Although we applaud the interactivist approach to language and communication taken in the target article, we notice that Shanker & King (S&K) give little attention to the theoretical frameworks developed by dynamical system theorists. We point out how the dynamical idea of causality, viewed as multidirectional across multiple scales of organization, could further strengthen the position taken in the target article.

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. (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)

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. Dynamical Systems 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)

First published in 1996, _The Embedded Self_ was lauded as "a brilliant and long overdue rapprochement between psychoanalysis and family therapy conceived by a practitioner trained and experienced in both modalities of treatment." Mary-Joan Gerson’s integrated presentation of psychodynamic and family systems theory invited therapists of either orientation to learn the tools and techniques of the other, to mutual benefit. Firmly grounded in detailed case presentations, her focus on family therapy examined its history, organizing concepts, and developmental approaches, (...) and addressed practical questions of diagnosis, clinical interaction, and referrals. A dozen years later, the psychoanalytic community is more open to integrating perspectives, and the growth of analysts working with couples and families necessitates an update of the material presented in _The Embedded Self_. Similarly, the family therapy community has deepened its interest in individual dynamics within systemic patterning. From a new and revised perspective on the possibilities of integration, Gerson covers the latest research in neuroscience and the transmission of affect within intimate relationships, with a new chapter on attachment theory and emotionally focused therapy. Sections on narrative therapy and psychoanalytically-oriented family therapy are expanded as well. _The Embedded Self_ was a sterling introduction to family systems theory and therapy, and enhanced the work of analysts and family and couples therapists alike. The second edition proves no different in its context but wider in its scope, further enhancing the work of the family therapist interested in individual dynamics, and preparing the psychodynamically-oriented therapist who seeks to extend her craft from the dyad to the triad, and beyond. (shrink)

Dynamical systems theory (DST) is a branch of mathematics that assesses abstract or physical systems that change over time. It has a quantitative part (mathematical equations) and a related qualitative part (plotting equations in a state space). Nonlinear dynamical systems theory applies the same tools in research involving phenomena such as chaos and hysteresis. These approaches have provided different ways of investigating and understanding cognitive systems in cognitive science and neuroscience. The ‘ (...) class='Hi'>dynamical hypothesis’ claims that cognition is and can be understood as dynamical systems. Common consequences for such an approach include rejecting understanding cognition as information processing in nature, including eschewing explanatory roles for computation or representation. Contemporary applications of DST include mouse‐tracking studies in cognitive science and nonrepresentational perspectives on motor control in neuroscience. Such work has philosophical implications concerning the boundaries of cognition, explanation, and representations. DST offers powerful methodology and theories that raise many topics of philosophical significance. (shrink)

This chapter contains sections titled: Dynamical Systems Theory and Coupling Haugeland's Theory of Systems and the Coupling of Components Clark's Theories of Systems and Coupling Conclusion.

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 dynamical systems. Introduction Elements of dynamical systems theory Entropy in communication theory Entropy in dynamical systems theory Comparison with other accounts Product versus process randomness. (shrink)

The overall goal of this target article is to demonstrate a mechanism for an embodied cognition. The particular vehicle is a much-studied, but still widely debated phenomenon seen in 7–12 month-old-infants. In Piaget's classic “A-not-B error,” infants who have successfully uncovered a toy at location “A” continue to reach to that location even after they watch the toy hidden in a nearby location “B.” Here, we question the traditional explanations of the error as an indicator of infants' concepts of objects (...) or other static mental structures. Instead, we demonstrate that the A-not-B error and its previously puzzling contextual variations can be understood by the coupled dynamics of the ordinary processes of goal-directed actions: looking, planning, reaching, and remembering. We offer a formal dynamic theory and model based on cognitive embodiment that both simulates the known A-not-B effects and offers novel predictions that match new experimental results. The demonstration supports an embodied view by casting the mental events involved in perception, planning, deciding, and remembering in the same analogic dynamic language as that used to describe bodily movement, so that they may be continuously meshed. We maintain that this mesh is a pre-eminently cognitive act of “knowing” not only in infancy but also in everyday activities throughout the life span. Key Words: cognitive development; dynamical systems theory; embodied cognition; infant development; motor control; motor planning; perception and action. (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)

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)

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.

