Using the concepts of chaotic dynamicalsystems, we present an interpretation of dynamic neural activity found in cortical and subcortical areas. The discovery of chaotic itinerancy in high-dimensional dynamicalsystems with and without a noise term has motivated a new interpretation of this dynamic neural activity, cast in terms of the high-dimensional transitory dynamics among “exotic” attractors. This interpretation is quite different from the conventional one, cast in terms of simple behavior on low-dimensional attractors. Skarda and (...) Freeman (1987) presented evidence in support of the conclusion that animals cannot memorize odor without chaotic activity of neuron populations. Following their work, we study the role of chaotic dynamics in biological information processing, perception, and memory. We propose a new coding scheme of information in chaos-driven contracting systems we refer to as Cantor coding. Since these systems are found in the hippocampal formation and also in the olfactory system, the proposed coding scheme should be of biological significance. Based on these intensive studies, a hypothesis regarding the formation of episodic memory is given. Key Words: Cantor coding; chaotic itinerancy; dynamic aspects of the brain; dynamic associative memory; episodic memory; high-dimensional dynamicalsystems; SCND attractors. (shrink)
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 dynamicalsystems 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)
The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamicalsystems 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)
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 dynamicalsystems 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)
Dynamicalsystems 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 dynamicalsystems 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)
This paper reviews some major episodes in the history of the spatial isomorphism problem of dynamicalsystems theory. In particular, by analysing, both systematically and in historical context, a hitherto unpublished letter written in 1941 by John von Neumann to Stanislaw Ulam, this paper clarifies von Neumann's contribution to discovering the relationship between spatial isomorphism and spectral isomorphism. The main message of the paper is that von Neumann's argument described in his letter to Ulam is the very first (...) proof that spatial isomorphism and spectral isomorphism are not equivalent because spectral isomorphism is weaker than spatial isomorphism: von Neumann shows that spectrally isomorphic ergodic dynamicalsystems with mixed spectra need not be spatially isomorphic. (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 dynamicalsystems. ;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 dynamicalsystems, 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)
Context is an important construct in many domains of cognition, including learning, memory, and emotion. We used dynamicalsystems methods to demonstrate the episodic nature of experience by showing a natural separation between the scales over which within-context and between-context relationships operate. To do this, we represented an individual's emails extending over about 5 years in a high-dimensional semantic space and computed the dimensionalities of the subspaces occupied by these emails. Personal discourse has a two-scaled geometry with smaller (...) within-context dimensionalities than between-context dimensionalities. Prior studies have shown that reading experience and visual experience have a similar two-scaled structure. Furthermore, the recurrence plot of the emails revealed that experience is predictable and hierarchical, supporting the constructs of some influential theories of memory. The results demonstrate that experience is not scale-free and provide an important target for accounts of how experience shapes cognition. (shrink)
Human participants and recurrent (“connectionist”) neural networks were both trained on a categorization system abstractly similar to natural language systems involving irregular (“strong”) classes and a default class. Both the humans and the networks exhibited staged learning and a generalization pattern reminiscent of the Elsewhere Condition (Kiparsky, 1973). Previous connectionist accounts of related phenomena have often been vague about the nature of the networks’ encoding systems. We analyzed our network using dynamicalsystems theory, revealing topological and (...) geometric properties that can be directly compared with the mechanisms of non-connectionist, rule-based accounts. The results reveal that the networks “contain” structures related to mechanisms posited by rule-based models, partly vindicating the insights of these models. On the other hand, they support the one mechanism (OM), as opposed to the more than one mechanism (MOM), view of symbolic abstraction by showing how the appearance of MOM behavior can arise emergently from one underlying set of principles. The key new contribution of this study is to show that dynamicalsystems theory can allow us to explicitly characterize the relationship between the two perspectives in implemented models. (shrink)
The problem of the direction of time is reconsidered in the light of a generalized version of the theory of abstract deterministic dynamicalsystems, 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)
Dynamicalsystems 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 dynamicalsystems 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.
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.
