O-Theory
O-theory is a scientific framework that describes the emergence of increasingly complex systems—from fundamental particles to neural organisms—based on the principle of dual closure.
Related lemma's: Dual Closure, Big History, Hypercycle, Autocatalytic set, major transitions, hierarchy, systems science
O-theory (Complexity Theory)
Developed by Dutch biologist Gerard Jagers op Akkerhuis, O-theory (theoperatortheory.info) is a framework that describes a basic form of stepwise increase in complexity in nature[1]. This increase ranges from subatomic particles to organisms with nervous systems. Systems at each level are defined by a common organizational principle.
Background and Origin
O-theory emerged from an integrative study of natural hierarchies that revealed classical approaches to classification often conflate different types of logic. To address this issue, Jagers op Akkerhuis proposed a framework based on closure, specifically the concept of Dual Closure, to identify levels of complexity. The focus on dual closure provides a method for identifying when a new kind of system has emerged[2].
Dual Closure and the Operator Hierarchy
Although closure is discussed in studies by prominent scientists, it is somewhat neglected as a scientific topic in and of itself [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]. It can take on different shapes. In O-theory, the focus is on a combination of closures. The first type is processual (functional) closure, which involves a cycle of change processes, such as the citric acid cycle. The second type is spatial (structural) closure, which contains a processual closure and mediates its interactions with the outside world. An example is a bacterium's membrane keeping metabolic molecules together. When both types occur in dependence, O-theory speaks of dual closure. The new unit of organization is called an "operator."
The operator hierarchy is the sequence of operators, starting with hadrons (e.g., protons or neutrons) and progressing through atoms, molecules, bacterial cells, and increasingly complex organisms, such as protozoa, plants, and animals (Figure 1). At each level, dual closure reappears in a new form brought about by the previous level's operators and depending on the physical or biological context. Importantly, the causes of dual closure vary from level to level, but the abstract pattern remains the same.
Figure 1: The operator hierarchy includes seven types of operators in four clusters. The first type is that of the hadron (level 1. Proton). Further dual closures lead to the following operator types and levels (with example): Atom (level 2. Nitrogen atom). Molecule (level 3. Water). Cell (level 4. Bacteria/archaea). Multicellular (level 5.1. Cyanobacteria). Hostcell, classically called eukaryotic cell (level 5.2. Paramecium). Multi-hostcellular, classically called eukaryotic multicellular (level 6: Sunflower). Neuron memon, classically an animal with neural network (level 7. Horse). Left side, vertical: Clusters. Clusters are displayed in different colors. (Modified after Jagers op Akkerhuis 2001 [16].
Higher-Order Regularities
Beyond its stepwise progression, the operator hierarchy exhibits patterns of higher-order regularity [17]. One such pattern is "multiness"—the formation of a new operator when a jointure of multiple components from the previous level leads to dual closure. Examples include quarks combining to hadrons, atoms combining to molecules, cells combining to multicellular organisms, and eukaryotic cells combining to eukaryotic multicellulars (Figure 1). In O-theory, eukaryotic cells are called host cells because the nucleus often disintegrates during cell division, while the mitochondria, as energy-providing, bacterial, endosymbiotic, guests of their host, always remain present.
Regular occurrences of multiness allow the operator hierarchy to be split into four major clusters (Figure 1):
1. Hadrons
2. Atom-based operators (atoms and molecules)
3. Cell-based operators (bacterial cells and multicellulars, eukaryotic cells and multicellulars)
4. Neural network-based operators (currently only the neuronmemon)
The fourth cluster includes animals with a neural network that has dual closure. Within O-theory, however, they are called memons to distinguish them from unicellular “animals”. The simplest of these is the neuron memon, which arises when neurons form and interact to create a neural network (processual closure) with an interface of sensors and activators (spatial closure) inside a multihostcellular organism.
Extrapolation and Predictive Power
The operator hierarchy allows for logical extrapolation due to its formal consistency—each level resulting from the same principle (dual closure). This opens up new research directions, such as investigating why the number of operator types seems to double with each successive cluster (1, 2, 4, and possibly 8) and whether other forms of closure recurrence besides multiness exist.
Scientific and Philosophical Applications
O-theory offers new conceptual tools and definitions that are applicable across multiple domains of science and philosophy:
* Definition of an organism: All operators that are at least as complex as a cell (bacterial/archaeal) are labeled organisms [18]. In Figure 1 these are the operators of level 4 and higher.
* Definition of life: Life can be seen as a common property of all organisms [19]. When viewed in this manner, life is not a tangible entity, but rather an abstraction. According to O-theory, life's defining characteristic is the presence of dual closure with complexity equal to or greater than a bacterial or archaeal cell. This criterion implicitly selects operators labeled as organisms. All organismic operators consume energy when active [18].
* Hierarchy theory: O-theory introduces a new analysis of hierarchy along three axis [20]. The first axis, called ‘upward’, is that of the operator hierarchy. The second axis, called ‘outward’, focuses on groupings op operators, e.g. from organisms to populations, communities and ecosystems. The third axis, called ínward’, examines an operator's internal organization. Starting with a cat, one could focus on its organs, tissues, cells, or chromosomes. These additions lead to three "dimensions" for analyzing complexity that should not be mixed. Distinguishing these three dimensions helps unravelling mixed hierarchies [21].
