Nonlinear Dynamics

The thesis of this paper is that panpsychism theory is very close to jungian theory, especially thinking of the quantum psychoid aspects of C.G.Jung and W.Pauli theory: a psyche that touches matter and matter with a “latent psyche”. The two theories seem to describe the same reality, an animation of matter in a spiritual sense, as the jungian Self seems to do at a higher level.The complexity theory appears instead to be a description of reality still nomothetic.

Человек – это память. Чтобы понять, что такое человек, необходимо понять, что такое память.

The discovery of sensitive dependence on initial conditions (SDIC) in nonlinear models runs counter to the textbook vision of CM, a vision guided by an almost exclusive focus on linear systems. Therefore, it is important to clearly distinguish between linear and nonlinear systems along with establishing some basic terminology (§I). The notions of SDIC and chaos also need clarification, since they play crucial roles in sensitive dependence (SD) arguments. This will require some discussion of Lyapunov exponents as well as the (...) relationship between nonlinear dynamics and chaos (§II and Appendix). For the sake of concreteness, it will also be useful to focus on the Laplacean vision for classical particle mechanics (e.g., Bishop 2002b, 2003 and 2005a), particularly the crucial notion of unique evolution (§III). The SD argument can then be stated in a clear form and its defenses, criticisms and limitations assessed in the more general context of nonlinear dynamics (§IV). Concluding remarks follow (§V). (shrink)

This paper dealing with extension of the Einstein eld equations using apparatus of contemporary generalization of the classical Lorentzian geometry named in literature Colombeau distributional geometry, see for example [1], [2], [3], [4], [5], [6], [7] and [32]. The regularizations of singularities presented in some solutions of the Einstein equations is an important part of this approach. Any singularities present in some solutions of the Einstein equations recognized only in the sense of Colombeau generalized functions [1], [2] and not classically. (...) In this paper essentially new class Colombeau solutions to Einstein eld equations is obtained. The vacuum energy density of free scalar quantum field  with a distributional background spacetime also is considered. It has been widely believed that, except in very extreme situations, the influence of gravity on quantum fields should amount to just small, sub-dominant contributions. Here we argue that this belief is false by showing that there exist well-behaved spacetime evolutions where the vacuum energy density of free quantum fields is forced, by the very same background distributional spacetime such distributional BHs, to become dominant over any classical energy density component. This semiclassical gravity effect finds its roots in the singular behavior of quantum fields on curved spacetimes. In particular we obtain that the vacuum fluctuations have a singular behavior on BHs horizon. (shrink)

Can stable regularities be explained without appealing to governing laws or any other modal notion? In this paper, I consider what I will call a ‘Humean system’—a generic dynamical system without guiding laws—and assess whether it could display stable regularities. First, I present what can be interpreted as an account of the rise of stable regularities, following from Strevens [2003], which has been applied to explain the patterns of complex systems (such as those from meteorology and statistical mechanics). Second, since (...) this account presupposes that the underlying dynamics displays deterministic chaos, I assess whether it can be adapted to cases where the underlying dynamics is not chaotic but truly random—that is, cases where there is no dynamics guiding the time evolution of the system. If this is so, the resulting stable, apparently non-accidental regularities are the fruit of what can be called statistical necessity rather than of a primitive physical necessity. (shrink)

In 1900, the physicist Henri Bénard exhibited the spontaneous formation of cells in a layer of liquid heated from below. Six or seven decades later, drastic reinterpretations of this experiment formed an important component of ‘chaos theory’. This paper therefore is an attempt at writing the history of this experiment, its long neglect and its rediscovery. It examines Bénard’s experiments from three different perspectives. First, his results are viewed in the light of the relation between experimental and mathematical approaches in (...) fluid mechanics, leading to a re-examination of the long-term reception of Bénard’s results among fluid dynamicists up to the chaos craze, whereby the traditional emphasis placed on mathematical physics is counterbalanced by greater attention to experimental approaches. Second, we focus on Bénard’s own way of using his results as analogies that could help grasp something about the reason why inorganic matter may structure itself in ways reminiscent of living forms. This is shown to resonate strongly with Prigogine’s work in the 1960s and 1970s. Third, Bénard’s adoption of the cinematograph as his preferred experimental instrument is interpreted as having reinforced his long-misunderstood belief that he had exhibited a form of self-organization essential to the understanding of life.Keywords: Bénard cells; Henri Poincaré; Chaos; Fluid mechanics; Cinematograph; Self-organization. (shrink)

