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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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IV. Ecosmomics: An Independent, UniVersal, Source Code-Script of Generative Complex Network Systems

Kauffman, Stuart. Investigations. New York: Oxford University Press, 2000. More conceptual insights into a view of Earth life that creates itself by means of intentional, autonomous agents which continually expand the niche of animate complexity. Kauffman’s frontier thinking offers glimpses of a “fourth law of thermodynamics,” a “general biology” for emergent life, autocatalytic biospheres, and a “coconstructing cosmos.”

Kauffman, Stuart. The Origins of Order: Self-Organization and Selection on Evolution. New York: Oxford University Press, 1993. A breakthrough work that reports on biologist and physician Kauffman’s decades of research studies on a deep theoretical basis for the innate self-organization of complex living systems which is in creative effect prior to the winnowing action of natural selection. (Also see Kauffman’s At Home in the Universe in Part III,An Organic Universe.)

Kelso, Scott and David Engstrom. The Complementary Nature. Cambridge: MIT Press, 2006. This important work is mainly noted in Current Vistas and by an extensive review in Recent Writings.

Khelifi, Mounir, et al. A Relative Multifractal Analysis. Chaos, Solitons and Fractals. Vol. 140, 2020. University of Monastir, Tunisia mathematicians provide a further finesse of nature’s infinite self-similar formulations. We also cite amongst a wide array of international 2020 papers such as Multifractal Analysis of Embryonic Eye Structures in Mice (Sijilmassi, Ouafa, et al, Universidad Complutense de Madrid, 138), The Origin of Collective Phenomena in Firm Sizes (Ji, Guseon, et al, Graduate School of Future Strategy, KAIST, S. Korea, 136), Using Network Science to Unveil Badminton Performance Patterns (Gomez, Miguel-Angel, et al, Universidad Politécnica de Madrid, 135), A Symbiosis between Cellular Automata and Genetic Algorithms (Cerruti, Umberto, et al, University of Torino, 134), and The Fractal Description Model of Rock Fracture Networks (LiLi, Sui, et al, North China Institute of Science, 129). Our aim is to document in this consummate year how every manifest social, biologic and physical phase is deeply guided by common mathematic sources.

The University of Monastir is a Tunisian multidisciplinary university with its own financial and administrative autonomy located on the Gulf of Hammamet, south of Tunis. It was founded in 2004 following the reform of the university higher education system and is organized in 5 Faculties, 2 graduate schools and 9 institutes.

Kiel, L. Douglas. Knowledge Management, Organizational Intelligence and Learning, and Complexity. UNESCO-EOLSS Joint Committee. Knowledge for Sustainable Development. Volume 1. Paris: UNESCO Publishing; Oxford: EOLSS Publishers, 2002. A good primer on complexity sciences. As these become more familiar, they are motivating organizations to become dynamic, adaptive, ecologically sensitive and constantly learning.

These discoveries focus on both order and disorder in the universe and on the increasing complexity and similarities across universal process, and have led to a new paradigm in the sciences – the self-organizing paradigm that focuses on how form and structure are produced in a dynamic and creative universe. (854) There is a growing recognition that the same processes that lead to a self-organizing universe have also led to the tremendous complexity of human cultures and human affairs. (855)

Krakauer, David, ed. Worlds Hidden in Plain Sight: The Evolving Idea of Complexity at the Santa Fe Institute 1984 – 2019. Santa Fe, NM: Santa Fe Institute Press, 2019. The SFI evolutionary biologist and current president gathers 35 years of contributions from events, seminars, projects, talks, and more which can well track the revolutionary discovery of a natural anatomy, physiology, cerebral, and cultural essence. A 1984 - 1999 section notes Mavericks such as John Holland, Murray Gell-Mann, and Simon Levin. 2000 - 2014 turns to Unifers like Harold Morowitz, Jessica Flack and Brian Arthur. 2015 and Beyond then completes 37 chapters with entries by Luis Bettencourt, Geoffrey West, Mirta Galesic, Simon DeDeo, Samuel Bowles, and Jennifer Dunne.

