With the advent of computers in the experimental labs, dynamic systems have become a new tool for research on problem solving and decision making. A short review of this research is given and the main features of these systems (connectivity and dynamics) are illustrated. To allow systematic approaches to the influential variables in this area, two formal frameworks (linear structural equations and finite state automata) are presented. Besides the formal background, the article sets out how the task (...) demands of system identification and system control can be realised in these environments, and how psychometrically acceptable dependent variables can be derived. (shrink)

I examine explanations’ realist commitments in relation to dynamical systems theory. First I rebut an ‘explanatory indispensability argument’ for mathematical realism from the explanatory power of phase spaces (Lyon and Colyvan 2007). Then I critically consider a possible way of strengthening the indispensability argument by reference to attractors in dynamical systems theory. The take-home message is that understanding of the modal character of explanations (in dynamical systems theory) can undermine platonist arguments from explanatory indispensability.

We define a mathematical formalism based on the concept of an ‘‘open dynamical system” and show how it can be used to model embodied cognition. This formalism extends classical dynamical systems theory by distinguishing a ‘‘total system’’ (which models an agent in an environment) and an ‘‘agent system’’ (which models an agent by itself), and it includes tools for analyzing the collections of overlapping paths that occur in an embedded agent's state space. To illustrate the way this formalism can (...) be applied, several neural network models are embedded in a simple model environment. Such phenomena as masking, perceptual ambiguity, and priming are then observed. We also use this formalism to reinterpret examples from the embodiment literature, arguing that it provides for a more thorough analysis of the relevant phenomena. (shrink)

Although its roots can be traced to the 19th century, progress in the study of nonlinear dynamical systems has taken off in the last 30 years. While pertinent source material exists, it is strewn about the literature in mathematics, physics, biology, economics, and psychology at varying levels of accessibility. A compendium research methods reflecting the expertise of major contributors to NDS psychology, Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data examines the techniques proven to be (...) the most useful in the behavioral sciences. The editors have brought together constructive work on new practical examples of methods and application built on nonlinear dynamics. They cover dynamics such as attractors, bifurcations, chaos, fractals, catastrophes, self-organization, and related issues in time series analysis, stationarity, modeling and hypothesis testing, probability, and experimental design. The analytic techniques discussed include several variants of the fractal dimension, several types of entropy, phase-space and state-space diagrams, recurrence analysis, spatial fractal analysis, oscillation functions, polynomial and Marquardt nonlinear regression, Markov chains, and symbolic dynamics. The book outlines the analytic requirements faced by social scientists and how they differ from those of mathematicians and natural scientists. It includes chapters centered on theory and procedural explanations for running the analyses with pertinent examples and others that illustrate applications where a particular form of analysis is seen in the context of a research problem. This combination of approaches conveys theoretical and practical knowledge that helps you develop skill and expertise in framing hypotheses dynamically and building viable analytic models to test them. (shrink)

It is often claimed (1) that levels of nature are related by supervenience, and (2) that processes occurring at particular levels of nature should be studied using dynamical systems theory. However, there has been little consideration of how these claims are related. To address the issue, I show how supervenience relations give rise to ‘supervenience functions’, and use these functions to show how dynamical systems at different levels are related to one another. I then use this analysis to (...) describe a graded approach to non-reductive physicalism, and to critically assess Davidson’s arguments for psychological anomaly. I also show how this approach can inform empirical research in cognitive science. (shrink)

Dynamical systems are mathematical structures whose aim is to describe the evolution of an arbitrary deterministic system through time, which is typically modeled as (a subset of) the integers or the real numbers. We show that it is possible to generalize the standard notion of a dynamical system, so that its time dimension is only required to possess the algebraic structure of a monoid: first, we endow any dynamical system with an associated graph and, second, we prove that such (...) a graph is a category if and only if the time model of the dynamical system is a monoid. In addition, we show that the general notion of a dynamical system allows us not only to define a family of meaningful dynamical concepts, but also to distinguish among a cluster of otherwise tangled notions of reversibility, whose logical relationships are finally analyzed. (shrink)

