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IV. Ecosmomics: An Independent Source Script of Generative, Self-Similar, Complex Network Systems

Mainzer, Klaus. Symmetry and Complexity: The Spirit and Beauty of Nonlinear Science. Singapore: World Scientific, 2005. A new book by the chair of philosophy of science at the University of Augsburg and director of its Institute of Interdisciplinary Informatics. Not seen yet, we quote from the publisher’s website.

Cosmic evolution leads from symmetry to complexity by symmetry breaking and phase transitions. The emergence of new order and structure in nature and society is explained by physical, chemical, biological, social and economic self-organization, according to the laws of nonlinear dynamics. All these dynamical systems are considered computational systems processing information and entropy….In the complex world of globalization, it strongly argues for unity in diversity.

Mainzer, Klaus. The Concept of Law in Natural, Technical and Social Systems. European Review. 22/S1, 2014. In a special issue on Basic Ideas in Science: The Concept of Law, the Technical University of Munchen philosopher, who has been writing about complexity since the 1990s, contrasts a prior phase of Newtonian mechanism with a Dynamic Concept of Laws that has arisen over this period. Rather than linear fixations, an actual nature of malleable, evolving intricacies and activities across scales of life and mind is being found. It is now known that genomes, brains, economies, and every milieu dynamically organize themselves in a similar way. As the quote notes, by 2014 their universal manifestion is proven from quanta to media, which then reveals a persistent, scale-free invariance. For a companion paper herein, see General Laws and Centripetal Science by Gerard Jagers.

Natural Laws of Self-organization: Laws of nonlinear dynamics do not only exhibit instability and chaos, but also self-organization of structure and order. The intuitive idea is that global patterns and structures emerge from locally interacting elements such as atoms in laser beams, molecules in chemical reactions, proteins in cells, cells in organs, neurons in brains, agents in markets, and so on. Complexity phenomena have been reported from many disciplines (e.g. biology, chemistry, ecology, physics, sociology, economics, and so on) and analysed from various perspectives such as Schrodinger’s order from disorder, Prigogine’s dissipative structure, Haken’s synergetics, Langton’s edge of chaos, etc. (S8)

Manukyan, Liana, et al. A Living Mesoscopic Cellular Automaton Made of Skin Scales. Nature. 544/173, 2017. University of Geneva and the Swiss Institutes of Bioinformatics researchers seek a better translation from natural mathematics into manifest biological form by way of this generative method. See also How the Lizard Gets Its Speckled Scales in the same issue by Leah Edelstein-Keshet, a University of British Columbia mathematician.

In vertebrates, skin colour patterns emerge from nonlinear dynamical microscopic systems of cell interactions. Here we show that in ocellated lizards a quasi-hexagonal lattice of skin scales, rather than individual chromatophore cells, establishes a green and black labyrinthine pattern of skin colour. We analysed time series of lizard scale colour dynamics over four years of their development and demonstrate that this pattern is produced by a cellular automaton (a grid of elements whose states are iterated according to a set of rules based on the states of neighbouring elements) that dynamically computes the colour states of individual mesoscopic skin scales to produce the corresponding macroscopic colour pattern. Our study indicates that cellular automata are not merely abstract computational systems, but can directly correspond to processes generated by biological evolution. (Abstract)

Markovic, Dimitrije and Claudius Gros. Power Laws and Self-Organized Criticality in Theory and Nature. Physics Reports. 536/2, 2014. In a 21st century tutorial that would please Johann Wolfgang, Goethe University, Frankfurt, physicists can quantify via sophisticated mathematics the presence of a natural vitality that repeats in constant sequential and structural kind everywhere. Its essence is a dynamic balance of order and disorder, form and fracture, separate entities and integral wholes, as found via a scale-invariance from solar flares to neural cognition and Internet sites. By these propensities, it is proposed that a good way to understand life’s evolution is an on-going endeavor toward states of “highly optimized tolerance,” i.e. an optimizing process. In regard, a true “universality” of the same pattern and process from cosmos to civilization can be now affirmed. We cite its long Abstract.

