More than a simple expository history, A Thousand Years of Nonlinear History sketches the outlines of a renewed materialist philosophy of history in the tradition of Fernand Braudel, Gilles Deleuze, and F lix Guattari, while also engaging the critical new understanding of material processes derived from the sciences of dynamics.Following in the wake of his groundbreaking War in the Age of Intelligent Machines, Manuel De Landa presents a radical synthesis of historical development over the last one thousand years. More (...) than a simple expository history, A Thousand Years of Nonlinear History sketches the outlines of a renewed materialist philosophy of history in the tradition of Fernand Braudel, Gilles Deleuze, and F lix Guattari, while also engaging the critical new understanding of material processes derived from the sciences of dynamics. Working against prevailing attitudes that see history as an arena of texts, discourses, ideologies, and metaphors, De Landa traces the concrete movements and interplays of matter and energy through human populations in the last millennium. De Landa attacks three domains that have given shape to human societies: economics, biology, and linguistics. In every case, what one sees is the self-directed processes of matter and energy interacting with the whim and will of human history itself to form a panoramic vision of the West free of rigid teleology and naive notions of progress, and even more important, free of any deterministic source of its urban, institutional, and technological forms. Rather, the source of all concrete forms in the West's history are shown to derive from internal morphogenetic capabilities that lie within the flow of matter-energy itself. (shrink)

Behaviors of chaotic systems are unpredictable. Chaotic systems are deterministic, their evolutions being governed by dynamical equations. Are the two statements contradictory? They are not, because the theory of chaos encompasses two levels of description. On a higher level, unpredictability appears as an emergent property of systems that are predictable on a lower level. In this talk, we examine the structure of dynamical theories to see how they employ multiple descriptive levels to explain chaos, bifurcation, and other complexities of (...) class='Hi'>nonlinear systems.. (shrink)

Wright & Liley contrast their theory that the global dynamics of the EEG are linear with that of Freeman, who hypothesizes an EEG governed by (nonlinear) deterministic-chaotic dynamics. A “call for further discussion” on the part of the authors is made as to how either theory fits with experimental findings indicating that EEG dynamics are non-linear but stochastic.

