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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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IV. Ecosmomics: Independent, UniVersal, Complex Network Systems and a Genetic Code-Script Source

2. Biteracy: Natural Algorithmic Computation

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: A parallel, companion endeavor to complex systems science is this active field of computational program studies. From Alan Turing’s morphogenesis to Stephen Wolfram’s cellular automata, Gordana Dodig-Crnkovic’s informational basis and many more, a natural genesis is known to involve and be suffused by analog/digital (George Dyson 2020) codings. As they work their way, some manner of selective optimization seems to be going on. In its genetic algorithmic form (John Holland) a deep affinity becomes evident amongst this whole mathematic emergence.

2023: The endeavor to perceive a natural mathematic animation can be traced back to Alan Turing in the 1950s and Gottfried Leibniz long before. In our global 21st century, digital/analog versions spread across a wide spectrum. We cite an array of advocates below, and note Susan Stepney, George Dyson, Laura Schaposnik, Tanya Latty amongst many innovators.

Bernini, Andrea, et al. Process Calculi for Biological Processes. Natural Computing. 17/2, 2018.
Caucheteux, Charlotte and Jean-Remi King. Brains and Algorithms Partially Converge in Natural Language Processing. Communications Biology. 5/134, 2022.
Dowek, Gillis. Computation, Proof, Machine: Mathematics Enters a New Age. Cambridge: Cambridge University Press, 2015.
Dyson, George. Analogia: The Emergence of Technology beyond Programmable Control. New York: Farrar, Straus and Giroux, 2020.
Gregor, Karol and Frederic Besse. Self-Organizing Intelligent Matter: A Blueprint for an AI Generating Algorithm. arXiv:2010.07627.
Hsu, Sheryl, et al. A Physarum-inpsired Approach to the Euclidean Steiner Tree Problem. Nature Scientific Reports. 22/14536, 2022.

Krause, Andrew, et al. Recent Progress and Open Frontiers for Turing’s Theory of Morphogenesis. Philosophical Transactions of the Royal Society A. November, 2021.
Krenn, Mario, et al. Predicting the Future of AI with AI: An Exponent Growing Knowledge Network. arXiv:2210.00881.
Molina, Daniel, et al. Comprehensive Taxonomies of Nature-and Bio-inspired Optimization. Cognitive Computation. 12/897, 2020.
Nichol, Daniel, et al. Model Genotype-Phenotype Mappings and the Algorithmic Structure of Evolution. Journal of the Royal Society Interface.16/20190332, 2019.
Stepney, Susan and Andrew Adamatzky, eds. Inspired by Nature. International: Springer, 2018.
Wolfram, Stephen. The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics. arXiv:2204.05123.

, . A New Kind of Science: A 15-Year View. https://backchannel.com/a-new-kind-of-science-a-15-year-view-4f5668abe54f. A May 16, 2017 posting by Stephen Wolfram on this anniversary of his 1000 page title opus. It appears on his Backchannel blog website, along with news from frontiers of global computer technology and services. To wit, the 21st century has indeed become a “computational universe,” as algorithmic programs historically come to supersede physical mathematics. He then notes how his popular Mathematica software is lately involved with neural network and linguistic features and operations. In closing, the motivation remains to elucidate and fulfill Gottfried Leibniz’s quest for a common, natural symbolic discursive language.

Evolutionary Biology and the Theory of Computing. simons.berkeley.edu/programs/evolution2014. A Simons Foundation program in the spring of 2014 whose organizers include Christos Papadimitriou and Leslie Valiant. Various seminars were Evolutionary Biology Boot Camp (January tutorial) with Eugene Koonin; Computational Theories of Evolution, Nick Barton organizer, with speakers such as Richard Watson, Chrisantha Fernando, Adi Livnat, and Steven Frank; and New Directions in Probabilistic Models of Evolution. (RW and CF abstracts noted separately) The vital multifaceted content might be summed by a slide from Papadimitriou’s “Evolution and Algorithms:” The special affinity between computation and biology: There is “innate explicit code” in Life.