This work addresses a broad range of questions which belong to four fields: computation theory, general philosophy of science, philosophy of cognitive science, and philosophy of mind. Dynamical system theory provides the framework for a unified treatment of these questions. ;The main goal of this dissertation is to propose a new view of the aims and methods of cognitive science--the dynamical approach . According to this view, the object of cognitive science is a particular set of dynamical systems, which (...) I call "cognitive systems". The goal of a cognitive study is to specify a dynamical model of a cognitive system, and then use this model to produce a detailed account of the specific cognitive abilities of that system. The dynamical approach does not limit a-priori the form of the dynamical models which cognitive science may consider. In particular, this approach is compatible with both computational and connectionist modeling, for both computational systems and connectionist networks are special types of dynamical systems. ;To substantiate these methodological claims about cognitive science, I deal first with two questions in two different fields: What is a computational system? What is a dynamical explanation of a deterministic process? ;Intuitively, a computational system is a deterministic system which evolves in discrete time steps, and which can be described in an effective way. In chapter 1, I give a formal definition of this concept which employs the notions of isomorphism between dynamical systems, and of Turing computable function. In chapter 2, I propose a more comprehensive analysis which is based on a natural generalization of the concept of Turing machine. ;The goal of chapter 3 is to develop a theory of the dynamical explanation of a deterministic process. By a "dynamical explanation" I mean the specification of a dynamical model of the system or process which we want to explain. I start from the analysis of a specific type of explanandum--dynamical phenomena--and I then use this analysis to shed light on the general form of a dynamical explanation. Finally, I analyze the structure of those theories which generate explanations of this form, namely dynamical theories. (shrink)

. Interpreted dynamical systems are dynamical systems with an additional interpretation mapping by which propositional formulas are assigned to system states. The dynamics of such systems may be described in terms of qualitative laws for which a satisfaction clause is defined. We show that the systems Cand CL of nonmonotonic logic are adequate with respect to the corresponding description of the classes of interpreted ordered and interpreted hierarchical systems, respectively. Inhibition networks, artificial neural networks, logic (...) programs, and evolutionary systems are instances of such interpreted dynamical systems, and thus our results entail that each of them may be described correctly and, in a sense, even completely by qualitative laws that obey the rules of a nonmonotonic logic system. (shrink)

Dynamical systems theory (DST) is gaining popularity in cognitive science and philosophy of mind. Recently several authors (e.g. J.A.S. Kelso, 1995; A. Juarrero, 1999; F. Varela and E. Thompson, 2001) offered a DST approach to mental causation as an alternative for models of mental causation in the line of Jaegwon Kim (e.g. 1998). They claim that some dynamical systems exhibit a form of global to local determination or downward causation in that the large-scale, global activity of the system (...) governs or constrains local interactions. This form of downward causation is the key to the DST model of mental causation. In this paper I evaluate the DST approach to mental causation. I will argue that the main problem for current DST approaches to mental causation is that they lack a clear metaphysics. I propose one metaphysical framework (Gillett, 2002a/b/c) that might deal with this deficiency. (shrink)

It is argued that the theory of situated cognition together with dynamic systems theory can explain the core of artistic practice and aesthetic experience, and furthermore paves the way for an account of how artist and audience can meet via the artist’s work. The production and consumption of art is an embodied practice, firmly based in perception and action, and supported by features of the local, agent-centered and global, socio-cultural contexts. Artistic creativity and aesthetic experience equally result from (...) the dynamic interplay between agent and context, allowing for artist and viewer to relate to the artist’s work in similar ways. (shrink)

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an ad hoc partition of an underlying phase space (...) description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed. (shrink)

Dynamicism has provided cognitive science with important tools to understand some aspects of “how cognitive agents work” but the issue of “what makes something cognitive” has not been sufficiently addressed yet, and, we argue, the former will never be complete without the later. Behavioristic characterizations of cognitive properties are criticized in favor of an organizational approach focused on the internal dynamic relationships that constitute cognitive systems. A definition of cognition as adaptive-autonomy in the embodied and situated neurodynamic domain (...) is provided: the compensatory regulation of a web of stability dependencies between sensorimotor structures, is created and preserved during a historical/developmental process. We highlight the functional role of emotional embodiment: internal bioregulatory processes coupled to the formation and adaptive regulation of neurodynamic autonomy. Finally, we discuss a “minimally cognitive behavior program” in evolutionary simulation modelling suggesting that much is to be learned from a complementary “minimally cognitive organization program”. (shrink)

