IV. Ecosmomics: An Independent, UniVersal, Source Code-Script of Generative Complex Network Systems
Livio, Mario. The Golden Ratio. New York: Broadway Books, 2002. Which is mathematical Fibonacci series found in evidence throughout nature. In so doing, it takes on fractal qualities as motifs repeat themselves with a nested self-similarity, much like Russian dolls.
Loose, Martin, et al. Protein Self-Organization: Lessons from the Min System. Annual Review of Biophysics. 40/315, 2011. This chapter by Dresden University (Loose), Max Planck Institute (Karsten Kruse), and Saarland University (Petra Schwille) scientists is a good example of the shift in biological research to admit and study the deep, creative, presence and play of “Collective dynamic behavior: a system that emerges from the interactions of a large number of components” at each and every phase from biomolecules to cells, organisms, and onto fish schools and bird flocks.
One of the most fundamental features of biological systems is probably their ability to self-organize in space and time on different scales. Despite many elaborate theoretical models of how molecular self-organization can come about, only a few experimental systems of biological origin have so far been rigorously described, due mostly to their inherent complexity. The most promising strategy of modern biophysics is thus to identify minimal biological systems showing self-organized emergent behavior. One of the best-understood examples of protein self-organization, which has recently been successfully reconstituted in vitro, is represented by the oscillations of the Min proteins in Escherichia coli. (Abstract, 315)
Lorenz, Dirk, et al. The Emergence of Modularity in Biological Systems. Physics of Life Reviews. 8/2, 2011. With coauthors Alice Jeng and Michael Deem, Rice University biophysicists cite Herbert Simon’s 1962 classic image, which a half century later can be verified as a natural, dynamic persistence for life to form into distinct, viable modules or communities at every nested phase and moment. Section 2.2.4 is “Spontaneous Emergence of Modularity as a Phase Transition,” while 3.2 is “Modularity in Metabolic Networks, Gene Networks, and Protein-Protein Interactions Networks,” and 3.6 “Social Networks,” indeed an iterative, developmental universality. See also “Modularity, Comparative Embryology and Evo-Devo” by Shigeru Kuratani in this journal (332/1, 2009), and “Hierarchical Evolution of Animal Body Plans” in Developmental Biology (337/1, 2010) by Jiankui He and Michael Deem.
In our review of the empirical evidence, we will show that natural and man-made systems employ modularity to a non-zero extent. That is, we will show that the polynomial approximation achieved by modularity and hierarchy has evolved in real networks. Modularity has been observed in all parts of biology on scales from proteins and genes to cells, to organs, to ecosystems. Proteins are often made up of almost independent modules, which may be exchanged through evolution. Topological Analysis of networks of genes or proteins has revealed modularity as well. Motifs and modules have been found in transcriptional regulation networks, and modules have been found across all scales in metabolic networks. Animal body plans can also be decomposed into clear structural or functional units. Food webs also show compartmentalization. Thus, a hierarchy of modules can be observed that spans many scale of biology. (130)
Ma’ayan, Avi. Complex Systems Biology. Journal of the Royal Society Interface. Vol. 14/Iss. 134, 2017. The director of the Mount Sinai Center for Bioinformatics, New York City, provides a succinct survey of this thirty year scientific endeavor to perceive and quantify a natural and social anatomy and physiology. We note for 1987 James Gleick’s Chaos book and the Santa Fe Institute (which I visited that summer). Into the later 2010s, as noted, e.g., in Figure 1, an expansive, self-similar synthesis from iconic cellular form and function to a dynamic cities can be achieved whence many almost exact copies of agents populate new complex environments and complex environments gradually congeal into complex agents. See also Lean Big Data Interpretation in Systems Biology and Systems Pharmacology by Ma’ayan, et al in Trends in Pharmacological Sciences (35/9, 2014).
Mainzer, Klaus. Challenges of Complexity in the 21st Century. European Review. 17/2, 2009. An “Interdisciplinary Introduction” to a special issue on the topic, whose articles by Jean-Marie Lehn, Peter Schuster, Wolf Singer, and Gunter Schiepek and others range from systems chemistry to self-organizing brains and psychotherapies. But however aptly dynamic self-organization can bring a novel theoretical explanation to every such realm, it has yet to dawn that a radically kind of genesis universe is thus implied and revealed.
Structures in nature can be explained by the dynamics and attractors of complex systems. They result from collective patterns of interacting elements that cannot be reduced to the features of single elements in a complex system. Nonlinear interactions in multi-component systems often have synergetic effects that can neither be traced back to single causes nor be forecast in the long run. The mathematical formalism of complex dynamical systems is taken from statistical physics. (223)
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)
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)
McDonough, John and Andrzej Herczyhski. Fractal Patterns in Music. arXiv:2212.12497. grace and move our human scores, an actual music and songs of the spheres. The opus chosen are Handel’s The Harmonious Blacksmith, Haydn’s Piano Sonata No. 53, The Planets: Uranus by Holst, onto Sonata in A Major by Scarlatti and others. By one more melodious composition our 21st century and 2020s complexity sciences continue to perceive and listen to a common veracity and universal reprise. See also Kulkarni, Suman, et al. Information Content of Note Transitions in the Music of J. S. Bach by Suman Kulkarni, et al at 2301.00783.
If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms. While a variety of statistical tools have been proposed to analyze time series in sound, no consensus has as yet exists as a good measure of complexity in music. Here we offer a new approach based on the self-similarity of the melodic lines at various temporal scales. Our definition of the fractal dimension is based on a temporal scaling hierarchy and the tonal contours of its musical motifs. These concepts are tested on “musical” Cantor Sets and Koch Curves and then applied to selected masterful compositions spanning five centuries. (Excerpt)
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)
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.”
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