The Impact of the Paradigm of Complexity on the Foundational Frameworks of Biology and Cognitive Science (original) (raw)
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A major challenge of interdisciplinary description of complex system behaviour is whether real systems of higher complexity levels can be understood with at least the same degree of objective, "scientific" rigour and universality as "simple" systems of classical, Newtonian science paradigm. The problem is reduced to that of arbitrary, many-body interaction (unsolved in standard theory). Here we review its causally complete solution, the ensuing concept of complexity and applications. The discovered key properties of dynamic multivaluedness and entanglement give rise to a qualitatively new kind of mathematical structure providing the exact version of real system behaviour. The extended mathematics of complexity contains the truly universal definition of dynamic complexity, randomness (chaoticity), classification of all possible dynamic regimes, and the unifying principle of any system dynamics and evolution, the universal symmetry of complexity. Every real system has a non-zero (and actually high) value of unreduced dynamic complexity determining, in particular, "mysterious" behaviour of quantum systems and relativistic effects causally explained now as unified manifestations of complex interaction dynamics. The observed differences between various systems are due to different regimes and levels of their unreduced dynamic complexity. We outline applications of universal concept of dynamic complexity emphasizing cases of "truly complex" systems from higher complexity levels (ecological and living systems, brain operation, intelligence and consciousness, autonomic information and communication systems) and show that the urgently needed progress in social and intellectual structure of civilisation inevitably involves qualitative transition to unreduced complexity understanding (we call it "revolution of complexity").
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This essay is a trial on giving some mathematical ideas about the concept of biological complexity, trying to explore four different attributes considered to be essential to characterize a complex system in a biological context: decomposition, heterogeneous assembly, selforganization, and adequacy. It is a theoretical and speculative approach, opening some possibilities to further numerical and experimental work, illustrated by references to several researches that applied the concepts presented here.
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Contemporary scientific knowledge is built on both methodological and epistemological reductionism. The discovery of the limitations of the reductionist paradigm in the mathematical treatment of certain physical phenomena originated the notion of complexity, both as a pattern and process. After clarifying some very general terms and ideas on biological evolution and biological complexity, the article will tackle to seek to summarize the debate on biological complexity and discuss the difference between complexities of living and inert matter. Some examples of the major successes of mathematics applied to biological problems will follow; the notion of an intrinsic limitation in the application of mathematics to biological complexity as a global, relational, and historical phenomenon at the individual and species level will also be advanced.
From Newton-Boltzmann paradigms to complexity: a bridge to bio-systems
We discuss the theoretical foundations of classical physical systems looking for the theoretical basis of complex systems. We propose to define complex any living system or any artificial system with the basic properties of life. The theory of dynamical systems, suitable to describe any physical system in the absence of appreciable quantum effects, is based on the paradigms of Newton concerning the deterministic evolution, and Boltzmann-Gibbs concerning the probabilistic aspects. Though reversibility is a general mathematical property shared by physical ordered systems, the chaotic and borderline dynamical systems are physically irreversible because of the intrinsic limits in the accuracy of initial conditions. Complex systems have a large information content that can be transmitted by self reproduction. They are surrounded by a fluctuating environment and on long time scales change following Darwin's paradigm of evolution. It defines a philogenetic time arrow that points toward an increasing information content and project richness unlikely the time arrow of the second principle of thermodynamics that points towards increasing local disorder and large scale uniformity. We outline how borderline physical systems exhibit coherent structures for short times, but evolve to a Boltzmann equilibrium on long time scales. As a possible model for a generic complex system (a prototype) we propose an ensemble of Von Neumann automata which move on a network interacting among themselves and with the environment. Such a model, suggested for instance by the urban mobility and the clonotipic immune system, is under investigation to detect how the macroscopic variables depend on the level of sophistication of the automata.
Knowledge Manifestation in Biological Systems Dynamics
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Recognizing anticipation as a specific form of knowledge and taking specific form of knowledge realization in a physical system (a program for Feynman's universal reversible quantum computer) one gets a definite algebraic property of quantum system's dynamics, which appeares to be closely related with characteristic features of biological systems. This means that physical description of biological systems at quantum level must anyhow contain explicit logical component evoked by the system's intrinsic knowledge. On physical level the fact of such knowledge existance manifest itself in global algebraic properties of its dynamics. Evolution of biological systems in such approach turns out to be an evolution of certain set of interaction constants of system's hamiltonian which makes it possible to implement logical operations as summands of the system's evolution operator.
Understanding biological complexity: lessons from the past
FASEB journal : official publication of the Federation of American Societies for Experimental Biology, 2003
Advances in molecular biology now permit complex biological systems to be tracked at an exquisite level of detail. The information flow is so great, however, that using intuition alone to draw connections is unrealistic. Thus, the need to integrate mathematical biology with experimental biology is greater than ever. To achieve this integration, obstacles that have traditionally prevented effective communication between theoreticians and experimentalists must be overcome, so that experimentalists learn the language of mathematics and dynamical modeling and theorists learn the language of biology. Fifty years ago Alan Hodgkin and Andrew Huxley published their quantitative model of the nerve action potential; in the same year, Alan Turing published his work on pattern formation in activator-inhibitor systems. These classic studies illustrate two ends of the spectrum in mathematical biology: the detailed model approach and the minimal model approach. When combined, they are highly syner...
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The paper discusses how systems biology is working toward complex accounts that integrate explanation in terms of mechanisms and explanation by mathematical models—which some philosophers have viewed as rival models of explanation. Systems biology is an integrative approach, and it strongly relies on mathematical modeling. Philosophical accounts of mechanisms capture integrative in the sense of multilevel and multifield explanations, yet accounts of mechanistic explanation (as the analysis of a whole in terms of its structural parts and their qualitative interactions) have failed to address how a mathematical model could contribute to such explanations. I discuss how mathematical equations can be explanatorily relevant. Several cases from systems biology are discussed to illustrate the interplay between mechanistic research and mathematical modeling, and I point to questions about qualitative phenomena (rather than the explanation of quantitative details), where quantitative models are still indispensable to the explanation. Systems biology shows that a broader philosophical conception of mechanisms is needed, which takes into account functional-dynamical aspects, interaction in complex networks with feedback loops, system-wide functional properties such as distributed functionality and robustness, and a mechanism’s ability to respond to perturbations (beyond its actual operation). I offer general conclusions for philosophical accounts of explanation.