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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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VI. Earth Life Emergence: Development of Body, Brain, Selves and Societies

A. A Survey of Common Principles

Frank, Steven. The Invariances of Power Law Distributions. arXiv:1604.04883. The UC Irvine mathematical biologist continues his insightful articulation of intrinsic natural patterns and processes across evolutionary nature. Search here and the e-print site for more papers. In this entry, scaling relations from trees to forests are seen to reveal a universal invariance similar to form and function phenomena found in kind everywhere else. Once again we seem to be closing on a grand genesis vista from universe to human by way of some such genomic influence just waiting to be discovered. See also his Common Probability Patterns Arise from Simple Invariances at 1602.03559.

Why does the complexity of nature reduce to such a simple pattern? Why do things as different as tree size and enzyme rate follow similarly simple patterns? Here, I analyze such patterns by their invariant properties. For example, a common pattern should not change when adding a constant value to all observations. Stretch invariance corresponds to the conservation of the total amount of something, such as the total biomass and consequently the average size. Rotational invariance corresponds to pattern that does not depend on the order in which underlying processes occur, for example, a scale that additively combines the component processes leading to observed values. I use tree size as an example to illustrate how the key invariances shape pattern. A simple interpretation of common pattern follows. That simple interpretation connects the normal distribution to a wide variety of other common patterns through the transformations of scale set by the fundamental invariances. (Abstract)

Frank, Steven and Jordi Bascompte. Invariance in Ecological Pattern. arXiv:1906.06979. UC Irvine and University of Zurich system theorists join their common studies across life’s evolutionary and environmental species to presently be able to advance and affirm nature’s infinite propensity to repeat self-similar forms and processes in kind at each and every creaturely and communal scale and instance.

The abundance of different species in a community often follows the log series distribution. Why does the complexity and variability of ecological systems reduce to such simplicity? This article proposes a more general answer based on the concept of invariance, the property by which a pattern remains the same after transformation. Invariance has a long tradition in physics. By bringing this unifying invariance approach into ecology, one can see that the log series pattern of species abundances dominates when the consequences of density dependent processes are invariant to addition or multiplication. Recognizing how these invariances connect pattern to process leads to a synthesis of previous approaches. (Abstract excerpt)

Frey, Erwin, et al. Protein Pattern Formation. arXiv:1801.01365. Ludwig Maximilian University and MPI Biochemistry researchers continue to articulate how life’s biomolecular substance and sustenance arises from and exemplifies nature’s dynamical self-organization processes. That is to say, besides all the biochemical reactions, an independent universal source of formative topologies seems at generative work.

Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. A prominent example of intracellular patterns are the oscillatory pole-to-pole oscillations of Min proteins in E. coli whose biological function is to ensure precise cell division. More generally, these functional modules of cells serve as model systems for self-organization, one of the core principles of life. Here we review recent theoretical and experimental advances in the field of intracellular pattern formation, focusing on general design principles and fundamental physical mechanisms. (Abstract)

In summary, protein pattern formation plays key roles in many essential biological processes from bacteria to animals, including cell polarisation and division. Combined theoretical and experimental approaches have established important principles of pattern-forming protein systems. Perhaps the most crucial feature that has emerged from these research efforts is the identification of the cytosol as a depot. This depot enables the system to store proteins and redistribute them throughout the system. Cytosolic diffusion is the key process that detects the local shape of the membrane, and it is this explicit dependence on geometry that is imprinted on membrane-bound protein patterns. (15)

Friedman, Eric and Adam Landsberg. Hierarchical Networks, Power Laws, and Neuronal Avalanches. Chaos. 23/1, 2013. University of California, Berkeley, and Scripps College, Claremont, mathematicians illustrate three tiers or aspects of nature’s ubiquitous complex systems. The paper describes the above phenomena with reference to an independent, universal source and activity. Its presence in critically self-organized, nested brain dynamics is then exemplary evidence. With this in place, it is recorded that similarly everywhere else in cosmos and civilization can be found this repetitive manifestation. In the second decade of this century and millennium, we seem to be reaching a revolutionary veracity throughout the worldwide literature of a genesis uniVerse, whence all this natural appearance results from and expresses its own iterative genetic source code.

