, Volume 17, Issue 3, pp 223–352

Categorical Ontology of Complex Spacetime Structures: The Emergence of Life and Human Consciousness

Original Paper

DOI: 10.1007/s10516-007-9011-2

Cite this article as:
Baianu, I.C., Brown, R. & Glazebrook, J.F. Axiomathes (2007) 17: 223. doi:10.1007/s10516-007-9011-2


A categorical ontology of space and time is presented for emergent biosystems, super-complex dynamics, evolution and human consciousness. Relational structures of organisms and the human mind are naturally represented in non-abelian categories and higher dimensional algebra. The ascent of man and other organisms through adaptation, evolution and social co-evolution is viewed in categorical terms as variable biogroupoid representations of evolving species. The unifying theme of local-to-global approaches to organismic development, evolution and human consciousness leads to novel patterns of relations that emerge in super- and ultra- complex systems in terms of colimits of biogroupoids, and more generally, as compositions of local procedures to be defined in terms of locally Lie groupoids. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ may be found with the help of generalized van Kampen theorems in algebraic topology such as the Higher Homotopy van Kampen theorem (HHvKT). Primordial organism structures are predicted from the simplest metabolic-repair systems extended to self-replication through autocatalytic reactions. The intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution is investigated in terms of categories of many-valued, Łukasiewicz–Moisil logic algebras and then compared with those obtained for (non-commutative) quantum logics. The claim is defended in this essay that human consciousness is unique and should be viewed as an ultra-complex, global process of processes. The emergence of consciousness and its existence seem dependent upon an extremely complex structural and functional unit with an asymmetric network topology and connectivities—the human brain—that developed through societal co-evolution, elaborate language/symbolic communication and ‘virtual’, higher dimensional, non-commutative processes involving separate space and time perceptions. Philosophical theories of the mind are approached from the theory of levels and ultra-complexity viewpoints which throw new light on previous representational hypotheses and proposed semantic models in cognitive science. Anticipatory systems and complex causality at the top levels of reality are also discussed in the context of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. The presence of strange attractors in modern society dynamics gives rise to very serious concerns for the future of mankind and the continued persistence of a multi-stable biosphere. A paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics is suggested to unfold now in physics, mathematics, life and cognitive sciences, thus leading to the realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics.


Space, time, chronotopoids and spacetime, ST ST in automata vs. quantum automata and organisms Categorical ontology and the theory of levels Relational biology principles What is life and life’s multiple logics, LM- and Q-logic Organismic categories and relational patterns Abelian vs. non-Abelian theories Commutativity limitations in logics, mathematics, physics and emergent systems Łukasiewicz–Moisil logic algebras of genetic networks and interactomes Homo erectus, habilis and sapiens Australopithecus and chimpanzees (PanThe emergence of hominins and hominoides Cognitive science Mental representations and intentionality Brentano, Harman, Dennett, Field and Fodor’s philosophy of the mind Higher dimensional algebra of brain functions Higher Homotopy-General Van Kampen Theorems (HHvKT) and Non-Abelian Algebraic Topology (NAAT) Non-commutativity of diagrams and non-Abelian theories Non-Abelian categorical ontology Non-commutative topological invariants of complex dynamic state spaces Double groupoids and quantum double groupoids Natural transformations in molecular and relational biology Molecular class variables (mcv) Natural transformations and the Yoneda-Grothendieck Lemma/construction The Primordial MR and Archea unicellular organisms Evolution and memory evolutive systems (MES) The Thalamocortical model, categorical limits, colimits and MES Biogroupoids Variable groupoids, variable categories, variable topology and atlas structures Irreversibility and open systems Selective boundaries vs. horizons Universal temporality Occam’razor and reductionist approaches Super-complex systems and brain dynamics Global and local aspects of biological evolution in terms of colimits of variable biogroupoids Chains and compositions of local procedures (COLPs) of locally Lie groupoids in the evolution and co-evolution of species What is consciousness and synaesthesia? The human mind, human consciousness and brain dynamics viewed as non-Abelian ultra-complex processes Emergence of human consciousness through co-evolution/social interactions and symbolic communication Rosetta biogroupoids as models of human social interactions Objectivation and memes Anticipation and feedforward Systems of internal representations, propositional attitudes and sentence-analogs Tarskian compositional semantics Moral duality and strange attractors of modern society dynamics 

Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.FSHN and NPRE Departments, AFC–NMR and NIR Microspectroscopy FacilityUniversity of Illinois at Urbana–ChampaignUrbanaUSA
  2. 2.School of InformaticsUniversity of WalesBangor, GwyneddUK
  3. 3.Department of Mathematics and Computer ScienceEastern Illinois UniversityCharlestonUSA

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