Excessive use of social media is a developing concern in the twenty-first century. This issue needs to be addressed before it has any more significant consequences than what we are currently experiencing. As a preventive technique, advertisements and awareness-raising campaigns about the detrimental impact of digital technologies are used. The application of novel mathematical techniques and terminologies in this field of study will have significant potential to enhance healthy living by preventing certain ailments. This is the most compelling justification for (...) conducting a new study with the most up-to-date techniques at our disposal. This study investigates clear and concise transmission in order to generate a deterministic mathematical model of social media addiction S M A using the fractal-fractional derivative operator. Also, the analysis of the S M A model in terms of the invariant domain, the existence of a positive invariant solution, and equilibria assumptions are stated in a detailed manner. Besides that, the basic reproduction number ℝ 0 < 1 is computed, demonstrating that the proposed methodology is more efficacious. The Atangana-Baleanu FF differential operators are recently defined in FF differential operators that are applied to characterize the S M A model’s mathematical algorithm. We investigated the numerical behaviour of the S M A in three ways: changing the fractional-order α as well as the fractal-dimension ℘ ; changing α while keeping ℘ constant; and changing ℘ while keeping α constant. Our examined visualizations and simulation studies using MATLAB for the numerical modelling of the aforementioned system showed that the novel developed Atangana-Baleanu FF differential operators produce remarkable results when compared to the classical frame. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 12.3 (2005) 235-237 [Access article in PDF] Determined by Chaos: The Nonlinear Dynamics of Free Will Jessica Wahman Keywords free will, chaos theory, determinism, materialism In "antidepressants and the Chaotic Brain: Implications for the Respectful Treatment of Selves," Douglas Heinrichs provides an intriguing justification of individuated and longer term therapy for depressive clients. He does not reject medication as a therapeutic strategy, nor (...) does he question the materialist basis of the traditional medical model. Rather, he offers a physically deterministic account of depression that is at the same time compatible with a sense of human agency and individuality. Heinrichs suggests that human physiology and its psychiatric disorders are better accounted for by the nonlinear dynamics of chaos theory than by the traditional account of neurotransmitter production and reuptake. Because the latter, microscopic, explanation suggests a direct cause-and-effect relationship between synaptic activity and subjective affect, it cannot account for the wide variation of responses to the same medications, nor can it satisfy the client's fears that her drug-induced well-being is not fully hers to control. Chaos theory, he asserts, can provide a better explanation by treating the human organism as a complex holistic system whose patterns resemble a topographical map of probability more than they do a unidirectional vector model of cause to effect. Like the weather, human affect and behavior are physically determined but difficult to predict, and so careful attention to both the individual history of the client and the uniqueness of responses to medication are a necessary part of any successful therapeutic program.Connected to this theory of nonlinear physiology is Heinrichs's account of autonomy and agency under this rubric. He notes that a psychology based on chaos theory is not only compatible with the notion of free will, it can better explain why the successful use of medication actually increases freedom and autonomy instead of limiting it. It is here that I wish to focus my comments, because his interpretation of free will may give us, to borrow a phrase from Daniel Dennett, a "variet[y] of free will worth wanting" (1984, title page). Free will, in this case, is not a metaphysical ability to act above and beyond our material causes, but is instead a property of the material system itself, namely when that system feels itself capable of greater psychic mobility around the topographical map of probabilistic patterns.According to this model, our ability to reason, plan, and act on the decisions we make is itself a [End Page 235] part of our chaotically determined neurologic system. When we are healthy, we are able to reason in our best interests and act on those reasons. This is modeled as an ability for the organism to metaphorically "move about" the map of its own possibilities, and more important, to both enter and escape certain states, known as chaotic attractors, into which it is likely to be drawn. "Where" we wind up, psychologically speaking, at any point in time is determined by our own system, and so we may say that in such a case we are autonomous and our choices are made freely. Depression, on the other hand, can be compared to a deep groove in the map, a chaotic attractor that is hard to escape, and so the system quite literally becomes "stuck in a rut." This is subjectively experienced as the tendency for thought processes and activities to fall into negative and self-defeating patterns despite the best efforts of the client to escape these habits. So long as the organism does not have a sense of being "trapped" in an attractor (whether a depressive or, for example, manic or compulsive state), then that organism may be said to be free. Medication and the therapy that accompanies it, so far as it facilitates our ability to escape deep chaotic attractors, promotes our own freedom of will. If a car cannot spin its way out of a ditch, does the tow truck hinder or promote its freedom by hauling it back onto solid pavement where it may again... (shrink)

The theoretical framework adopted in the exact sciences, for constructing and testing deterministic theories on the one hand, and modelling and analysis of observed phenomena on the other, is often implicitly assumed to be that of structural stability. In view of recent developments in nonlinear dynamics, it is argued here that in general it may not be possible to assume strict determinism and structural stability simultaneously; either strict determinism holds, in which case the fragility framework may turn (...) out to be the appropriate framework for the study of certain phenomena in the exact sciences, or ‘structural stability’ is restored at the expense of introducing stochasticity. In this sense a certain degree of indeterminacy may be unavoidable even at the classical level. (shrink)

Clarifies the central elements of the "stuckness" feeling in the traditional framework for free will and determinism in psychology, based on the inherent dependence on context and the assumed need of free will to be independent of context. These central elements are examined from the relatively overlooked perspective of time. A large part of the stuckness is revealed to stem from the linear assumption of time, rather than the linear nature of causality, as usually assumed. Suggestions are offered for (...) overcoming this overlooked perspective to overcome the stuckness. Alternative assumptions of time are shown to offer a fresh framework for resolving the free will/determinism problem. It is suggested that nonlinear approaches to time offer several advantages in the framing of the issues, including the integration of possibility and the past, without time and causality being sacrificed in the process. 2012 APA, all rights reserved). (shrink)

