Chaos

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.

The unreduced many-body interaction problem solution, absent in usual science framework, reveals a new quality of emerging multiple, equally real but mutually incompatible system configurations, or “realisations”, giving rise to the universal concept of dynamic complexity and chaoticity. Their imitation by a single, “average” realisation or trajectory in usual theory (corresponding to postulated “exact” or perturbative problem solutions) is a rough simplification of reality underlying all stagnating and emerging problems of conventional (unitary) science, often in the form of missing, or (...) “dark”, entities and “hidden variables”. We show how the application of unreduced interaction problem solution and the ensuing concept of dynamic complexity provides the desired causally complete and intrinsically unified solutions to respective unitary science problems in the entire range of complexity levels, from elementary particles and cosmology to emergent consciousness and modern development crisis, implying real, essential and urgently needed progress. (shrink)

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)

Various processes are often classified as both deterministic and random or chaotic. The main difficulty in analysing the randomness of such processes is the apparent tension between the notions of randomness and determinism: what type of randomness could exist in a deterministic process? Ergodic theory seems to offer a particularly promising theoretical tool for tackling this problem by positing a hierarchy, the so-called ‘ergodic hierarchy’, which is commonly assumed to provide a hierarchy of increasing degrees of randomness. However, that notion (...) of randomness requires clarification. The mathematical definition of EH does not make explicit appeal to randomness; nor does the usual way of presenting EH involve a specification of the notion of randomness that is supposed to underlie the hierarchy. In this paper we argue that EH is best understood as a hierarchy of random behaviour if randomness is explicated in terms of unpredictability. We then show that, contrary to common wisdom, EH is useful in characterising the behaviour of Hamiltonian dynamical systems. (shrink)

We survey and clarify some recent appearances of the term ‘emergence’. We distinguish epistemological emergence, which is merely a limitation of descriptive apparatus, from ontological emergence, which should involve causal features of a whole system not reducible to the properties of its parts, thus implying the failure of part/whole reductionism and of mereological supervenience for that system. Are there actually any plausible cases of the latter among the numerous and various mentions of ‘emergence’ in the recent literature? Quantum mechanics seems (...) to offer one, in the Bell properties of entangled particles, but other apparently promising candidates, such as non‐linear dynamical systems investigated by complexity studies and chaos theory, seem on careful analysis to display only epistemological emergence. We examine the consequences for physicalism of admitting ontological emergence in the micro‐physical. (shrink)

Complex phenomena – like structures or processes – are intriguing scientists around the world. There are many reasons why complexity is a popular topic of research. Having that all in mind I would like to focus in this introductory article on one example of complexity, that is structural complexity where complex geometrical patterns appear as the result of the simple rules of an algorithm – known as the chaos game. Therefore the aim of this paper is an invitation to more (...) advanced research on complexity. (shrink)

Unified and causal complex-dynamic origin of standard (special and general) relativistic and quantum effects revealed previously at the lowest levels of world interaction dynamics is explicitly generalised to all higher levels of unreduced interaction processes, thus additionally confirming the causally complete character of complex-dynamical, naturally quantised relativity, which does not contain any artificially added, abstract postulates. We demonstrate some elementary applications of this generalised quantum relativity at higher levels of complex brain and social interaction dynamics.

Inhere we expand the concept of Holobiont to incorporate niche construction theory in order to increase our understanding of the current planetary crisis. By this, we propose a new ontology, the Ecobiont, as the basic evolutionary unit of analysis. We make the case of Homo Sapiens organized around modern cities (technobionts) as a different Ecobiont from classical Homo Sapiens (i.e. Hunter- gatherers Homo Sapiens). We consider that Ecobiont ontology helps to make visible the coupling of Homo Sapiens with other biological (...) entities under processes of natural and cultural evolution. Not to see this coupling hidden systemic risks and enhance the probability of catastrophic events. So Ecobiont ontology is necessary to understand and respond to the current planetary crisis. -/- . (shrink)

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)

In this paper, we investigate the ultimate bound set and positively invariant set of a 3D Lorenz-like chaotic system, which is different from the well-known Lorenz system, Rössler system, Chen system, Lü system, and even Lorenz system family. Furthermore, we investigate the global exponential attractive set of this system via the Lyapunov function method. The rate of the trajectories going from the exterior of the globally exponential attractive set to the interior of the globally exponential attractive set is also obtained (...) for all the positive parameters values a,b,c. The innovation of this paper is that our approach to construct the ultimate bounded and globally exponential attractivity sets assumes that the corresponding sets depend on some artificial parameters ; that is, for the fixed parameters of the system, we have a series of sets depending on λ and m. The results contain the known result as a special case for the fixed λ and m. The efficiency of the scheme is shown numerically. The theoretical results may find wide applications in chaos control and chaos synchronization. (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)