We show that in networks with a hierarchical architecture, critical dynamical behaviors can emerge even when the underlying dynamical processes are not critical. This finding provides explicit insight into current studies of the brain's neuronal network showing power-law avalanches in neural recordings, and provides a theoretical justification of recent numerical findings. Our analysis shows how the hierarchical organization of a network can itself lead to power-law distributions of avalanche sizes and durations, scaling laws between anomalous exponents, and universal functions—even in the absence of self-organized criticality or critical points. This hierarchy-induced phenomenon is independent of, though can potentially operate in conjunction with, standard dynamical mechanisms for generating power laws. (Abstract)

Many real-world networks are hierarchically organized into layers of modules and submodules, one prominent example being the neuronal network of the human brain. A central but still largely unexplored question is how an underlying hierarchical structure can affect a network's dynamical behavior. In this paper, we develop a renormalization analysis to uncover some important implications of hierarchical architecture in a network. Our main result reveals the interesting role of hierarchy in generating robust power-law behavior in networks, a fact which helps explain recent results on neuronal cascades in human brains. In addition, we show that other properties of these networks are consistent with the experimental data on brain networks and suggest new experiments to improve our understanding of brain networks and behavior. The ideas developed in this paper should be broadly applicable to many other network settings which exhibit a hierarchical modular (HM) structure, ranging from engineered to biological to social systems. (Lead Paragraph)

Friston, Karl. A Free Energy Principle for a Particular Physics. arXiv:1906.10184. The Wellcome Centre for Human Neuroimaging, London collegial neurotheorist posts a 148 page draft manuscript which seeks to join his self-composing and cognizing Bayesian brain theories with a conducive, natural, cosmic affinity. Search KF as this view gains a growing number of supporters. Akin to Integrated Information theory (Tononi) and other entries, these fluid perceptions take on their own iterative course in quest of better explanations, albeit in arcane terms which ought to gain a common clarity.

This monograph attempts a theory of every 'thing' that can be distinguished from other things in a statistical sense. The ensuing independencies, mediated by Markov blankets (see below), speak to a recursive composition of ensembles (things) at increasingly higher spatiotemporal scales. This decomposition provides a broad description of small things via quantum mechanics and the Schrodinger equation, then statistical mechanics and related fluctuation theorems, and through to big things in classical mechanics. Our main contribution is to examine the implications of Markov blankets for self-organisation to nonequilibrium steady-state. In so doing, we recover an information geometry and accompanying free energy principle that allows one to interpret the internal states as they represent and infer external states. (Abstract edits)

In statistics and machine learning, the Markov blanket for a node in a graphical model contains all the variables that shield the node from the rest of the network. This means that the Markov blanket of a node is the only knowledge needed to predict the behavior of that node and its children. In a Bayesian network, the values of the parents and children of a node evidently give information about that node. In a Bayesian network, the Markov blanket of node A includes its parents, children and the other parents of all of its children. (WikiPedia)

Gallos, Lazaros, et al. Scaling Theory of Transport in Complex Biological Networks. Proceedings of the National Academy of Sciences. 104/7746, 2007. Biophysicists at CCNY Levich Institute and Bar-Ilan University develop a theoretical framework for this ubiquitous property invariantly found from proteins to people.

We study transport in real-world biological networks and via a model, which possess both self-similar properties and the scale-free character in their degree distribution. We explain our results with theoretical arguments and simulation analysis. We use approaches from renormalization theory in statistical physics that enable us to exploit the self-similar characteristics of the fractal networks and develop a scaling theory of transport, which we use to address the effects of the modularity and the degree inhomogeneity of the substrate.

