Nonlinear Dynamics

The article presents the empirical confirmation to the black hole and white hole juxtapose theory. The author based the experiment on the multi- mission multi-spectral space telescope data conducted remotely with the NASA Data Challenge and Harvard- Smithsonian Micro-Observatory. Since the loss of the original manuscript, the author reformulated the mathematics during the research. The observation developed a resonance observation technique that observed the white hole to the moon’s direction with the sun. The data reduction of the white hole and (...) other observations provides an explanation for the undetected gravitons and some empirical physical features of the white hole. (shrink)

The article summarizes the software tool on astrophysical analysis with multi-wavelength space telescope data. It recaps the evidence analysis conducted on the Kerr-Newman black hole (KNBH). It was written prior to the article Research on the Kerr-Newman Black Hole in M82 Confirms Black Hole and White Hole Juxtapose not soon after the experiment. The conducted analysis suggested Hawking radiation is caused by the movement of ergosurfaces of the BH and serves as the primal evidence for black hole and white hole (...) juxtapose. A later data exploration was conducted with the radiation trails in the multi-wavelength data. The evidences produced corroborates with Yale professor Priyamvada Natarajan's black hole seeds theory. It implies that the electromagnetic dynamic of fusion and fission temperature determines the pressure of surface tension on the macro particles, and the mass density of the BH is determined by the electromagnetic tension between the outer ergosurface and inner ergosurface. The ring singularity of the BH and the Penrose-Hawking singularity of the BH determine the spin and gravitational singularity of the BH. Inside the ergosurfaces, the BH singularities' backward inflow causes the vicinity's rate on feeding the BH. It makes the active galactic nuclei (AGN) a semi-closed system. The density pressure is released on threshold. During the mass exchange observed by energy momentum upon the AGN's open, the macroparticle composition of the BH changes with the galactic event. This causes the expansion rate of the galaxy and contraction rate of the BH. AGN types and their relative motions determine the expansion rate of the cosmic universe in a generalized quantitative thinking. The article concludes that BH spin is caused by the asymmetric motions of AGN in the BH system. A set of the nuclear resonance caused by BH and white hole (WH) oscillation is processed with the same set of data. (shrink)

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

The 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.

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

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

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

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

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)

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)

From his earliest work forward, phenomenologist Maurice Merleau-Ponty attempted to develop a new ontology of nature that would avoid the antinomies of realism and idealism by showing that nature has its own intrinsic sense which is prior to reflection. The key to this new ontology was the concept of form, which he appropriated from Gestalt psychology. However, Merleau-Ponty struggled to give a positive characterization of the phenomenon of form which would clarify its ontological status. Evan Thompson has recently taken up (...) Merleau-Ponty’s ontology as the basis for a new, “enactive” approach to cognitive science, synthesizing it with concepts from dynamic systems theory and Francisco Varela’s theory of autopoiesis. However, Thompson does not quite succeed in resolving the ambiguities in Merleau-Ponty’s account of form. This article builds on an indication from Thompson in order to propose a new account of form as asymmetry, and of the genesis of form in nature as symmetry-breaking. These concepts help us to escape the antinomies of Modern thought by showing how nature is the autoproduction of a sense which can only be known by an embodied perceiver. (shrink)

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

Some have suggested that certain classical physical systems have undecidable long-term behavior, without specifying an appropriate notion of decidability over the reals. We introduce such a notion, decidability in (or d- ) for any measure , which is particularly appropriate for physics and in some ways more intuitive than Ko's (1991) recursive approximability (r.a.). For Lebesgue measure , d- implies r.a. Sets with positive -measure that are sufficiently "riddled" with holes are never d- but are often r.a. This explicates Sommerer (...) and Ott's (1996) claim of uncomputable behavior in a system with riddled basins of attraction. Furthermore, it clarifies speculations that the stability of the solar system (and similar systems) may be undecidable, for the invariant tori established by KAM theory form sets that are not d-. (shrink)