Evolutionary biology is an intellectually rich field which has advanced remarkably through a synergistic interplay between deep understanding of biology and mathematical techniques, especially from probability and statistics. Over the past several decades, the role of computer science in studying biology has grown enormously, and computation has now become an indispensable part of the intellectual mix. Many current problems in evolutionary biology push the limits of computation, and new algorithmic insights are needed to make progress. The objective of this program is to promote the interaction between theoretical computer scientists and researchers from evolutionary biology, physics, probability, and statistics. The participants of the program will collaborate to identify and tackle some of the most important theoretical and computational challenges arising from evolutionary biology. The major themes of the program will be sound mathematical modeling, rigorous methods for statistical estimation, and computational scalability. (Conference Summary)

During the past decade, models and theories of evolution have been articulated which were inspired by computational considerations: examples are Valiant's evolvability, and the theory of mixability for the role of sex. The purpose of this workshop is to showcase and advance this strand of research, and also to expose it to the feedback and criticism of biologists and mathematicians. A second goal of the workshop is to highlight research questions in evolutionary biology which might benefit from computational insights and methodology, such as intractability proofs and novel algorithmic paradigms. (Computational Theories of Evolution)

Aerts, Diederik, et al. Quantum Entanglement in Physical and Cognitive Systems. arXiv:1903.09103. A seven person team based at Brussels Free University with other postings in Switzerland, the UK and Chile enter their latest work-in-progress toward a theoretical and conceptual, quantum and classical, physical and biological, cosmic integrative whole. Into mid 2019, per the second quote, as new understandings join quantum and human phenomena, we can begin to glimpse a universal Copernican revolution. Physics and people are at last reunited, which in turn implies a lively, literate ecosmos. On this eprint site, over a hundred papers by D. Aerts, this group, and many colleagues can be accessed going back to 2008. An example is The Emergence and Evolution of Integrated Worldviews by DA with Liane Gabora at 1001.1399. Another current posting is Quantum-Theoretic Modeling in Computer Science at 1901.04299 and Quantum Entanglement in Corpuses of Documents 1810.12114.

We provide a general description of the phenomenon of entanglement in bipartite systems, as it manifests in micro and macro physical systems, as well as in human cognitive processes. We do so by observing that when genuine coincidence measurements are considered, the violation of the 'marginal laws', in addition to the Bell-CHSH inequality, is also to be expected. The situation can be described in the quantum formalism by considering the presence of entanglement not only at the level of the states, but also at the level of the measurements. (Abstract excerpt)

But nowadays the predictions of quantum theory are no longer put into question, not only as regards entanglement, which has been shown to be preservable over distances of a thousand kilometers, but also with respect to many other effects such the delocalization of large organic molecules. On the other hand, the debate about the profound meaning of the theory never stopped, and in fact has constantly renewed and expanded over the years, so much so that one can envisage this will produce in the end a Copernican-like revolution in the way we understand the nature of our physical reality. Such a debate, however, is not confined to physicists or philosophers of science, but also reached new fields of investigation, in particular that of psychology, due to the development of that research domain called ‘quantum cognition.’ (2)

Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the others, even when the particles are separated by a large distance.

In physics, the CHSH inequality can be used in the proof of Bell's theorem, which states that certain consequences of entanglement in quantum mechanics cannot be reproduced by local hidden variable theories. Experimental verification of violation of the inequalities is seen as experimental confirmation that nature cannot be described by local hidden variables theories. CHSH stands for John Clauser, Michael Horne, Abner Shimony, and Richard Holt, who described it in 1969.

Al-Mehairi, Yaared, et al. Compositional Distributional Cognition. arXiv:1608.03785. Oxford University computer scientists including Bob Coecke and Martha Lewis contribute a technical paper which in translation expresses innate affinities between its mathematics and widely removed linguistic and quantum dimensions. The ICS reference below about cerebral computation is from The Harmonic Mind by Paul Smolensky and Geraldine Legendre. CatCo is a paper by Coecke, et al in Linguistic Analysis (36/1/345, 2011). See also companion August postings from this group such as Quantum Algorithms for Compositional Natural Language Processing (1608.01406).