This paper explores whether human proactivity can be considered an expression of free will. The discussion involves two paradigms, which are mutually complementary and encompass psychological proactivity and reactivity. Both paradigms raise the question of linear and non-linear determinism, which inevitably leads to the issue of free will. The analysis attempts to find a compromise between linear and non-linear determinism through the approach of human dialectical complexity (Lebed & Bar-Eli, 2013). This refers to the relationships of two types (...) of complex subsystems within a human: the perceptual-motor dynamic system (PMDS), which is mostly determined by linear impacts and expressed through reactive behavior, and the “free-will”Footnote1 complex system (FCS), which is mostly determined by non-linear redundant determinism and expressed through proactive dynamics. In summary, it is concluded that there cannot be a categorical assertion of the permanent existence of free will in human functioning. The human dialectical complexity expressed by both proactivity and reactivity causes the “floating” presence of free will depending on the prevalence of proactive control factors and the non-linear determination of a living human system. (shrink)

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)

Behaviors of chaotic systems are unpredictable. Chaotic systems are deterministic, their evolutions being governed by dynamical equations. Are the two statements contradictory? They are not, because the theory of chaos encompasses two levels of description. On a higher level, unpredictability appears as an emergent property of systems that are predictable on a lower level. In this talk, we examine the structure of dynamical theories to see how they employ multiple descriptive levels to explain chaos, bifurcation, and other complexities of (...) class='Hi'>nonlinear systems. (shrink)

The domain of nonlinear dynamical systems and its mathematical underpinnings has been developing exponentially for a century, the last 35 years seeing an outpouring of new ideas and applications and a concomitant confluence with ideas of complex systems and their applications from irreversible thermodynamics. A few examples are in meteorology, ecological dynamics, and social and economic dynamics. These new ideas have profound implications for our understanding and practice in domains involving complexity, predictability and determinism, equilibrium, control, planning, individuality, (...) responsibility and so on. Our intention is to draw together in this volume, we believe for the first time, a comprehensive picture of the manifold philosophically interesting impacts of recent developments in understanding nonlinear systems and the unique aspects of their complexity. The book will focus specifically on the philosophical concepts, principles, judgments and problems distinctly raised by work in the domain of complex nonlinear dynamical systems, especially in recent years. -Comprehensive coverage of all main theories in the philosophy of Complex Systems -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields are also included. (shrink)

A tight control of intracellular [Ca2+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{2+}$$\end{document}] is essential for the survival and normal function of cells. In this study we investigate key mechanistic steps by which calcium is regulated and calcium oscillations could occur using in silico modeling of membrane transporters. To do so we give a deterministic description of intracellular Ca2+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{2+}$$\end{document} dynamics using nonlinear dynamics in order to understand Ca2+\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{2+}$$\end{document} signaling. We first present the ordinary differential equations system for cell calcium kinetics and make a preliminary work on Sobol indices. We then describe and analyze complex transporters action. Besides, we analyze the whole system. We finally perform numerical simulations and compare our results to real data. (shrink)

The signals in numerous complex systems of engineering can be regarded as nonlinear parameter trend with noise which is identically distributed random signals or deterministic stationary chaotic signals. The commonly used methods for parameter estimation of nonlinear trend in signals are mainly based on least squares. It can cause inaccurate estimation results when the noise is complex. This paper proposes a calibration method for this issue in the case of single parameter via nonstationarity measure from the perspective of (...) the stationarity of residual sequence. Some numerical studies are conducted for validation. Results of numerical studies show that the proposed calibration method performs well for various models with different noise strengths and types and can significantly improve the accuracy of initial estimates obtained by least squares method. This is the first time that the nonstationarity measure is applied to the parameter calibration. All these results will be a guide for future studies of other parameter calibrations. (shrink)