The book opens with a yearly topical list from initial glimpses of a nonlinear physics across astral and material systems all the way to active societies and economies. 2019 titles are Humans in Ecological Networks and Eco-Evolutionary Synthesis. A prime SFI founder George Cowan saw the promise of an iconic, common motif which similarly recurred everywhere. Three and a half decades later, as we try to document, a self-organizing complex adaptive network system of node element and link relation within a whole, viable entity seems to well fulfill this goal. I visited SFI in 1987 to hear a talk by Morowitz, when one sensed that a new animate frontier was opening. We cite a prescient 1992 affirmation by Murray Gell-Mann, another founder, along with a 2015 verification by David Krakauer.

Ultimately, we can argue that it is the self-similarity of the structure of fundamental physical law that dictates the continuing usefulness of mathematics. At the modest level of earlier science, this sort of self-similarity is strikingly apparent. Electricity, gravitation, and magnetism all have the same force, and Newton suggested that there might be some short-range force. Now that scientists are paying attention to scaling phenomena, we see in the study of complex systems astonishing power laws extending over many orders of magnitude. The renormalization group turns out to apply not only to condensed matter but to numerous other subjects. The biological and social sciences are just as much involved in these discoveries of scaling behavior as the physical sciences. We are always dealing with nature consonant and conformable to herself. So the approximate self-similarity of the laws of nature runs the gamut from underlying laws of physics to the phenomenological laws of the most complex realms. (Murray Gell-Mann, 1992, 38-39)

For the last few decades we have been steadily surveying the landscape of complex phenomena, and it is gratify that along the way we find that complex systems nominally unrelated bear strong family resemblances. These similarities include how the structure of evolutionary adaption looks a lot like the mathematics of learning, that the distribution of energy within a body made of tissues and fluids follows rules similar to those governing the flow of energy in a society, that networks within cells adhere to the geometric principles we find on the internet, and that the rise and fall of ancient civilizations follow a sequence similar to the present growth of urban centers. (David Krakauer, 2015, 230)

Krishnagopal, Sanjukta, et al. Synchronization Patterns: From Network Motifs to Hierarchical Networks. arXiv:1607.08798. In this prepost of a paper to appear in Philosophical Transactions A, Technical University of Berlin physicists including Eckehard Scholl try to define these common characteristics of a universally nonlinear nature. Of special note is a choice of brain neural networks as a prime exemplar, as if a cerebral microcosm for all complex, self-organizing systems. In regard, as their presence becomes evident from quantum to cultural realms, an analogous macrocosm may once again well accord with human qualities

We investigate complex synchronization patterns such as cluster synchronization and partial amplitude death in networks of coupled Stuart-Landau oscillators with fractal connectivities. The study of fractal or self-similar topology is motivated by the network of neurons in the brain. This fractal property is well represented in hierarchical networks, for which we present three different models. In addition, we introduce an analytical eigensolution method and provide a comprehensive picture of the interplay of network topology and the corresponding network dynamics, thus allowing us to predict the dynamics of arbitrarily large hierarchical networks simply by analyzing small network motifs. We also show that oscillation death can be induced in these networks, even if the coupling is symmetric, contrary to previous understanding of oscillation death. Our results show that there is a direct correlation between topology and dynamics: Hierarchical networks exhibit the corresponding hierarchical dynamics. This helps bridging the gap between mesoscale motifs and macroscopic networks. (Abstract)

The work presented here is of particular interest for neuroscience where recently a lot of emphasis has been put on the relation between structural connectivity and functional connectivity in the brain. Evidence from empirical studies suggests that the presence of a direct anatomical connection between two brain areas is associated with stronger functional interactions between these two areas. Our results support these empirical results through theoretical investigation. In addition, they can give valuable insight because they provide a completely analytical framework while employing a complex hierarchical structure that mimics the hierarchical nature of neurons in the brain. The fractal or self-similar hierarchical organization of neural networks is studied in [83–86]. The advantage of this theoretical study is that it allows for investigating the interplay of dynamics and topology on every scale, from the smallest to the largest structural level as well as the investigation of dynamics of each individual node. (16)

