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IV. Ecosmomics: A Survey of Nonlinear Complex Network Sciences

This central chapter will portray the genomic basis of a 21st century animate revolution by way of sorting into circa 2000, 2010, and 2020 phases. We do so to convey a scientific ascent from homo to anthropo and Earthropo sapience, along with how this subject field went through stages of early, disparate takes to a maturing coalescence and onto a current distillation and synthesis into one, common, gender=based, naturome code.

2000: We ought to open with a referral to prior intimations. As noted in An Anthropocosmic Code, at the heart of wisdom is a luminous relation by which to relate Earth and heaven, human and Divine. This correspondence recurs at each scale and instance because everything arises from and epitomizes a singular, complementary source. Our engendered microcosm is thus an iconic reflection of a numinous macrocosm. The opus work, then as now, is to realize that this existant abide is distinguished by an innate, discernable quality. That is to say, it comes with a code we are made and meant to read and write. A favorite image is Yin and Yang, whose feminine and masculine aspects reside within a triune, familial whole.

But this portal was set aside as a 17th to 20th mechanical science (a necessary spiral turn) went on to reduce cosmos and matter to benthic particles and theories, sans nay identity or purpose. Only just now is a novel humankind compass finding an ordained multi-level, iterative arrangement, this time over the temporal expanse of an evolutionary genesis. Its late version is expressed by Rosetta-like translations of the sciences of nonlinear, self-organizing, networked complexity. Here is an indicative quotation from the day, followed brief entries to rudimentary topics and approaches, then just getting going.

In the 1980’s and 1990’s we are witnesses to a new paradigmatic shift in science. Theorists in many fields are moving away from linear, reductionist, simple cause-effect models toward confronting the challenges of complex adaptive systems. Such systems are found in fields as diverse as astrophysics and economics, cerebral neurobiochemistry and cognitive psychology. (Harold Morowitz, Jerome Singer)

Nonequilibrium Thermodynamics A theory of energy and information flow, usage, and dissipation for open living systems. (Ilya Prigogine)

Fractal Geometry Nature displays the same shapes and topologies with fractional dimensions at every scale. (Benoit Mandelbrot)

Complex Adaptive Systems Many agents (neurons, people) in local interaction, guided by rules or norms give rise to an emergent order. (John Holland, Murray Gell-Mann)

Self-Organization As these systems proceed without central direction, they arrange into a nested scale of whole entities. (Stuart Kauffman, et al)

Universality Similar self-organized complex adaptive network dynamics are found throughout nature from cosmos to civilization. (Eugene Stanley, Mark Buchanan)

Modularity Complex systems tend to form modular, symbiotic components and processes from genes to societies. (Herbert Simon, Gunter Wagner)

Autopoiesis Such bounded, animate systems make and maintain themselves by referring to an internal description. (Humberto Maturana, Francisco Varela)

Self-Organized Criticality Whereby complex dynamic systems seem to become poised at the edge of order and chaos. (Per Bak)

Scale-Free Networks Elemental nodes interlink from cellular metabolisms to ecosystems and the Internet. (Albert-Laszlo Barabasi, Duncan Watts)

Synergetics A more physically based theory of a universal self-organization. (Herman Haken, Scott Kelso)

Artificial Life Computer simulation of molecular, genetic, organic, social and economic societies and their evolution. (Chris Langton, Chris Adami)

Cellular Automata A computational process based on simple, algorithmic rules which self-assemble into an emergent order. (Stephen Wolfram)

Hierarchy Theory Evolving organisms and ecosystems deploy into a scalar sequence and arrangement. (Stan Salthe, Niles Eldredge)

Neural Networks The brain is built and works by multiple networks of neurons, synapses and axons in constant flux due to weighted inputs and experience. (John Hopfield, Stephen Grossberg)

Connectionism A cognitive theory of how neurons compute and handle information, aka parallel distributed processing. (David Rumelhart)

Synchronicity Phenomena from electrons and fireflies to planetary orbits synchronize in unison, which gives rise to orderly forms. (Steven Strogatz)

A vital observation is that few generic components or activities distinguish the ubiquitous system. Whether bacterial assemblies, financial investors or a scientific endeavor as we just saw, many entities interact, and communicate, guided by common rules and norms, from which an overall, adaptive organization arises . A reciprocal interplay of free agents and local interactions, nodes and links in network terms, can be indentified in each case. In this guise they can be seen to form complements of particulate and holistic, discrete and systematic, dot and connect phases.

As this natural activity goes through its cycle or spiral of self-emergence, a standard sequence is traced. In its initial stages, units or elements (microbes, neurons, organisms, researchers) propagate and compete. As densities increase, a modular division of labor occurs. Constant dialogue occurs whether by chemicals, electric potentials, behaviors or language. In time cooperation succeeds over competition. At a threshold of viable coherence, a new whole scale of relative individuality is achieved. We now move on to a 2010 writeup I did for readers who asked for an accessible, introductory survey.

2010: As Habitable UniVerse above documents an ongoing revolution unto an organic genesis ecosmos, it ought to be an equivalent genetic code. A concurrent endeavor of theoretical mathematics across physical, biologic and cultural phases is indeed describing a natural uniVerse to human genotype. In response, I posted a Global Glossary of some 32 working terminologies, subject, personal views, and more within a broad nonlinear complex network systems approach. The topical array from 10 years before has is now reached a stage of gaining mature, evidential definitions. A good book introduction is Complexity: A Guided Tour by the Portland State University scientist Melanie Mitchell (Oxford, 2009). We open quotes from this work, a subject listing, which then can be sorted sorts into certain areas.