Complexity arises from interaction dynamics, but its forms are co-determined by the operative constraints within which the dynamics are expressed. The basic interaction dynamics underlying complex systems is mostly well understood. The formation and operation of constraints is often not, and oftener under appreciated. The attempt to reduce constraints to basic interaction fails in key cases. The overall aim of this paper is to highlight the key role played by constraints in shaping the field of complex systems. Following (...) an introduction to constraints, the paper develops the roles of constraints in specifying forms of complexity and illustrates the roles of constraints in formulating the fundamental challenges to understanding posed by complex systems. (shrink)
The received view about emergence and reduction is that they are incompatible categories. I argue in this paper that, contrary to the received view, emergence and reduction can hold together. To support this thesis, I focus attention on dynamicalsystems and, on the basis of a general representation theorem, I argue that, as far as these systems are concerned, the emulation relationship is sufficient for reduction (intuitively, a dynamical system DS1 emulates a second dynamical system (...) DS2 when DS1 exactly reproduces the whole dynamics of DS2). This representational view of reduction, contrary to the standard deductivist one, is compatible with the existence of structural properties of the reduced system that are not also properties of the reducing one. Therefore, under this view, by no means are reduction and emergence incompatible categories but, rather, complementary ones. (shrink)
Dynamicalsystems 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)
Both natural and engineered systems are fundamentally dynamical in nature: their defining properties are causal, and their functional capacities are causally grounded. Among dynamicalsystems, 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 dynamicalsystems (...) 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)
After more than 15 years of study, the 1/f noise or complex-systems approach to cognitive science has delivered promises of progress, colorful verbiage, and statistical analyses of phenomena whose relevance for cognition remains unclear. What the complex-systems approach has arguably failed to deliver are concrete insights about how people perceive, think, decide, and act. Without formal models that implement the proposed abstract concepts, the complex-systems approach to cognitive science runs the danger of becoming a philosophical exercise in (...) futility. The complex-systems approach can be informative and innovative, but only if it is implemented as a formal model that allows concrete prediction, falsification, and comparison against more traditional approaches. (shrink)
A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamicalsystems theory measures can similarly be interpreted as typicality measures. However, a justification why these measures are a good choice of typicality measures is missing, and the paper attempts to fill this gap. The paper first argues that Pitowsky's justification of typicality measures does not fit the bill. Then a first proposal of how to justify typicality measures is presented. (...) The main premises are that typicality measures are invariant and are related to the initial probability distribution of interest. The conclusions are two theorems which show that the standard measures of statistical mechanics and dynamicalsystems are typicality measures. There may be other typicality measures, but they agree about judgements of typicality. Finally, it is proven that if systems are ergodic or epsilon-ergodic, there are uniqueness results about typicality measures. (shrink)
I examine explanations’ realist commitments in relation to dynamicalsystems 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 dynamicalsystems theory. The take-home message is that understanding of the modal character of explanations (in dynamicalsystems theory) can undermine platonist arguments from explanatory indispensability.