Kulkarni, Suman, et al. Information Content of Note Transitions in the Music of J. S. Bach.. arXiv:2301.00783. University of Pennsylvania and CCNY interdisciplinary theorists including Danielle Bassett open with an appreciation of our human social love of tuneful melodic compositions, as they now become amenable to 21st mathematical sciences of network forms, linguistics, and so on. It is noted that these findings hold to the same scale and metre as everywhere else in nature. See also Fractal Patterns in Music by John McDonough and Andrzej Herczyhski at arXiv:2221.12497, and The Song of the Cell by Siddhartha Mukherjee (Scribner, 2022).

Music has a complex structure that expresses emotion and conveys information, which people process through an imperfect cognitive gestalt version of reality. To address and analyze this wide issue, we study J. S. Bach's music by way of network science and information theory. Bach's work is highly structured over wide range of fugues and choral pieces that we view as a network of note transitions to quantify the information in each piece and how they can be grouped together. Our findings shed new light network properties of Bach's music and gain insight into features that make networks of information effective for communication. (Excerpt)

Lee, Deokjae, et al. Universal Mechanism for Hybrid Percolation Transitions. Nature Scientific Reports. 7/5723, 2017. A Korean - Hungarian collaboration of Seoul National University and Central European University systems physicists cites another example whence physical materiality can be seen to innately possess generic, commonly repetitive, formative features.

Hybrid percolation transitions (HPTs) induced by cascading processes have been observed in diverse complex systems such as k-core percolation, breakdown on interdependent networks and cooperative epidemic spreading models. Here we present the microscopic universal mechanism underlying those HPTs. We show that the discontinuity in the order parameter results from two steps: a durable critical branching (CB) and an explosive, supercritical (SC) process, the latter resulting from large loops inevitably present in finite size samples. This crossover mechanism and scaling behavior are universal for different HPT systems. Our result implies that the crossover time O(N1/3) is a golden time, during which one needs to take actions to control and prevent the formation of a macroscopic cascade, e.g., a pandemic outbreak. (Abstract)

Percolation is a prototypical model of disorder, which is often used to illustrate the emergence and the resilience of a giant cluster as links between individuals are added and deleted one by one, respectively. A giant cluster at a transition point in the mean field limit is to good approximation a critical branching (CB) tree with unit mean number of offspring. The giant cluster of recovered nodes at a transition point of a simple epidemiological model, the so-called susceptible/infective/removed (SIR) model, is one of such percolating clusters grown in the CB processes. Percolation transition is known as a robust continuous transition. (1)

Lehn, Jean-Marie. Toward Self-Organization and Complex Matter. Science. 295/2400, 2002. A cross-fertilization between complex systems, biological evolution, and chemistry leads to a synthesis of self-organization and selection as a science of dynamically adaptive “informed matter.”

Self-organization is the driving force that led to the evolution of the biological world from inanimate matter. The inclusion of dissipative nonequilibrium processes, like those present in the living world, constitutes a major goal and challenge for supramolecular chemistry. (2400) Multilevel hierarchical self-organization enables the progressive buildup of more and more complex systems in a sequential temporal ordered fashion. (2401)

Lesne, Annick and Michel Lagues. Scale Invariance: From Phase Transitions to Turbulence. Germany: Springer, 2012. Parisian physicists achieve a dedicated volume to express current realizations of nature’s own propensity to reliably repeat in kind the same structures and dynamics across universe to human scales, indeed from physics to people. By way of mathematic theories, albeit in abstractions as self-organized criticality, a robust veracity of a fractal-like “universality” is described from cosmic condensed matter to chemical, polymeric realms, biological systems, and onto somatic physiologies. See also From Newton to Mandelbrot by D. Stauffer, E. Stanley, and A. Lesne (Springer 2017) for a further excursion.