All the systems I described above consist of large networks of individual components (ants, cells, neurons, stock-buyers, Web-site creators), each typically following relative simple rules, with no central control or leader. It is the collective actions of vast numbers of components that give rise to the complex, hard to predict, and changing patterns of behavior that fascinate us. (12)

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)


Agent-Based Modeling, Artificial Life, Autopoiesis, Biosemiotics, Cellular Automata, Chaos Theory, Complex Adaptive Systems, Computational Information, Developmental Systems Theory , Dissipative Structures, Dynamical Systems Theory, Econophysics, Emergence, Fractal Geometry, General Systems Theory, Hierarchy Theory, Multi-Agent Systems, Neural Networks, Non-equilibrium Thermodynamics, Nonlinear Phenomena, Renormalization Group Theory, Scale-Free Networks, Scale Invariance, Self-Organized Criticality, Self-Organization, Small-World Network, Statistical Physics, Swarm Intelligence, Synergetics, Synergy, Universality.

Generic Complex System Agent-Based Modeling, Complex Adaptive System, Multi-Agent Systems

Complexity Sciences Nonlinear Phenomena, (Dynamical) Chaos Theory, Emergence

Computer-Based Techniques Cellular Automata, (Digital) Computation Information, Swarm Intelligence

Earlier & Other Versions General Systems Theory, Statistical Physics, Nonequilibrium Thermodynamics, Renormalization Group Theory

Topological Aspects Fractal Geometry, Self-Similarity, Hierarchy, Scale Invariance

CS Features Self-Organization, Autopoiesis, Scale-Free Networks, Self-Organized Criticality, Synergy, Small World, Universality

Field Specific Approaches Dynamical Systems Theory (Evolution), Developmental Systems Theory (Psychology), Neural Networks (Brain), Biosemiotics (Language), Econophysics (Social)

Agent-Based Modeling “An agent-based model (ABM) is a class of simulations for the interactions of autonomous agents (both individual and collective entities such as organizations or groups) with a view to assessing their effects on the system as a whole. It combines elements of game theory, complex systems, emergence, computational sociology, multi-agent systems, and evolutionary programming. (Wikipedia) A tendency carried over from reductive particle or object analysis has been to place more weight on the entity or element component of a CS rather than the connections.

Artificial Life “While processes of self-organization, reproduction, learning, adaptation and evolution are in nature confined to the biological sphere, they can be duplicated in principle in computer simulations.” This approach researches via high speed computations how digital and analog equations are able to graphically simulate and model life from the bottom-up. Since organic forms do follow from genomic programs, it became rather easy to do.

Autopoiesis A neologism coined by Chilean biologists Humberto Maturana and Francisco Varela in the 1970s to emphasize how living systems are involved with “self-making” as they strive to maintain a bounded viability. This occurs by referring to and reapplying the internal descriptive processes that originally constituted them. In this view, all life from an original ur-protocell to multicellular organisms is characterized by a propensity to form and maintain closed entities with their own included meaning. An accessible book by these scholars is Tree of Knowledge (1992) while >i>The Enactive Mind by Varela, Evan Thompson, and Eleanor Rosch takes the theory to cognitive domains.

Biosemiotics “Biosemiotics is an interdisciplinary research agenda investigating the myriad forms of communication and signification found in and between living systems. It is thus the study of representation, meaning, sense, and the biological significance of codes and sign processes, from genetic code sequences to intercellular signaling processes to animal display behavior to human semiotic artifacts such as language and abstract symbolic thought.” (International Society for Biosemiotic Studies)

Cellular Automata Wikipedia has an extensive but technical posting for this computation driven approach. The term means the use of graphic “cells” or boxes to which one of two values are typically ascribed. As various software programs run they spin out highly intricate forms, some of which look a lot like organisms. A famous initiator and theorist is Stephen Wolfram as per his 2002 tome A New Science of Life.

Chaos Theory “A field of study in mathematics, physics, economics and philosophy to observe the behavior of dynamical systems that are highly sensitive to initial conditions, often referred to as the butterfly effect. Small differences in initial conditions yield widely diverging outcomes for chaotic systems, rendering long-term prediction generally not possible.” This misnomer has stuck since the 1980s from early inklings that apparently chaotic behavior actually exhibits mathematical regularities. James Gleick’s popular 1987 Chaosbook is a landmark introduction to the whole endeavor.

Complex Adaptive Systems Again CAS are distinguished by many semi-autonomous parts or entities engaged in relational interaction, via communication by tacit rules or norms, from which emerges novel, feasible, organizations. The presence of this complementarity might even be taken to infer masculine and feminine principles.

Computational Information “In physics and cosmology, digital physics is a collection of theoretical perspectives based on the premise that the universe is describable by information, and therefore computable.” All these areas involve hyperfast computers, so often slip into such as emphasis. In its purview, software algorithms iteratively and recursively which give rise to increasingly complex, material ‘hardware’ forms.

Developmental Systems Theory “Developmental systems theory (DST) is a collection of models of biological development and evolution that argue that the emphasis the modern evolutionary synthesis places on genes and natural selection as explanation of living structures and processes is inadequate. DST embraces a range of positions, from a need to include more explanatory reasons than genes and natural selection, to the view that evolutionary theory profoundly misconceives the nature of living processes.” A main formulator is biotheorist Susan Oyama’s 2001 work Cycles of Contingency.

Dissipative Structures A term associated with nonequilibrium thermodynamics with regard to open systems that receive and process energy and information to maintain and foster their viability with any excess dissipated. A closed system, by contrast, has no such outside inputs, and is a inappropriate standard carried over from inorganic, equilibrium phenomena studies.

Dynamical Systems Theory Another DST, this time as an employ of complexity insights by Indiana University psychologists Esther Thelen, Linda Smith, and others to study the kinetic, behavioral, linguistic and cognitive maturation of infants and children. The approach has caught on and is now used by many practitioners such as Scott Kelso, Alan Fogel, Marc Lewis, Kathleen Nelson, and in the Netherlands, Paul van Geert.

Econophysics An interdisciplinary field that combines statistical, many-body physics with nonlinear dynamics to illume complicated economics issues and policies. A main founder is Boston University systems sage Eugene Stanley. From tentative beginnings in the 1990s, the field has taken hold worldwide. The technical journal Physica A: Statistical Physics and others now contain many papers as an example of the welling meld of physics and complex systems.