On an influential account, chaos is explained in terms of random behaviour; and random behaviour in turn is explained in terms of having positive Kolmogorov-Sinai entropy (KSE). Though intuitively plausible, the association of the KSE with random behaviour needs justification since the definition of the KSE does not make reference to any notion that is connected to randomness. I provide this justification for the case of Hamiltonian systems by proving that the KSE is equivalent to a generalized version of (...) Shannon's communication-theoretic entropy under certain plausible assumptions. I then discuss consequences of this equivalence for randomness in chaotic dynamicalsystems. Introduction Elements of dynamicalsystems theory Entropy in communication theory Entropy in dynamicalsystems theory Comparison with other accounts Product versus process randomness. (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 dynamicalsystems, 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 dynamicalsystems give rise to higher-level (...)dynamical structures. (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 dynamicalsystems 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 dynamicalsystems 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)
This study attempts to describe the notion of the ‘self’ using dynamicalsystems language based on the results of our robot learning experiments. A neural network model consisting of multiple modules is proposed, in which the interactive dynamics between the bottom-up perception and the top-down prediction are investigated. Our experiments with a real mobile robot showed that the incremental learning of the robot switches spontaneously between steady and unsteady phases. In the steady phase, the top-down prediction for the (...) bottom-up perception works well when coherence is achieved between the internal and the environmental dynamics. In the unsteady phase, conflicts arise between the bottom-up perception and the top-down prediction; the coherence is lost, and a chaotic attractor is observed in the internal neural dynamics. By investigating possible analogies between this result and the phenomenological literature on the ‘self', we draw the conclusions that the structure of the ‘self’ corresponds to the ‘open dynamic structure’ which is characterized by co-existence of stability in terms of goal-directedness and instability caused by embodiment; the open dynamic structure causes the system's spontaneous transition to the unsteady phase where the ‘self’ becomes aware. (shrink)
Traditional approaches to modeling cognitive systems are computational, based on utilizing the standard tools and concepts of the theory of computation. More recently, a number of philosophers have argued that cognition is too subtle or complex for these tools to handle. These philosophers propose an alternative based on dynamicalsystems theory. Proponents of this view characterize dynamicalsystems as (i) utilizing continuous rather than discrete mathematics, and, as a result, (ii) being computationally more powerful than (...) traditional computational automata. Indeed, the logical possibility of such super-powerful systems has been demonstrated in the form of analog artificial neural networks. In this paper I consider three arguments against the nomological possibility of these automata. While the first two arguments fail, the third succeeds. In particular, the presence of noise reduces the computational power of analog networks to that of traditional computational automata, and noise is a pervasive feature of information processing in biological systems. Consequently, as an empirical thesis, the proposed dynamical alternative is under-motivated: What is required is an account of how continuously valued systems could be realized in physical systems despite the ubiquity of noise. (shrink)
In this work, we provide conditions to obtain fixed point theorems for parallel dynamicalsystems over graphs with maxterms and minterms as global evolution operators. In order to do that, we previously prove that periodic orbits of different periods cannot coexist, which implies that Sharkovsky’s order is not valid for this kind of dynamicalsystems.
. Interpreted dynamicalsystems are dynamicalsystems 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 dynamicalsystems, 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)
Cognitive science's basic premises are under attack. In particular, its focus on internal cognitive processes is a target. Intelligence is increasingly interpreted, not as a matter of reclusive thought, but as successful agent-environment interaction. The critics claim that a major reorientation of the field is necessary. However, this will only occur when there is a distinct alternative conceptual framework to replace the old one. Whether or not a serious alternative is provided is not clear. Among the critics there is some (...) consensus, however, that this role could be fulfilled by the concept of a 'behavioral system'. This integrates agent and environment into one encompassing general system. We will discuss two contexts in which the behavioral systems idea is being developed. Autonomous Agents Research is the enterprise of building behavior-based robots. DynamicalSystems Theory provides a mathematical framework well suited for describing the interactions between complex systems. We will conclude that both enterprises provide important contributions to the behavioral systems idea. But neither turns it into a full conceptual alternative which will initiate a major paradigm switch in cognitive science. The concept will need a lot of fleshing out before it can assume that role. (shrink)
According to the received view, reduction is a deductive relation between two formal theories. In this paper, I develop an alternative approach, according to which reduction is a representational relation between models, rather than a deductive relation between theories; more specifically, I maintain that this representational relation is the one of emulation. To support this thesis, I focus attention on mathematical dynamicalsystems and I argue that, as far as these systems are concerned, the emulation relation is (...) sufficient for reduction. I then extend this representational model-based view of reduction to the case of empirically interpreted dynamicalsystems, as well as to a treatment of partial, approximate, and asymptotic reduction. (shrink)
The proposed model is put forward as a template for the dynamicalsystems 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 dynamicalsystems models must be clarified.
