Comments:

133 pages, October 2, 2010

Abstract:

An attempt is made from the viewpoint of the recent theory of ontological levels [2],[40],[137],[206]-[209] to understand the origins and emergence of life, the dynamics of the evolution of organisms and species, the ascent of man and the co-emergence, as well as co-evolution of human consciousness within organised societies. The new concepts developed 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 [1],[194],[197]. 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 highest and 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 collection of sets may be a \emph{class}, instead of a set [59],[176]-[177]; it may also be called a `super-set', or a \emph{meta-set}; a `theorem' about theorems is a \emph{meta-theorem}, and a `theory' about theories is a \emph{`meta-theory'}. In the same sense that a statement about propositions is a higher-level $\$ rather than a simple proposition, a global process of subprocesses is a \emph{meta-process}, and the emergence of higher levels of reality \emph{via} such meta-processes results in the objective existence of \emph{ontological meta-levels}. It is also attempted here to classify more precisely the levels of reality and species of organisms than it has been thus far reported. The selected approach for our broad-- but 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, Category Theory (CT) and Higher Dimensional Algebra (HDA). 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. Such relatively new concepts are defined in the appropriate sequence beginning with the concept of groupoid which is fundamental to all algebraic topology studies [63], [69], and that also turns out to be essential to numerous applications in mathematical biology [11]-[23],[34],[74], including those of higher dimensional groupoids in theoretical neuroscience [38],[69]-[70]. An 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 [33],[39]. This novel algebraic topology concept of \emph{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. Fundamentally inter--related, higher homotopy and holonomy groupoid 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. All key concepts pertaining to this context are here defined for a self-contained presentation, notwithstanding the difficulties associated with understanding the essence of life, the human mind, consciousness and its origins. One can define pragmatically the human brain in terms of its neurophysiological functions, anatomical and microscopic structure, but one cannot as readily observe and define the much more elusive human mind which depends both upon a fully functional human brain and its training or education by the human society. Human minds that do not but weakly interact with those of any other member of society are partially disfunctional, and this creates increasing problems with the society integration of large groups of people that only interact weakly with all the other members of society. Obviously, it does take a fully functional mind to observe and understand the human mind. It is then claimed that human consciousness is an \emph{unique} phenomenon which should be regarded as a composition, or combination of ultra-complex, global processes of subprocesses, at a \emph{meta-level} not sub--summed by, but compatible with, human brain dynamics [11]--[23],[33]. Thus, a defining characteristic of such conscious processes involves a \emph{combination of global procedures} or meta-processes-- such as the parallel processing of both image and sound sensations, perceptions and emotions, decision making and learned reflexes, etc.-- that ultimately leads to the ontological meta-level of the ultra-complex, human mind. In this monograph we shall not attempt to debate if other species are capable of consciousness, or to what extent, but focus instead on the ultra-complex problems raised by human consciousness and its emergence. Current thinking [87], [91],[182],[186],[188], [190], [195]-[196],[203],[247] considers the actual emergence of human consciousness [83],[91],[186],[190],[261] --and also its ontic category-- to be critically dependent upon the existence of both a human society level of \emph{minimal} (tribal) organization [91],[186],[190], and that of an extremely complex structural --functional unit --the human brain with an \emph{asymmetric} network topology and a dynamic network connectivity of very high-order [187],[218], [262]. Then, an extension of the concept of coevolution of human consciousness and society leads one to the concept of \emph{social consciousness} [190]. One arrives also at the conclusion that the human mind and consciousness are the result not only of the \emph{co-evolution} of man and his society [91],[186],[190], but that they are, in fact, the result of the original \emph{co-emergence} of the meta-level of a minimally-organized human society with that of several, ultra-complex human brains. Unlike the myth of only one Adam and one Eve being the required generator of human society, our co-emergence concept leads necessarily to the requirement of several such `primitive' human couples co-existing in order to generate both a minimally organized society and several, minimally self-conscious, interacting \emph{H. sapiens} minds that shaped the first Rosetta groupoids of \emph{H. sapiens} into human tribes. The human `spirit' and society are, thus, \emph{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. Theories of the mind are thus considered in the context of a novel ontological theory of levels. 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 [40],[69]. Our novel approach to meta-systems and levels using Category Theory and HDA mathematical representations is also applicable--albeit in a modified form--to supercomputers, complex quantum computers, man--made neural networks and novel designs of advanced artificial intelligence (AI) systems (AAIS). Anticipatory systems and complex causality at the top levels of reality are also discussed in the context of Complex Systems Biology (CSB), psychology, sociology and ecology. A paradigm shift towards \emph{non-commutative}, or more generally, non-Abelian theories of highly complex dynamics [33],[40],[69] 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. \bigskip \textsc{Keywords:} \textit{{\it Categorical Ontology of Super-Complex and Ultra-Complex System Dynamics,Higher Dimensional Algebra of Networks,Theoretical Biology and Variable Groupoids, Non-Abelian Quantum Algebraic Topology and Quantum Double Groupoids, Higher Homotopy-General van Kampen theorems; autistic children, advanced artificial intelligence and biomimetics}} http://planetmath.org/?op=getobj&from=collab&id=170 2000 \textit{Mathematics Subject Classification}: 16B50, 68Q15.

Rights:

Copyright@2010 by I.C. Baianu et al.

Download:

uiucs31New38rd2.pdf

Links:

No messages.