Emergence “In philosophy, systems theory, science, and art, emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. Emergence is central to the theories of integrative levels and of complex systems.” This abstract term for regnant, cognizant life is often posed as a positive alternative to a mechanical, reductive disassembly of nature. A prime expositor is theologian Philip Clayton, as conveyed in his Mind and Emergence: From Quantum to Consciousness (Oxford, 2004).

Fractal Geometry A fractal is "…a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole.” A mathematical fractal results from a software equation or algorithm that is recursively run again and again. A fractal shape is too irregular to be described by planar Euclidean geometry, and has a ‘self-similar’ affinity across its myriad nested dimensions. Natural objects approximated by fractals are clouds, mountain ranges, lightning bolts, coastlines, snow flakes, flora like cauliflower and broccoli, and animal coloration patterns, that is just about everything.

General Systems Theory From the 1950s into the 1980s, along with its cousin cybernetics, this was the main school in prescient search for holistic integrations of an organismic nature. A tacit inspiration was the hope of finding a common code everywhere. An expositor was Ludwig Von Bertalanffy in a 1968 book by this title, another opus is Living Systems by James G. Miller (McGraw Hill, 1976).

Hierarchy Theory “Hierarchies are ordinations, as from smaller to larger, or from simpler to more complex. In science-related discourses there have been two forms of hierarchy theory, one based on scale (extension) and another on descriptive complexity (intension).” (Stan Salthe) This is an approach based on the conception that nature consistently arrays itself into scales of beings and becomings.

Multi-Agent Systems Another phrasing of a generic CAS, akin to ABS above, that may be variously adopted by a discipline, e.g. as Applied Anthropology used to model the spread of an epidemic in Baltimore. The phrase gives the impression of still another technique, which it is not.

Neural Networks Brain development and cognitive function has been a major area of CS application as cerebral anatomy and activity become exemplars of self-organization. In CalTech’s John Hopfield proposed the theory in 1982 to explain how neurons are entrained by way of synapses and axons into myriad webworks. As we think, neural nets ever change their ‘weights,’ emphasis, or presence based on the content they receive and convey. A computational version called artificial neural networks or ANN has found use in simulating ecosystems and many other areas.

Nonequilibrium Thermodynamics (This is an edited introduction from A Thermodynamics of Life.) “The sterile, mechanical universe of 19th century theories was conceived as a closed, isolated system tending to equilibrium. As predicted by the second law of thermodynamics, it inexorably expires as available energy is spent as entropy. But a recent revision is underway by which life has become known as an open system infused and organized by a flow of energy and information. The gloomy fate has been superseded by far-from-equilibrium version which can describe and qualify the florescent rise of life and its human phase.”

Nonlinear Phenomena “Nonlinear” has been a generic banner for complexity studies, in contrast to earlier, mainly physical sciences that understandably dealt with simpler “linear” cause and effect. But complex self-organization is not straight-forward, it is affected by small influences at its outset (e.g., the so-called butterfly effect), so that resultant forms and activities can be locally unpredictable. However, as Statistical Physics avers below, large-scale patterns tend to average out and are reliable in outcome.

Renormalization Group Theory “In theoretical physics, the renormalization group refers to a mathematical apparatus that allows one to investigate the changes of a physical system by views at different distance scales.” Renormalization group is formally related to "scale invariance," a symmetry that appears the same at all scales.” We cite this term, first used by the 1975 Nobel physicist Kenneth Wilson, because it occurs in some CS papers.

Scale-Free Networks Simpler object interconnections such as telephones are equal point to point, or ‘random graphs,’ with no characteristic geometry. In the late 1990s Notre Dame physicists Albert-Laszlo Barabasi and Reka Albert realized that nonlinear nature and society was actually graced by a distinctive type of arrangement whereof certain nodes or hubs had many links, while most other had only a few. This insight has since grown into a major field of complex system research. As a result, the same scale or form is repeated in self-similar fashion over and over, e.g., food webs, brains or social media. The Internet is a prime example, which might imply cerebral propensities.

Scale Invariance This is another phrase to denote CS propensities to repeat in kind again and again, often in a layered emergence of the same animate pattern and process. “Self-similarity” is also used to describe this recurrence. Its iconic representation would be geometric fractals, whose infinite repetition arises from iterations of mathematical, software-like equations. Such a constant recapitulation across every natural and social realm from galaxies to Gaia could be taken to infer the presence of an innate, implicate, cosmic genetic-like source.

Self-Organized Criticality A concept mainly from the late Danish scientist Per Bak, well told in his How Nature Works (Springer, 1996), to explain how natural phenomena seems to reside in a dynamic, creative state or zone poised between order and chaos. The phrase and theory is now widely used from origin of life studies to brain cerebration. As a comment, we include this quote from Complexity and Criticality (2005) by Kim Christensen and Nicholas Moloney, which notes a need to get clear, common definitions.

“The word `complexity' takes on a variety of meanings depending on the context, and its official definition is continuously being revised. This is because complexity is a rapidly developing field at the forefront of mathematics, physics, geophysics, economics and biology. And yet, nobody agrees on a clear and concise theoretical formalism with which to study 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 behaviour. Self-organized criticality is a cooperative feature emerging from the repeated application of the microscopic laws of a system of interacting parts.”

Self-Organization “The process where a structure or pattern appears in a system without a central authority or external direction. A globally coherent pattern appears from the local interaction of the elements that makes up the system, thus the organization is achieved in a way that is parallel and distributed. The most robust and unambiguous examples of self-organizing systems are from the physics of non-equilibrium processes. Self-organization is also relevant in chemistry, where it is also synonymous with self-assembly. The concept of self-organization is central to the description of biological systems, from the subcellular to the ecosystem level.” (Wikipedia)

“Self-organization is the spontaneous often seemingly purposeful formation of spatial, temporal, spatio-temporal structures or functions in systems composed of few or many components. In physics, chemistry and biology self-organization occurs in open systems driven away from thermal equilibrium. The process of self-organization can be found in many other fields also, such as economy, sociology, medicine, technology.” (Scholarpedia) As opposed to any mechanical or architectural artifact, which are made by outside control, or preset plans, an iconic property of complex systems is their ability to arrange into increasingly multifaceted forms and viability. A prime articulator has been the polymath physician Stuart Kauffman, in his brilliant writings over some 40 years.