The past decade has witnessed significant advances in our understanding of nonlinear systems, both theoretically and experimentally. In turn, these insights have led to applications over a broad range of subjects, as well as to new interpretations of complex behavior. Inevitably, it seems, there has been a concomitant rush to re-interpret various well-understood aspects of thermodynamic behavior in manybody systems by means of these mechanisms. It is perhaps useful, therefore, to examine these notions critically, and in doing so we (...) are able to illuminate somewhat the origins of, and motivations for, various dubious descriptions of these systems. Among other things, one notices in such discussions an unfortunate focus on “randomness,” rather than on the actual role of probabilities in describing the phenomena. Although valuable insights into some areas of complex behavior have arisen from studies of so-called “deterministic chaos,” we can detect no influence they may have on the predictions of statistical mechanics, and thus conclude that they are of little relevance to the thermodynamic behavior of large systems. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Chaos and LiteratureCarl Matheson and Evan KirchhoffIChaos theory was the intellectual darling of pop-science writers of the late 1980s. 1 In their eyes, it would provide a new paradigm by which to describe the world, one that liberated scientists from clockwork determinism—or, alternatively, from incomprehensible randomness. In an introductory textbook of the period, Robert Devaney called chaos theory “the third great scientific revolution of the 20th century, along (...) with relativity and quantum mechanics.” Similar attitudes propagated into philosophy; for example, Stephen Kellert argued that an acceptance of chaos theory would involve a reconfiguration of scientific methodology. 2It was in the domain of literary theory, however, that chaos found its most enthusiastic reception in the humanities, and the enthusiasm lives on. Many literary theorists display no hesitation in touting the supposedly revolutionary implications of chaos science. Katherine Hayles, the chief among them, argues that because the concept of order has undergone a “radical reevaluation” in recent decades, “textuality is conceived in new ways within critical theory and literature, and new kinds of phenomena are coming to the fore within an emerging field known as the science of chaos” (CO, p. 1). She infers that the new “paradigm of orderly disorder” (CB, p. xiii) represented by chaos theory signifies a conceptual revolution in modern culture as a whole. 3 She attempts to establish a parallel between chaos theory and various poststructuralist philosophical positions, including those of Derrida and Foucault, claiming that this new paradigm “may well prove to be as important to the second half of the century as the field concept was to [End Page 28] the first half” (CB, p. xiii), and that chaos may soon be “on a par with evolution, relativity, and quantum mechanics in its impact on the culture” (CO, p. 4). Other theorists make claims for the interpretive power of chaos; according to William Demastes, “chaos theory can help in comprehending several paths that the theatre has followed since the inception of postmodernism” (p. 242). 4 By a conservative estimate, over fifty papers have been published which link chaos theory to literature or literary theory. Clearly, the idea that chaos theory has application outside of science is not restricted to one or two over-eager humanists.In this essay, we wish to address some of the claims which concern the relationship between chaos science and the study of literature. Three such claims are:a. There are significant similarities between the science of chaos, contemporary literary theory, and/or philosophy.b. We can trace a common etiology for chaos theory and poststructuralist criticism. The two are so intimately related that they are really different formulations of a common claim, as filtered through two different fields.c. The science of chaos can help us interpret and understand specific literary works, and perhaps contemporary literature in general.However, before assessing the relationship between chaos and literature, we will briefly introduce chaos theory itself and demonstrate that even a minimal understanding is sufficient to undercut the supposed revolutionary significance of chaos theory. 5IIChaotic systems are deterministic: an exact description of a system at any given time, together with the laws of nature that apply to it, will entail the entire future behavior of the system. In this sense, chaotic systems form a subclass of classical systems (and are to be distinguished from quantum systems, which are indeterministic). However, chaotic systems differ from the systems studied throughout most of the history of science in two major ways. First, the differential equations used to model them are nonlinear, while the history of mathematical physics is largely devoted to a treatment of linear differential equations. Technical issues aside, the ramifications of nonlinearity are: (i) equations which are impossible to solve using the general strategies designed for [End Page 29] linear equations; and consequently (ii) the need for solutions by methods of numerical approximation, generally performed on a computer. Second, chaotic systems exhibit a feature known as “sensitive dependence”—or, more colorfully, as “the butterfly effect,” a figure of speech intended to evoke the worry that our long-term forecasts of the weather can be hopelessly disrupted by the atmospheric fluctuations due to a single butterfly... (shrink)