Emergence is much discussed by both philosophers and scientists. But, as noted by Mitchell (2012), there is a significant gulf; philosophers and scientists talk past each other. We contend that this is because philosophers and scientists typically mean different things by emergence, leading us to distinguish being emergence and pattern emergence. While related to distinctions offered by others between, for example, strong/weak emergence or epistemic/ontological emergence (Clayton, 2004, pp. 9–11), we argue that the being vs. pattern distinction better captures what (...) the two groups are addressing. In identifying pattern emergence as the central concern of scientists, however, we do not mean that pattern emergence is of no interest to philosophers. Rather, we argue that philosophers should attend to, and even contribute to, discussions of pattern emergence. But it is important that this discussion be distinguished, not conflated, with discussions of being emergence. In the following section we explicate the notion of being emergence and show how it has been the focus of many philosophical discussions, historical and contemporary. In section 3 we turn to pattern emergence, briefly presenting a few of the ways it figures in the discussions of scientists (and philosophers of science who contribute to these discussions in science). Finally, in sections 4 and 5, we consider the relevance of pattern emergence to several central topics in philosophy of biology: the emergence of complexity, of control, and of goal-directedness in biological systems. (shrink)

I investigate the role of stability in cosmology through two episodes from the recent history of cosmology: Einstein’s static universe and Eddington’s demonstration of its instability, and the flatness problem of the hot big bang model and its claimed solution by inflationary theory. These episodes illustrate differing reactions to instability in cosmological models, both positive ones and negative ones. To provide some context to these reactions, I also situate them in relation to perspectives on stability from dynamical systems theory and (...) its epistemology. This reveals, for example, an insistence on stability as an extreme position in relation to the spectrum of physical systems which exhibit degrees of stability and fragility, one which has a pragmatic rationale, but not any deeper one. (shrink)

The file on this site provides the slides for a lecture given in Hangzhou in May 2018, and the lecture itself is available at the URL beginning 'sms' in the set of links provided in connection with this item. -/- It is commonly assumed that regular physics underpins biology. Here it is proposed, in a synthesis of ideas by various authors, that in reality structures and mechanisms of a biological character underpin the world studied by physicists, in principle supplying detail (...) in the domain that according to regular physics is of an indeterminate character. In regular physics mathematical equations are primary, but this constraint leads to problems with reconciling theory and reality. Biology on the other hand typically does not characterise nature in quantitative terms, instead investigating in detail important complex interrelationships between parts, leading to an understanding of the systems concerned that is in some respects beyond that which prevails in regular physics. It makes contact with quantum physics in various ways, for example in that both involve interactions between observer and observed, an insight that explains what is special about processes involving observation, justifying in the quantum physics context the replacement of the unphysical many-worlds picture by one involving collapse. The link with biology furthermore clarifies Wheeler’s suggestion that a multiplicity of observations can lead to the ‘fabrication of form’, including the insight that this process depends on very specific ‘structures with power’ related to the 'semiotic scaffolding' of the application of sign theory to biology known as biosemiotics. -/- The observer-observed 'circle' of Wheeler and Yardley is a special case of a more general phenomenon, oppositional dynamics, related to the 'intra-action' of Barad's Agential Realism, involving cooperating systems such as mind and matter, abstract and concrete, observer and observed, that preserve their identities while interacting with one another in such a way as to act as a unit. A third system may also be involved, the mediating system of Peirce linking the two together. Such a situation of changing connections and separations may plausibly lead in the future to an understanding of how complex systems are able to evolve to produce 'life, the universe and everything'. -/- (Added 1 July 2018) The general structure proposed here as an alternative to a mathematics-based physics can be usefully characterised by relating it to different disciplines and the specialised concepts utilised therein. In theoretical physics, the test for the correctness of a theory typically involves numerical predictions, corresponding to which theories are expressed in terms of equations, that is to say assertions that two quantities have identical values. Equations have a lesser significance in biology which typically talks in terms of functional mechanisms, dependent for example on details of chemistry and concepts such as genes, natural selection, signals and geometrical or topologically motivated concepts such as the interconnections between systems and the unfolding of DNA. Biosemiotics adds to this the concept of signs and their interpretation, implying novel concepts such as semiotic scaffolding and the semiosphere, code duality, and appreciation of the different types of signs, including symbols and their capacity for abstraction and use in language systems. Circular Theory adds to this picture, as do the ideas of Barad, considerations such as the idea of oppositional dynamics. The proposals in this lecture can be regarded as the idea that concepts such as those deriving from biosemiotics have more general applicability than just conventional biology and may apply, in some circumstances, to nonlinear systems generally, including the domain new to science hypothesised to underlie the phenomena of present-day physics. -/- The task then has to be to restore the mathematical aspect presumed, in this picture, not to be fundamental as it is in conventional theory. Deacon has invoked a complex sequence of evolutionary steps to account for the emergence over time of human language systems, and correspondingly mathematical behaviour can be subsumed under the general evolutionary mechanisms of biosemiotics (cf. also the proposals of Davis and Hersh regarding the nature of mathematics), so that the mathematical behaviour of physical systems is consistent with the proposed scheme. In conclusion, it is suggested that theoretical physicists should cease expecting to find some universal mathematical ‘theory of everything’, and focus instead on understanding in more detail complex systems exhibiting behaviour of a biological character, extending existing understanding. This may in time provide a more fruitful understanding of the natural world than does the regular approach. The essential concepts have an observational basis from both biology and the little-known discipline of cymatics (a discipline concerned with the remarkable patterns that specific waveforms can give rise to), while again computer simulations also offer promise in providing insight into the complex behaviours involved in the above proposals. -/- References -/- Jesper Hoffmeyer, Semiotic Scaffolding of Living Systems. Commens, a Digital Companion to C. S. Peirce (on Commens web site). Terrence Deacon, The Symbolic Species, W.W. Norton & Co. Karen Barad, Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning, Duke University Press. Philip Davis and Reuben Hersh, The Mathematical Experience, Penguin. Ilexa Yardley, Circular Theory. (shrink)