Small-World Networks “In mathematics, physics and sociology a small-world network is a type of mathematical graph in which most nodes are not neighbors of one another, but most nodes can be reached from every other by a small number of hops or steps. Social networks, the connectivity of the Internet, and gene networks all exhibit small-world network characteristics.” Circa 1998 Duncan Watts and Stephen Strogatz came up with this mathematical model and name as another perspective on and attribute of scale-free networks, based on how close or remote “nodes” are to each other.

Statistical Physics “A condensed matter or many-body physics that endeavors to explain and predict the macroscopic properties and behavior of a system on the basis of known characteristics and interactions of its microscopic constituents, usually when the number of such constituents is very large. In the past years, the field has branched into complex systems because it was realized that both studied the spontaneous activity of many agents with relational behaviors. An entry example (2010) of this merger might be the Centre for Statistical Mechanics and Complexity, University of Rome, website (Google).

Swarm Intelligence An AI scheme that deals with natural and societal systems composed of many interactive ‘individuals’ that coordinate via distributed control, which engenders self-organization. Examples are colonies of ants and termites, schools of fish, flocks of birds, herds of land animals, along with some artifacts as robot motions.

Synergetics Another method to explain the formation and self-organization of patterns and structures in open systems far from thermodynamic equilibrium. It was fostered from the 1970s by Hermann Haken, a University of Stuttgart laser physicist. In its idiom, self-organization requires a 'macroscopic' system, consisting of many nonlinearly interacting subsystems. A Springer series in Synergetics has published dozens of technical volumes since 1977.

Synergy “Synergy, in general, may be defined as two or more agents working together to produce a result not obtainable by any of the agents independently.” We mention as abstraction in the mix, as used by Peter Corning in his Nature’s Magic: Synergy in Evolution and the Fate of Humankind(2003) about innate propensities for cooperation. Symbiosis would be another take.

Universality “In statistical mechanics, universality is the observation that there are properties for a large class of systems that are independent of the dynamical details of the system.” A word used across the sciences and humanities, which for complexity science means the same dynamical system in evidence from galaxies to genomes to Gaia. Its archetypal attributes would be many interactive agents, scale-free networks, and nested self-organization. If such a ubiquitous repetition can be succinctly articulated, it well infers an independent, creative source, and illumes, as wisdom teaches, nature’s manifest, illustrative repetition. Please see our new, extensive 2020 Introduction and throughout for a vital 21st century affirmation.

A Complex Systems Timeline This arcane array, whereof each vernacular phrase denotes a certain attribute, begs translation unto a familiar human and earth account, as our new introduction attempts. Historically, this movement began in the 1960s with the general systems theory school. A prescient 1980 work The Self-Organizing Universe by Erich Jantsch conveyed its promise. Another milestone was Mitchell Feigenbaum’s 1982 finding that apparent chaos, such as turbulent fluid flow, in fact exhibited mathematical regularities. A breakthrough 1987 book was James Gleick’s Chaos: Making a New Science, which brought the endeavor to popular awareness.

As the usual course, the 21st century complexity project diversified and morphed into technical detail and preferences, aided by computer capacities not before possible. Since the 2000s, scientific studies spread across all natural and societal realms from cosmos to civilization, from astrophysics and genomics to psychology and economics, as these novel insights brought a heretofore elusive theoretical explanation. Each domain from galactic clusters to life’s origin, animal behaviors, disease epidemics, conversational speech, and so on was found to exemplify a complex adaptive system of many interactive agents and interlinked nodes.

In mid course writings on nonlinear systems began to cite and include both modes of a dynamical, recurrent complexity (phenotype) which was so obvious that there must be inferred cause (genotype) from it all arose. Some examples are Self-Organization in Complex Ecosystems by Jordi Bascompte and Richard Sole (2006), and Marten Scheffer’s Critical Transition in Nature and Society (2009). A 2008 paper Collective Behavior in Animal Groups: Theoretical Models and Empirical Studies by Irene Giardina and colleagues at the University of Rome contends that since starling flocks or tuna schools are so composed of autonomous members in beneficial group formations, they clearly infer a mathematic and physical origin.

In the same period, researchers realized that complexity studies and statistical physics were actually dealing with the same phenomena, albeit with different approaches and terms. But what is not yet seen or possible at that time was a philosophia view of a self-creative universe with dual domains of emergent phenotype development and immanent genetic-like source.

2020: To be cited here and in the new site introduction.

Bornholdt, Stefan and Stuart Kauffman. Revisiting the Statistical Mechanics Perspective on Cellular Regulation. arXiv:1902.00483.

Coveney, Peter, et al. Bridging the Gaps at the Physics-Chemistry-Biology Interface. Philosophical Transactions of the Royal Society A. Vol. 374/Iss. 2080, 2016.

Feistel, Rainer and Werner Ebeling. Physics of Self-Organization and Evolution. Weinheim: Wiley-VCH, 2011.

Frame, Michael and Amelia Urry. Fractal Worlds: Grown, Built, and Imagined. New Haven: Yale University Press, 2016.

Holovatch, Yurij, et al. Complex Systems: Physics beyond Physics. European Journal of Physics. 38/023002, 2017.

Lesne, Annick and Michel Lagues. Scale Invariance. Germany: Springer, 2012.

Lin, Yi, et al. Systems Science. Boca Raton: CRC Press, 2012.

Ma’ayan, Avi. Complex Systems Biology. Journal of the Royal Society Interface. Vol. 14/Iss. 134, 2017.

Mero, Laszlo. The Logic of Miracles. New Haven: Yale University Press, 2018.

Meyers, Robert, ed., 2nd edition. Encyclopedia of Complexity and Systems Science. Berlin: Springer, 2020.

Mitchell, Melanie. Complexity: A Guided Tour. Oxford: Oxford University Press, 2009.

Munoz, Miguel. Colloquium: Criticality and Dynamical Scaling in Living Systems. arXiv:1712.04499.