Garcia-Ruiz, Ronald and Adam Vernon. Emergence of Simple Patterns in Many-Body Systems from Macroscopic Objects to the Atomic Nucleus. arXiv:1911.04819. . R. Garcia Ruiz is posted at CERN Geneva and MIT, while A. Vernon is with KU Leuven, Belgium and the University of Manchester. Among an increasing number of reports, this entry with 175 references is a good example to date of a global scientific endeavor now able to quantify a substantial nature that everywhere gives rise to common forms and flows by its own propensities. With a root basis in nuclear shell clusters, a recurrent regularity spreads in kind across micro-physical and macro-biological realms. As the second quote cites, iconic mathematical shapes can found throughout, aka “magic numbers.” See also Underlying Structure of Collective Bands and Self-Organization in Quantum Systems by Takaharu Otsuka, et al at arXiv:1907.10759, and Magic Number Colloidal Clusters as Minimum Free Energy Structures by Junwei Wang, et al in Nature Communications (9/5259, 2018.)

Strongly correlated many-body systems often display the emergence of simple patterns and regular behavior of their global properties. Phenomena such as clusterization, collective motion and shell structures are commonly observed across different size, time, and energy scales in our universe. Although at the microscopic level their individual parts are described by complex interactions, the collective behavior of these systems can exhibit strikingly regular patterns. This contribution provides an overview of the experimental signatures that are used to identify the emergence of structures and collective phenomena in distinct physical systems, along with macroscopic examples. (Abstract)

Throughout nature, driving forces give rise to the arrangement of constituents in many-body systems at almost every size. On biological scales, this manifests in collective phenomena and pattern formation such as the phyllotaxis of plants, where growth patterns appear in the leaves or flowers around a plant stem. A striking example is observed in the seeds in a sunflower head, which follows the Fibonacci sequence. Complex many-body systems often form clusters to minimise their energy by interactions between neighbours and their mean field. This can form “magic” numbers, as in the atomic nucleus, where certain integer numbers of constituents of a given system result in greater stability of its collective whole. Another instance is the abundance distribution of isotopes in the universe following nucleosynthesis. (2, edits)

In nuclear physics, a magic number is a number of nucleons (either protons or neutrons, separately) such that they are arranged into complete shells within the atomic nucleus. The seven most widely recognized magic numbers as of 2019 are 2, 8, 20, 28, 50, 82, and 126. For protons, this corresponds to the elements helium, oxygen, calcium, nickel, tin, and lead. (Wikipedia)

Giometto, Andrea, et al. Scaling Body Size Fluctuations. Proceedings of the National Academy of Sciences. 110/4646, 2013. École Polytechnique Fédérale de Lausanne, Swiss Federal Institute of Aquatic Science and Technology, and Università di Padova, researchers describe a ubiquitous natural propensity to reiterate “universal forms” across spatial and temporal, evolutionary and environmental occasions, as the extended quotes attest.


The size of an organism matters for its metabolic, growth, mortality, and other vital rates. Scale-free community size spectra (i.e., size distributions regardless of species) are routinely observed in natural ecosystems and are the product of intra- and interspecies regulation of the relative abundance of organisms of different sizes. Intra- and interspecies distributions of body sizes are thus major determinants of ecosystems’ structure and function. We show experimentally that single-species mass distributions of unicellular eukaryotes covering different phyla exhibit both characteristic sizes and universal features over more than four orders of magnitude in mass. Remarkably, we find that the mean size of a species is sufficient to characterize its size distribution fully and that the latter has a universal form across all species. We show that an analytical physiological model accounts for the observed universality, which can be synthesized in a log-normal form for the intraspecies size distributions. We also propose how ecological and physiological processes should interact to produce scale-invariant community size spectra and discuss the implications of our results on allometric scaling laws involving body mass. (Abstract)

Why should a continuous, gap-free spectrum of organismic sizes emerge from the ecological and evolutionary processes that shape their ecosystems? The origins and the implications of the absence of preferential body sizes, which is routinely observed across a variety of ecosystems regardless of broad differences in climatic and environmental conditions, have been attracting much interest from field and theoretical ecologists. Scale invariance, epitomized by power-law probability distributions, requires regularities of the component parts (the species’ size distributions) making up the whole [the community size spectra (i.e., the probability distributions of size regardless of species)]. In particular, a necessary condition for scaling community size spectra is the lack of peaks that pinpoint frequent occurrences, and therefore excess abundance (and vice versa) within any given range of sizes. Such features are particularly interesting if robust to environmental fluctuations because their dynamic origin could lie in the self-organization of complex adaptive systems. (4646)

Gisiger, T. Scale Invariance in Biology: Coincidence or Footprint of a Universal Mechanism? Biological Reviews. 76/2, 2001. After an introduction to dynamical systems in their physical embodiment, their power law self-similarity properties are shown to pervade biological and neurological realms so as to affirm a ‘universality’ throughout nature.

