Chaos

We review the recently proposed universal concept of dynamic complexity and its new mathematics based on the unreduced interaction problem solution. We then consider its progress-bringing applications at various levels of complex world dynamics, including complex-dynamical nanometal physics and living condensed matter, unreduced nanobiosystem dynamics and the integral medicine concept, causally complete management of complex economical and social dynamics, and the ensuing concept of truly sustainable world governance.

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)

Recent work by Frigg et. al. and Mayo-Wilson have called attention to a particular sort of error associated with attempts to model certain complex systems: structural modeling error. The assessment of the degree of SME in a model presupposes agreement between modelers about the best way to individuate natural systems, an agreement which can be more problematic than it appears. This problem, which we dub “the system individuation problem” arises in many of the same contexts as SME, and the two (...) often compound one another. This paper explores the common roots of the two problems in concerns about the precision of predictions generated by scientific models, and discusses how both concerns bear on the study of complex natural systems, particularly the global climate. (shrink)

Understanding (physics, philosophy, and psychology as) a constant variable.

The unreduced solution to the arbitrary interaction problem, absent in the standard theory framework, reveals many equally real and mutually incompatible system configurations, or "realizations". This is the essence of universal dynamic undecidability, or multivaluedness, and the ensuing causal randomness (unpredictability), non-computability, irreversible time flow (evolution, emergence), and dynamic complexity of every real system, object, or process. This creative undecidability of real-world dynamics provides causal explanations for "quantum mysteries", relativity postulates, cosmological problems, and the huge efficiency of high-complexity phenomena, such (...) as life, intelligence, and consciousness, giving rise to extended applications, far beyond the critical limits of usual science paradigm. (shrink)

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.

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)

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.

There is a persistent confusion about determinism and predictability. In spite of the opinions of some eminent philosophers, it is possible to understand that the two concepts are completely unrelated. In few words we can say that determinism is ontic and has to do with how Nature behaves, while predictability is epistemic and is related to what the human beings are able to compute. An analysis of the Lyapunov exponents and the Kolmogorov-Sinai entropy shows how deterministic chaos, although with an (...) epistemic character, is non subjective at all. This should clarify the role and content of stochastic models in the description of the physical world. (shrink)

Starting for the good results reached in physics researchers in economics and finance have been interested in testing nonlinear dependence and chaos in economic models and data. A wide variety of reasons for this interest have been suggested, including an attempt to improve the forecasting accuracy of linear time series models and to better explain the dynamics of the underlying variables of interest using a richer class of models than that permitted by limiting the set to the linear case. But (...) chaos theory has not had the same impact in the economics as it has in the hard sciences like physics. The literature did not provide a solid support for chaos as a consequence of the high noise level that exists in most economic time series, the relatively small sample sizes of data, and the weak robustness of chaos tests for these data. (shrink)

The stories we tell in our attempt to make sense of the world, our myths and religion, literature and philosophy, science and art, are the comforting vehicles we use to transmit ideas of order. But beneath the quest for order lies the uneasy dread of fundamental disorder. True chaos is hard to imagine and even harder to represent, especially without some recourse to the familiar coherency of order. In this book, Martin Meisel considers the long effort to conjure, depict, and (...) rationalize extreme disorder, with all the passions, excitements, and compromises the act has provoked. In seven chapters--"Shaping Chaos," "Nothing and Something," "Number," "Carnival," "War," "Energy," and "Entropy"--Meisel builds a rough history from major social, psychological, and cosmological turning points in the imagining of chaos. He uses examples from literature, philosophy, painting, graphic art, science, linguistics, music, and film, particularly exploring the remarkable shift in the eighteenth and nineteenth centuries from conceiving of chaos as disruptive to celebrating its liberating and energizing potential. Discussions of Sophocles, Plato, Lucretius, Calderon, Milton, Haydn, Blake, Faraday, Chekhov, Faulkner, Wells, and Beckett, among others, are matched with incisive readings of art by Brueghel, Rubens, Goya, Turner, Dix, Dada and the futurists. Meisel addresses the revolution in mapping energy and entropy and the manifold impact of thermodynamics. Known for his pathbreaking studies of literature, drama, and the visual arts, Meisel uses this chaotic frame to elaborate on larger concerns of purpose, mortality, meaning, and mind. (shrink)

This study presents the fundamental concepts and technical details of a U-model-based control system design framework, including U-model realisation from classic model sets, control system design procedures, and simulated showcase examples. Consequently, the framework provides readers with clear understandings and practical skills for further research expansion and applications. In contrast to the classic model-based design and model-free design methodologies, this model-independent design takes two parallel formations: it designs an invariant virtual controller with a specified closed-loop transfer function in a feedback (...) control loop and it determines the real controller output by resolving the inverse of the plant U-model. It should be noted that this U-control provides a universal control system design platform for many existing linear/nonlinear and polynomial/state-space models and it complements many existing design approaches. Simulation studies are used as examples to demonstrate the analytically developed formulations and guideline for potential applications. (shrink)

This article focuses on three recent discussions on determinism in the philosophy of science. First, determinism and predictability will be discussed. Then, second, the paper turns to the topic of determinism, indeterminism, observational equivalence and randomness. Finally, third, there will be a discussion about deterministic probabilities. The paper will end with a conclusion.

