Chaos

Instead of postulated fixed structures and abstract principles of usual positivistic science, the unreduced diversity of living world reality is consistently derived as dynamically emerging results of unreduced interaction process development, starting from its simplest configuration of two coupled homogeneous protofields. The dynamically multivalued, or complex and intrinsically chaotic, nature of these real interaction results extends dramatically the artificially reduced, dynamically single-valued projection of standard theory and solves its stagnating old and accumulating new problems, “mysteries” and “paradoxes” within the unified (...) and causally complete picture of intrinsically evolving, dynamically complex reality. The permanently unfolding complexity progress thus revealed is fundamentally unlimited and does not need to stop at the directly observed diversity of usual matter complexity. The exciting, but rigorously substantiated and objectively inevitable prospects of further civilisation complexity development towards its superior levels of genuine sustainability and global Noosphere are outlined, with practically important conclusions for today’s critical problem solution. (shrink)

From the beginning of chaos research until today, the unpredictability of chaos has been a central theme. It is widely believed and claimed by philosophers, mathematicians and physicists alike that chaos has a new implication for unpredictability, meaning that chaotic systems are unpredictable in a way that other deterministic systems are not. Hence, one might expect that the question ‘What are the new implications of chaos for unpredictability?’ has already been answered in a satisfactory way. However, this is not the (...) case. I will critically evaluate the existing answers and argue that they do not fit the bill. Then I will approach this question by showing that chaos can be defined via mixing, which has never before been explicitly argued for. Based on this insight, I will propose that the sought-after new implication of chaos for unpredictability is the following: for predicting any event, all sufficiently past events are approximately probabilistically irrelevant. (shrink)

A review of James Glieck's _Chaos: Making a New Science_, noting how nonmonotonic functions self-referentially take on their own values and lead to complexity without randomness.

Economies making a transition from centrally planned socialism to market capitalism can experience chaotic hysteresis. This can arise from elements of the previous system persisting even as institutions are transformed with the system possibly experiencing chaos during this conflict. A model of investment cycles accompanied by technological stagnation shows this phenomenon which can be viewed from a cusp catastrophe perspective. Empirical tests of Soviet investment and construction data provide incomplete support for the cusp structure with chaos. Nonlinear structures are found (...) with bifurcation effects for all cases and possibly chaotic dynamics for five-year lagged construction data. (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)

Thesis --University of Stellenbosch, 2004.

"Cosmos or Chaos: Theodicy, Love, and Existential Choice," explores in detail the social-psychological dimensions of cosmology and the tension between the ideas of cosmos and chaos in the history of Western thought, as these are manifested in philosophy, science, "pure" reason, and religion. In the process, the author seeks to provide the foundation for a viable existentialist social ethic, drawing upon the works of Camus, Sartre, Bergson, Unamuno, Dostoevsky, and the teachings of Theravada Buddhism. ;The dissertation is divided into six (...) parts. Part One establishes the conceptual framework of the project. Here a connection is made between the theodicy problem and the "cosmos compulsion," the often desperate human need to believe in the existence of an orderly and coherent universe and to deny the chaos in nature, society, and the self. Part Two traces the themes of cosmos and chaos in early Greek philosophy, beginning with the pre-Socratics and culminating with the synthesis offered by Aristotle. An analysis of modern and post-modern science follows in Part Three, highlighting in particular the faith-driven thought of Albert Einstein, the correspondences between the insights of thermodynamics and process philosophy, and the parallels to be found between existentialism and quantum theory. Superstring theory is dismissed as yet another vain, quasi-religious attempt at a "theory of everything" influenced by the cosmos compulsion. So-called "chaos theory" is discussed in depth and revealed to be somewhat of a misnomer. Part Four is comprised primarily of existentialist critiques of reason, logic, mathematics, language, and systematic thought in general. Part Five more closely focuses on the theodicy problem, first through an examination of its historical class nature, then with a critical review of the different responses to theodicy offered by existentialist thinkers, both religious and atheistic . This is used to make normative pronouncements and to articulate an existentialist social ethic, leading to Part Six, which examines how cosmos and chaos take shape in the various types of love, concluding with an appeal to the synthesis of eros and agape presented in the works of Dostoevsky. (shrink)

Three main features of the mythos and logos relationship will be examined in this article; beginning with the symbolic elaboration fantasy binds chaos and how beings/forces of the universe are classified by it. A second concern studies two strategies of thought to face chaos: one, unfolding the mythical assumption of a beings /powers distribution filling the universe forever and, another, based on a metaphysical supposition of the existence of 'something' eternal and infinite from which everything stems. It is about dogma (...) and myth antagonism as a way to deal with chaos. Finally, how myth involves and triggers thought before the undetermined is stressed. At this point of the reflection, Blumenberg's thesis on the special relation between mythos and logos —as a way to proceed by a distancing order— is profitable; also, Lacan/Zîzêk's notion of Real as an account of how the undetermined moves to familiar and known things is included as a complement. (shrink)