The problem of the direction of time is reconsidered in the light of a generalized version of the theory of abstract deterministic dynamical systems, thanks to which the mathematical model of time can be provided with an internal dynamics, solely depending on its algebraic structure. This result calls for a reinterpretation of the directional properties of physical time, which have been typically understood in a strictly topological sense, as well as for a reexamination of the theoretical meaning of the (...) widespread time-reversal invariance of classical physical processes. (shrink)

The new kid on the block in cognitive science these days is dynamic systems. This way of thinking about the mind is, as usual, radically opposed to computationalism - - the hypothesis that thinking is computing. The use of dynamic systems is just the latest in a series of attempts, from Searle's Chinese Room Argument, through the weirdnesses of postmodernism, to overthrown computationalism, which as we all know is a perfectly nice hypothesis about the mind that (...) never hurt anyone. (shrink)

Our approach aims at accounting for causal claims in terms of how the physical states of the underlying dynamical system evolve with time. Causal claims assert connections between two sets of physicals states—their truth depends on whether the two sets in question are genuinely connected by time evolution such that physical states from one set evolve with time into the states of the other set. We demonstrate the virtues of our approach by showing how it is able to account for (...) typical causes, causally relevant factors, being ‘the’ cause, and cases of overdetermination and causation by absences. (shrink)

Stocks and flows are building blocks of dynamic systems: Stocks change through inflows and outflows, such as our bank balance changing with withdrawals and deposits, or atmospheric CO2 with absorptions and emissions. However, people make systematic errors when trying to infer the behavior of dynamic systems, termed SF failure, whose cognitive explanations are yet unknown. We argue that SF failure appears when people focus on specific system elements, rather than on the system structure and gestalt. Using (...) a standard SF task, SF failure decreased by a global as opposed to local task format; individual global as opposed to local processing styles; and global as opposed to local perceptual priming. These results converge toward local processing as an explanation for SF failure. We discuss theoretical and practical implications on the connections between the scope of attention and understanding of dynamic systems. (shrink)

Efforts to bridge emotion theory with neurobiology can be facilitated by dynamic systems (DS) modeling. DS principles stipulate higher-order wholes emerging from lower-order constituents through bidirectional causal processes cognition relations. I then present a psychological model based on this reconceptualization, identifying trigger, self-amplification, and self-stabilization phases of emotion-appraisal states, leading to consolidating traits. The article goes on to describe neural structures and functions involved in appraisal and emotion, as well as DS mechanisms of integration by which they interact. (...) These mechanisms include nested feedback interactions, global effects of neuromodulation, vertical integration, action-monitoring, and synaptic plasticity, and they are modeled in terms of both functional integration and temporal synchronization. I end by elaborating the psychological model of emotion–appraisal states with reference to neural processes. (shrink)

Both natural and engineered systems are fundamentally dynamical in nature: their defining properties are causal, and their functional capacities are causally grounded. Among dynamical systems, an interesting and important sub-class are those that are autonomous, anticipative and adaptive (AAA). Living systems, intelligent systems, sophisticated robots and social systems belong to this class, and the use of these terms has recently spread rapidly through the scientific literature. Central to understanding these dynamical systems is their complicated (...) organisation and their consequent capacities for re- and self- organisation. But there is at present no general analysis of these capacities or of the requisite organisation involved. We define what distinguishes AAA systems from other kinds of systems by characterising their central properties in a dynamically interpreted information theory. (shrink)

Progress in the last few decades in what is widely known as “Chaos Theory” has plainly advanced understanding in the several sciences it has been applied to. But the manner in which such progress has been achieved raises important questions about scientific method and, indeed, about the very objectives and character of science. In this presentation, I hope to engage my audience in a discussion of several of these important new topics.

The proposed model is put forward as a template for the dynamical systems approach to embodied cognition. In order to extend this view to cognitive processing in general, however, two limitations must be overcome. First, it must be demonstrated that sensorimotor coordination of the type evident in the A-not-B error is typical of other aspects of cognition. Second, the explanatory utility of dynamical systems models must be clarified.