During a century from the Van der Waals mean field description of gases in the 1870s until the introduction of the renormalization group (RG) in the 1970s, thermodynamics and statistical physics were unable to account for the incredible universality observed in critical phenomena. The success of RG techniques is not only to solve this challenge of critical behaviour in thermal transitions but to introduce useful tools across a wide field where a system exhibits scale invariance. Since then, a new physics of scaling laws and critical exponents allows quantitative descriptions of numerous occasions, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos and turbulence. The chapters are jointly written by an experimentalist and a theorist.

Lin, Yi, et al. Systems Science. Boca Raton: CRC Press, 2012. Yi Lin is a mathematican with academic appointments across China and the USA, and several texts on nonlinear theories to his credit. Coauthor Xiaojun Duan, with a Chinese PhD in systems engineering, professes at the National University of Defense Technology, Changsha. She drew upon her course material for the book’s topical range from historical backgrounds and nonlinear dynamics to self-organization, complex adaptive systems, synergetics, nonequilibrium thermodynamics, fractals, chaotic behavior, nested networks, emergence, and onto “open complex giant systems” of global and cosmic scale. The extraordinary volume is of such merit we offer an exemplary array of quotes.

But this edition is unique among its genre by achieving from an Eastern hemisphere an innovative appreciation of such ubiquitous natural generative phenomena. As also noted in Yi Lin and Shoucheng OuYang 2010 (search), Western science, as is well known, tends to particulate material reduction and a mechanist cosmos, life, and human devoid of source or destiny. From a holistic Asian perspective, a once and future accord can be realized, per the quotes, whence this 21st century systems vision is seen as confirmation of ancient organic procreative essences. Indeed, the arcane terms above are interpreted as new encounters with and versions of an eternal, independent Tao, with its “dialectics” of agent and relation, node and link, entity and empathy, surely masculine Yang and feminine Yin, as they reciprocally spiral into manifest development. (While the word dialectics is used often, no mention of Marxism is ever made.)

In short, the characteristics of systems science require scholars of different backgrounds to talk and to conduct research together so that they can potentially discover implicit connections underlying the artificially separated disciplines. Through integrations of multiple fields, commonalities of systems can be discovered so that practical problems can be resolved. (16)

One of the main theoretical contributions of (Ludwig von) Bertalanffy is the introduction of emergence into systems science. This concept has created an overall and long-lasting influence to the development of systems science. Its philosophical foundation is dialectics. Reductionism and holism, and analytical thinking and synthetic thinking, have always been pairs of opposites in the development of science. In the past several hundred years, science has advocated reductionism and denounced holism and emphasized on analytic thinking and despised synthetic thinking. To establish systems and to open up the research of complexity, there is a need to revisit these two pairs of opposites and to go beyond reductionism and analytic thinking in order to reestablish the dominance of holism and synthetic thinking on the basis of modern science. (19)

In Chinese society since antiquity, the philosophical thought that all worldly things give birth while in opposition to each other and mutually support and react to each other has been well accepted and widely recognized. However, this philosophical thought has not been rigorously described using scientific language. Also, it could not explain the ultimate whys and hows of things in terms of analytically describing interactions. (107) Synergetics is an interdisciplinary science that studies the formation and self-organization of patterns and structures appearing in open systems that are far from thermodynamic equilibrium. (107) In short, in the theory of synergetic, cooperation, orderliness, order parameters, and slow-change and fast-change variables are all products of competition. Through conflicts, opposites are unified, with the unification, there are still opposites. This fundamental law of dialectics plays out vividly in synergetics. (114)

When one looks at the mechanism for chaotic and random phenomena to appear and to evolve from the angle of behavioral forms, he or she can define these phenomena as due to self-organization. It is the foundation for all evolutionary processes to take place, be they natural or historical, physical or chemical, biological or human or societal. No matter what properties the systems’ components possess, and no matter which level they are situated at, these processes are similar, and their attributes are all self-organization. (115) From molecules to the universe, from cells to societies, all the objects that are so seemingly different possess one common attribute without a single exception: they evolve in the direction of an increasing degree of orderliness. Such evolutions are spontaneous. (115)