This paper discusses possible correspondences between the dynamicalsystems 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)
Laws of nature have been traditionally thought to express regularities in the systems which they describe, and, via their expression of regularities, to allow us to explain and predict the behavior of these systems. Using the driven simple pendulum as a paradigm, we identify three senses that regularity might have in connection with nonlinear dynamicalsystems: periodicity, uniqueness, and perturbative stability. Such systems are always regular only in the second of these senses, and that sense (...) is not robust enough to support predictions. We thus illustrate precisely how physical laws in the classical regime of dynamicalsystems fail to exhibit predictive power. *R. G. Holt gratefully acknowledges the support of the National Center for Physical Acoustics at Oxford, Mississippi, and the Office of Naval Research. (shrink)
The distinction at the heart of van Gelder’s target article is one between digital computers and dynamicalsystems. But this distinction conflates two more fundamental distinctions in cognitive science that should be keep apart. When this conflation is undone, it becomes apparent that the “computational hypothesis” (CH) is not as dominant in contemporary cognitive science as van Gelder contends; nor has the “dynamical hypothesis” (DH) been neglected.
The theory of dynamicalsystems 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)
The "dynamicalsystems" model of cognitive processing is not an alternative computational model. The proposals about "computation" that accompany it are either vacuous or do not distinguish it from a variety of standard computational models. I conclude that the real motivation for van Gelder's version of the account is not technical or computational, but is rather in the spirit of natur-philosophie.
In a series of recent papers, two of which appeared in this journal, a group of philosophers, physicists, and climate scientists have argued that something they call the `hawkmoth effect' poses insurmountable difficulties for those who would use non-linear models, including climate simulation models, to make quantitative predictions or to produce `decision-relevant probabilites.' Such a claim, if it were true, would undermine much of climate science, among other things. Here, we examine the two lines of argument the group has used (...) to support their claims. The first comes from a set of results in dynamicalsystems theory associated with the concept of `structural stability.' The second relies on a mathematical demonstration of their own, using the logistic equation, that they present using a hypothetical scenario involving two apprentices of Laplace's omniscient demon. We prove two theorems that are relevant to their claims, and conclude that both of these lines of argument fail. There is nothing out there that comes close to matching the charac. (shrink)
Cognitive agents are dynamicalsystems but not quantitative dynamicalsystems. Quantitative systems are forms of analogue computation, which is physically too unreliable as a basis for cognition. Instead, cognitive agents are dynamicalsystems that implement discrete forms of computation. Only such a synthesis of discrete computation and dynamicalsystems can provide the mathematical basis for modeling cognitive behavior.
In 1973, Nickles identified two senses in which the term `reduction' is used to describe the relationship between physical theories: namely, the sense based on Nagel's seminal account of reduction in the sciences, and the sense that seeks to extract one physical theory as a mathematical limit of another. These two approaches have since been the focus of most literature on the subject, as evidenced by recent work of Batterman and Butterfield, among others. In this paper, I discuss a third (...) sense in which one physical theory may be said to reduce to another. This approach, which I call `dynamicalsystems reduction,' concerns the reduction of individual models of physical theories rather than the wholesale reduction of entire theories, and specifically reduction between models that can be formulated as dynamicalsystems. DS reduction is based on the requirement that there exist a function from the state space of the low-level model to that of the high-level model that satisfies certain general constraints and thereby serves to identify quantities in the low-level model that mimic the behavior of those in the high-level model - but typically only when restricted to a certain domain of parameters and states within the low-level model. I discuss the relationship of this account of reduction to the Nagelian and limit-based accounts, arguing that it is distinct from both but exhibits strong parallels with a particular version of Nagelian reduction, and that the domain restrictions employed by the DS approach may, but need not, be specified in a manner characteristic of the limit-based approach. Finally, I consider some limitations of the account of reduction that I propose and suggest ways in which it might be generalised. I offer a simple, idealised example to illustrate application of this approach; a series of more realistic case studies of DS reduction is presented in another paper. (shrink)
There is presently considerable interest in the phenomenon of "self-organisation" in dynamicalsystems. The rough idea of self-organisation is that a structure appears "by itself in a dynamical system, with reasonably high probability, in a reasonably short time, with no help from a special initial state, or interaction with an external system. What is often missed, however, is that the standard evolutionary account of the origin of multi-cellular life fits this definition, so that higher living organisms are (...) also products of self-organisation. Very few kinds of object can selforganise, and the question of what such objects are like is a suitable mathematical problem. Extending the familiar notion of algorithmic complexity into the context of dynamicalsystems, we obtain a notion of "dynamical complexity". A simple theorem then shows that only objects of very low dynamical complexity can self organise, so that living organisms must be of low dynamical complexity. On the other hand, symmetry considerations suggest that living organisms are highly complex, relative to the dynamical laws, due to their large size and high degree of irregularity. In particular, it is shown that since dynamical laws operate locally, and do not vary across space and time, they cannot produce any specific large and irregular structure with high probability in a short time. These arguments suggest that standard evolutionary theories of the origin of higher organisms are incomplete. (shrink)
Lewis's dynamicalsystems emotion theory continues a tradition including Merleau-Ponty, von Bertallanfy, and Aristotle. Understandably for a young theory, Lewis's new predictions do not follow strictly from the theory; thus their failure would not disconfirm the theory, nor their success confirm it – especially given that other self-organizational approaches to emotion (e.g., those of Ellis and of Newton) may not be inconsistent with these same predictions.