Bruineberg and colleagues highlight work using Markov blankets to demarcate the bounds of the mind. This echoes earlier attempts to demarcate the bounds of the mind from a dynamical systems perspective. Advocates of mechanistic explanation have challenged the dynamical approach to independently motivate the application of the formalism, a challenge that Markov blanket theorists must also meet.

Neural organization contains a wealth of facts from all areas of brain research and provides a useful overview of physiological data for those working outside the immediate field. Furthermore, it gives a good example that the approach of dynamical system theory together with the concepts of cooperative and competitive interaction can be fruitful for an interdisciplinary approach to cognition.

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)

From his earliest work forward, phenomenologist Maurice Merleau-Ponty attempted to develop a new ontology of nature that would avoid the antinomies of realism and idealism by showing that nature has its own intrinsic sense which is prior to reflection. The key to this new ontology was the concept of form, which he appropriated from Gestalt psychology. However, Merleau-Ponty struggled to give a positive characterization of the phenomenon of form which would clarify its ontological status. Evan Thompson has recently taken up (...) Merleau-Ponty’s ontology as the basis for a new, “enactive” approach to cognitive science, synthesizing it with concepts from dynamic systems theory and Francisco Varela’s theory of autopoiesis. However, Thompson does not quite succeed in resolving the ambiguities in Merleau-Ponty’s account of form. This article builds on an indication from Thompson in order to propose a new account of form as asymmetry, and of the genesis of form in nature as symmetry-breaking. These concepts help us to escape the antinomies of Modern thought by showing how nature is the autoproduction of a sense which can only be known by an embodied perceiver. (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)

It is now widely accepted that qualitative and quantitative research traditions, rather than being seen as opposed to or in competition with each other should be used, where appropriate, in some kind of combination. How this combining is to be understood ontologically, and therefore epistemologically, however, is not always clear. Rather than endlessly discussing the relationship between different approaches, this paper explores some of the assumptions of the ontologies that underpin such apparent differences, arguing that approaches which declare themselves to (...) be distinct theoretically are often surprisingly similar methodologically. It is argued that dominant ontologies and epistemologies struggle with the conceptualisation and representation of particularity, difference, process, interactions through time, multiple and de-centred forms of causation, and dynamic structure. Complexity/dynamic systems theory is then introduced and examined for its potential to offer the basis of a different kind of ontology: one which is able not only to accommodate these things, but which is itself based upon them. In conclusion, the implications of this perspective are discussed in relation to the problems that have been identified, particularly in relation to the conceptualisation of 'context'. (shrink)

Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations' solutions, such as orbital resonances and horseshoe (...) orbits. Poincaré wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating. (shrink)

Dynamic systems theory (DS) provides tools for exploring how simpler elements can interact to produce complex psychological configurations. It may, as Lewis demonstrates, provide means for explicating relationships between two reductionist approaches to overlapping sets of phenomena. The result is a description of psychological phenomena at a level that begins to achieve the richness we would hope to achieve in examining psychological life as it is experienced and explored in psychoanalysis.

It is now widely accepted that qualitative and quantitative research traditions, rather than being seen as opposed to or in competition with each other ( ; ) should be used, where appropriate, in some kind of combination (; ). How this combining is to be understood ontologically, and therefore epistemologically, however, is not always clear. Rather than endlessly discussing the relationship between different approaches, this paper explores some of the assumptions of the ontologies that underpin such apparent differences, arguing that (...) approaches which declare themselves to be distinct theoretically are often surprisingly similar methodologically. It is argued that dominant ontologies and epistemologies struggle with the conceptualisation and representation of particularity, difference, process, interactions through time, multiple and de‐centred forms of causation, and dynamic structure. Complexity/dynamic systems theory is then introduced and examined for its potential to offer the basis of a different kind of ontology: one which is able not only to accommodate these things, but which is itself based upon them. In conclusion, the implications of this perspective are discussed in relation to the problems that have been identified, particularly in relation to the conceptualisation of ‘context’. (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)

This chapter contains sections titled: How is the Combining of Qualitative/Quantitative Methods to be Understood? ‘Critical Connections’? Problems Conceptualising and Researching Difference, Specificity and Context Complexity Theory: Redefining Order (and Chaos)? A Complexity‐Based Ontology Conceptualising Difference, Specificity and Context Conclusion Notes References.