Rosas, Fernando, et al. An Information-Theoretic Approach to Self-Organization. arXiv:1808.05602.

Thurner, Stefan, et al. Introduction to the Theory of Complex Systems. Oxford: Oxford University Press, 2018.

View the 183 Bibliographic Entries

A. An Array of 21st Century Decipherments

1. Network Physics: A Cosmic Connectome

The first title phrase is meant to distinguish this 21st century scientific endeavor from a long, albeit necessary particle focus in this subject field. It reports the expansive witness of nature’s scale-free mode of dynamic interconnections everywhere, originally due much around 2000 to Albert-Laszlo Barabasi and Reka Albert, then Notre Dame University physicists, search each name. In contrast to prior random or Erdos-Renyi graphs, e.g., telephones, natural phenomena from galaxies to genomes, organisms, societies and languages are finely interconnected by a “preferential attachments and growth” of node elements and relational linkages. As such, they contain larger and smaller modules, hubs and communities with more influence. An ever growing list includes galactic and quantum networks, multiplex neural nets, animal and human groupings, onto power grids and Internet websites.

The initial model applied so well that it has, with much updating and expansion, been adopted by every scientific field and realm, as ALB notes in a 2012 Nature Physics article entitled The Network Takeover. Network Science texts by Mark Newman, Shlomo Havlin, Barabasi, and others show how robust this notice of equally real communicative interactions between parts, objects, entities has become. For one instance, their universal presence is evident when one can find daily arXiv e-print site postings such as The Network behind the Cosmic Web (1604.03236) and Mapping Out Narrative Structures and Dynamics Using Networks (1604.03029), where both papers cite these same principles. Publications such as Journal of Complex Networks and Network Neuroscience post theoretical advances such as multiplex core/periphery modes and simplical complexes, along with anatomy, physiology and biomedical applications.

After two decades, we can report a revolution from ecosmos to ecologies that a common structural topology and dynamic growth becomes evident at each phase and instance. This discovery then well implies an independent, universally exemplified, mathematical source. Thus we add Cosmic Connectomics as a subtitle.

2020:

Albert, Reka and Albert-Laszlo Barabasi. Statistical Mechanics of Complex Networks. Reviews of Modern Physics. 74/1, 2002.

Aleta, Alberto and Yamir Moreno. Multllayer Networks in a Nutshell. Annual Review of Condensed Matter Physics. 10, 2019.

Battiston, Federico, et al. Network beyond Pairwise Interactions: Structure and Dynamics. arXiv: 2006.01764.

Biamonte, Jacob, et al. Complex Networks: From Classical to Quantum. arXiv:1702.08459.

Bianconi, Ginestra. Multilayer Networks: Structure and Function. Oxford: Oxford University Press, 2018.

Boguna, Marian, et al. Network Geometry. arXiv:2001.03241

Chavalarias, David. From Inert Matter to the Global Society: Life as Multi-level Networks of Processes. Philosophical Transactions of the Royal Society B. February, 2020.

Cimini, Giulio, et al. The Statistical Physics of Real-World Networks. arXiv:1810.05095.

Gysi, Deisy and Katja Nowick. Construction, Comparison and Evolution of Networks in Life Sciences and Other Disciplines. Journal of the Royal Society Interface. May 2020.

Holse, Petter. Modern Temporal Network Theory. European Physical Journal B. 88/9, 2016.

Mariani, Manuel, et al. Nestedness in Complex Networks: Observation, Emergence, and Implications. Physics Reports. Volume 813, 2019

Newman, Mark. Networks: An Introduction. New York: Oxford University Press, 2018.

Vespignani, Alessandro. Twenty Years of Network Science. Nature. 558/528, 2018.

View the 141 Bibliographic Entries

2. Biteracy: Natural Algorithome Programs

The present Cosmic Code chapter reports a broad array of scientific encounters with nature’s generative propensity to form evolutionary self-organizations of complexity and cognition. From our humankind vista, a revolutionary perception can be noticed of an independent, mathematical program-like agency in procreative effect. Here we collect a range of computational, algorithmic, information-based, cellular automata, meta-biology, evolutionary optimization, analog/digital software, DNA data and more entries. These endeavors often refer to Gottfried Leibniz, to Greece before, and later espeically to Alan Turing so as to trace a heritage in search of an “alphabetic calculus” and “Mathesis Universalis.” In regard, the perennial quest (magnum opus, great work) was in much part to decipher and read a natural logos, a constant source code to avail as an edifying guidance.

This introduction is a 2018 update because recent contributions seem at last to be reaching a robust affirmation. We might list Stephen Wolfram, Gregory Chaitin, Sara Walker, Hector Zenil, Enrico Borriello, Anne Condon, Leroy Cronin, Agoston Eiben, Hyunju Kim, Doug Moore, Paul Davies and more. The achievement is closing upon a common code program behind nature’s universal proclivity to become poised at a reciprocal self-organized criticality, see also Universality Affirmations herein.

Another aspect is in need of airing and review. The phrase “mindless mathematics” has been bandied about (Aguirre 2018), which infers that cosmic nature (or lack thereof) is bereft prescription or purpose. But in actuality a mathematical domain can take two different forms. One is a pure or applied mode, such as arithmetic. Each day on the arXiv preprint site some 200 entries appear under Mathematics. But its Computer Science section reports on computational software which does carry information. Each day some 300 contributions are listed. So we may have an arithmetic to which “mindless” might apply, and maybe an “algorithmetic” version that does contain, or has a fmindful capacity for narrative message.

And finally, we introduce “Biteracy,” a word which does not come up in a Google search. As the section title alludes, natural algorithms have roots in John Holland’s 1970’s original genetic version, with many extensions since, see Xin-She Yang. But we refer to John A. Wheeler’s familiar “bit to it” arc which courses from an informative (quantum) origin through an oriented evolution to vital human observers and recorders. An inference could be that we regnant peoples arrive as the way a participatory uniVerse learns to decipher, read, and intentionally take forth its own genomic endowment.

