Dual closure (operator theory)
"Dual closure" describes the processes causing a system called an "operator," as well as its typical organization.
Related lemma's: closure, big history, autocatalytic set, hypercycle, systems science, O-theory
Dual Closure
Dual closure is a core concept within Operator Theory (O-theory, theoperatortheory.info), a theoretical framework for understanding hierarchical organization in nature, developed by the Dutch biologist Gerard Jagers op Akkerhuis [1], [2]. Successive dual closures cause the emergence of a ranked series with discrete levels of entities of increasingly complex type known as operators, ranging from hadrons, to animals with nervous systems.
Conceptual Foundation
The concept of closure - whether temporal, spatial, or causal - has long been present in scientific and philosophical discourse. However it has rarely been recognized as a prominent topic. Possibly the earliest use is that by Rene Descartes[3] who described vortices of motion as closed systems of interaction. Later, Henri Bergson[4] linked individuality to naturally isolated, closed systems. More recent theoretical contributions include the works of: Monod on cybernetic closure in cellular regulation[5], Rosen on metabolism-replacement systems and closure to efficient causation[6], Maturana and Varela on the concept of autopoiesis[7], Kauffman on autocatalytic chemical sets[8] and Hofstadter on recursive self-reference (strange loops)[9]. Other studies of closure in system theory, autonomy, and biological organization include the works of e.g. Teilhard de Chardin[10], Heylighen[11], Moreno and Mossio[12], Huxley[13], Eigen and Schuster[14], Chandler and van den Vijver[15], Letelier[16], Soto-Andrade[17], Ellis[18], Ganti[19] [20], Holland[21].
These studies share a common emphasis on systems distinguished by some form of closure. O-theory builds on insights from these studies by introducing the concept of dual closure. Dual closure refers to the co-emergence of two forms of closure. The first is the closure of a series of process steps, also called processual or functional closure. This takes the form of a closed loop of transformations over time and is close to the use of closure in mathematics. The second is the formation of a "container" around the process loop, also called spatial or structural closure. It is of a topological nature, and acts as a boundary that limits the dynamics of the elements of the processual closure. When both closures interact, O-theory speaks of dual closure.
Paradigmatic examples include an atom and a cell (Figure 1).
The nucleus of an atom is held together by the exchange of pions between protons and neutrons. This exchange mutually changes their states. The positive charge of the protons in the nucleus then attracts electrons to form an electron shell.
A bacterial cell combines a metabolic cycle that sustains itself with a membrane that encloses the metabolism. In each example, the interaction between the two closures creates a self-sustaining, cohesive system; an operator. If there were only one closure, the cell membrane would merely be a vesicle. Meanwhile, the cell's hypercyclic metabolic reactions would float in the solute, which would allow for random mixing and prevent material unity. Therefore, material and organizational unity require dual closure.
Scientific Rationale of Dual Closure
The primary aim of O-theory is to provide a coherent, extrapolative model of the evolution of complexity that bridges the fields of physics, chemistry, biology, and cognitive science. In order to support such extrapolation, the operator hierarchy must employ a generative principle that applies uniformly across all levels involved[22].
Applications and Scientific Relevance
Dual closure has potential applications in evolutionary biology, systems theory, artificial life, and the foundations of artificial intelligence. Recent work positions the operator hierarchy as a complexity metric applicable from fundamental particles to hypothetical post-biological systems, with links to evolutionary theory and thermodynamics[23].
References
- ↑ Akkerhuis, Gerard A.J.M. Jagers op; van Straalen, Nico M. (1999). "Operators, the Lego‐bricks of nature: Evolutionary transitions from fermions to neural networks". World Futures. 53 (4): 329–345. doi:10.1080/02604027.1999.9972746. ISSN 0260-4027.
- ↑ Jagers op Akkerhuis, G. A. J. M. (2010). The operator hierarchy. A chain of closures linking matter, life and artificial intelligence. Alterra scientific contributions 34.