The hope of finding new methods of predicting the course of historical processes could be connected with the recent developments of the theory of self-organisation, also called synergetics. It provides us with knowledge of constructive principles of co-evolution of complex social systems, co-evolution of countries and geopolitical regions being at different stages of development, integration of the East and the West, the North and the South. Due to the growth of population on the Earth in blow-up regime, the general and (...) local instability of development is increasing. The social world seems to go towards a unity, a sustainable commonwealth through pulsations rather than monotonously. It goes via alternation of disintegration, even if partial, and getting more powerful integrations of structures. There is a path of multiple reduction of temporal and material expenses, a path of a resonant excitation of desirable and — no less important — feasible in a given social system structure. In the case of the right topology of integration of geopolitical structures an arising whole organisation can accelerate its tempo of evolution. 1999 Elsevier Science Ltd. All rights reserved. (shrink)

Reaction-diffusion systems which have reaction term satisfying f(-q) = -f(q) tend strongly to form striped patterns. Haken’s slaving principle is used to derive differential equations for unstable mode amplitudes close to the Turing instability. This connects a dynamical symmetry to pattern selection, with possible relevance to biological and chemical pattern-forming phenomena.

While many different mechanisms contribute to the generation of spatial order in biological development, the formation of morphogenetic fields which in turn direct cell responses giving rise to pattern and form are of major importance and essential for embryogenesis and regeneration. Most likely the fields represent concentration patterns of substances produced by molecular kinetics. Short range autocatalytic activation in conjunction with longer range “lateral” inhibition or depletion effects is capable of generating such patterns (Gierer and Meinhardt, 1972). Non-linear reactions are (...) required, and mathematical criteria were derived to design molecular models capable of pattern generation. The classical embryological feature of proportion regulation can be incorporated into the models. The conditions are mathematically necessary for the simplest two-factor case, and are likely to be a fair approximation in multi-component systems in which activation and inhibition are systems parameters subsuming the action of several agents. Gradients, symmetric and periodic patterns, in one or two dimensions, stable or pulsing in time, can be generated on this basis. Our basic concept of autocatalysis in conjunction with lateral inhibition accounts for self-regulatory biological features, including the reproducible formation of structures from near-uniform initial conditions as required by the logic of the generation cycle. Real tissue form, for instance that of budding Hydra, may often be traced back to local curvature arising within an initially relatively flat cell sheet, the position of evagination being determined by morphogenetic fields. Shell theory developed for architecture may also be applied to such biological processes. (shrink)

The paper addresses the formation of striking patterns within originally near-homogenous tissue, the process prototypical for embryology, and represented in particularly purist form by cut sections of hydra regenerating, by internal reorganisation of the pre-existing tissue, a complete animal with head and foot. The essential requirements are autocatalytic, self-enhancing activation, combined with inhibitory or depletion effects of wider range – “lateral inhibition”. Not only de-novo-pattern formation, but also well known, striking features of developmental regulation such as induction, inhibition, and proportion (...) regulation can be explained on this basis. The theory provides a mathematical recipe for the construction of molecular models with criteria for the necessary non-linear interactions. It has since been widely applied to different developmental processes. (shrink)

This summary of the original paradigm of the universal science of complexity starts with the discovered exact origin of the stagnating "end" of conventional, unitary science paradigm and development traditionally presented by its own estimates as the only and the best possible kind of scientific knowledge. Using a transparent generalisation of the exact mathematical formalism of arbitrary interaction process, we show that unitary science approach and description, including its imitations of complexity and chaoticity, correspond to artificial and ultimately strong reduction (...) of the natural plurality of unreduced interaction results called realisations to a single, "average" or "exact", realisation. This severe reduction of the natural world dynamics in unitary science underlies all its unsolvable "mysteries" and "paradoxes", persisting "difficult problems", and finally the modern "end" of the progress of just that, actually very special kind of knowledge, whose irreducible limits lead to the modern deep crisis of the global civilisation development. We show then how the rigorously substantiated restoration of the full richness of real-world dynamics within the intrinsically unified knowledge of the universal science of complexity provides not only the causally complete solution to the old and new problems of unitary science but opens practically unlimited possibilities for the new progress of science and civilisation as a result of this crucial extension, which we call complexity revolution. The unreduced analysis of the universal complexity science shows that at the current critical bifurcation point of development, we have only two incompatible possibilities and emerging tendencies, either the dangerously growing degradation within the dominating unitary science and thinking limits (irrespective of purely empirical technology power becoming even dangerous here) or the new golden age of scientific discoveries and civilisation progress with the qualitatively extended approach and results of unreduced complexity science and the new thinking it implies. (shrink)