2020:

Kaznatcheev, Artem. Evolution is Exponentially More Powerful with Frequency-Dependent Selection. bioRxiv. May 3, 2020.

Brabazon, Anthony, et al. Natural Computing Algorithms. Berlin: Springer, 2015.

Condon, Anne, et al. Will Biologists Become Computer Scientists? EMBO Reports. 19/9, 2018.

De Castro, Leandro Nunes. Fundamentals of Natural Computing. Boca Raton: Chapman & Hall/CRC, 2006.

Domingos, Pedro. The Master Algorithm. New York: Basic Books, 2015.

Erwig, Martin. Once Upon an Algorithm: How Stories Explain Computing. Cambridge: MIT Press, 2017.

Manca, Vincenzo. The Principles of Informational Genomics. Theoretical Computer Science. 701/190, 2017.

Mayfield, John. The Engine of Complexity: Evolution as Computation. New York: Columbia University Press, 2013.

Sommaruga, Giovanni and Thomas Strahm, eds. Turing’s Revolution. Switzerland: Birkhauser, 2015.

Stepney, Susan, et al, eds. Computational Matter. International: Springer, 2018.

Valiant, Leslie. Nature's Algorithms for Learning and Prospering in a Complex World. New York: Basic Books, 2013.

Wolfram, Stephen. Logic, Explainability and the Future of Understanding. Complex Systems. 28/1, 2019.

Xu, Lei. Bayesian Ying-Yang Harmony Learning. Applied Informatics. Online June, 2016.

View the 98 Bibliographic Entries

3. A Rosetta Ecosmos Literacy: Systems Linguistics

This module began in 2004 as a place to convey perceptions of an innate natural textuality written in an edifying script that newly literate humans were invited and meant to decipher and read. Into the later 2000s, as the complexity sciences grew in veracity, it was realized that fractal scales and dynamic self-organizations could apply to and are ingrained across written literature and spoken conversation. This project has variously expanded in the 2010s to a quantum compositionality (Coecke, Aerts), a statistical physics basis (Burridge), mathematic patterns in mythologies (Kenna, et al), and so on. Other sections such as The Book of Naturome, An Informational Source and Emergent Genetic Information also have apropos citations.

2020: As many other sections, the realization that even our vernacular languages and lingua franca are reflections of nature’s complex regulatory systems, which are expressed from quantum origins to paper and ebook libraries, has not yet come into public awareness. Again, we offer the 2020 Introduction and resource website as a way to make known this vital dispensation just in our midst.

Baez, John and Mike Stay. Physics, Topology, Logic and Computation: A Rosetta Stone. Coecke, Bob, ed. New Structures in Physics. Berlin: Springer, 2011.

Bloch, William Goldbloom. The Unimaginable Mathematics of Borges’ Library. Oxford: Oxford University Press, 2008.

Bost, Xavier and Vincent Labatut. Extraction and Analysis of Fictional Character Networks. ACM Computing Surveys. 52/5, 2019.

Burridge, James. Spatial Evolution of Human Dialects. Physical Review X. 7/031008, 2017.

De Looze, Laurence. The Letter and the Cosmos. Toronto: University of Toronto Press, 2016.

Esposti, Mirko, et al, eds. Creativity and Universality in Language. Switzerland: Springer International, 2016.

Kenna, Ralph, et al, eds. Maths Meets Myths: Quantitative Approaches to Ancient Narratives. International: Springer, 2017.

Massip-Bonet, Angels and Albert Bastardas-Boada, eds. Complexity Perspectives on Language, Communication and Society. Berlin: Springer, 2013.

Mufwene, Salikoko, et al. Complexity in Language: Developmental and Evolutionary Perspectives. Cambridge: Cambridge University Press, 2017.

Torre, Ivan, et al. On the Physical Origin of Linguistic Laws and Lognormality in Speech. Royal Society Open Science. 6/8, 2019.

Westling, Louise. The Logos of the Living World. New York: Fordham University Press, 2014.

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4. Universality Affirmations: A Critical Complementarity

This is a new 2016 section to report an increasing scientific witness and confirmation of an evolutionary developmental genesis that iteratively repeats itself in exemplary kind at every phase and instance from universe to us. A distillation is underway from self-organizing, complex adaptive network systems to a single, iconic particle/wave, DNA/AND, node/link complementarity and whole triality. So as we track the global literature, citations of a true “universality” are now being admitted. We cite next a summary for a 2018 Stochastic Models in Ecology and Evolutionary Biology conference, (search Venice), as a good example.

Living systems are characterized by the emergence of recurrent dynamical patterns at all scales of magnitude. Self-organized behaviors are observed both in large communities of microscopic components - like neural oscillations and gene network activity - as well as on larger levels - as predator-prey equilibria, to name a few. Such regularities are deemed to be universal in the sense they are due to common mechanisms, independent of the details of the system. This belief justifies investigation through quantitative models able to grasp key features while disregarding inessential complications.

Fast forward to 2020, this perception has become known as a “self-organized criticality” between opposite but reciprocal domains of more or less order in dynamic balance. As our worldwide learning curve rises, new entries from physics to neuroscience (Stuart Kauffman, William Bialek, Miguel Munoz, Dante Chialvo, et al) report that living systems seem to seek and prefer an active repose between such complementary states. These dual, polar states take on archetypal modes such as conserve and create, maintain and evolve. A technical version of this natural attractor is cited as a chimera condition (Zakharova, Bastidas, et al) whence “coherence and incoherence” coexist at the same time.

Another salient indication is the wide-ranging employ of (artificial) neural networks, along with genetic sequencing techniques, to study disparate realms from quantum phases to the gamut of cosmic, creaturely and societal realms. In similar regard, algorithmic, self-organizing map, astroinformatic, statistical physics, phylogenetic tree and other methods are being repurposed to quantify areas from galaxies and chemistry to language and ecosystems.

