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A category theory and higher dimensional algebra approach to complex systems biology, meta-systems and ontological theory of levels: emergence of life, society, human consciousness and articial intelligence. (English) Zbl 1340.92017

Summary: In this monograph we present a novel approach to the problems raised by higher complexity in both nature and the human society, by considering the most complex levels of objective existence as ontological meta-levels, such as those present in the creative human minds and civilised, modern societies. Thus, a “theory” about theories is called a “meta-theory”. In the same sense that a statement about propositions is a higher-level \(\langle proposition\rangle\) rather than a simple proposition, a global process of subprocesses is a “meta-process”, and the emergence of higher levels of reality “via” such meta-processes results in the objective existence of “ontological meta-levels”. The new concepts suggested for understanding the emergence and evolution of life, as well as human consciousness, are in terms of globalisation of multiple, underlying processes into the meta-levels of their existence. Such concepts are also useful in computer aided ontology and computer science. The selected approach for our broadbut also in-depth-study of the fundamental, relational structures and functions present in living, higher organisms and of the extremely complex processes and meta-processes of the human mind combines new concepts from three recently developed, related mathematical fields: algebraic topology (AT), category theory (CT) and higher dimensional algebra (HDA), as well as concepts from multi-valued logics. Several important relational structures present in organisms and the human mind are naturally represented in terms of universal CT concepts, variable topology, non-abelian categories and HDA-based notions. The unifying theme of local-to-global approaches to organismal development, biological evolution and human consciousness leads to novel patterns of relations that emerge in super- and ultra-complex systems in terms of global compositions of local procedures. This novel AT concept of “combination of local procedures” is suggested to be relevant to both ontogenetic development and organismal evolution, beginning with the origin of species of higher organisms; such concepts may provide a formal framework for an improved understanding of evolutionary biology and the origin of species on multiple levels-from molecular to species and biosphere levels. It is claimed that human consciousness is an “unique” phenomenon which should be regarded as a composition, or combination of ultra-complex, global processes of subprocesses, at a “meta-level” supported by, and compatible with, the human brain dynamics. Thus, a defining characteristic of such conscious processes involves a “combination of global procedures” or meta-processes – that may also involve parallel processing of both image and sound sensations, perceptions, emotions and decision making, etc. – that ultimately leads to the ontological meta-level of the ultra-complex, human mind. Then, an extension of the concept of co-evolution of human consciousness and society leads one to the concept of “social consciousness”. One arrives also at the conclusion that the human mind and consciousness are the result not only of the “co-evolution” of man and his society, but that they are, in fact, the result of the original “co-emergence” of the meta-level of a minimally-organized human society with that of several, ultra-complex human brains. The human “spirit” and society are, thus, “completely inseparable” – just like the very rare Siamese twins. Therefore, the appearance of human consciousness is considered to be critically dependent upon the societal co-evolution, the emergence of an elaborate language-symbolic communication system, as well as the existence of “virtual”, higher dimensional, non-commutative processes that involve separate space and time perceptions in the human mind. Two fundamental, logic adjointness theorems are considered that provide a logical basis for categorical representations of functional genome and organismal networks in variable categories and extended toposes, or topoi, “classified” (or encoded) by multi-valued logic algebras; their subtly nuanced connections to the variable topology and multiple geometric structures of developing organisms are also pointed out. Our ultra-complexity viewpoint throws new light on previous semantic models in cognitive science and on the theory of levels formulated within the framework of categorical ontology. A paradigm shift towards “non-commutative”, or more generally, 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. The presence of strange attractors in modern society dynamics, and especially the emergence of new meta-levels of still-higher complexity in modern society, gives rise to very serious concerns for the future of mankind and the continued persistence of a multi-stable biosphere if such ultra-complexity, meta-level issues continue to be ignored by decision makers.

MSC:

92C42 Systems biology, networks
92B05 General biology and biomathematics
68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
03G20 Logical aspects of Łukasiewicz and Post algebras
03G12 Quantum logic
18A15 Foundations, relations to logic and deductive systems
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
93B15 Realizations from input-output data
18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)
18G55 Nonabelian homotopical algebra (MSC2010)
55U40 Topological categories, foundations of homotopy theory
91E99 Mathematical psychology
91D30 Social networks; opinion dynamics
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