- ↑ Descartes, R. (1644). Principles of philosophy, part II
- ↑ Bergson, Henri (1908). L'evolution creatrice. Paris: F. Alcan. Search this book on
- ↑ Monod, J. (1970). Le hasard et la nécessité. Editions du Seuil
- ↑ Rosen, R (1973). Foundations of Mathematical Biology. Elsevier. doi:10.1016/c2013-0-11404-3. ISBN 978-0-12-597203-1. Search this book on
- ↑ Maturana, H. R., & Varela, F. J. (1972). Autopoiesis and cognition: the realization of the living. Boston studies in the philosophy and history of science. Dordrecht: Reidel.
- ↑ Kauffman, Stuart A (1993-06-10). The Origins of Order: Self-Organization and Selection in Evolution. Oxford University PressNew York, NY. doi:10.1093/oso/9780195079517.001.0001. ISBN 978-0-19-507951-7. Search this book on
- ↑ Hofstadter, Douglas R. (2008). I am a strange loop (Paperback first published ed.). New York, NY: Basic Books, a member of the Perseus Books Group. ISBN 978-0-465-03079-8. Search this book on
- ↑ Teilhard de Chardin, P (1969). The future of man. Editions du Seuil. pp. 109–110. Search this book on
- ↑ Heylighen, F. (1990 pp. 335-342). Relational Closure: a mathematical concept for distinction-making and complexity analysis. In R. Trappl (Ed.), Cybernetics and Systems '90. World Science, Singapore
- ↑ Moreno, Alvaro; Mossio, Matteo (2015). Biological Autonomy: A Philosophical and Theoretical Enquiry. History, Philosophy and Theory of the Life Sciences. Dordrecht: Springer. ISBN 978-94-017-9836-5. Search this book on
- ↑ Huxley, Julian (2022). The Individual in the Animal Kingdom. The MIT Press. Cambridge: The MIT Press. ISBN 978-0-262-36998-5. Search this book on
- ↑ Eigen, Manfred; Schuster, Peter (1979). "The Hypercycle". SpringerLink. doi:10.1007/978-3-642-67247-7.
- ↑ Chandler, Jerry L. R., ed. (2000). Closure: emergent organizations and their dynamics. Annals of the New York Academy of Sciences. New York, NY: The New York Academy of Sciences. ISBN 978-1-57331-248-6. Search this book on
- ↑ Letelier, Juan-Carlos; Cárdenas, María Luz; Cornish-Bowden, Athel (2011). "From L'Homme Machine to metabolic closure: Steps towards understanding life". Journal of Theoretical Biology. 286: 100–113. doi:10.1016/j.jtbi.2011.06.033.
- ↑ Soto-Andrade, J., Jaramillo-Riveri, S., & Letelier, J.-C. (2011). Ouroboros avatars: A mathematical exploration of self-reference and metabolic closure.
- ↑ Ellis, George F. R. (2020-10-01). "The Causal Closure of Physics in Real World Contexts". Foundations of Physics. 50 (10): 1057–1097. doi:10.1007/s10701-020-00366-0. ISSN 1572-9516. PMC 7431902 Check
|pmc=value (help). PMID 32836326 Check|pmid=value (help). - ↑ Gánti, Tibor; Gánti, Tibor (2003). Chemoton theory. Mathematical and computational chemistry. New York, NY: Kluwer Acad./Plenum. ISBN 978-0-306-47785-0. Search this book on
- ↑ Gánti, Tibor (2003). Chemoton theory. Mathematical and computational chemistry. New York: Kluwer Academic/Plenum Publishers. ISBN 978-0-306-47785-0. Search this book on
- ↑ Holland, John H. (2012-07-13). Signals and Boundaries: Building Blocks for Complex Adaptive Systems. The MIT Press. doi:10.7551/mitpress/9412.001.0001. ISBN 978-0-262-30589-1. Search this book on
- ↑ Jagers op Akkerhuis, Gerard A. J. M. (2024). "The Third Law of Evolution and The Future of Life". Library of Ethics and Applied Philosophy. doi:10.1007/978-3-031-73205-8. ISSN 1387-6678.
- ↑ Jagers op Akkerhuis G. A. J. M. (2022). The Operator Theory: A Yardstick for Complexity from Quarks to Memons? Relationships with Evolution and Thermodynamics. In: G. Y. Georgiev M. Shokrollahi-Far. (Eds.): Efficiency in Complex Systems. Self-Organization Towards Increased Efficiency
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