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)

In this article, the dynamical behaviors of two classes of chaotic systems are considered based on generalized Lyapunov function theorem with integral inequalities. Explicit estimations of the ultimate bounds are derived. The results presented in this article contain the existing results as special cases. Computer simulation results show that the proposed method is effective. © 2014 Wiley Periodicals, Inc. Complexity 21: 363–369, 2015.

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)

Nicht Stabilität, sondern Instabilität sei der Grundcharakter der Natur, so hören wir von Jan Schmidt als Auftakt zu seinem Buch „Das Andere der Natur“ (Hirzel-Verlag, 2015). „Das Eine der Natur“, welches reduktionistisch zu erfassen ist, soll durch ein „Anderes“ ergänzt werden. Von dieser anderen Seite her zeigt sich „Natur ... auch (als) instabil, komplex, chaotisch, zufällig, emergent...“, und aus dieser Sicht des Naturgeschehens heraus will der Autor eine Philosophie der Instabilität entwerfen. Der gelernte Physiker und Philosoph lehrt an der Hochschule (...) Darmstadt (hda) Wissenschafts- und Technikphilosophie. Sein Buch beleuchtet das Thema „Instabilitäten“ aus vielen Blickwinkeln. Was sind Instabilitäten, was Selbstorganisation, was ist Zeit, was Zufall, was Kausalität? Diese Erkenntnisse bezieht der Autor dann auf den Kosmos, auf die Evolution bis hin zum menschlichen Gehirn und seinen Leistungen. Mit dieser Rezension gehe ich ausführlich auf dieses lesenswerte Buch ein. (shrink)

A dynamical system is called chaotic if small changes to its initial conditions can create large changes in its behavior. By analogy, we call a dynamical system structurally chaotic if small changes to the equations describing the evolution of the system produce large changes in its behavior. Although there are many definitions of “chaos,” there are few mathematically precise candidate definitions of “structural chaos.” I propose a definition, and I explain two new theorems that show that a set of models (...) is structurally chaotic if it contains a chaotic function. I conclude by discussing the relationship between structural chaos and structural stability. (shrink)

Climatology is a paradigmatic complex systems science. Understanding the global climate involves tackling problems in physics, chemistry, economics, and many other disciplines. I argue that complex systems like the global climate are characterized by certain dynamical features that explain how those systems change over time. A complex system's dynamics are shaped by the interaction of many different components operating at many different temporal and spatial scales. Examining the multidisciplinary and holistic methods of climatology can help us better understand the nature (...) of complex systems in general. -/- Questions surrounding climate science can be divided into three rough categories: foundational, methodological, and evaluative questions. "How do we know that we can trust science?" is a paradigmatic foundational question (and a surprisingly difficult one to answer). Because the global climate is so complex, questions like "what makes a system complex?" also fall into this category. There are a number of existing definitions of `complexity,' and while all of them capture some aspects of what makes intuitively complex systems distinctive, none is entirely satisfactory. Most existing accounts of complexity have been developed to work with information-theoretic objects (signals, for instance) rather than the physical and social systems studied by scientists. -/- Dynamical complexity, a concept articulated in detail in the first third of the dissertation, is designed to bridge the gap between the mathematics of contemporary complexity theory (in particular the formalism of "effective complexity" developed by Gell-Mann and Lloyd [2003]) and a more general account of the structure of science generally. Dynamical complexity provides a physical interpretation of the formal tools of mathematical complexity theory, and thus can be used as a framework for thinking about general problems in the philosophy of science, including theories, explanation, and lawhood. -/- Methodological questions include questions about how climate science constructs its models, on what basis we trust those models, and how we might improve those models. In order to answer questions about climate modeling, it's important to understand what climate models look like and how they are constructed. Climate model families are significantly more diverse than are the model families of most other sciences (even sciences that study other complex systems). Existing climate models range from basic models that can be solved on paper to staggeringly complicated models that can only be analyzed using the most advanced supercomputers in the world. I introduce some of the central concepts in climatology by demonstrating how one of the most basic climate models might be constructed. I begin with the assumption that the Earth is a simple featureless blackbody which receives energy from the sun and releases it into space, and show how to model that assumption formally. I then gradually add other factors (e.g. albedo and the greenhouse effect) to the model, and show how each addition brings the model's prediction closer to agreement with observation. After constructing this basic model, I describe the so-called "complexity hierarchy" of the rest of climate models, and argue that the sense of "complexity" used in the climate modeling community is related to dynamical complexity. -/- With a clear understanding of the basics of climate modeling in hand, I then argue that foundational issues discussed early in the dissertation suggest that computation plays an irrevocably central role in climate modeling. "Science by simulation" is essential given the complexity of the global climate, but features of the climate system--the presence of non-linearities, feedback loops, and chaotic dynamics--put principled limits on the effectiveness of computational models. This tension is at the root of the staggering pluralism of the climate model hierarchy, and suggests that such pluralism is here to stay, rather than an artifact of our ignorance. Rather than attempting to converge on a single "best fit" climate model, we ought to embrace the diversity of climate models, and view each as a specialized tool designed to predict and explain a rather narrow range of phenomena. Understanding the climate system as a whole requires examining a number of different models, and correlating their outputs. This is the most significant methodological challenge of climatology. -/- Climatology's role contemporary political discourse raises an unusually high number of evaluative questions for a physical science. The two leading approaches to crafting policy surrounding climate change center on mitigation (i.e. stopping the changes from occurring) and adaptation (making post hoc changes to ameliorate the harm caused by those changes). Crafting an effective socio-political response to the threat of anthropogenic climate change, however, requires us to integrate multiple perspectives and values: the proper response will be just as diverse and pluralistic as the climate models themselves, and will incorporate aspects of both approaches. I conclude by offering some concrete recommendations about how to integrate this value pluralism into our socio-political decision making framework. (shrink)