The target paper of Schoeller, Perlovsky, and Arseniev is an essential and timely contribution to a current shift of focus in neuroscience aiming to merge neurophysiological, psychological and physical principles in order to build the foundation for the physics of mind. Extending on previous work of Perlovsky et al. and Badre, the authors of the target paper present interesting mathematical models of several basic principles of the physics of mind, such as perception and cognition, concepts and emotions, instincts and learning. (...) Their conceptualization helps to clarify the distinction between conscious and unconscious aspects of mind that is often neglected and further provide a clear description of the mental hierarchy, which extends from physical objects in the physical world to abstract ideas in the mental/subjective realm. While we agree that identification of a few fundamental principles is a first step toward developing the physics of the mind, and we concur with the selection of those principles in the target review paper, we think that the theory of the physics of mind would much benefit from considering also the most basic principles that are common for the physics/matter/brain and the mind/subjectivity/cognition. In this respect, such basic principles as time and space, as well as criticality, self-organization, and emergence seem to be the most interesting. (shrink)

This work builds on the Volterra series formalism presented in Dreisigmeyer and Young to model nonconservative systems. Here we treat Lagrangians and actions as ‘time dependent’ Volterra series. We present a new family of kernels to be used in these Volterra series that allow us to derive a single retarded equation of motion using a variational principle.

The models of the electric charge and magnetic moment are presented based on the nonlinear response of a vacuum on the applied electric and magnetic fields. The model of the electric charge contains one parameter—the radius of charge—and predicts one value of the electric charge for all elementary particles independently on the value of this radius. Different values of this parameter for the electron are discussed.

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)

Nonlinear patterns of change arise frequently in the analysis of repeated measures from longitudinal studies in psychology. The main feature of nonlinear development is that change is more rapid in some periods than in others. There generally also are strong individual differences, so although there is a general similarity of patterns for different persons over time, individuals exhibit substantial heterogeneity in their particular response. To describe data of this kind, researchers have extended the random coefficient model to accommodate nonlinear trajectories (...) of change. It can often produce a statistically satisfying account of subject-specific development. In this review we describe and illustrate the main ideas of the nonlinear random coefficient model with concrete examples. (shrink)

v. 1. Theory of continuous Fokker-Planck systems -- v. 2. Theory of noise induced processes in special applications -- v. 3. Experiments and simulations.

A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic reviews of the relevant material are provided. Further chapters are devoted to the stability of invariant sets, bifurcation theory, chaotic dynamics and the transition to chaos. In the final two chapters the authors approach the subject from a measure-theoretical (...) point of view and compare results to those given for the geometrical or topological approach of the first eight chapters. Includes about one hundred exercises. A Windows-compatible software programme called DMC, provided free of charge through a website dedicated to the book, allows readers to perform numerical and graphical analysis of dynamical systems. Also available on the website are computer exercises and solutions to selected book exercises. See www.cambridge.org/economics/resources. (shrink)

