The dynamical systems approach in cognitive science offers a potentially useful perspective on both brain and behavior. Indeed, the importation of formal tools from dynamical systems research has already paid off for our field in many ways. However, like some other theoretical perspectives in cognitive science, the dynamical systems approach comes in both moderate or pragmatic and “fundamentalist” varieties ( Jones & Love, 2011 ). In the latter form, dynamical systems theory can rise to some stirring rhetorical heights. However, as argued here, it also triggers a number of serious and specific reservations.

One cannot help but admire the target articles for their aspirations. In a discipline that can sometimes get caught up in trivialities, it is undeniably bracing to read work that strives for such a broad reach. There are, to be sure, other admirable aspects to these articles, including the value they attach to formalization and their focus on real‐time performance rather than abstract competence. Particularly agreeable is the view that organized behavior arises from a system with underlying reservoirs of flexibility (Riley et al., p. 24), an insight that makes it possible to accommodate “quasi‐regularity”: the appearance of structured exceptions amid apparent regularity (see Plaut, McClelland, Seidenberg, & Patterson, 1996). And yet, when the authors of one target article allow that “the reader … can get off the highway at any point” (Silberstein & Chemero, p. 5), I must. For one thing, I find myself in need of a rest stop after navigating through the jargon in which these papers traffic: ultra‐fast dynamics, reciprocal embodiment, tensegrity, scale‐free variation, strange loops, flows of energy, symmetry breaking, diffusion, synergies, self‐organized criticality … collapse. I hasten to acknowledge that such technical language would be entirely acceptable if it were clear that the underlying ideas genuinely required it. However, at least in some instances, highfalutin terms are applied to what appear to be fairly pedestrian concepts. For example, in the piece by Riley et al. (p. 4), the dynamical expression “exquisite context sensitivity” is invoked in connection with the observation that “most simple cognitive judgments … vary with task requirements.” Why is this “exquisite” context sensitivity, as opposed to ordinary, garden‐variety context sensitivity? Similarly, Gibbs and van Orden (p. 17) assert that “All communicative impairments have a pragmatic dimension in that they seem somewhat out of balance … as though the critical states of options to be enacted were insufficiently constrained by the near‐term history of the discourse … possibly due to an amplification of the frustration that underdetermines all utterances before the fact.” How does this differ from saying that the choice of words in speech is insufficiently sensitive to the preceding context? What does “critical state” add to the more prosaic “decision,” and what do “frustration” and “underdetermination” add to the more conventional notion of competition? Another source of reservations, again common to all the target articles, is a more or less rejectionist attitude toward longer standing approaches. “Cognitive science,” we are told, “has reached an impasse” (Riley et al., p. 2). “The dynamics of cognition are radically different from what is often assumed” (Dixon et al., p. 3), and “To move forward, cognitive science must turn and embrace complexity to equip itself with the tools and concepts that will enable the needed sea change” (Riley et al., p. 2). I am reluctant to make this turn, for at least three reasons. I will refer to these, respectively, as (a) the Explanatory Donut Hole, (b) the Holmesian Fallacy,1 and (c) the Computationalism Canard.

1. The Explanatory Donut Hole The perspective taken in all of the target articles is strikingly abstract and universalist, appealing to principles that are purported to span domains and levels of description. Indeed, the framework presumes to characterize cognition at large: “Cognition, because it involves the activity of physical elements, must consume energy. Energy consumption will change the local gradients of energy and matter, and therefore the speed at which energy flows through the system, that is, the rate of diffusion. Thus, the activity that is cognition must change the rate of diffusion in the complex physical materials in which it occurs” (Dixon et al., p. 14). The unifying impulse that is evident here goes hand in hand with an insistent holism. For example, Dixon and colleagues assert that behavioral differences across individuals and in neuropsychological syndromes “reflect differences in system‐wide dynamical properties … rather than reflecting differences or deficits in specific components” (p. 10). Paradoxically, however, alongside this universalist/holistic perspective, one finds a subtle but pervasive nominalism. For example, we are told that “Peoples’ pragmatic choices in speaking derive from a perpetually iterated dynamic process, whereby multiple simultaneous conflicting constraints self‐organize into people’s in‐the‐moment potentials for utterances and meaningful experiences” (Gibbs & van Orden, p. 12). As a result, “each spoken utterance is a singular event” (Gibbs & van Orden, p. 14). In a similar vein, according to Riley and colleagues, “endlessly innovative motor solutions draw on exquisite context sensitivity as well as ultrafast action” (p. 13). Complexity gives rise to such unbounded variety that every individual behavior must be treated as an irreducibly unique entity. The approach leaves a gaping empty space between these two levels—the universal and the individual—and it is this gap that I am christening the Explanatory Donut Hole. In other approaches, this gap would be filled through a consideration of mechanism, including the internal structure of the machinery that gives rise to the relevant form of behavior. The present articles warn us away from this anti‐revolutionary way of theorizing. To focus on internal structure is to fall into a “component‐dominant” view (Dixon et al., p. 10), a merely “historical response to complexity” (Riley et al). Such “neo‐mechanistic approaches,” we are told, “must not be fundamentally explanatory” (Silberstein & Chemero, p. 1). In order to avoid distasteful discussions of system components, one option is to reduce those components to such a microscopic level that their individual causal properties are essentially pointless to discuss in isolation, like those of molecules in a fluid. It is apparently in this spirit that the brain is portrayed simply as “the complex physical materials” within which cognition occurs (Dixon et al., p. 14). After all, if “sensory and mechanical feedback” can “induce large‐scale changes in architecture completely reorganizing connectivity” (Riley et al., p. 13), then any discussion of functional neuroanatomy, above the level of the individual neuron, would indeed seem misguided. The Explanatory Donut Hole gives rise to a kind of obscurantism. The open space between holistic and microscopic levels makes it difficult to discern, as we read about dynamics: the dynamics of what? If we cannot talk about components, what is it that is “interacting?” The problem is finessed to some extent by focusing on explanations that focus exclusively on a global level, for example, Dixon’s idea that neuropsychological conditions “reflect differences in system‐wide dynamical properties,” or the following description of dual‐task performance from Riley and van Orden: “Pitting the priority of motor activities against cognitive activities, the flexible cognitive system absorbs and dissipates motor perturbations without a performance breakdown, reorganizing to sustain the same accuracy in cognitive performance of the dual‐task condition” (p. 22). Whether this analysis is valid or not, it seems unlikely that useful explanations for behavior are always to be found at such an abstract level. Indeed, neuropsychology itself seems to provide clear counter‐examples. Parkinson’s disease, for instance, is well known to involve dysfunction in a discrete, functionally coherent component of the brain. Obviously, dynamical formalisms may be extremely useful in understanding the ramifications of this component‐based problem, but one cannot get things off the ground if there is a refusal to talk seriously about isolable system components with meaningful causal properties. The same point could be made about hippocampal amnesia, or cortical blindness, or even limb amputation.