And it ought to be noticed that this epic discovery (see Ecosmomics intro) appears to imply and represent gender principles, yang and yin once again within a Taome trinity. How neat it would be if a bicameral sapiensphere learning on her/his own, could gain such 2020 binocular vision of a family ecosmos. And how wonderful if political parties locked destructive conflict could reinvent themselves as entity/empathy, animus/anima, particle/pattern, me + we = US mutually beneficial halves

2020: From general systems theory in the 1960s, the 1980s Santa Fe Institute and further afield, the deep motivation of the complexity science project was to find a singular source code which infinitely recurs in self-similar kind everywhere. This once and future work, decipherment and avail can be the built-in heart secret dispensation we so need. It is our main purpose, via EarthKinder 2020, to bring this vital realization into common public. (Please view these missives as a work in process)


Bala, Arun. Complementarity beyond Physics. Basingstoke, UK: Palgrave Macmillan, 2017.

Chialvo, Dante. Life at the Edge: Complexity and Criticality in Biological Function. arXiv:1810.11737.

Daniels, Bryan, et al. Criticality Distinguishes the Ensemble of Biological Regulatory Networks. Physical Review Letters. 121/138102, 2018.

Hidalgo, Jorge, et al. Cooperation, Competition and the Emergence of Criticality in Communities of Adaptive Systems. Journal of Statistical Mechanics. March/033203, 2016.

Kartvelishvili, Guram, et al. The Self-Organized Critical Multiverse. arXiv:2003.12594.

Kim, Hyunju, et al. Universal Scaling Across Biochemical Networks of Earth. Science Advances. 5/eaau0149, 2019.

Munoz, Miguel. Colloquium: Criticality and Dynamical Scaling in Living Systems. Reviews of Modern Physics. 90/031001, 2018.

Roli, Andrea, et al. Dynamical Criticality. Journal of Systems Science and Complexity. 31/3, 2018.

Tadic, Bosiljka. Self-Organized Criticality and Emergent Hyperbolic Networks. European Journal of Physics. 40/2, 2019.

Villani, Marco, et al. Evolving Always-Critical Networks. Life. 10/3, 2020.

Wilting, Jens and Viola Priesemann. 25 Years of Criticality in Neuroscience. arXiv:1903.05129.

Zurn, Perry and Danielle Bassett. Network Architectures Supporting Learnability. Philosophical Transactions of the Royal Society B February 2020.


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B. Our Own HumanVerse Genome Studies

In Part III, The Information Computation Turn, we saw how space, time, matter and energy is becoming seen as suffused by an informative, program-like quality. Part IV, Cosmic Code, went on to document such an independent procreative system, while Part V, A Quickening Evolution, reported humankind’s nascent integral synthesis of the oriented, gestation of life, mind and self-cognizance. This extensive Part VI, Earth Life Emergence, will attempt to show how these innate, genetic-like, complementary principles are in similar manifestation everywhere. To continue this scenario, its most familiar exemplar, of course, is the genome code that informs the form, function and life span of every organism and person. Since circa 2001, with the sequencing of the human genome, a whole scale revision has been underway as to what constitutes genetic phenomena, broadly considered, which is still being worked out. This section will try to chronicle the many concerted efforts, see also Systems Biology and Genetics above.

While the last half of the 20th century from the 1953 DNA double helix sought to find the nucleotide and associated biomolecules, as readers know, a “systems” turn has begun to study the equally present dynamic regulatory networks that connect all the pieces. In regard, what defines a “gene” is still in abeyance, e. g. strings of codons. With this expansion, a new aspect known as “epigenetics” has opened opens to many external, environmental influences in effect beyond a point molecular locus. So once again the universal complex archetypes of a discrete elemental mode - DNA, along with the interactive relations - AND, with their informative content and communication, are well exemplified.

With these advances, as readers know a multitude of “-omics” have sprung up and taken across every organic scientific field and stage. Proteome, metabolome, cellular interactome, a neural connectome, are among many, each distinguished by an interplay of nodes and links. Thus an emergent genetic phenomena accrues as a fertile cosmos becomes graced with a genome-like essence everywhere. As an example, the popular “major evolutionary transitions” emergence by John Maynard Smith and Eors Szathmary (search & shown next) whence life’s episodic procession from suitable biochemicals to our human phase is at each step facilitated by a novel informative basis. Its linguistic version, one could even say “languagome,” is covered in A Cultural Code.

2020:

Barabasi, Daniel and Albert-Laszlo Barabasi. A Genetic Model of the Connectome. Neuron 105/1, 2020.

Cobb, Matthew. Life’s Greatest Secret: The Race to Crack the Genetic Code. New York: Basic Books, 2015.

Cowen, Lenore, et al. Network Propagation: A Universal Amplifier of Genetic Associations. Nature Review Genetics. 18/551, 2020.

Eraslan, Gokcen, et al. Deep Learning: New Computational Modelling Techniques for Genomics. Nature Reviews Genetics. 20/7, 2019.

Field, Dawn and Neil Davies. Biocode: The New Age of Genomics. New York: Oxford University Press, 2015.

Koonin, Eugene and Artem Novozhilov. Origin and Evolution of the Universal Genetic Code. Annual Review of Genetics. 51/45, 2017.

McGillivray, Patrick, et al. Network Analysis as a Grand Unifier in Biomedical Data Science. Annual Review of Biomedical Data Science. Vol. 1, 2018.

Mukherjee, Siddhartha. The Gene: An Intimate History. New York: Scribner, 2016.

Watson, James, et al. DNA: The Story of the Genetic Revolution. New York: Knopf, 2017.

Zimmer, Carl. She Has Her Mother’s Laugh: The Powers, Perversions, and Potential of Heredity. New York: Dutton, 2018.

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1. Paleogenomics, Archaeogenomics: Natural Ancestry

This circa 2015 section is added to gather historic expansions of genetic research techniques so as to begin to recover and reconstruct all manner of prior entities, migrations, timelines and more. By this vista, a temporal “paleo” evolutionary retrospect across a span biospheric creatures from insects to sapiens can be perceived. As the entries describe, incipient attempts began in the 1980s and 1990s to recreate the DNA genomes of hominids and primates. After the 2001 Human Genome project, aided by sophisticated instruments and computer informatics, it became increasingly possible to sequence any present or past entity from Neanderthals and hominids to dinosaurs and onto invertebrates.