In the spirit of complex systems, we should try not to look at these examples as physical processes or reactions between chemical reactants, but instead as systems made of many particles, or 'agents,’ which interact with each other via certain rules. (163) These findings might therefore illustrate how an ecosystem self-organizes into a critical state as the web of interactions between species and individuals develops. (185) Scale invariance is very common in nature, but it is only since the early 1970s that the mathematical tools necessary to define it more clearly were introduced. (204)

Grimm, Volker, et al. Pattern-Oriented Modeling of Agent-Based Complex Systems. Science. 310/987, 2005. This international collaboration with ten authors describes a novel method of understanding ecological systems, and how it may be applied throughout scientific fields. Autonomous, adaptive agents are everywhere: immune cells, plants, citizens, investors, and so on. Their collective behavior can be quantified by “individual-based” (IBM) or “pattern-oriented” (POM) modeling by “bottom-up” simulations, seen as another name for complex adaptive systems (CAS). These approaches have been implemented by studies of ultra complex and stratified ecosystems. As a reflection, one more recognition of a quite different natural materiality via its universal creative complementarity.

Agent-based complex systems are dynamics networks of many interacting agents; examples include ecosystems, financial markets, and cities. (987) In particular, experiments contrasting hypotheses for the behavior of interacting agents will lead to an accumulation of theory for how the dynamics of systems from molecules to ecosystems and economies emerge from bottom-level processes. This approach may change our whole notion of scientific theory, which until now has been based on the theories of physics. (991)

Harte, John. Toward a Synthesis of the Newtonian and Darwinian Worldviews. Physics Today. October, 2002. In this 2001 Leo Szilard Award Lecture, a theoretical ecologist attempts to join the universality of physical systems and the interdependent detail of ecosystems by way of complexity principles.

A self-similar pattern, as the phrase is used in the study of fractals, is one that looks the same on all spatial scales….My students and I have been employing a variety of analytical methods, including renormalization-group techniques developed for the study of scaling in self-similar phenomena in physics, to understand better the origins, implications, and interconnections of the power-law and self-similar relationships one finds in ecology. (33) I suggest that particularity and contingency, which characterize the ecological sciences, and generality and simplicity, which characterize the physical sciences, are miscible, and indeed necessary, ingredients in the quest to understand humankind’s home in the universe. (34)

Haugland, Sindre, et al. Self-Organized Alternating Chimera States in Oscillatory Media. Nature Scientific Reports. 5/9883, 2015. Technische Universität München, Nonequilibrium Chemical Physics, researchers including Katharina Kirscher, contribute to studies upon nature’s substantial propensity to switch between orderly or chaotic conditions. A biological example is the unihemispheric sleep pattern of avian animals which varies from synchronization to incoherence. We thus find another instance whence cosmos and life seems to persist in a dynamic poise of complementary modes. See also Spatially Organized Dynamical States in Chemical Oscillator Networks by Mahesh Wickramasinghe and Istvan Kiss in PLoS One (8/11, 2013) for another Taoist tango.

Oscillatory media can exhibit the coexistence of synchronized and desynchronized regions, so-called chimera states, for uniform parameters and symmetrical coupling. In a phase-balanced chimera state, where the totals of synchronized and desynchronized regions, respectively, are of the same size, the symmetry of the system predicts that interchanging both phases still gives a solution to the underlying equations. We observe this kind of interchange as a self-emerging phenomenon in an oscillatory medium with nonlinear global coupling. An interplay between local and global couplings renders the formation of these alternating chimeras possible. (Abstract)

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