Book Review of "Trinity in Relation: Creation, Incarnation, and Grace in an Evolving Cosmos" by Gloria L. Schaab.

Chaos theory not only stretched the concept of chaos well beyond its traditional semantic boundaries, but it also challenged fundamental tenets of physics and science in general. Hence, its present and potential impact on the Western worldview cannot be underestimated. I will illustrate the relevance of chaos theory in regard to modern Western thought by tracing the concept of order, which modern thinkers emphasised as chaos’ dichotomic counterpart. In particular, I will underline how the concern of seventeenth-century natural philosophers with (...) order and conservation oriented the production of their concept of nature. Moreover, I will match this resulting world of natural facts with both the classical construction of the cosmos , and the nineteenth-century physico-chemical structure of conservation laws. Furthermore, I will recall the challenges to the deterministic and determinable modern scientific framework. These challenges arose from within the hard sciences, and they were often understood as a temporary lack of knowledge. I will argue that scientists long failed to acknowledge results that were at odds with their expectations, which were deeply engrained in modern Western thought, and which even harked back to the classical theoretical framework. Finally, I will suggest a link between the cultural earthquake that shook Western societies during the ‘long sixties,’ and the questioning of scientific expectations, which chaos theory defied. (shrink)

In this article I examine two mathematical definitions of observational equivalence, one proposed by Charlotte Werndl and based on manifest isomorphism, and the other based on Ornstein and Weiss’s ε-congruence. I argue, for two related reasons, that neither can function as a purely mathematical definition of observational equivalence. First, each definition permits of counterexamples; second, overcoming these counterexamples will introduce non-mathematical premises about the systems in question. Accordingly, the prospects for a broadly applicable and purely mathematical definition of observational equivalence (...) are unpromising. Despite this critique, I suggest that Werndl’s proposals are valuable because they clarify the distinction between provable and unprovable elements in arguments for observational equivalence. (shrink)

(2013). My Life in Chaos. World Futures: Vol. 69, The Complexity of Life and Lives of Complexity, pp. 248-268.

There are different kinds of uncertainty. I outline some of the various ways that uncertainty enters science, focusing on uncertainty in climate science and weather prediction. I then show how we cope with some of these sources of error through sophisticated modelling techniques. I show how we maintain confidence in the face of error.

In this eclectic and interdisciplinary work, chaos pioneer Ralph Abraham traces the history of consciousness through a rediscovery of the three forces that drive it: chaos, gaia, and eros-the mind, body and spirit of evolution. With startling originality and clarity of vision, Abraham employs photographs, timelines, charts, and an engaging format to sweep the reader along on this wild ride through math, science, mythology, philosophy, and whole of history.

A cura di Ignazio Licata, Ammar J. Sakaji Jeffrey A. Barrett, Enrico Celeghini, Leonardo Chiatti, Maurizio Consoli, Davide Fiscaletti, Ervin Goldfain, Annick Lesne, Maria Paola Lombardo, Mohammad Mehrafarin, Ronald Mirman, Ulrich Mohrhoff, Renato Nobili, Farrin Payandeh, Eliano Pessa, L.I Petrova, Erasmo Recami, Giovanni Salesi, Francesco Maria Scarpa, Mohammad Vahid Takook, Giuseppe Vitiello This volume comes out from an informal discussion between friends and colleagues on the answer:what topic do you think as fundamental in theoretical physics nowadays? Obviously wereceived different answers (...) according to the disposition and the different research areas, and answersin superposition state too. And yet some attractors have emerged pointing out the keys forthe Physicists conception of Nature, all of them converging towards a group of stronglyinterconnectedproblems. Let's see them one by one:. The concept of particle identity in Quantum Mechanics (QM) and Quantum Field Theory (QFT);. The relationship between QM and QFT, in particular the non -local aspects in Field Theory andthe problem of non-perturbative solutions;. The local/global problem in the relationship between particle physics and cosmology;. The role of Renormalization group in describing the meso and macroscopic emergent behaviour;. The possible extension of Poincaré symmetry group and Quantum cosmology;. Higgs "mechanism" and the origin of mass. (shrink)