A companion effort is the ENCODE: Encyclopedia of DNA Elements project, which began in 2003 and proceeds apace with advanced genome sequencing. In February 2015 a similar discernment of the multifaceted Human Epigenome was announced. Together with the molecular nucleotide substrate, this much expanded appreciation of genetic phenomena promises many benefits. If we might reflect upon and extrapolate these abilities, collaborative human beings over round Earth might well seem to be the universe’s way, billions of years on, to achieve a whole-scale self-sequence of its own natural genetic code.

2020: A revolutionary approach and window is thus opened for kinderkind sapience to turn about and revision how it all came to be. And so to muse, what manner of self-realizing, selecting and cocreating phenomenal occasion are we coming upon?

Benitez-Burraco, Antonio and Dan Dediu. Ancient DNA and Language. Journal of Language Evolution. 3/1, 2018.

Ermini, Luca, et al. Major Transitions in Human Evolution Revisited: A Tribute to Ancient DNA. Journal of Human Evolution. Volume 79, 2015.

Harris, Eugene. Ancestors in Our Genome: The New Science of Human Evolution. Oxford: Oxford University Press, 2014.

Llamas, Bastien, et al. Human Evolution: A Tale from Ancient Genomes. Philosophical Transactions of the Royal Society B. Vol.372/Iss.1713, 2016.

Paabo, Svante. Neanderthal Man: In Search of Lost Genomes. New York: Basic Books, 2011.

Racimo, Fernando, et al. Beyond Broad Strokes: Sociocultural Insights from the Study of Ancient Genomes. Nature Reviews Genetics. June 2020.

Reich, David. Ancient DNA and the New Science of the Human Past. New York: Pantheon, 2018.

Skoglund, Pontus and Iain Mathieson. Ancient Human Genomics: The First Decade. Annual Review of Genomics and Human Genetics. Vol. 19, 2018.

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2. The Deep Affinity of Genomes and Languages

Around 1970, the linguist Roman Jakobson and the biopsychologist Jean Piaget opined that these prime informational domains ought to have common similarities. The familiar phrase Book of Life, along with analogous usage of language terms in genetics was popular at the time. Over subsequent decades, as gathered herein, parallels between the two code scripts grew in veracity and value, often as an insightful cross-comparison. We post this 2016 section because recent contributions strongly confirm an innate, natural continuity. A March 2016 issue of the Philosophical Transactions of the Royal Society A on “DNA as Information” (J. Cartwright) supports this view by novel rootings of genome phenomena in mathematics, physics and chemistry.

2020: As our worldwise personsphere arises to learn on her/his own, a ecosmic textual, poetic narrative naturone seems at last being presently translated and legible.

Bolshoy, Alexander, et al. Genome Clustering: From Linguistic Models to Classification of Genetic Texts. Berlin: Springer, 2010.

Cartwright, Julyan, et al. DNA as Information. Philosophical Transactions of the Royal Society A. Vol.374/Iss.2063, 2016.

Faltynek, Dan, et al. On the Analogy between the Genetic Code and Natural Language by Sequence Analysis. Biosemiotics. Online April, 2019.

Igamberdiev, Abir and Nikita Shklovskiy-Kordi. Computational Power and Generative Capacity of Genetic Systems. BioSystems. 142-143/1, 2016.

List, Johann-Mattis, et al. Networks of Lexical Borrowing and Lateral Gene Transfer in Language and Genome Evolution. BioEssays. Online December, 2013.

Muskhelishvili, Georgi. DNA Information: Laws of Perception. Berlin: SpringerBriefs in Biology, 2015.

Searls, David. A Primer in Macromolecular Linguistics. Biopolymers. 99/3, 2013.

Zolyan, Suren and Renad Zhdanov. Genome as (hyper)Text: From Metaphor to Theory. Semiotica. 225/1, 2018.

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3. Whole Genome Regulatory Systems: DNA + AND

As our emergent sapiensphere proceeds to learn on her/his own, we add a 2015 section akin to other natural Systems units because genetic phenomena, with the internal components now identified and sequenced, are being seen and treated by the same informational, self-organized, complex modular network criticalities as everywhere else. In this Omics era whole genomes appear as a prime exemplar of this independent mathematical source. Nodal DNA nucleotides + connective AND networks array across dynamic scales to inform and guide life’s evolutionary gestation, each myriad creature, ourselves, and a celestial ovoGenesis. Gene regulatory networks (GRNs) which connect nucleotides and biomolecules are receiving concerted notice, as references attest.

2020: As genomes become altogether envisioned as composite wholes, they join other phases from quantome to neurome and geonome on the way to a nascent ecosmic Omicsphere.

Angelin-Bonnet, Olivia, et al. Gene Regulatory Networks. arXiv:1805.01098.

Capozziello, Salvatore, et al. The Chern-Simons Current in Systems of DNA-RNA Transcriptions. Annalen der Physik. 530/4, 2018.

Cortini, Ruggero, et al. The Physics of Epigenetics. arXiv:1509.04145.

Cowen, Lenore, et al. Network Propagation: A Universal Amplifier of Genetic Associations. Nature Reviews Genetics. 18/9, 2017.

Daniels, Bryan, et al. Logic and Connectivity Jointly Determine Criticality in Biological Gene Regulatory Networks. arXiv:1805.01447.

Finn, Elizabeth and Tom Misteli. Molecular Basis and Biological Function of Variability in Spatial Genome Organization. Science. 365/998, 2019.

Grimbs, Anne, et al. A System-Wide Network Reconstruction of Gene Regulation and Metabolism in Escherichia coli. arXiv:1803.05429.

Szedlak, Anthony, et al. Evolutionary and Topological Properties of Genes and Community Structures in Human Gene Regulatory Networks. PLoS Computational Biology. Online June, 2016.

Verd, Berta, et al. Modularity, Criticality, and Evolvability of a Developmental Gene Regulatory Network. eLife. 8/e43832, 2019.

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