This article proposes a new problem which is called the Stochastic Travelling Advisor Problem in network optimization, and it is defined for an advisory group who wants to choose a subset of candidate workplaces comprising the most profitable route within the time limit of day working hours. A nonlinear binary mathematical model is formulated and a real application case study in the occupational health and safety field is presented. The problem has a stochastic nature in travelling and advising times (...) since the deterministic models are not appropriate for such real-life problems. The STAP is handled by proposing suitable probability distributions for the time parameters and simulating the problem under such conditions. Many application problems like this one are formulated as nonlinear binary programming models which are hard to be solved using exact algorithms especially in large dimensions. A novel binary version of the recently developed gaining-sharing knowledge-based optimization algorithm to solve binary optimization problems is given. GSK algorithm is based on the concept of how humans acquire and share knowledge during their life span. The binary version of GSK depends mainly on two stages that enable BGSK for exploring and exploitation of the search space efficiently and effectively to solve problems in binary space. The generated simulation runs of the example are solved using the BGSK, and the output histograms and the best-fitted distributions for the total profit and for the route length are obtained. (shrink)

It is shown that time may be appreciated in at least two senses: chronological and dynamical. Chronological time is the time of our naïve acquaintance as transient beings. At its most extensive scale, it corresponds to history encompassing both the abiotic and the biotic universe. Dynamical time, deriving from classical mechanics, is the time embraced by most of the laws of physics. It concerns itself only with present conditions since it is held that that the past may be reconstructed from (...) the present and the future predicted from the present, a position known as Laplacian determinism.Nonlinear dynamics has shown the fallacy of this supposition: The concrete values that may be assumed in the variables of the equations of motion constituting the laws of physics as a result of the spontaneous or intentional interaction of subject or measuring systems and of object or measured systems cannot be of infinite precision. Indeed, even if they could be, it is not at all clear that they would permit Laplacian determinism because of what is thought to be the ubiquity of K-flow dynamics in nature in which even infinite past information leading to the present cannot yield prediction of the future. In consequence, nonlinear dynamics, in rebellion against dynamical time, generates a primitive form of history distinguishing past, present, and future that may be termed nonlinear dynamical hysteresis.When nonlinear dynamics came to be complemented with semiotic modulation through the implement of symbol-mediated language as first instantiated through the communicating as opposed to the merely dynamically interacting molecular complexes of the cell, what can be termed semiotic hysteresis was born. The paper attempts to show that indefinitely evolving complexity, sustainability, justice, and meaning are indissolubly bound with chronological time in the sense of semiotic hysteresis : This semiotic hysteresis yields the indefinite evolutionary time of the living condition—including culture. (shrink)

Contributions in modern theoretical physics and chemistry on the behavior of nonlinear systems, exemplified by Ilya Prigogine's work on the thermodynamics of open systems, attract growing attention in economics. Our purpose here is to relate the new orientation in the natural sciences to a particular nonorthodox strand of thought within economics. All that is needed for this purpose is some appreciation of the general thrust of the enterprise, which involves a shift of perspective from the determinism of conventional (...) physics to the nonteleological open-endedness, creative, and nondetermined nature of evolutionary processes. (shrink)

In talks given early in the 1990s, Jean-Michel Grandmont (1998) introduced the concept of the self-fulfilling mistake. This phenomenon can emerge when economic agents cannot distinguish between randomness and determinism, a situation that can occur when the underlying true dynamics are chaotic (Radunskaya, 1994), although such a situation could arise with other forms of complex nonlinear dynamics besides those involving chaotic dynamics. In such a situation, agents may be unable to discern the true dynamics and may adopt simple, (...) boundedly rational “rules of thumb” based on some kind of backward-looking adaptive expectations (Bullard, 1994). For certain kinds of underlying processes, agents may be able to mimic the actual dynamics with such an “incorrect” behavioral rule, an outcome known as a consistent expectations equilibrium (CEE), a concept formalized by Hommes (1998) as meaning that the two processes have identical means and also autocorrelation coefficients at all leads and lags. Sorger (1998) and Hommes and Sorger (1998) have shown how in some cases agents can learn to converge on such CEEs, or self-fulfillingly mistaken behavior. These models all involve discrete dynamics. The first realization that a discrete chaotic dynamic could be mimicked by a simple linear autocorrelation function is due to Bunow and Weiss (1979) and Sakai and Tokumaru (1980), the latter demonstrating the possibility for the case of the asymmetric tent map, a result studied in more depth by Brock and Dechert (1991) and Radunskaya (1994). (shrink)

