Reply to Commentators 1 Running head: REPLY TO COMMENTATORS

Searching for General Principles in Cognitive Performance: Reply to Commentators

Damian G. Stephen Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston, MA Guy Van Orden Center for Cognition, Action & Perception, Department of Psychology, University of Cincinnati, Cincinnati, OH

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Address correspondence to: Damian G. Stephen Wyss Institute for Biologically Inspired Engineering Harvard University 3 Blackfan Circle, Floor 5 Boston, MA 02115 Phone: (703) 300-3375 Email: [email protected] Or Guy Van Orden, CAP Center, ML 0376, University of Cincinnati Cincinnati, OH 45221-0376, USA. Phone: (513) 321-0425 Email: [email protected]

Reply to Commentators 2 The commentators expressed concerns regarding the relevance and value of noncomputational non-symbolic explanations of cognitive performance. But what counts as an “explanation” depends on the pre-theoretical assumptions behind the scenes of empirical science regarding the kinds of variables and relationships that are sought out in the first place, and some of the present disagreements stem from incommensurate assumptions. Traditional cognitive science presumes cognition to be a decomposable system of components interacting according to computational rules to generate cognitive performances (i.e., component-dominant dynamics). We assign primacy to interactiondominant dynamics among components. Though either choice can be a good guess before the fact, the primacy of interactions is now supported by much recent empirical work in cognitive science. Consequently, in the main, the commentators have failed so far to address the growing evidence corroborating the theory-driven predictions of complexity science. Keywords: complexity, explanation, interaction-dominance, computation, universality

Reply to Commentators 3 Searching for General Principles in Cognitive Performance: Reply to Commentators We thank the commentators and the authors of the target articles who contributed to this new debate format of TopiCS. We are indebted to the commentators in particular for spelling out the ways in which they see complexity science as problematic, and illustrating the ways in which complexity science is sometimes misunderstood. From the comments it is clear that basic assumptions and technical jargon of complexity theory do not circulate widely across the cognitive science community, and so they understandably become easy targets of complaint and parody. In that light Wagenmakers, van der Maas, and Farrell (this volume) may find interesting an actual explicit multistep outline for how to do empirical work in complexity science. One such outline in Kelso (2003) came out of work on motor coordination and perception, culminating in the 1995 publication of Dynamic Patterns: The Self-Organization of Brain and Behavior. Scott Kelso’s 1995 volume holds up still as a touchstone for ideas about complexity and detailed corroboration of the empirical flags of complexity and qualitative change in brain and behavior. Kelso also explains why the initial empirical focus must be the global dynamics of a system, only turning afterward to a system’s components. “It is difficult to isolate the components and study their dynamics. The reason is that the individual components seldom exist outside the context of the functioning whole, and have to be studied as such.” (Kelso, 2003, p. 50). The commentators made clear as well that we should have been more up front about our motivation in departing from conventional theories of cognition. We seek an alternative rooted in general principles, in part, to counter the present state of empirically motivated cognitive science. We see an endless variety of newly discovered effects

Reply to Commentators 4 yielding an indefinite catalog of special-purpose mechanisms. We worry that empirical cognitive science may begin to resemble a parody of reductionism because mechanisms accrue pretty much one to one with empirical effects – as though each empirical effect is visibly transparent to its underlying mechanism – a problem that has been called the effect = structure fallacy (Gibbs, 1994; Lakoff, 1987) and the module mistake (Van Orden & Kloos, 2003). The effect = structure fallacy originates in a physical metaphor of effect = cause. A manipulation of the task or stimulus environment – a change in task or stimulus conditions – causes observed changes in measured performance. The manipulation is the ultimate cause of the change in performance, which by definition, must be contingent on recovering information from proximal trigger stimuli, requiring some kind of mechanistic bridge across the causal structure of the body. Thus each newly discovered effect yields another bridging mechanism of brain or cognition. Yet the grounding of the logic remains purely metaphorical because, for all the intermediary mechanisms invoked, no actual causal chains are ever worked out in detail. Hence, “ultrafast” cognitive responses highlighted by Riley, Shockley, and Van Orden (this volume) are truly paradoxical in the dictionary sense: the fact of zero-net-delay responses is logically at odds with the premise that information requires processing time to be recovered in the first place. Van Rooij (this volume) understands the paradox and justly turns it around, asking for more details about how a complexity approach may escape paradox, while anticipating important details of the escape that we imagine. That is, neither “information processing” nor self-organization need be corralled within the time between a stimulus and a response. If “value assignments” exist before a stimulus is presented (e.g., due to a

