit the theoretical throne that has been occupied by computationalism for the past several decades. Whether or not this ultimately turns out to be right, one thing is certain: thinking about cognition dynamically is difficult. One reason is that the relevant mathematics is often formidable, even before one attempts to apply it to the behavior of natural cognitive agents. Another is that the dynamical approach demands that we think of cognition as essentially a matter of change in time. For most people, thinking about interactive processes seems intrinsically more challenging than thinking about static structures. Third, most contemporary cognitive scientists (including ourselves) have undergone lengthy training in how to conceptualize cognition in broadly computational terms (i.e., in terms of symbols and operations on symbol structures). But the dynamical approach is at odds with computationalism at many levels and in many ways. It demands a fundamental shift in one's theoretical worldview. The inevitable inertia of the human mind renders this shift quite difficult. For this reason, we are pleased that Mark Coulson and Stephen Nunn devoted considerable effort to thoughtful exposition of some central strands of Mind as Motion. Our experience has been that proper appreciation of the dynamical approach is impossible without first thoroughly working through some sufficient number of dynamical treatments of specific aspects of cognition. Skimming the material, or hearing about it second hand, just isn't enough; it cannot bring about the required perspectival shift. Coulson and Nunn do stop to put up some cautionary flags in quite appropriate places. Generally, however, they are concerned neither to endorse nor indict, and readers interested to understand how some dynamicists begin to tackle problems of language or development might find their discussions a useful point of entry. Incidentally, Coulson in his discussion of language mentions the chapters by Elman, Browman & Goldstein, and Petitot, but he neglects to even mention various other chapters relevant to language, such as those by Saltzman (on motor control in speech), Pollack (formal grammars), and Port, Cummins & McAuley (auditory and speech perception). In fact, of all major domains of cognition, it turned out to be language which received most attention in Mind as Motion. We found this surprising, in view of the widespread assumption that language is somehow especially appropriate for traditional computational modeling. Steve Torrance and Brendan Kitts both tackle more general issues. Interestingly, despite significant differences in tone, they conclude their discussions on the same note. Both suggest that Mind as Motion may be too antagonistic to mainstream computationalism. Torrance asks: Where does this leave computationalism as an approach to cognition? One possibility, short of killing it off, is to allow computational and dynamical accounts to co-exist in some manner-rather in the manner of Smolensky's approach. Another possibility is that there may be certain areas of cognition where dynamical approaches are best employed and others where computational approaches are most appropriate. Perhaps there is even a quite complex interplay between the two. Kitts is considerably more assertive, claiming that The point I would like to make-and I believe it is an obvious one-is that dynamical systems will not be ideal for every situation, and that other formal systems should be used if they provide a better description... Now, we agree (of course) that cognitive scientists should always use whatever theoretical framework happens to provide the best descriptions. We even agree that some aspects of cognition might (after all) turn out to be best described in traditional computational terms. The interesting, substantial issue is: which framework will in fact provide the best description of any given aspect of cognition? To address this, we must look closely at whatever evidence bears on the case. There is no place here for simple dogmatism on either side. Kitts' claim that it is "obvious" that the dynamical approach has certain limits is just as ill-founded as any blind faith that all cognition is best described dynamically. So, we agree with Kitts when he claims that the central question is: Do dynamical systems have features which enable them to model phenomena better than other models? But we find quite bizarre his claim that Despite...PVG's rhetoric, there is really no evidence either way. For there is already a vast amount of evidence upon which we can draw, and more becomes available every month. The evidence is of two basic kinds. First, we can look at the relative success of dynamical as opposed to computational models in describing any given aspect of cognition. Consider, for example, the huge range of empirical data on human decision making under uncertainty. Is that better captured by dynamical models, such as the one described in Motion as Motion by Busemeyer & Townsend, or by orthodox computational models? Clearly, there is a great deal of such evidence available, and in any given case it is hardly obvious in advance which side is right. Mind as Motion included some fifteen chapters presenting evidence in favor of dynamical treatment of a wide range of aspects of cognition. That alone does not close the case, but it does illustrate the fact that serious assessment of the dynamical hypothesis is a matter of taking a long hard look at the details. The second kind of evidence consists of general arguments concerning the merits of dynamical or computational treatment. There is already a long philosophical tradition discussing the many arguments concerning the computational hypothesis, and Mind as Motion did not purport to cover this terrain. What it did add to the debate was a series of general arguments favoring the dynamical approach. Kitts reformulates them as follows: PVG's argument that dynamical systems are better models comes down to three points: 1. The underlying physics of mental phenomena is continuous. 2. Differential equations have features such as slow and fast time scales, self-organization, and so on, which make them good for cognition. 