Some have argued that chaos, with its characteristic feature of sensitive dependence on initial conditions, should be sensitive to quantum events (Hobbs 1991; Kellert 1993). The upshot of these arguments is that classical chaos would then be indeterministic, but such a conclusion is dependent on which versions of quantum theory and solutions to the measurement problem are adopted (Bishop and Kronz 1999). In this essay, the relationship between quantum mechanics and sensitive dependence is placed in the general context of (...) class='Hi'>nonlinear dynamics and is investigated in detail, revealing further limitations and quali…cations on these sensitive dependence arguments. (shrink)

Some irrational numbers are "random" in a sense which implies that no algorithm can compute their decimal expansions to an arbitrarily high degree of accuracy. This feature of (most) irrational numbers has been claimed to be at the heart of the deterministic, but chaotic, behavior exhibited by many nonlinear dynamical systems. In this paper, a number of now classical chaotic systems are shown to remain chaotic when their domains are restricted to the computable real numbers, providing counterexamples to the (...) above claim. More fundamentally, the randomness view of chaos is shown to be based upon a confusion between a chaotic function on a phase space and its numerical representation in Rn. (shrink)

Between Calculability and Non-Calculability. Issues of Calculability and Predictability in the Physics of Complex Systems. The ability to predict has been a very important qualifier of what constitutes scientific knowledge, ever since the successes of Babylonian and Greek astronomy. More recent is the general appreciation of the fact that in the presence of deterministic chaos, predictability is severely limited (the so-called ‘butterfly effect’): Nearby trajectories diverge during time evolution; small errors typically grow exponentially with time. The system obeys deterministic laws (...) and still is unpredictable, seemingly a paradox for the traditional viewpoint of Laplacian determinisms. With the concept of deterministic chaos the epistemological issue about an adequate understanding of predictability is no longer just a mere philosophical topic. Physicists on the one hand recognize the limits of (long term) predictability, computability and even of scientific knowledge, on the other hand they work on concepts for extending the horizon of predictability. It is shown in this paper that physics of complex systems is useful to clarify the jungle of different meanings of the terms ‘predictability’ and ‘computability’ — also with philosophical implications for understanding science and nature. Today, from the physical point of view, the relevance of the concepts of predictability seems to be underestimated by philosophers as a mere methodological topic. In the paper I analyse the importance of predictability and computability in physics of complex systems. I show a way how to cope with problems of unpredictability and noncomputability. Nine different concepts of predictability and computability (i.e. open solution, sensitivity/chaos, redundancy/chance) are presented, compared and evaluated. (shrink)

A notion of quantum space-time is introduced, physically defined as the totality of all flows of quantum test particles in free fall. In quantum space-time the classical notion of deterministic inertial frames is replaced by that of stochastic frames marked by extended particles. The same particles are used both as markers of quantum space-time points as well as natural clocks, each species of quantum test particle thus providing a standard for space-time measurements. In the considered flat-space case, the fluctuations in (...) coordinate values with respect to stochastic frames are described by coordinate probability amplitudes related to irreducible stochastic phase space representations of the Poincaré group. Lagrangian field theory on quantum space-time is formulated. The ensuing equations of motion for interacting fields contain no singularities in their nonlinear terms, and therefore can be handled by methods borrowed from classical nonlinear analysis. (shrink)

Rift Valley Fever is a vector-borne disease mainly transmitted by mosquito. To gain some quantitative insights into its dynamics, a deterministic model with mosquito, livestock, and human host is formulated as a system of nonlinear ordinary differential equations and analyzed. The disease threshold $$\mathcal{R}_0$$ is computed and used to investigate the local stability of the equilibria. A sensitivity analysis is performed and the most sensitive model parameters to the measure of initial disease transmission $$\mathcal{R}_0$$ and the endemic equilibrium are (...) determined. Both $$\mathcal{R}_0$$ and the disease prevalence in mosquitoes are more sensitive to the natural mosquito death rate, d m . The disease prevalence in livestock and humans are more sensitive to livestock and human recruitment rates, $$\Uppi_l$$ and $$\Uppi_h$$, respectively, suggesting isolation of livestock from humans is a viable preventive strategy during an outbreak. Numerical simulations support the analytical results in further exploring theoretically the long-term dynamics of the disease at the population level. (shrink)