Reply to Commentators 5 history of task instructions or task experience), and they exist in a precise balance favoring equally each alternative response option, then this anticipatory poise could effectively restrict allowable maxima (or minima). The anticipatory poise in the complexity account is imagined to be a selforganizing critical state, a configuration of the mind and the body that can ignore irrelevant changes in the environment while limiting action trajectories to the prespecified response options – a customized, taut, metastable poise (Van Orden, Kloos & Wallot, 2011). A critical state lacks only the thinnest form of “symmetry breaking” disambiguation to close the loop and enact a response (compare Järvilehto, 1998). The inscrutably tiny and subtle minutia of change in an environment or person that can disambiguate poised alternatives explains why inherent uncertainty stands between a scientist and the proximal cause of a response behavior, which is why nature presents us with exclusively statistical portraits of performance outcomes (compare Gibbs & Van Orden, this volume). Admittedly, the previous hypothesis draws metaphorically on proofs of concept from ultrafast symmetry breaking in physical, chemical, and biological systems (Wallot & Van Orden, in press a). As a metaphor of anticipatory poise, however, critical states and symmetry breaking also reveal the way in which the causal metaphor of effect = structure is needlessly exclusive, imposing strict a priori limits on what may count as legitimate phenomena. Conventional effects combine average increases or decreases in the quantities of measured values, an extremely limited and misleading view of dynamics. However, conventional explanations, like all explanations, also reflect specific pre-theoretical commitments to what counts as “fact” and what counts as “explanation.”

Reply to Commentators 6 For example, when Newell (1990) and Simon (1973) “worried greatly about dynamics” (Eliasmith, this volume) they did so recognizing that tightly coupled and multiplicative dynamics pose problems for decomposition into components. To avoid such problems they limited their consideration to systems with components on separate, isolable timescales, and limited information processing between stimulus and response to a single timescale (the very idea of component-dominant dynamics that is seriously challenged by scaling phenomena, see Van Orden & Holden, 2002). In line with these assumptions, explanations became first the decomposition into key parameters and second the specification of the relationships among those parameters. That’s OK for decomposable systems, but what about systems in which the dynamics of components become interdependent (interaction-dominant dynamics) – the apparent dynamics of living beings for instance? Cognitivism requires that nature divide cognitive systems along fault lines of component-dominant dynamics yielding isolable component functions. Complex systems result when nature produces a system across a multiscale web of interactions blurring the borders between components as in fieldtheoretic physics (Bickhard, 2008). Navigating this distinction has already become an issue of how these complementary approaches can coexist in scientific discourse (Dale, 2008) and differences in jargon create obstacles for any coexisting approaches (Wagenmakers et al., this volume). Nevertheless, the details of theoretical commitments require specific languages, and by turn, language will reflect pre-theoretical commitments. Currently, the obstacles that jargons create may appear most obvious in confronting the unfamiliar jargon of complexity science. However the jargoned

Reply to Commentators 7 distinctions do not come out of nothing as Eliasmith (this volume) seems to believe, and the language habits from decades of cognitive science equally reflect pre-theoretical commitments. We suspect that significant misunderstandings in this debate stem from such unacknowledged or unidentified choices. In that light, for example, several commentators faulted the complex system’s approach for failing to be concrete – i.e., we failed to vindicate representations and computation – while the commentaries themselves illustrate the difficulty of keeping the mainstream story straight. The mind is computational, so we are told, and there are functionally independent components when it suits the localization of lesions in Parkinson’s disease (e.g., Botnivick, this volume; cf. Van Orden, 2010, on Parkinson’s disease), but we are told at the same time that functionally independent components compose only a minority of cognitive architectures and represent a “straw man” picture of cognitive science (Eliasmith, this volume). And, though we are told that the cognitive theorists have considered the interactions among mind, body, and environment, at the end of the day the only factors that matter are latent cognitive factors (Wagenmakers et al., this volume). In other words, several commentators have decided what will count as a viable cognitive explanation. If we or anyone else refuses to play by their rules they threaten to take their ball and go home, which might be OK if there were a strong tradition of successful empirical cognitive science, arriving at reliable explanations that are widely recognized inside and outside of cognitive science. Were that the case it would be prudent to remain skeptical of ‘revolutions’ or ‘paradigm shifts.’ But over half a century, empirical cognitive science has had its own difficulties winning over hearts and minds, even without our meddling (Bickle, 2003; Bickhard, 2001; Dennett, 1984; Harley, 2004;