We accommodate the Integrated Connectionist/Symbolic Architecture (ICS) of [32] within the categorical compositional semantics (CatCo) of [13], forming a model of categorical compositional cognition (CatCog). This resolves intrinsic problems with ICS such as the fact that representations inhabit an unbounded space and that sentences with differing tree structures cannot be directly compared. We do so in a way that makes the most of the grammatical structure available, in contrast to strategies like circular convolution. Using the CatCo model also allows us to make use of tools developed for CatCo such as the representation of ambiguity and logical reasoning via density matrices, structural meanings for words such as relative pronouns, and addressing over- and under-extension, all of which are present in cognitive processes. Moreover the CatCog framework is sufficiently flexible to allow for entirely different representations of meaning, such as conceptual spaces. Interestingly, since the CatCo model was largely inspired by categorical quantum mechanics, so is CatCog. (Abstract)

Barish, Robert, et al. An Information-Bearing Seed for Nucleating Algorithmic Self-Assembly. Proceedings of the National Academy of Sciences. 106/6054, 2009. Caltech biocomputer scientists working with co-author mentor Erik Winfree contend that “natural, mineral, chemical, and biological structures of great complexity” organize themselves from an initial seed source so infused with a genetic-like code. One might then wonder - did a genesis universe likewise originate in this way?

Thus, algorithmic self-assembly is universal both for computation and for construction. These features establish an analogy to developmental programs in biological organisms: ‘‘Genomic information’’ contained in a seed specifies a complex growth process guided by information processing. (6054) Thus, in addition to their technical relevance, the ability to study seeded growth processes using programmable DNA systems may open up new approaches for studying fundamental natural phenomena. (6059)

Beinhocker, Eric. Evolution as Computation: Integrating Self-Organization with Generalized Darwinism. Journal of Institutional Economics. 7/3, 2011. The McKinsey Global Institute, London, economics theorist presses his view of the physical, biological, and societal universe in terms of and as due to iterative, algorithmic, informative processes. By so doing, the work continues the major project of his 2006 The Origin of Wealth toward a vital synthesis of “self-organization with a generalized Darwinism.” This waxing school perceives complex adaptive systems as a natural ‘software’ that drives or generates the amplifying scales of life’s regnant intricacy.

This paper argues that information theory, rooted in modern thermodynamics, offers the potential to integrate these two perspectives in a common and rigorous framework. Both evolution and self-organization can be generalized as computational processes that can be applied to human social phenomena. Under this view, evolution is a process of algorithmic search through a combinatorial design space, while self-organization is the result of non-zero sum gains from information aggregation. Evolution depends on the existence of self-organizing forces, and evolution acts on designs for self-organizing structures. (Abstract, 1)

By now it should be clear that there is much self-organizing going on under the evolution as computation perspective. The algorithm captures free energy to search enormous combinatorial spaces in search of fit designs, creating novelty through changes in design modules and recombinations of modules to discover and realize previously unrealized designs. In this way, order and structure are (Non-monotonically) created. (21) To summarize, from the point of view of information theory and computation, it is almost impossible to talk about evolution without referring to self-organization, and vice versa. Evolution needs self-organization to bootstrap the process of evolutionary search and order creation, while self-organization leads to conditions where the logic differentiation, selection and retention can take hole. (23)

Beltran, Lester and Suzette Geriente. Quantum Entanglement in Corpuses of Documents. arXiv:1810.12114. Brussels Free University, Interdisciplinary Studies Group researchers led by Diederik Aerts explore how recent clarifications and integrative expansions of quantum theory can reveal how such deep phenomena is actively present even in human literary writings. As if a library of cosmos (taking license), in addition to fractal network complexities, our textual linguistic corpora is found to possess a physical affinity and generative source. And we note, by turns, this extant cosmos becomes graced by a natural narrative (more license). See also Quantum-Theoretic Modeling in Computer Science by these authors and group at 1901.04299 for a later finesse. A parallel effort goes on in Bob Coecke’s Oxford University group, such as The Mathematics of Text Structure at 1904.03478.