With the advent of the newest technologies, it is necessary for engineering to incorporate the integration of social responsibility and technical integrity. A possible approach to accomplishing this integration is by expanding the culture of the engineering profession so that it is more congruent with the complex nature of the technologies that are now being developed. Furthermore, in order to achieve this expansion, a shift in thinking is required from a linear or reductionist paradigm (atomistic, deterministic and dualistic) to a (...) nonlinear paradigm (holistic, chaotic and subjective). Three aspects of such a nonlinear paradigm (holism, transparency and responsiveness) enable an engineer to shift from “applying ethics” to “being ethical”. This culture change can be a basis for developing new curricula to satisfy the ABET-2000 requirements as well as for the practice of engineering in the 21st Century. (shrink)

Chaos, once considered antithetical to scientific law and order, is presently the subject of a vigorous and progressive scientific research program. "Chaos" as it is used in current scientific literature is a technical term: it refers to stochastic behavior generated by deterministic systems. This behavior has appeared in models of a wide range of phenomena including atmospheric patterns, population dynamics, celestial motion, heartbeat rhythms, turbulent fluids, chemical reactions and social structures. In general, chaos arises in the nonlinear dynamics of (...) complex systems. Grebogi, Ott and Yorke reflect the sentiment of the scientific community when they state that chaotic nonlinear dynamics has "fundamental implications." This dissertation explores these results in a philosophic context. ;The research is organized as follows: The Context of Science. Scientific results are achieved in and make sense in the practical context of research which includes both experiment and theory. Drawing on the work of Dyke, Galison, Garfinkel and Hacking, a philosophic context is described which more accurately reflects the significance of scientific results than do the contexts of discovery and justification. Models. Chaos theory is constituted by a family of numerical models. In this chapter, Giere's account of modeling is extended to both bio-medical and numerical models. Chaos in Scientific Models. This is a rather lengthy primer of chaos theory that is, although technically accurate, accessible to nonspecialists. It constitutes a road map for the primary literature on chaos. Chaos and Prediction. Chaos theory shows a limit of our science, namely, chaotic systems are deterministic yet unpredictable in the long run. The chapter includes a discussion of scientific determinism following Popper and, it concludes by providing evidence against the laplacian claim that deterministic systems are predictable. Chaos and Complexity. This shows what contribution chaos theory makes toward answering the challenge of organized complexity articulated by Weaver. It discusses attempts to characterize complexity and shows how the results of chaos theory can help. I draw on the work of Abraham, Arecchi, Atlan, Chaitin, Eckmann, Peacocke, Rosen, Ruelle, and others. Chaos theory provides a thoroughly nonvitalistic framework for understanding dynamical complexity in organic, as well as inorganic, systems. (shrink)

This paper outlines the qualitative foundations of a “quasiclassical” theory in which particles are pictured as spatially extended periodic excitations of a universal background field, interacting with each other via nonlinearity in the equations of motion for that field, and undergoing collapse to a much smaller volume if and when they are detected. The theory is based as far as possible directly on experiment, rather than on the existing quantum mechanical formalism, and it offers simple physical interpretations of such concepts (...) as mass, 4-momentum, interaction, potentials, and quantization; it may lead directly to the standard equations of quantum theory, such as the multiparticle Schrödinger equation, without going through the conventional process of “quantizing” a classical theory. The theory also provides an alternative framework in which to discuss wave-particle duality and the quantum “measurement problem”; in particular, it is suggested that the unpredictability of quantum phenomena may arise from “deterministic chaos” in the behavior of the background field. (shrink)

The fundamental problem on which Ilya Prigogine and the Brussels–Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of time (...) was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels–Austin Group, is to consider the observed direction of time to be a basic physical phenomenon due to the dynamics of physical systems. This essay focuses mainly on recent developments in the Brussels–Austin Group after the mid-1980s. The fundamental concerns are the same as in their earlier approaches (subdynamics, similarity transformations), but the contemporary approach utilizes rigged Hilbert space (whereas the older approaches used Hilbert space). While the emphasis on nonequilibrium statistical mechanics remains the same, their more recent approach addresses the physical features of large Poincare systems, nonlinear dynamics and the mathematical tools necessary to analyze them. (shrink)

La dialectique pour penser la non-linéarité, le complexe pensé dialectiquement : une nouvelle révolution paradigmatique ? Le débat est ouvert.

