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

Christensen, Kim and Nicholas Moloney. Complexity and Criticality. London: Imperial College Press, 2005. A technical work rooted in statistical mechanics that implies in part that self-organization in non-equilibrium systems may be a unifying concept for a emergent natural complexity.

For our purposes, complexity refers to the repeated application of simple rules in systems with many degrees of freedom that gives rise to emergent behavior not encoded in the rules themselves. (vii) Criticality refers to the behavior of extended systems at a phase transition where observables are scale free, that is, no characteristic scales exist for these observables. (vii) Criticality is therefore a cooperative feature emerging from the repeated application of the microscopic laws of a system of interacting ‘parts.’ (vii)

The science of complexity is highly interdisciplinary. It deals with dynamical systems composed of many interacting units, for example grains in granular media, rocks in the crust of the Earth, water droplets in the atmosphere, networks of organisms in biology or agents in economics, etc. (253)

Chua, Leon. Local Activity is the Origin of Complexity. International Journal of Bifurcation and Chaos. 15/11, 2005. Another example of growing efforts to identify a common complex system, but with dense mathematics it is hard to see how this feature can fit the bill. But the universality concept – that the same complex dynamics recurs everywhere throughout a nested nature –has long been the payoff.

Many scientists have struggled to uncover the elusive origin of “complexity,” and its many equivalent jargons, such as emergence, self-organization, synergetics, collective behaviors, nonequilibrium phenomena, etc…..The purpose of this paper is to show that all the jargons and issues cited above are mere manifestations of a new fundamental principle called local activity, which is mathematically precise and testable. (3435)

Chua, Leon, et al. A Nonlinear Dynamics Perspective of Wolfram’s New Kind of Science. Part V: Fractals Everywhere. International Journal of Bifurcation and Chaos. 15/12, 2005. The other four parts appeared over the last two years in this publication. A highly technical meditation on a “universal computation” by cellular automata and neural networks which manifests a self-similarity throughout an emergent world.

Cilliers, Paul. Difference, Identity, and Complexity. Philosophy Today. Spring, 2010. A synopsis of Cilliers and Rika Preiser’s edited work next in search of workable ways to understand nature’s self-organizing interplay of creative diversity and essential unity.

The argument in this essay is primarily one which resists an interpretation of deconstruction, and a post-structural understanding of difference, as an absolute free-play. Deconstruction acknowledges the inevitability of structure, and of its transformation. This “double movement” should be central when we think of institutions and organizations. (63)

Cilliers, Paul and Rika Preiser, eds. Complexity, Difference and Identity: An Ethical Perspective. Berlin: Springer, 2010. University of Stellenbosch, RSA, systems philosophers gather papers to address a troublesome issue in nonlinear studies – how to square a prolific spontaneity with an implied steady source. Its sections of Complexity, Difference, Identity, Ethics of Complexity, and Consequences strive toward a necessary reciprocity. See chapters by Cilliers and Collier herein, also Cilliers’ synopsis in Philosophy Today, (Spring 2010).

Corning, Peter. Nature’s Magic: Synergy in Evolution and the Fate of Humankind. Cambridge: Cambridge University Press, 2003. A consummate volume to convey this biologist’s thesis that cooperative effects between, for example, genes or individuals, are equally as important as the components themselves. The theory posits that when cooperation produces beneficial functional effects or synergies (some are not beneficial), these may be favored or selected (synergistic selection). This propensity then plays a causal role in the evolution of emergent complexity from the origin of life to human societies.

Corominas-Murtra, Bernat, et al. Hierarchy in Complex Systems. arXiv:1303.2503. A March 2013 posting by Corominas-Murtra and Ricard Sole, Universitat Pompeu Fabra, with Joaquin Goni and Carlos Rodgiguez-Caso, Indiana University, which is seen as confirming a half century later, Herbert Simon’s advocacy that regnant nature relies on hierarchical modularities for its robust maintanence. Indeed this 21st century Barcelona-Bloomington team can avail theoretical computations to develop 3D visualizations, which reveals an implicate source from which these nested, evolutionary structures arise. Ricard Sole acknowledges conversations in regard at the Santa Fe Institute with Douglas Erwin, Eric Smith, Geoffrey West and Murray Gell-Mann. See for example, Colm Ryan, et al. “Hierarchical Modularity and the Evolution of Genetic Interactomes across Species” in Molecular Cell (46/691, 2012) which also cites “general design principles” at work.