Temporal patterns in human movement, and in speech in particular, occur on multiple timescales. Regularities in such patterns have been observed between speech gestures, which are relatively quick movements of articulators (e.g., tongue fronting and lip protrusion), and also between rhythmic units (e.g., syllables and metrical feet), which occur more slowly. Previous work has shown that patterns in both domains can be usefully modeled with oscillatory dynamical systems. To investigate how rhythmic and gestural domains interact, an experiment was (...) conducted in which speakers performed a phrase repetition task, and gestural kinematics were recorded using electromagnetic articulometry. Variance in relative timing of gestural movements was correlated with variance in rhythmic timing, indicating that gestural and rhythmic systems interact in the process of planning and producing speech. A model of rhythmic and gestural planning oscillators with multifrequency coupling is presented, which can simulate the observed covariability between rhythmic and gestural timing. (shrink)

This article discusses the role of moment-to-moment affect dynamics in mental disorder and aims to integrate recent literature on this topic in the context of complex dynamical system theory. First, we will review the relevance of temporal and contextual aspects of affect dynamics in relation to psychopathology. Related to this, we will discuss recent insights resulting from a network view on affect dynamics in psychopathology. Next, we explore how we can reconcile literature findings from a perspective of complex (...) dynamical system theory. Finally, future directions with regard to personalized assessment of risk and diagnostic use are discussed. (shrink)

A fundamental link between system theory and statistical mechanics has been found to be established by the Kolmogorov entropy K. By this quantity the temporal evolution of dynamical systems can be classified into regular, chaotic, and stochastic processes. Since K represents a measure for the internal information creation rate of dynamical systems, it provides an approach to irreversibility. The formal relationship to statistical mechanics is derived by means of an operator formalism originally introduced by Prigogine. (...) For a Liouville operator L and an information operator $\tilde M$ acting on a distribution in phase space, it is shown that i[L, $\tilde M$ ]≡KI (I=identity operator). As a first consequence of this equivalence, a relation is obtained between the chaotic correlation time of a system and Prigogine's concept of a “finite duration of presence.” Finally, the existence of chaos in quantum systems is discussed with respect to the existence of a quantum mechanical time operator. (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.

It is widely believed that mathematics carries a substantial part of the explanatory burden in science. However, mathematics can also play important heuristic roles of a different kind, being a source of new ideas and approaches, allowing us to build toy models, enhancing expressive power and providing fruitful conceptualizations. In this paper, we focus on the application of dynamical systems theory (DST) within the extended cognition (EC) field of cognitive science, considering this case study to be a (...) good illustration of a general phenomenon. In the paper, we justify both a negative and a positive claim. The negative claim is that dynamical systems theory hardly plays any explanatory role in EC research. We justify our claim by analyzing several accounts of the explanatory role of mathematics and stressing the way mathematical arguments are used in explanations. Our positive claim is that even though, for now, DST has no explanatory power in many of the EC approaches, it still plays an important heuristic role there. In particular, using mathematical notions improves the expressive power of the language and gives a sense of understanding of the phenomena under investigation. The case study of EC allows us to identify and analyze this important role of mathematics, which seems to be neglected in contemporary discussions. (shrink)

A study of shifts in scientific strategies for measuring the living body, especially in dynamic systems theory: sheds light on Hegel's concept of measure in The Science of Logic, and the dialectical transition from categories of being to categories of essence; shows how Hegel's speculative logic anticipates and analyzes key tensions in scientific attempts to measure and conceive the dynamic agency of the body. The study's analysis of the body as having an essentially dynamic identity irreducible to measurement (...) aims to contribute to reconceiving the body, in a way that may be helpful to overcoming dualism. (shrink)