Shanker & King (S&K) trumpet the adoption of a “new paradigm” in communication studies, exemplified by ape language research. Though cautiously sympathetic, I maintain that their argument relies on a false dichotomy between “information” and “dynamicalsystems” theory, and that the resulting confusion prevents them from recognizing the main chance their line of thinking suggests.
This thesis is on information dynamics modeled using *dynamic epistemic logic*. It takes the simple perspective of identifying models with maps, which under a suitable topology may be analyzed as *topological dynamicalsystems*. It is composed of an introduction and six papers. The introduction situates DEL in the field of formal epistemology, exemplifies its use and summarizes the main contributions of the papers.Paper I models the information dynamics of the *bystander effect* from social psychology. It shows how augmenting (...) the standard machinery of DEL with a decision making framework yields mathematically self-contained models of dynamic processes, a prerequisite for rigid model comparison.Paper II extrapolates from Paper I's construction, showing how the augmentation and its natural peers may be construed as maps. It argues that under the restriction of dynamics produced by DEL dynamicalsystems still falls a collection rich enough to be of interest. Paper III compares the approach of Paper II with *extensional protocols*, the main alternative augmentation to DEL. It concludes that both have benefits, depending on application. In favor of the DEL dynamicalsystems, it shows that extensional protocols designed to mimic simple, DEL dynamicalsystems require infinite representations. Paper IV focuses on *topological dynamicalsystems*. It argues that the *Stone topology* is a natural topology for investigating logical dynamics as, in it, *logical convergence* coinsides with topological convergence. It investigates the recurrent behavior of the maps of Papers II and III, providing novel insigths on their long-term behavior, thus providing a proof of concept for the approach.Paper V lays the background for Paper IV, starting from the construction of metrics generalizing the Hamming distance to infinite strings, inducing the Stone topology. It shows that the Stone topology is unique in making logical and topological convergens coinside, making it the natural topology for logical dynamics. It further includes a metric-based proof that the hitherto analyzed maps are continuous with respect to the Stone topology. Paper VI presents two characterization theorems for the existence of *reduction laws*, a common tool in obtaining complete dynamic logics. In the compact case, continuity in the Stone topology characterizes existence, while a strengthening is required in the non-compact case. The results allow the recasting of many logical dynamics of contemporary interest as topological dynamicalsystems. (shrink)
Various aspects of the integrability of dynamicalsystems are discussed with the help of the singular point analysis. In particular the connection with the Painlevé property is described. Several examples will serve as illustrations.
Dynamicalsystems 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 dynamicalsystems 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)
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 dynamicalsystems theory.
In Robert West’s talk last week, dynamicalsystems theory (DST) was applied to a specific problem involving interacting symbolic systems, without much reference to how those systems are embodied or related to other types of systems. Despite this level of abstraction, DST can yield interesting results, though one might be left wondering if it really leads to understanding, or what it all means. In particular, Robert noted problems he has in convincing referees that the sort (...) of explanation he gave can give a useful understanding, and that it doesn’t invoke dubious notions with its references to emergence, holism, and mathematical openness. (shrink)