2. The Holmesian Fallacy For a behavioral nominalist, it is inappropriate to do science by making repeated measurements of supposedly stable behaviors. One must look elsewhere for data. The holist perspective supplies the solution: measure phenomena that pertain to global system dynamics. Thus, the preoccupation in this work with 1/f noise and related phenomena. Forget what you thought were the data, we are told; “The ‘noise’ is actually the behavioral signal” (Riley et al., p. 19). Two things concern me here. First, it is not clear how specific the information is that is provided by such phenomena as power laws or scale invariance. As the authors of the target articles themselves note, such patterns are seen in a wide variety of settings, and this includes settings well outside of psychology and neuroscience. How much can they then tell us about the processes at work in specific domains of human information processing? The second concern relates to what I am labeling the Holmesian Fallacy. There is a marked tendency in work focusing on 1/f noise (and related phenomena) to treat it like the critical clue in a detective story: the subtle, neglected detail that reveals, to the intelligent eye, the hidden truth in all that surrounds it. I personally find data concerning reaction‐time variability, for example, to be very interesting, but why should I believe that they hold the key to the entire story? A dynamicist can find chaos in the water dripping from my kitchen sink. However, this will be of little relevance in understanding how the plumbing in my house operates. This is true even if the power spectrum governing interdrip intervals varies as I turn the handle on the faucet. Sometimes what looks like a peripheral phenomenon may be just that.

3. The Computationalism Canard In addition to replacing traditional experimental measures, the target articles also propose to replace what they take to be the prevailing explanatory framework in cognitive science. “Dynamical systems … employ[s] differential equations rather than computation as the primary explanatory tool” (Silberstein & Chemero, p. 4). The crux of this distinction pertains to representation: “computation” involves it; dynamical cognitive science does not. Indeed, the dynamical approach is avowedly “anti‐representationalist” (Silberstein & Chemero, p. 6). “Synergies,” Riley and colleagues stress, “are not representations” (p. 9). “Representations are not needed to bridge perception and action” (Silberstein & Chemero, p. 5). The message is that one must choose: One may either use differential equations to explain phenomena, or one may appeal to representation. This strikes me as a false dilemma. As an illustration of how representation and dynamics can peacefully coexist, one may consider recent computational accounts of perceptual decision making. Here, we find models that can be understood as implementing statistical procedures, computing the likelihood ratio of opposing hypotheses (read: representations), or with equal immediacy as systems of differential equations (see Beck & Pouget, 2007; Bogacz et al., 2006). Another problem with the rejection of representation is that it seems to prohibit explanations that appeal to internal models of any kind. It seems difficult to account in any comprehensive way for human behavior without recourse to the idea of an internal model. Indeed, model‐based procedures appear fundamental even to simple reward‐based decision making in rodents (see Dickinson, 1985). The notion of an internal model seems necessarily to carry within it the idea of representation (see Davenport, 1999). At the same time, to reinforce the previous point, one can certainly describe the operation of an internal model in dynamical terms (see, e.g., Jordan & Rumelhart, 1992). The target articles cope with the problems arising from a rejection of representation in two ways. The first is to marginalize the issue: Dynamical systems theory, we are told, “removes the pressure to treat one portion of the system as representing other portions of the system—at least for many cognitive acts” (Silberstein & Chemero, p. 5, emphasis added). However, this move to isolate some forms of cognition from others violates a basic tenet of the dynamical approach, which is that nothing can be isolated from anything else. The other strategy involves an attempt to dissolve inherently representational processes into the dynamical ether through verbal slight of hand. It is hard to say what an “intention” or “goal” might be without appeal to some form of representation. According to Riley and colleagues, however, intentions simply “supply constraints to delimit overall degrees of freedom of the body...The constrained degrees of freedom realize a purpose or goal in behavior by limiting unrealized propensities for behavior to trajectories consistent with intentions” (p. 16). Problem solved! It is the above concerns that force me off the dynamicist “highway.” Taken together, they make it appear quite possible that this highway may turn out to be more of a blind alley. However, one point I want to emphasize in closing is that these problems do not stem from the embrace of dynamical formalisms, per se. Rather, they stem from the radical stance adopted in the target articles. The dynamical approach can be extremely productive, I believe, when it is applied in a fashion that admits discussion of internal system structure and of representation. Rather than setting up a choice between “component‐dominant” and “interaction‐dominant” approaches, we need to find a way of balancing between these two. The authors of the target articles are correct when they say that traditional approaches suffer from the lack of a dynamical perspective. However, the complementary mistake should also be avoided.