3. Computational models have failed so far to model cognition. We're not quite sure what Kitts means by "comes down to," but his list is a poor substitute for the series of six distinct arguments provided in "Its About Time" (pp.17-30). There, we summarized the arguments as follows: What we really want to know is: what general things do we already know about the nature of cognitive systems that suggest that dynamics will be the framework within which the most powerful models are developed? We know, at least, these very basic facts: that cognitive processes always unfold in real time; that their behaviors are pervaded by both continuities and discretenesses; that they are composed of multiple sub-systems which are simultaneously active and interacting; that their distinctive kinds of structure and complexity are not present from the very first moment, but emerge over time; that cognitive processes operate over many time scales, and events at different time-scales interact; and that they are embedded in a real body and environment. The dynamical approach provides a natural framework for the description and explanation of phenomena with these broad properties. The computational approach, by contrast, either ignores them entirely or handles them only in clumsy, ad hoc ways. (p.18) It would take too much space to demonstrate the point here, but we suggest that Kitts' scatterfire responses to his own substitutes for our arguments fall a long way short of rebutting this extensive array of considerations. (For example, one of our arguments was that any adequate framework for the description of natural cognition must be able to accommodate both continuous and discrete forms of change. Kitts transforms this into the claim that the "underlying physics of mental phenomena is continuous," which he then challenges. However, as far as we can see, the nature of the physical world at minute scales is not relevant.) More generally, we are still looking forward to the day when someone presents serious critical assessment of these arguments. Torrance, after presenting a sympathetic introduction to the dynamical approach and an overview of Mind as Motion, turns to the problem of how connectionism stands with respect to the dynamical and computational approaches, and indeed how those approaches stand with respect to each other. The latter question is taken up in quite a bit more detail in "The Dynamical Hypothesis in Cognitive Science" (forthcoming, Behavioral and Brain Sciences). Here we take the opportunity to clarify the status of connectionism. The neural networks used as models in connectionist research in cognitive science are typically dynamical systems of a quite specific kind (high-dimensional, homogeneous systems of "neural" processing units). However, these systems are sometimes configured and conceptualized in ways that are heavily based on traditional computational ways of thinking. For example, they are sometimes conceptualized in terms of the transformation of input representations into output representations, just like traditional computational models. At other times, connectionist systems are configured and conceptualized in thoroughly dynamical ways. Thus, some connectionist work is dynamical; indeed, as Mind as Motion demonstrates, much of the best dynamical work is connectionist in form. Meanwhile, other connectionist work amounts to a kind of ugly hybrid of dynamical and computational elements. Generally, we regard connectionism, as an intellectual movement within cognitive science, as a kind of unstable, transitional stage in the gradual progression from orthodox computationalism to full-blooded dynamicism. Kitts, obviously impatient with the opposition Mind as Motion deliberately sets up between dynamical and computational approaches, proposes that we think instead of a spectrum of "formal systems." These differ along dimensions such as "descriptive power," "computational power," and "analytical methods," thereby determining their suitability for modeling different aspects of cognition. A formal system in Kitts' sense is basically a set of possible states, some initial states, some rules governing mappings between states, and some output or final states. In attempting to encompass dynamical systems within the general category of formal systems as he defines them, however, Kitts is failing to appreciate the deep difference between the dynamical and computational approaches. The crucial point is that dynamical systems need not have anything corresponding to start or input states, or to final or output states, and state change need not be understood as discrete instantaneous mappings from one state to another. This may seem strange, but consider the solar system, and how we understand its behavior. For all practical purposes, there are no privileged start states, and no privileged ends states; no inputs and no outputs. All aspects of the system are continuously and continually changing and affecting each other's change. The complexities of its behavior are found in this temporal evolution, rather than in complex static structures transformed by simple discrete operations. Kitts' "formal systems" framework, vague and speculative as it is, is really little more than a set of square holes into which he is trying to force the round pegs of dynamics. From a thoroughly dynamical perspective, cognition looks very different than it does from the perspective Minsky, Newell, Simon, Chomsky and their heirs. In contrast to the a priori inventories of static symbols that are manipulated in discrete time by a cognitive engine sequestered from the rest of the physical world, the dynamical perspective sees cognition as a matter of continuous and ceaseless change in a system at all times shaped by coupling with the body and with spatiotemporal patterns in the environment. Wherever discrete, static or object-like cognitive entities can be found (such as 'concepts', 'words,' 'rules', etc.), it encourages us to describe the dynamics enabling these relative stabilities to exist. A major shift in thinking is required to appreciate cognition from this perspective and to see it as intrinsically embedded in the body and the world. There is no question that far more is at stake here than merely a choice of formal mechanism. Dynamicism-as Kitts properly suspected-entails a revolutionary change in the intellectual culture of cognitive science. Indeed, this is one of the most prominent themes in Mind as Motion. |
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