This article reports on a study that took a Dynamic Systems Theory perspective to second language motivational self system. More specifically, it investigated the influence of an Intensive English Reading course based on the Production-Oriented Approach upon the L2MSS of Chinese university English majorsfrom the DST perspective. To this end, two intact classes composed of 50 students were assigned into experimental group and control group, who responded to an L2MSS scale before and after the one-semester intervention. Eight and (...) five students were respectively selected using the purposive sampling method from the experimental and control groups for follow-up semi-structured interviews. The quantitative results revealed that the overall and dimensional levels of L2MSS were significantly strengthened over time in the EG while kept stable in the CG. The qualitative results suggested that the enhanced Ideal L2 Self of the participants stemmed from an attractor basin that was deepened by a number of attractors encompassing Output Tasks and Peer Performance. The interview results also showed that the increased L2 Learning Experience of the participants pertained to an attractor basin that was consolidated by an array of attractors containing Output Tasks, Teacher Guidance, Group Discussion, and Peer Assessment. The findings indicated that the attractors at the subjective and social dimensions in the POA-based course collectively worked together to cause changes in L2MSS among the participants. The implications for intervening L2 motivation from a POA approach in English as a Foreign Language classrooms were discussed. (shrink)

The concepts and powerful mathematical tools of Dynamical Systems Theory (DST) yield illuminating methods of studying cognitive processes, and are even claimed by some to enable us to bridge the notorious explanatory gap separating mind and matter. This article includes an analysis of some of the conceptual and empirical progress Dynamical Systems Theory is claimed to accomodate. While sympathetic to the dynamicist program in principle, this article will attempt to formulate a series of problems (...) the proponents of the approach in question will need to face if they wish to prolong their optimism. The main points to be addressed involve the reductive tendencies inherent in Dynamical Systems Theory, its somewhat muddled position relative to connectionism, the metaphorical nature DST-C exhibits which hinders its explanatory potential, and DST-C's problematic account of causality. Brief discussions of the mathematical and philosophical backgrounds of DST, seminal experimental work and possible adaptations of the theory or alternative suggestions (dynamicist connectionism, neurophenomenology, R&D theory) are included. (shrink)

Marr's seminal work laid out a program of research by specifying key questions for cognitive science at different levels of analysis. Because dynamic systems theory focuses on time and interdependence of components, DST research programs come to very different conclusions regarding the nature of cognitive change. We review a specific DST approach to cognitive-level processes: dynamic field theory. We review research applying DFT to several cognitive-level processes: object permanence, naming hierarchical categories, and inferring intent, that demonstrate the (...) difference in understanding of behavior and cognition that results from a DST perspective. These point to a central challenge for cognitive science research as defined by Marr—emergence. We argue that appreciating emergence raises questions about the utility of computational-level analyses and opens the door to insights concerning the origin of novel forms of behavior and thought. We contend this is one of the most fundamental questions about cognition and behavior. (shrink)

One of the major divergences between dynamical systems theory and symbolism lies in their views on the role of representation in cognition. From the perspective of development, the cognitive development could be divided into three levels: sensorimotor, imagery representation and linguistic representation. It is claimed that representation is not a sufficient condition though it is necessary for cognition. However, it does not mean that the authors agree with the notion of strong coupling in dynamicism that completely (...) rejects representation. (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)

Years ago, when I was an undergraduate math major at the University of Wyoming, I came across an interesting book in our library. It was a book of counterexamples t o propositions in real analysis (the mathematics of the real numbers). Mathematicians work more or less like the rest of us. They consider propositions. If one seems to them to be plausibly true, then they set about to prove it, to establish the proposition as a theorem. Instead o f setting (...) out to prove propositions, the psychologists, neuroscientists, and other empirical types among us, set out to show that a proposition is supported by the data, and that it is the best such proposition so supported. The philosophers among us, when they are not causing trouble by arguing that AI is a dead end or that cognitive science can get along without representations, work pretty much like the mathematicians: we set out to prove certain propositions true on the basis of logic, first principles, plausible assumptions, and others' data. But, back to the book of real analysis counterexamples. If some mathematician happened t o think that some proposition about continuity, say, was plausibly true, he or she would then set out to prove it. If the proposition was in fact not a theorem, then a lot of precious time would be wasted trying to prove it. Wouldn't it be great to have a book that listed plausibly true propositions that were in fact not true, and listed with each such proposition a counterexample to it? Of course it would. (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 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)