In a preceding issue of Faith and Philosophy Stewart Goetz criticized a paper of mine in which I try to show that libertarians need not be committed to the principle of alternative possibilities (PAP) and that Frankfurt-style counterexamples to PAP are no threat to libertarianism. In my view, the main problem with Goetz’s arguments is that Goetz does not properly understand my position. In this paper, I respond to Goetz by summarizing my position in as plain a way as possible. (...) Goetz’s charge against my position has two parts, first, that it isn’t libertarian and, second, that it provides no good reason for libertarians to abandon PAP. This paper briefly presents my answers to these two parts of Goetz’s charge. (shrink)

I shall argue that compatibilism cannot resist in a principled way the temptation to prepunish people. Compatibilism thus emerges as a much more radical view than it is typically presented and perceived, and is seen to be at odds with fundamental moral intuitions.

What is the thesis of determinism? Though it is obvious that in principle there is more than one possible thesis that might be given this name, it seems to be the case that philosophers working on the free will problem have gradually gravitated towards a more-or-less standard definition, minor variations on which can now be found widely scattered through the free will literature. I call it the ‘entailment definition’ and it states, roughly, that determinism is the thesis that (...) for any given time, a complete statement of the facts about that time, together with a complete statement of the laws of nature, entails every truth as to what happens after that time. In this paper, I argue that acceptance of the entailment definition has been a mistake—and that we need a definition of determinism which, by contrast with the entailment definition, makes explicit mention of the notion of natural necessity. (shrink)

David Hume has traditionally been assumed to be a soft determinist or compatibilist, at least in the ‘reconciling project’ that he presents in Section 8 of the first Enquiry, entitled ‘Of liberty and necessity.’ Indeed, in encyclopedias and textbooks of Philosophy he is standardly taken to be one of the paradigm compatibilists, rivalled in significance only by Hobbes within the tradition passed down through Locke, Mill, Schlick and Ayer to recent writers such as Dennett and Frankfurt. Many Hume scholars also (...) concur in viewing him as a determinist, for example Norman Kemp Smith, Barry Stroud, A. J. Ayer, Paul Russell Don Garrett, Terence Penelhum, George Botterill, John Bricke, and John Wright. My main purpose in this paper will be to provide the evidence to substantiate this traditional interpretation, which has hitherto been widely assumed rather than defended. In the absence of such a defence, the consensus has been left open to challenge, most notably in a recent paper and a subsequent book by James Harris, who boldly claims that Hume ‘does not subscribe to determinism of any kind, whether Hobbesian or merely nomological.’. (shrink)

Most readers will agree with the starting assumptions of Klee that contemporary science and philosophy assume a primarily micro-deterministic view of nature–and that this has long been the case, or was at least until the 1970s. Defending a strict micro-determinism, Klee argues that concepts of emergence that seemingly are opposed to micro-determinist doctrine can be shown, on analysis, to be ultimately consistent with a thoroughgoing philosophy of micro-determinism. An exception is made, however, in the case of my own (...) view, labeled “direct macro-determinism,” which he describes as “ultimately more troublesome” but then disposes of as being based on “simplistic analogies” and “metaphors” and “too weak to be conclusive.”. (shrink)

(1991). Different forms of causation in dynamical systems: Determinism, pattern generation, and information. World Futures: Vol. 30, No. 4, pp. 221-237.

There has been a long-standing debate about the relationship of predictability and determinism. Some have maintained that determinism implies predictability while others have maintained that predictability implies determinism. Many have maintained that there are no implication relations between determinism and predictability. This summary is, of course, somewhat oversimplified and quick at least in the sense that there are various notions of determinism and predictability at work in the philosophical literature. In this essay I will focus (...) on what I take to be the Laplacean vision for determinism and predictability. While many forms of predictability are inconsistent with this vision, I argue that a suitably restricted notion of predictability, consistent with the practice of physicists, is implied by the Laplacean notion of determinism. It is argued that limitations on predictability are of an in principle nature in the Appendix. (shrink)