Power laws and distributions with heavy tails are common features of many complex systems. Examples are the distribution of earthquake magnitudes, solar flare intensities and the sizes of neuronal avalanches. Previously, researchers surmised that a single general concept may act as an underlying generative mechanism, with the theory of self organized criticality being a weighty contender. The power-law scaling observed in the primary statistical analysis is an important, but by far not the only feature characterizing experimental data. The scaling function, the distribution of energy fluctuations, the distribution of inter-event waiting times, and other higher order spatial and temporal correlations, have seen increased consideration over the last years. Leading to realization that basic models, like the original sandpile model, are often insufficient to adequately describe the complexity of real-world systems with power-law distribution.

Consequently, a substantial amount of effort has gone into developing new and extended models and, hitherto, three classes of models have emerged. The first line of models is based on a separation between the time scales of an external drive and a an internal dissipation, and includes the original sandpile model and its extensions, like the dissipative earthquake model. Within this approach the steady state is close to criticality in terms of an absorbing phase transition. The second line of models is based on external drives and internal dynamics competing on similar time scales and includes the coherent noise model, which has a non-critical steady state characterized by heavy-tailed distributions. The third line of models proposes a non-critical self-organizing state, being guided by an optimization principle, such as the concept of highly optimized tolerance.

We present a comparative overview regarding distinct modeling approaches together with a discussion of their potential relevance as underlying generative models for real-world phenomena. The complexity of physical and biological scaling phenomena has been found to transcend the explanatory power of individual paradigmal concepts. The interaction between theoretical development and experimental observations has been very fruitful, leading to a series of novel concepts and insights. (Abstract)

Mazzolini, Andrea, et al. Statistics of Shared Components in Complex Component Systems. arXiv:1707.08356. When this chapter about a independent, recurrent, genetic-like code was first posted in 2004, it was mainly a report of sporadic efforts by disparate researchers and schools, couched in abstract terms. Some 13 years on, University of Turin and Sorbonne University, Paris, biophysicists here describe a common complexity in exemplary evidence across a wide natural and social range from microbes to literature. As intimated and sought through history, in 1960s general systems theory, a 1980s goal for the Santa Fe Institute, at long last, with many similar entries by way of novel worldwide collaborations, are such inklings of its historic, revolutionary articulation.

Many complex systems are modular. Such systems can be represented as "component systems", such as LEGO bricks in LEGO sets. In other component systems, instead, the underlying functional design and constraints are not obvious a priori, and their detection is often a challenge, requiring a clear understanding of component statistics. Importantly, some quantitative invariants appear to be common to many systems, most notably a broad distribution of component abundances, which often resembles the well-known Zipf's law. Here, we specifically focus on the statistics of shared components, i.e., the distribution of the number of components shared by different system-realizations. To account for the effects of component heterogeneity, we consider a simple null model, which builds system-realizations by random draws from a universe of possible components. Surprisingly, this model can positively explain important features of empirical component-occurrence distributions obtained from data on bacterial genomes, LEGO sets, and book chapters. (Abstract excerpts)

A large number of complex systems in very different contexts - ranging from biology to linguistics, social sciences and technology - can be broken down to clearly defined basic building blocks or components. For example, books are composed of words, genomes of genes, and many technological systems are assemblies of simple modules. Once components are identified, a specific realization of a system (e.g., a specific book, a LEGO set, a genome) can be represented by its parts list, which is the subset of the possible elementary components (e.g. words, bricks, genes),with their abundances, present in the realization. (1)

The striking similarities of laws governing both component abundance and occurrence found in empirical systems of very different origins (LEGO sets, genomes, book chapters) support the idea that the concept of “component system” defined in this work can capture in a unified framework a large class of complex systems with some common global properties. Such “universal” phenomena may be regarded as emergent properties due to system heterogeneity, which transcend the specific design, generative process or selection criteria at the origin of a system. Analogous phenomena occur, for example, in ecosystems, where emergent species-abundance distributions appear for forests, birds or insects. (9)