Berges, Jurgen. Scaling Up Quantum Simulations. Nature. 569/339, 2019. . A Heidelberg University physicist lauds a paper Self-Verifying Variational Quantum Simulation of Lattice Models by eleven University of Innsbruck researchers in the same issue (Kokail, 569/355) about a composite digital-analog computational method which can span and join quantum and classical phases. Once again this complementarity is found to work best.

It is difficult to carry out and verify digital quantum simulations that use many quantum bits. A hybrid device based on a digital classical computer and an analog quantum processor suggests a way forward.

Bernini, Andrea, et al. Process Calculi for Biological Processes. Natural Computing. 17/2, 2018. Some 17 years since the 2001 human genome sequence that led to a new integrative phase, University of Siena, Sassari, and Pisa, Italy and Pontifical Xavierian University, Cali, Columbia biomathematicians propose that a deeper affinity between systems biology and computational operations exists and should be fostered. By turns, life naturally seems to compute and iterate her/his self into developmental and organismic evolution. An Algorithmic Systems Biology is then scoped out going forward. See also the Springer conference series Computational Methods in Systems Biology.

Systems biology is a research area devoted to developing computational frameworks for modeling biological systems in a holistic fashion. This paper surveys a specific computational approach to systems biology, based on the so-called process calculi, a formalism for describing concurrent systems. We start from a basic process calculus that is then extended with increasingly expressive features to better reflect the biological aspects of interest. We then compare the expressive power of the resulting calculi, mentioning if they are supported by software tools. From this comparison we derive some suggestions on the most suitable frameworks for dealing with specific cases of interest. (Abstract)

There is a substantial analogy between the above view of biological systems and the concurrent systems studied in computer science. These are made of a possibly huge number of independent processing units that perform concurrent computations, exchange information with each other via communications, have a discrete nature and are often endowed with stochastic features. This analogy makes process calculi, a formalism for specifying concurrent systems, a natural candidate for modeling biological entities. (346)

In computer science, the process calculi (or process algebras) are a diverse family of related approaches for formally modelling concurrent systems. Process calculi provide a tool for the high-level description of interactions, communications, and synchronizations between a collection of independent agents or processes. They also provide algebraic laws that allow process descriptions to be manipulated and analyzed, and permit formal reasoning about equivalences between processes. (Wikipedia)

Bonnici, Vincenzo and Vincenzo Manca. Informational Laws of Genome Structures. Nature Scientific Reports. 6/28840, 2016. University of Verona computational biologists exemplify the mid 2010 frontiers of an integral organic cosmos as written as complex systems from physical to genetic phases which can be parsed by a linguistic analysis. It is said that a genome is essentially a text, a descriptive document amenable to information theory. For more examples, we cite papers in Mind Over Matter, and throughout, that speak in terms of grammar, dictionaries, encyclopedias, libraries, and so on. See also Recurrence Distance Distributions in Computational Genomics in American Journal of Bioinformatics and Computational Biology (3/1, 2015), and Infogenomics Tools: A Computational Suite for Informational Analyses of Genomes in Journal of Bioinformatics and Proteomics Review (1/1, 2015), by the authors.