The fault ride-through capability and fault current issues are the main challenges in doubly fed induction generator- based wind turbines. Application of the bridge-type fault current limiter was recognized as a promising solution to cope with these challenges. This paper proposes a nonlinear sliding mode controller for the BFCL to enhance the FRT performance of the DFIG-based WT. This controller has robust performance in unpredicted voltage sag level and nonlinear features. Theoretical discussions, power circuit, and nonlinear control consideration of the (...) SMC-based BFCL are conducted, and then, its performance is verified through time-domain simulations in the PSCAD/EMTDC environment. To reduce the chattering phenomenon and decrease the reaching time, it used the exponential reaching law for designed SMC. Also, the SMC-based BFCL performance is compared with the conventional and PI controller-based BFCL for both symmetrical and asymmetrical short-circuit faults. Simulation results reveal that the SMC-based BFCL provides better performance compared with the conventional and PI controller-based BFCL to enhance the FRT. (shrink)

This essay explores the metaphorical use of the area of nonlinear dynamics popularly known as "chaos theory," surveying its use in one particular field: legal theory. After sketching some of the mistakes encountered in these efforts, I outline the possibility of the fruitful use of nonlinear dynamics for thinking about our legal system. I then offer some general lessons to be drawn from these examples-both cautionary maxims and a limited defense of cross-disciplinary borrowing. I conclude with some reflections on the (...) nature of arguments that seek to establish intellectual authority or epistemic merit by analogical reasoning. (shrink)

Chaotic dynamics has been hailed as the third great scientific revolution in physics this century, comparable to relativity and quantum mechanics. In this book, Peter Smith takes a cool, critical look at such claims. He cuts through the hype and rhetoric by explaining some of the basic mathematical ideas in a clear and accessible way, and by carefully discussing the methodological issues which arise. In particular, he explores the new kinds of explanation of empirical phenomena which modern dynamics can deliver. (...) Explaining Chaos will be compulsory reading for philosophers of science and for anyone who has wondered about the conceptual foundations of chaos theory. (shrink)

We examine a case in which non-computable behavior in a model is revealed by computer simulation. This is possible due to differing notions of computability for sets in a continuous space. The argument originally given for the validity of the simulation involves a simpler simulation of the simulation, still further simulations thereof, and a universality conjecture. There are difficulties with that argument, but there are other, heuristic arguments supporting the qualitative results. It is urged, using this example, that absolute validation, (...) while highly desirable, is overvalued. Simulations also provide valuable insights that we cannot yet (if ever) prove. (shrink)

Recenzja książki: Andrzej Pelczar, Czas i dynamika. O czasie w równaniach różniczkowych i układach dynamicznych, OBI--Kraków, Biblos-Tarnów 2003, ss. 117.

The big news about chaos is supposed to be that the smallest of changes in a system can result in very large differences in that system's behavior. The so-called butterfly effect has become one of the most popular images of chaos. The idea is that the flapping of a butterfly's wings in Argentina could cause a tornado in Texas three weeks later. By contrast, in an identical copy of the world sans the Argentinian butterfly, no such storm would have arisen (...) in Texas. The mathematical version of this property is known as sensitive dependence. However, it turns out that sensitive dependence is somewhat old news, so some of the implications flowing from it are perhaps not such “big news” after all. Still, chaos studies have highlighted these implications in fresh ways and led to thinking about other implications as well. -/- In addition to exhibiting sensitive dependence, chaotic systems possess two other properties: they are deterministic and nonlinear (Smith 2007). This entry discusses systems exhibiting these three properties and what their philosophical implications might be for theories and theoretical understanding, confirmation, explanation, realism, determinism, free will and consciousness, and human and divine action. (shrink)

It is shown that the famous Lyapunov exponents cannot be used as the numerical characteristic for distinguishing different kinds of attractors, such as the equilibrium point, the limit closed curve, the stable torus and the strange attractor.

In a theoretical simulation the cooperation of two insects is investigated who share a large number of maximally entangled EPR-pairs to correlate their probabilistic actions. Specifically, two distant butterflies must find each other. Each butterfly moves in a chaotic form of short flights, guided only by the weak scent emanating from the other butterfly. The flight directions result from classical random choices. Each such decision of an individual is followed by a read-out of an internal quantum measurement on a spin, (...) the result of which decides whether the individual shall do a short flight or wait. These assumptions reflect the scarce environmental information and the small brains’ limited computational capacity. The quantum model is contrasted to two other cases: In the classical case the coherence between the spin pairs gets lost and the two butterflies act independently. In the super classical case the two butterflies read off their decisions of whether to fly or to wait from the same internal list so that they always take the same decision as if they were super correlated. The numerical simulation reveals that the quantum entangled butterflies find each other with a much shorter total flight path than in both classical models. (shrink)