The theory of dynamical systems allows one to describe the change in a system' 's macroscopic behavior as a bifurcation in the underlying dynamics. We show here, from the example of depressive syndrome, the existence of a correspondence between clinical and electro-physiological dimensions and the association between clinical remission and brain dynamics reorganization. On the basis of this experimental study, we discuss the interest of such results concerning the question of normality versus pathology in psychiatry and the relationship between (...) mind and brain. (shrink)

This paper discusses possible correspondences between the dynamical systems characteristics observed in our previously proposed cognitive model and phenomenological accounts of immanent time considered by Edmund Husserl. Our simulation experiments in the anticiparatory learning of a robot showed that encountering sensory-motor flow can be learned as segmented into chunks of reusable primitives with accompanying dynamic shifting between coherences and incoherences in local modules. It is considered that the sense of objective time might appear when the continuous sensory-motor flow (...) input to the robot is reconstructed into compositional memory structures through the articulation processes described. (shrink)

Dynamic systems theory is a way of describing the patterns that emerge from relationships in the universe. In the study of interpersonal relationships, within and between species, the scientist is an active and engaged participant in those relationships. Separation between self and other, scientist and subject, runs counter to systems thinking and creates an unnecessary divide between humans and animals.

This paper proposes a model for implementation of intrinsic natural language sentence meaning in a physical language understanding system, where 'intrinsic' is understood as 'independent of meaning ascription by system-external observers'. The proposal is that intrinsic meaning can be implemented as a point attractor in the state space of a nonlinear dynamical system with feedback which is generated by temporally sequenced inputs. It is motivated by John Searle's well known critique of the then-standard and currently still influential computational theory of (...) mind, the essence of which was that CTM representations lack intrinsic meaning because that meaning is dependent on ascription by an observer. The proposed dynamical model comprises a collection of interacting artificial neural networks, and constitutes a radical simplification of the principle of compositional phrase structure which is at the heart of the current standard view of sentence semantics because it is computationally interpretable as a finite state machine. (shrink)

Dynamicism has provided cognitive science with important tools to understand some aspects of “how cognitive agents work” but the issue of “what makes something cognitive” has not been sufficiently addressed yet and, we argue, the former will never be complete without the latter. Behavioristic characterizations of cognitive properties are criticized in favor of an organizational approach focused on the internal dynamic relationships that constitute cognitive systems. A definition of cognition as adaptive-autonomy in the embodied and situated neurodynamic domain (...) is provided: the compensatory regulation of a web of stability dependencies between sensorimotor structures is created and preserved during a historical/developmental process. We highlight the functional role of emotional embodiment: internal bioregulatory processes coupled to the formation and adaptive regulation of neurodynamic autonomy. Finally, we discuss a “minimally cognitive behavior program” in evolutionary simulation modeling suggesting that much is to be learned from a complementary “minimally cognitive organization program”. (shrink)

The question whether cognition is subserved by internal processes in the brain (internalism) or extends in to the world (active externalism) has been vigorously debated in recent years. I show how internalist and externalist ideas can be pursued in a common framework, using (1) open dynamical systems, which allow for separate analysis of an agent's intrinsic and embodied dynamics, and (2) supervenience functions, which can be used to study how low-level dynamical systems give rise to higher-level dynamical structures.

The Visual World Paradigm (VWP) presents listeners with a challenging problem: They must integrate two disparate signals, the spoken language and the visual context, in support of action (e.g., complex movements of the eyes across a scene). We present Impulse Processing, a dynamical systems approach to incremental eye movements in the visual world that suggests a framework for integrating language, vision, and action generally. Our approach assumes that impulses driven by the language and the visual context impinge minutely on (...) a dynamical landscape of attractors corresponding to the potential eye-movement behaviors of the system. We test three unique predictions of our approach in an empirical study in the VWP, and describe an implementation in an artificial neural network. We discuss the Impulse Processing framework in relation to other models of the VWP. (shrink)

We show how a simple nonlinear dynamical system (the discrete quadratic iteration on the unit segment) can be the basis for modelling the embryogenesis process. Such an approach, even though being crude, can nevertheless prove to be useful when looking with the two main involved processes:i) on one hand the cell proliferation under successive divisions ii) on the other hand, the differentiation between cell lineages. We illustrate this new approach in the case of Caenorhabditis elegans by looking at the early (...) stages of embryogenesis, up to several hundreds of cells (lima bean larval stage). We show how the many results that have been obtained by several groups can be interpreted in terms of values for the parameters controlling the dynamical system. Furthermore, we can extend the model to the cases of genetic mutations. More precisely the teratogenetic and lethal effects are associated with abnormal variation of the control parameters with time. (shrink)

In this paper we will discuss some basic aspects of the global theory of dynamical systems. Rather than entering in technical derivations, we will try to emphasize the main points of the concept of dynamical systems which lead us to the generalization presented here, as well as some results that are easily generalized. Besides, some considerations of philosophical nature will be made.