Most of the recent work in chaos theory has been the development of data analysis tools for analyzing chaotic data. It is based upon the results of the application of these tools that many researchers have made claims that such phenomena as heartbeats, planetary orbits, and chemical reactions are chaotic. ;The first part of my dissertation is concerned with investigating the standard methods that are used to determine whether a system is chaotic, and the requirements of these methods. I begin (...) by explaining chaos theory, and providing a generally accepted definition of chaos. I then explain the current methods that have been developed for experimentally studying chaotic systems. With this in mind, I turn to a more theoretical investigation of the reliability of these methods. Within the framework of formal learning theory, I discuss the conditions under which a scientist can reliably determine whether a system is chaotic. ;Generalizing this problem leads to the philosophical center of my dissertation: an investigation that relates how the conceptions of reliability of the scientists who work with chaos theory fit into a larger philosophical picture of reliable knowledge, and whether and in what sense or senses scientists are justified in their beliefs that particular systems are chaotic. ;I argue that Alvin Goldman is correct in a general sense; cashing out "justified" as "produced by a process that reliably produces true beliefs" captures a very strong intuition about knowledge and justification. I also argue that defining reliability, as Goldman does, in terms of "truth-ratios" does not capture our intuitions about reliability, and is often ill-defined. Instead, we need to define a reliable process as one which does one of two things: either the process always produces true beliefs, or the process gives specific conditions under which it will fail to produce true beliefs. ;Finally, I return to the discussion of a particular instance of scientific knowledge, the knowledge that a system is chaotic. I argue that, under my conception of reliabilism, and under certain conditions, scientists are in fact justified in their beliefs that particular dynamical systems in nature are chaotic. (shrink)

What happens to scientific knowledge when researchers outside the natural sciences bring elements of the latest trend across disciplinary boundaries for their own purposes? Researchers in fields from anthropology to family therapy and traffic planning employ the concepts, methods, and results of chaos theory to harness the disciplinary prestige of the natural sciences, to motivate methodological change or conceptual reorganization within their home discipline, and to justify public policies and aesthetic judgments. Using the recent explosion in the use of chaos (...) theory, _Borrowed Knowledge and the Challenge of Learning across Disciplines _examines the relationship between science and other disciplines as well as the place of scientific knowledge within our broader culture. Stephen H. Kellert’s detailed investigation of the myriad uses of chaos theory reveals serious problems that can arise in the interchange between science and other knowledge-making pursuits, as well as opportunities for constructive interchange. By engaging with recent debates about interdisciplinary research, Kellert contributes a theoretical vocabulary and a set of critical frameworks for the rigorous examination of borrowing. (shrink)

This dissertation shows that an alternative theoretical approach from physics--chaos theory--offers a viable basis for improved understanding of human beings and their behavior. Chaos theory provides achievable frameworks for potential identification, assessment, and adjustment of human behavior patterns. ;Most current psychological models fail to address the metaphysical conditions inherent in the human system, thus bringing deep errors to psychological practice and empirical research. Freudian, Jungian and behavioristic perspectives are inadequate psychological models because they assume, either implicitly or explicitly, that the (...) human psychological system is a closed, linear system. On the other hand, Adlerian models that require open systems are likely to be empirically tenable. Logically, models will hold only if the model's assumptions hold. ;The innovative application of chaotic dynamics to psychological behavior is a promising theoretical development because the application asserts that human systems are open, nonlinear and self-organizing. Chaotic dynamics use nonlinear mathematical relationships among factors that influence human systems. This dissertation explores these mathematical relationships in the context of a sample model of moral behavior using simulated data. ;Mathematical equations with nonlinear feedback loops describe chaotic systems. Feedback loops govern the equations' value in subsequent calculation iterations. For example, changes in moral behavior are affected by an individual's own self-centeredness, family and community influences, and previous moral behavior choices that feed back to influence future choices. ;When applying these factors to the chaos equations, the model behaves like other chaotic systems. For example, changes in moral behavior fluctuate in regular patterns, as determined by the values of the individual, family and community factors. In some cases, these fluctuations converge to one value; in other cases, they diverge in still other cases, they oscillate periodically among two or more precise values. ;At certain values, the equations iterate random results, with no convergence, divergence or periodicity: "chaos." At still other values, the equations behave chaotically for many iterations; then a periodic oscillation emerges from the chaos. These emergent patterns provide a significantly better model fit to the dynamic reality of psychological behavior because qualitatively reorganized behavior is logically possible and incorporated in the model's metaphysical assumptions. (shrink)

Chaos, order and the transitions between them — these are issues which are being intensively debated in many different sciences at present. These debates are by no means restricted to the natural sciences. Numerous popularizations confirm the existence of a broad following which is intensely interested in the phenomenon. This provided the background against which the Institute Vienna Circle organized a symposion, as international as it was interdisciplinary, entitled “Order and Chaos in Nature and Society”, held on 18 – 21 (...) November 1992. The program was organized by Heinz-Otto Peitgen and Rainer Hegselmann, both at the University of Bremen. (shrink)