Universality of Fractal Structures Fractal is a concept with a wide-ranging significance. There are fractal phenomena in nature, societies, and human thoughts. It can be categorized into four main classes: natural fractals, time fractals, social fractals, and thought fractals. Natural fractals include geometric fractals, functional fractals, information fractals, energy fractals, etc. Time fractals mean such systems that have the property of self-similarity along the time axis. Social fractals include those self-similar phenomena seen in human activities and societal phenomena. Thought fractals stand for those self-similarities existing in human knowledge and consciousness. (157)

Philosophical Significance of Fractal Theory The fractal theory points out the dialectical relationship between wholes and parts of the objective world. It destroys the membrane between wholes and parts and locates the media and bridges that connect parts and wholes. That is there are self-similarities between wholes and parts. The Fractal theory provides a new methodology for people to comprehend the whole from parts and a different basis for people to fathom infiniteness from finiteness. Additionally, the fractal theory further deepens and enriches the universal connectedness of the world and the unitarity principle of the cosmos. (158)

Science and Theories of Complexity After the 1970s, nonlinear science, as represented by dissipative structures, synergetics, catastrophe theory, chaos theory, fractal theory, hypercycle theory, etc., made great advances and has shaken the determinism that has ruled physics, geometry, and mathematics for over 300 years. Determinism enabled physics to express various behaviors in predictable forms. However, natural, biological, ecological, social, and economic systems are fully filled with nonlinearity and complexity. Thus, investigations of such systems cannot be placed on reductionism. Instead, the thought of wholeness has to be employed. Complex adaptive systems theory represents an important theoretical achievement. Since entering the 1990s, complex systems and complexity have been a hot topic of scientific activities. (199)

Three Begets All Things of the World The origin of systems thinking in China can be traced back to Lao Tzu of the time of spring and Autumn over more than 2000 years ago. Lao Tzu is one of the earliest philosophers, who considered such questions as: Where and how is the world from? Where is it going to? In chapter 42 of Tao De Ching, Lao Tzu says that “Tao breeds one, one breeds two, two breeds three, and three begets all things of the world.” Why did Lao Tzu jump directly from “three” to “all things.”? It is because throughout Chinese history, yin and yang have represented complementary opposites; through these opposites, the colorful world has been formed. By using the point of view of the present systems science, the significance of “three” can be quite clearly illustrated. (202)

Basics of Complex Adaptive Systems Complex systems represent one of the current main research directions in systems science, while complex adaptive systems (CASs) stand for a class of very representative complex systems. (221) This point of view of interactions is very instructive. When agents are said to be the basis of the whole, it does not mean that the isolated and separated agents form the foundation of the whole. If it were so, one would have returned to the point of view of reductionism. It is the interactions between the agents and between the agents and their environments that contribute the foundation of the whole. When one says that “the whole is greater than the sum of its parts,” he or she talks about the “added value” created by these interactions. The rich and colorful behavioral patterns of CASs come from these increased values. (225) Third, the thought of adaptability organically links together the macrocosm and microcosm. Through the interactions between agents and between agents and their respective environments, changes in individual agents become the foundations of changes in the whole system so that these changes of different levels are considered at the same time. (225)

In principle, the fundamental properties of open complex giant systems are the same as those of general systems, including wholeness, correlation, systemhood, orderliness and dynamics, (along with) hierarchy, evolution, and emergence. (246) The treatment of such open complex giant systems as the human brain, human body, and geological system have gone beyond the total scientific achievement of the past 200 or more years on the basis of reductionism. It can be concluded that there is a need to organically combine the wholeness theory of the Chinese culture with reductionism in order to guide the investigations of open complex giant systems. (246)

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