Locke & Bogin (L&B) suggest that theoretical principles of ontogenetic development apply to language evolution. If this is the case, then evolutionary theory should utilize epigenetic theories of development to theorize, model, and elucidate the evolution of language wherever possible. In this commentary, I evoke principles of dynamic systems theory to evaluate the evolutionary phenomena presented in the target article.

Dynamical systems promise to elucidate a notion of top–down causation without violating the causal closure of physical events. This approach is particularly useful for the problem of mental causation. Since dynamical systems seek out, appropriate, and replace physical substrata needed to continue their structural pattern, the system is autonomous with respect to its components, yet the components constitute closed causal chains. But how can systems have causal power over their substrates, if each component is sufficiently caused by (...) other components? Suppose every causal relation requires background conditions, without which it is insufficient. The dynamical system is structured with a tendency to change background conditions for causal relations anytime needed substrates for the pattern's maintenance are missing; under the changed background conditions, alternative causal relations become sufficient to maintain the pattern. The system controls the background conditions under which one or another causal relation can subserve the system's overall pattern, while the components remain causally closed under their given background conditions. (shrink)

This book focuses on showing how the ideas central to the new wave oj dynamic systems studies may also form the basis for a new and distinctive theory of human development where both global order and local variability in behaviour emerge together from the same organising dynamical interactions. This also sharpens our understanding of the weaknesses of the traditional formal, structuralist theories. Conversely, dynamical models have their own matching set of problems, many of which are consiously explored here. (...) Less readily acknowledged, the youthfulness of this field means that many of the studies presented here struggle to pass beyond speculative metaphor. Nonetheless, the field is shown to be one of vigour, intelligence and great promise. (shrink)

From birth to 15 months infants and caregivers form a fundamentally intersubjective, dyadic unit within which the infant’s ability to recognize gender/sex in the world develops. Between about 18 and 36 months the infant accumulates an increasingly clear and subjective sense of self as female or male. We know little about how the precursors to gender/sex identity form during the intersubjective period, nor how they transform into an independent sense of self by 3 years of age. In this Theory and (...) Hypothesis article I offer a general framework for thinking about this problem. I propose that through repetition and patterning, the dyadic interactions in which infants and caregivers engage imbue the infant with an embodied, i.e., sensori-motor understanding of gender/sex. During this developmental period gender/sex is primarily an intersubjective project. From 15 to 18 months there are few reports of newly appearing gender/sex behavioral differences, and I hypothesize that this absence reflects a period of developmental instability during which there is a transition from gender/sex as primarily inter-subjective to gender/sex as primarily subjective. Beginning at 18 months, a toddler’s subjective sense of self as having a gender/sex emerges, and it solidifies by 3 years of age. I propose a dynamic systems perspective to track how infants first assimilate gender/sex information during the intersubjective period ; then explore what changes might occur during a hypothesized phase transition, and finally, review the emergence and initial stabilization of individual subjectivity-the period from 18 to 36 months. The critical questions explored focus on how to model and translate data from very different experimental disciplines, especially neuroscience, physiology, developmental psychology and cognitive development. I close by proposing the formation of a research consortium on gender/sex development during the first 3 years after birth. (shrink)

Economic logic impinges on contemporary political theory through both economic reductionism and economic methodology applied to political decision-making (through game theory). The authors argue that the sort of models used are based on mechanistic and linear methodologies that have now been found wanting in physics. They further argue that complexity based self-organization methods are better suited to model the complexities of economy and polity and their interactions with the overall social system.

Dynamical simulations of male and female mating strategies illustrate how traits such as restrictedness constrain, and are constrained by, local ecology. Such traits cannot be defined solely by genotype or by phenotype, but are better considered as decision rules gauged to ecological inputs. Gangestad & Simpson's work draws attention to the need for additional bridges between evolutionary psychology and dynamical systems theory.

Dynamical systems are mathematical objects meant to formally capture the evolution of deterministic systems. Although no topological constraint is usually imposed on their state spaces, there is prima facie evidence that the topological properties of dynamical systems might naturally depend on their dynamical features. This paper aims to prepare the grounds for a systematic investigation of such dependence, by exploring how the underlying dynamics might naturally induce a corresponding topology.