McLeish, Tom. Are There Ergodic Limits to Evolution? Interface Focus. 5/6, 2015. n this Are There Limits to Evolution? issue, a Durham University biophysicist tries to apply a physical theory about relevant landscape searches whereof “random” micro phases are averaged out to a predictable “fitness optima” result. But a Google of “ergodic” brings a variety of definitions, so an effort to clarify its usage would serve its usage. In any event, an affinity of “statistical mechanics and evolutionary dynamics” is seen to support innate tendencies for evolution to converge on similar forms and ways.

We examine the analogy between evolutionary dynamics and statistical mechanics to include the fundamental question of ergodicity — the representative exploration of the space of possible states (in the case of evolution this is genome space). Several properties of evolutionary dynamics are identified that allow a generalization of the ergodic dynamics, familiar in dynamical systems theory, to evolution. (Abstract)

For several generations of thinkers in the field of evolutionary dynamics, there has been a fruitful conversation with the concepts and methodologies of statistical mechanics [1]. The analogy arises, because random mutation between alleles at the genotype level induces a coarse-grained diffusion within the space of coded structures at the phenotype level, in a similar way that intermicrostate dynamics generates the sampling of macrostates in statistical mechanics. So divergence among genotypes (e.g. in bacteria) may nonetheless map onto a convergence in phenotype, in a manner isomorphic to the mapping of large numbers of configurational microstates into the same macrostate in statistical mechanics. There are three principal common ingredients that make the analogy between statistical mechanics and evolution fruitful: (i) a very large space of states; (ii) a coarse-grained set of properties that emerge from the microscopic states; and (iii) a stochastic dynamical process that moves the system from one state, or set of states, to another. (1)

Mero, Laszlo. The Logic of Miracles. New Haven: Yale University Press, 2018. The Eötvös Loránd University, Budapest mathematician and psychologist provides a well reasoned rebuttal and alternative to Nassim Taleb’s 2010 The Black Swan (2010) about a chaotic unpredictability that besets complex natural and social societies. But if we refuse to accept this and press on for an inherent basis which underlies sufficiently regular events, one does actually appear. The approach involves a stronger perception of an infinite fractal self-similarity and scale-invariance across all natural to cultural realms. A further avail of ubiquitous scale-free networks braces the argument. Of course wild stuff happens, but not without some modicum of meaning and trace to a relatively reliable source.

We live in a much more turbulent world than we like to think, but the science we use to analyze economic, financial, and statistical events mostly disregards the world’s essentially chaotic nature. We need to get used to the idea that wildly improbable events are actually part of the natural order. The renowned Hungarian mathematician and psychologist László Mérő explains how the wild and mild worlds (which he names Wildovia and Mildovia) coexist, and that different laws apply to each. Even if we live in an ultimately wild universe, he argues, we’re better off pretending that it obeys Mildovian laws. Doing so may amount to a self fulfilling prophecy and create an island of predictability in a very rough sea. Perched on the ragged border between economics and complexity theory, Mérő proposes to extend the reach of science to subjects previously considered outside its grasp: the unpredictable, unrepeatable, highly improbable events we commonly call “miracles.”

Meyers, Robert, editor-in-chief. Encyclopedia of Complexity and Systems Science. Berlin: Springer, 2009. The 11 volume, 10,000 page compendium is now available, with a full listing of its 592 topical contents in 15 sections, and preface, posted on the Springer web citation. A broad range is covered, but constrained within narrowly defined sections such as Cellular Automata, Mathematical Basis of, which are muchly technical and pedantic. An author count averages 15 men to 1 woman, better than the Britannica. Some articles of note might be "Complex Gene Regulatory Networks' by Sui Huang and Stuart Kauffman, "Self-Organizing Systems" by Wolfgang Banzhaf, and Eric Chaisson's "Exobiology and complexity." We quote at length from its synopsis of this scientific frontier which languishes without a common terminology and vision so as to reveal a universally recurrent genesis cosmos.