* evolution theory: Dual closure is proposed as a third law of evolution, supplementing the two laws of variation and selection [20].
Scientific Status
O-theory exists for about three decades. It is based on well-established scientific principles and draws from physics, biology, and systems theory. Rather than introducing new physical laws, it reorganizes and integrates existing knowledge through a unifying logical structure. The famous Dutch mathematician and Spinoza laureate Prof. Henk Barendregt recognized it as a metatheory [22]. It is seen as a useful tool for theoretical modeling, empirical research, and interdisciplinary discourse, including applications in astrobiology, Big History, complexity science and artificial intelligence, [23], [24], [25], [26], [27], [28]
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- ↑ 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
- ↑ 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
- ↑ Teilhard de Chardin, P (1969). The future of man. Editions du Seuil. pp. 109–110. Search this book on
- ↑ 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, Humberto R.; Varela, Francisco J. (1980). Autopoiesis and cognition: the realization of the living. Boston studies in the philosophy of science. Dordrecht, Holland ; Boston: D. Reidel Pub. Co. ISBN 978-90-277-1015-4. Search this book on
- ↑ Eigen, Manfred; Schuster, Peter (1979). "The Hypercycle". SpringerLink. doi:10.1007/978-3-642-67247-7.
- ↑ 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.
- ↑ 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
- ↑ Chandler, Jerry L. R.; Vijver, Gertrudis van de, eds. (2000). Closure: emergent organizations and their dynamics. Annals of the New York Academy of Sciences. New York, NY: New York Academy of Sciences. ISBN 978-1-57331-248-6. Search this book on
- ↑ 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
- ↑ 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.
- ↑ 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
- ↑ 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). - ↑ Akkerhuis, Gerard Jagers op (2001). "Extrapolating a Hierarchy of Building Block Systems Towards Future Neural Network Organisms". Acta Biotheoretica. 49 (3): 171–189. doi:10.1023/A:1011949326096. ISSN 0001-5342.
- ↑ Akkerhuis, Gerard Jagers op (2001). "Extrapolating a Hierarchy of Building Block Systems Towards Future Neural Network Organisms". Acta Biotheoretica. 49 (3): 171–189. doi:10.1023/A:1011949326096. ISSN 0001-5342.
- ↑ 18.0 18.1 Jagers op Akkerhuis, Gerard A. J. M. (2010). "Towards a Hierarchical Definition of Life, the Organism, and Death". Foundations of Science. 15 (3): 245–262. doi:10.1007/s10699-010-9177-8. ISSN 1233-1821.
- ↑ Cleland, Carol E. (2012). "Life without definitions". Synthese. 185 (1): 125–144. doi:10.1007/s11229-011-9879-7. ISSN 0039-7857.
- ↑ 20.0 20.1 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 0001-5342.
- ↑ Szathmáry, Eörs; Smith, John Maynard (1995). "The major evolutionary transitions". Nature. 374 (6519): 227–232. doi:10.1038/374227a0. ISSN 0028-0836.
- ↑ Barendregt, H. (2016, pp 61-64). Reflections on the Operator Theory. In G. A. J. M. Jagers op Akkerhuis (Ed.), Evolution and transitions in complexity. The science of hierarchical organization in nature. Springer International Publishing AG, Cham, Switzerland.
- ↑ Helman, Daniel S. (2022). "Finding or Creating a Living Organism? Past and Future Thought Experiments in Astrobiology Applied to Artificial Intelligence". Acta Biotheoretica. 70 (2). doi:10.1007/s10441-022-09438-2. ISSN 0001-5342.
- ↑ Chatterjee, Atanu; Georgiev, Georgi; Iannacchione, Germano (2017). "Aging and efficiency in living systems: Complexity, adaptation and self-organization". Mechanisms of Ageing and Development. 163: 2–7. doi:10.1016/j.mad.2017.02.009.
- ↑ Stoelhorst J.-W. (2016), pp 175-182). Major transitions, Operator Theory, and Human Organization. In G. A. J. M. Jagers op Akkerhuis (Ed.), Evolution and transitions in complexity. The science of hierarchical organization in nature. Springer International Publishing AG, Cham, Switzerland.
- ↑ Georgiev G.Y., Chatterjee, A. (2016). The road to a measurable quantitative understanding of self-organization and evolution. In G. A. J. M. Jagers op Akkerhuis (Ed.), Evolution and transitions in complexity. The science of hierarchical organization in nature. Springer International Publishing AG, Cham, Switzerland.
- ↑ Zwart, H. (2016). What comes next? The operator theory as an operationalization of the Teilhardian view on cosmogenesis. In G. A. J. M. Jagers op Akkerhuis (Ed.), Evolution and transitions in complexity. The science of hierarchical organization in nature. Springer International Publishing AG, Cham, Switzerland.
- ↑ Cottam, Ron; Ranson, Willy (2017), "And Yet It Moves", Bridging the Gap between Life and Physics, Cham: Springer International Publishing, pp. 103–133, ISBN 978-3-319-74532-9