Reply to Commentators 8 Harnard, 1990; Searle, 1980, 1990; Stanovich, 2004; Thelen & Smith, 1994; Uttal, 1990, 2001, 2007; Watkins, 1990; Weldon, 1999). Yet, except for van Rooij (this volume) computation is put forward in the commentaries as the more rigorous alternative, with no mention of inherent weaknesses (on the latter point, e.g., see Bell, 1999; Van Orden, 2008). Consider, however, that in order for computation to proceed, meaning must be localized in some internal unit of processing be it a “representation,” a “symbol,” “subsymbol,” or “microfeature.” It is only possible to compute “1 + 2 = 3” or “pet + fish = guppy” if the respective symbols have rigidly defined semantic content. Computation can’t work the way it is supposed to if the semantic content is flexibly context-dependent (Turvey & Moreno, 2006; van Rooij, this volume), requiring a limitless syntax listing all the possible contexts of semantic content (Fodor, 2000). Likewise, connectionism supports only a weak combinatorial idea of emergence in which locally meaningful tokens are reshuffled into various configurations without any net gain in cognitive content (Boogerd, Bruggeman, Richardson, Stephan, & Westerhoff, 2005; Cariani, 1997). Thus, the functional independence of semantic tokens is not simply a rhetorical inconvenience; it is a requirement for computation to provide reliable solutions. Like any scientific tool, computational modeling has a finite scope, but this fact is not evident when the commentators equate computation with dynamical systems theory, a popular false claim. Computable systems are a subset of nonlinear dynamical systems in which mathematical iterations of state variables are governed by a finite number of parameters. Complexity, in this case, is limited to algorithmic complexity, measured in the number of bits of an “input.” However, dynamical systems exhibit another kind of

Reply to Commentators 9 complexity, emphasized by Riley et al. (this volume), expressing universal properties. That is, they exhibit the same universal patterns of change in their behavior irrespective of their material composition (Solé, Manrubia, Benton, Kauffman, & Bak, 1999; Stanley et al., 1996). Crucially, systems that express universality do so at the cost of a finite set of parameters. So in this strict theoretical sense, cognitive performance that exhibits universality cannot be equated with a computational model although, practically, computational modeling retains its utility as the same essential workhorse. Universality is identified using statistical methods that probe the dynamics of cascades, methods that estimate how variation propagates through the measured behavior of a system – and all empirical approaches share the concern over variation in measured values. Consequently, we find it puzzling that conventional accounts have so far mostly ignored the structured patterns of variation predicted in complexity science, sometimes accounting for virtually all of the variance that is to be explained (Gilden, 2001; 2009). Equally puzzling is the claim by Howes (this volume) that “what is important for cognitive science is … how [reliably a theory] predicts empirical observations.” This admonition suggests that he is unaware that specific power-law scaling relations and fractal behavior were predictions derived from complexity science, that ultrafast action is a prediction from symmetry breaking, that exquisite context sensitivity is a prediction inherent to strongly nonlinear dynamical systems and complexity (Rosen, 1991), that the elaborate changes in variation that anticipate emergence of a new problem solution were predicted from the patterns surrounding emergent qualitative change in thermodynamics, a hypothesis that has been further tested and corroborated in discerning rules in card-sort