The science and tools of complexity and systems science include theories of self-organization, complex systems, synergetics, dynamical systems, turbulence, catastrophes, instabilities, nonlinearity, stochastic processes, chaos, neural networks, cellular automata, adaptive systems, and genetic algorithms. Examples of near-term problems and major unknowns that can be approached through complexity and systems science include: The structure, history and future of the universe; the biological basis of consciousness; the integration of genomics, proteomics and bioinformatics as systems biology; human longevity limits; the limits of computing; sustainability of life on earth; predictability, dynamics and extent of earthquakes, hurricanes, tsunamis, and other natural disasters; the dynamics of turbulent flows; lasers or fluids in physics, microprocessor design; macromolecular assembly in chemistry and biophysics; brain functions in cognitive neuroscience; climate change; ecosystem management; traffic management; and business cycles. All these seemingly quite different kinds of structure formation have a number of important features and underlying structures in common. These deep structural similarities can be exploited to transfer analytical methods and understanding from one field to another.

Mikhailov, Alexander. From Cells to Societies: Models of Complex Coherent Action. Berlin: Springer, 2002. Using the approach to self-organizing systems known as synergetics, general principles are found to characterize the collective behavior of populations of interactive agents whether microbes or cultures.

Miller, James G. Living Systems. New York: McGraw-Hill, 1976. A classic treatise on the nested, hierarchical organization of biological and social life wherein 20 critical subsystems that process either matter-energy or information repeat at each subsequent level. These similar, isomorphic features “thread out” at each stage from the genetic to the global. The resultant field of Living Systems Theory has been elaborated in the journals Behavioral Science and its successor Systems Research and Behavioral Science.

Minkel, J. R. Hollow Universe. New Scientist. April 27, 2002. A report from the physics frontier of an encounter with an information based, fine-grained, holographic cosmos whereby the same “image,” “message” or “system” plays out everywhere in its emergent development.

Maybe.…nature is storing the data about its most basic building blocks like a hologram. In a conventional hologram, a laser beam bouncing off an object is mixed with another laser beam and the resulting interference pattern is recorded on a flat surface. Shine new light onto the recording, and a three dimensional image leaps out. If nature works like this, then information somehow lives on the boundary of any region of spacetime. The material stuff within that boundary, the objects that we perceive and touch, is just the unpacked, higher-dimensional manifestation of that hologram. That is the holographic principle. (24)

Mitchell, Melanie. Complexity: A Guided Tour. Oxford: Oxford University Press, 2009. The Portland State University and Santa Fe Institute computer scientist, with John Holland and Douglas Hofstadter as doctoral mentors, draws on her two decades of experience and public lectures to offer an accessible entry to this multi-faceted endeavor. With an emphasis on computational simulations, nature’s propensities for scale-free networks, power laws, cellular automata, genetic algorithms, cross-communication, evolvability, and so on, along with their proponents, are clearly explained. But in a tacit response to our male scientific culture (every one else mentioned), which seems unable to cognitively perceive or admit intrinsic patterns, the search for or possibility of universal, independent abiding principles is mostly dismissed. Altogether a good introduction.

Now I can propose a definition of the term complex system: a system in which large networks of components with no central control and simple rules of operation give rise to complex collective behavior, sophisticated information processing, and adaptation via learning or evolution. (13) Systems in which organized behavior arises without an internal or external controller or leader are sometimes called self-organizing. Since simple rules produce complex behavior in hard-to-predict ways, the macroscopic behavior of such systems is sometimes called emergent. Here is an alternative definition of a complex system: a system that exhibits nontrivial emergent and self-organizing behaviors. (13)

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