A Conceptual Construction of Complexity Levels Theory in Spacetime Categorical Ontology: Non-Abelian Algebraic Topology, Many-Valued Logics and Dynamic Systems
نویسندگان
چکیده
A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Supercomplex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in superand ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the R. Brown School of Informatics, University of Wales, Dean St., Bangor, Gwynedd LL57 1UT, UK e-mail: [email protected] J. F. Glazebrook Department of Mathematics and Computer Science, Eastern Illinois University, 600 Lincoln Ave., Charleston, IL 61920-3099, USA e-mail: [email protected] I. C. Baianu (&) FSHN and NPRE Departments, AFC-NMR and NIR Microspectroscopy Facility, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA e-mail: [email protected] 123 Axiomathes DOI 10.1007/s10516-007-9010-3
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