Reply to Commentators 10 tests of executive function (Anastas, Stephen, & Dixon, 2011) and in insight problems (Stephen, Boncoddo, Magnuson, & Dixon, 2009). In addition, starting from a conceptual basis in chaos theory, the complexity approach is closing in from anther direction on an explicit theory of anticipatory poise (Stepp & Turvey, 2009), with accompanying predictions corroborated in tests using the structured variation associated with chaos and 1/f scaling (Stephen & Dixon, 2011; Stepp, Chemero, & Turvey, 2011). Last but not least, deviations in 1/f scaling laws appear to be predicted by the locus of changes in control, the relative increases or decreases in involuntary or voluntary sources of control (Kloos & Van Orden, 2010). In short, we are testing theory-driven hypotheses and failing so far to reject them. Widely observed scaling laws and newly observed multifractal variation in cognitive performance provide evidence that cognitive activities are the product of multiplication among interdependent random factors (Ihlen & Vereijken, 2010; Holden et al., 2009), because interaction-dominant dynamics predicted these phenomena. If sources of variation were additive, we could entertain the hope of recovering independent parameters, but as it stands, the parameters may be neither independent nor recoverable (Holden, Choi, Amazeen, & Van Orden, 2011; Van Orden, Kello, & Holden, 2010). The diagnostic facts of the matter are these: the nature of the interactions among a system’s components can be established empirically in “phenomena that pertain to global system dynamics” (Botnivick, this volume) without any knowledge of the interacting components. So the broad-strokes desideratum may require more inclusive contemporary theory-constitutive-metaphors than effect = cause, possibly those of multiscale selforganizing structures analogous to turbulent fluid flow.

Reply to Commentators 11 That said, we simply remain committed to pursuing explanations of cognitive performance that can accommodate reliable and compelling empirical evidence. Hence, we place our theoretical money on interactions rather than components. Pursuing an interaction-dominant explanation involves pursuing an explanation built around the propagation of variation through a heterogeneous field of matter (a body) with energy flowing on a variety of scales (metabolism). With respect to energy, this insight can be got in part from the primary metabolic function of the neuron (Davia, 2005), which sits at the root of the logic of neuroimaging. The existence of order in human behavior depends on a flow of matter and energy through the body, as an open system; that is the root metaphor of order in contemporary science (e.g., Hollis, Kloos & Van Orden, 2009). No variation in behavior can occur without energy flow, and the propagation of variation in the activities of autonomous beings should provide clues to their coordination with the environment (Hooker, 2011). Indeed, the relationship between energy flow and (fractal) variation is borne out empirically in the coordination of a cognitive system with perceptual information in the environment (Stephen & Hajnal, 2011; Stephen, Arzamarski, & Michaels, 2010) These are heady ideas and we are far from delivering formal equivalence. Nonetheless, the complex systems approach has managed to achieve new insights from among the maddening details of observable variation, in variation that was conventionally discarded as uninteresting noise. We are confident that this program of research can achieve further insights, which will involve modeling the statistics of measured variation across multiple scales of space and time (e.g., Holden et al., 2009; Thornton & Gilden, 2005). Power spectra have been informative as they have been

Reply to Commentators 12 immensely informative to physicists, biologists, and engineers (Bronzino, 2000). And 1/f relationships and multiplicative cascades will resist formal equivalence to their componential models (e.g., Holden et al., 2011). However, fractal variation in 1/f noise is only one analytical route to testing for multiplicative cascades, and self-organized criticality is only one formalism with which to make sense of multiplicative cascades. Failing either one, complexity science has more general ways of testing multiplicative cascade dynamics (Chhabra & Jensen, 1989). In either case, pre-theoretical preferences for independent components and computation simply do not add up to behavior because evidence of universality in complexity cannot be sidestepped (Ihlen & Vereijken, 2010; Wallot & Van Orden, in press b). It is the service of criticism to draw attention to where terminology and assumptions need clarification and correction, but further skepticism will need, first, to be upfront about its own pre-theoretical commitments and, then, to provide a solid alternative account of why changes in fractal variation should ever predict cognitive outcomes, why – to use Botnivick’s (this volume) metaphor – dripping faucets might actually predict changes in the plumbing. The complex-systems approach has progressed beyond a disagreement with the tenets of information-processing or computational cognitive science. It now harbors a steadily growing body of reliable positive evidence that contradicts or grossly surprises conventional thinking. If we are wrong about our interpretation of this evidence, then we must depend upon our skeptics to tell us how to better understand these many discoveries. The complex-systems approach has been clear throughout about the commitment to multiplicative interactions among processes and about its expectations that cognitive

Reply to Commentators 13 activities self-organize from multiscale variation. For now, the good news is that multiplicative interactions and multiscale variation continue to gain ground in predicting cognitive performance. And although a main current of this debate remains the disagreement on what counts as “explanation,” surely it becomes clear that we have tested and failed to reject sensible hypotheses predicting unexpected regularities in the arrhythmic variation of cognitive performance. Thus ultimately the debate will move beyond the immediate concerns of the commentators.

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