We think that our informational indexes, and the laws relating them, confirm a very simple and general intuition. If life is information represented and elaborated by means of (organic) molecules, then the laws of information necessarily have to reveal the deep logic of genome structures. (5) Our investigation can be compared to the astronomical observations measuring positions and times in the orbits of celestial objects. Kepler’s laws arose from the regularities found in planetary motions, and from Kepler’s laws, the laws of mechanics emerged. This astronomical comparison, which was an inspiring analogy, revealed a surprising coincidence when ellipses were introduced in the representation of entropic and anti-entropic components. Kepler’s laws were explained by Newton’s dynamical and gravitational principles. Continuing our analogy, probably deeper informational principles are the ultimate reason for the laws that we found. (7)

Bossard, Jeremy, et al. Evolving Random Fractal Cantor Superlattices for the Infrared Using a Genetic Algorithm. Journal of the Royal Society Interface. Vol.13/Iss.114, 2016. As the technical quotes describe, Penn State electrical engineers achieve deep insights into a previously entangled, intractable nature. By novel finesses of fractal geometries, reliable self-similar patterns do indeed appear. Moreover this observation results from the employ of a genetic algorithm which can select an optimum solution in an evolutionary manner from a population of options. Once again in the 2010s, such arcane mysteries become at last amenable to humankind’s discernment. Nature is truly graced by an ordained form and function which we peoples are meant to read and carry forth.

Ordered and chaotic superlattices have been identified in Nature that give rise to a variety of colours reflected by the skin of various organisms. In particular, organisms such as silvery fish possess superlattices that reflect a broad range of light from the visible to the UV. Such superlattices have previously been identified as ‘chaotic’, but we propose that apparent ‘chaotic’ natural structures, which have been previously modelled as completely random structures, should have an underlying fractal geometry. Fractal geometry, often described as the geometry of Nature, can be used to mimic structures found in Nature, but deterministic fractals produce structures that are too ‘perfect’ to appear natural. Introducing variability into fractals produces structures that appear more natural. We suggest that the ‘chaotic’ (purely random) superlattices identified in Nature are more accurately modelled by multi-generator fractals. (Abstract)

In order to exploit the multi-generator Cantor bar fractal to generate superlattices with desired spectral properties, a GA was employed to evolve the superlattice structure. The GA is a robust stochastic optimizer that has been used to solve a variety of challenging electromagnetic design problems. The GA is a popular optimizer within the electromagnetics community, because it is simple to implement and capable of solving problems with many design parameters. The GA itself is inspired by Nature as it emulates the natural evolutionary process, so combining it with the multi-generator fractal model allows us to not only mimic the superlattice geometries identified in Nature, but also to evolve optimum designs as would happen in Nature. The operating principle of the GA comes from the Darwinian notion of natural selection, where a population of design candidates competes for survival at each iteration of the optimization process. (4)

Brabazon, Anthony, et al. Natural Computing Algorithms. Berlin: Springer, 2015. As Preface excerpt cites, University College, Dublin systems scholars provide a comprehensive version of many realizations that an evolutionary cosmos from physical to genomic, animal, plant, behavioral, and human economic realms is suffused with and animated by a multitude of algorithmic programs. The grand incentive is to properly discern, finesse and apply in kind to improve all aspects of biosphere and anthropocene abidance.

The field of natural computing has been proven to be successful problem solvers across domains as varied as management science, telecommunications, business analytics, bioinformatics, finance, marketing, engineering, architecture and design, to name but a few. The first (book) part covers a family of algorithms which are inspired by processes of evolution as well as introducing pivotal concepts in the design of natural computing algorithms such as choice of representation, diversity generation mechanisms, and the selection of an appropriate fitness function. The second illustrates a selection of algorithms which are inspired by the social behaviour of individuals (social computing) ranging from flocking behaviours to the food foraging behaviours of several organisms, including bats, insects and bacteria. The third part introduces a number of algorithms whose workings are inspired by the operation of our central nervous system (neurocomputing). The fourth discusses optimisation and classification algorithms which are metaphorically derived from the workings of our immune system. The fifth part provides an introduction to developmental and grammatical computing, where the creation of a model or structure results from a development process which is typically governed by a set of rules, a ‘grammar’. Physical computing is described in the sixth, with the primary emphasis being placed on the use of quantum inspired representations in natural computing. Two emerging paradigms in natural computing, chemical computing and plant inspired algorithms are introduced in part seven of the book. (Preface)

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