Cowan, George, et al, eds. Complexity. Reading, MA: Addison Wesley, 1994. A compendium of papers in search of unifying themes in terms of complex adaptive systems. The pioneers are represented: Philip Anderson, Brian Arthur, Per Bak, Walter Fontana, Murray Gell-Mann, Brian Goodwin, John Holland, Erica Jen, Stuart Kauffman, Melanie Mitchel, Peter Schuster, along with many others.

De Florio, Vincenzo. Systems, Resilience, and Organization: Analogies and Points of Contact with Hierarchy Theory. arXiv:1411.0092. A citation for publications on this site and in journals by the University of Antwerp mathematician. The endeavor often casts back to Gottfried Leibniz to propose a 2010s synthesis by way of a fractal self-similarity from cells to communities that could fulfill his prescience of a universally recurrent code script.

Deacon, Terrence. The Hierarchic Logic of Emergence: Untangling the Interdependence of Evolution and Self-Organization. Weber, Bruce and David Depew, eds. Evolution and Learning. Cambridge: MIT Press, 2003. An entry into recent work in process of the University of California at Berkeley biological anthropologist and author.

The contention of this paper is that biological evolution and evolutionary processes in general are a subset of processes drawn from a much larger set of novelty-producing processes that also includes self-assembly and self-organizing processes. (273) Evolutionary emergent systems can further interact to form multilayer systems of exceeding complexity. Indeed, this is the nature of complex organisms that is exemplified in the ascending levels of “self” that proceed from gene to cell to organism to lineage to species, and so on, in the living world. (302)

Deutsch, Andreas amd Sabine Dormann. Cellular Automaton Modeling of Biological Pattern Formation. International: Springer, 2018. Technical University of Dresden complexity bioscientists provide a latest tutorial about nature’s essential propensity to iteratively organize her/his self into viable, universal scales of emergent genesis. Some chapter and section titles are On the Origin of Patterns, Ontogeny and Phylogeny, and Physical Analogues, Morphogenesis.

The book introduces pattern-forming principles in biology and the various mathematical modeling techniques used to analyze them. Cellular automaton models are discussed for different types of cellular processes and interactions, such as random movement, cell migration, adhesive cell interaction, alignment and cellular swarming, growth processes, pigment cell pattern formation, tumor growth, and Turing-type patterns. The final chapter discusses potentials and limits of the cellular automaton approach in modeling various biological applications, along with future research directions. (Publisher)

Dingle, Kamaludin, et al. Input-Output Maps are Strongly Biased Towards Simple Outputs. Nature Communications. 9/761, 2018. By way of algorithmic information theory and system cartographic methods, Oxford University mathematicians KD, Chico Camargo and Ard Louis perceive an inherent tendency in complex network behavior to simplify and generalize themselves. The work merited notice as A Natural Bias for Simplicity by Mark Buchanan in Nature Physics (December 2018). See also by this group Deep Learning Generalizes because the Parameter-Function Map is Biased Towards Simple Functions at arXiv: 1805.08522.

Many systems in nature can be described using discrete input–output maps. Without knowing details about a map, there may seem to be no a priori reason to expect that a randomly chosen input would be more likely to generate one output over another. Here, by extending fundamental results from algorithmic information theory, we show instead that for many real-world maps, the a priori probability P(x) that randomly sampled inputs generate a particular output x decays exponentially with the approximate Kolmogorov complexity K~(x) of that output. We explore this strong bias towards simple outputs in systems ranging from the folding of RNA secondary structures to systems of coupled ordinary differential equations to a stochastic financial trading model. (Abstract)

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