The Evolution of Complexity - Abstracts.

Is the Variety Inevitable?

By Saulius Norvaisas

  • Institute of Mathematics and Informatics
  • Vilnius, Lithuania
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  • Abstract:

    Genetists [1], biologists [2], jurists [3], philosophers [4] consider the problems of variety emergence and its maintenance. At present it is obvious that the presence of sufficient variety in any evolutionary system enables up to avoid great disasters and increases the rate of evolution.

    P.Bak et al. showed in the model of self-organized criticality that complex systems evolve to a state such that even insignificant fluctuations can entail events of any size that have a power law distribution [5]. In this model perturbations are external. However, in the systems of sach a state there should appear a mechanism generating perturbations inside the system due to a feedback. That can be a result of nonlinear interaction of the quantities connected with order parameters (that express a quasistationary state of the self-organized system). Deterministic chaos generated in such a way is used for selective adaptation of the system itself (i.e. in the passage into another quasistationary state), thus maintaining dynamic homeostasis of the system.

    Though transference of this standpoint into the interpretation of social evolution phenomena does not cause essential contradictions, however, it is difficult so far define direct factors that ensure the generation of variety in different stages of evolution of the social system. It is noticed that in certain systems (including social ones) there appear constants (6% of necessary variety, 0.0008% of stabilizing selection and others) [6]. The ratio of constructed modules of a system (reflecting its order parameters) allow to judge of its "normality" and a possibility of changing. The models are proposed with explain the formation of conglomerate power law distribution in the most various systems [7]. However, the origin of "inovations" and the rate of adaptation of the system are not considered here. The report will propose a model in which the interaction of the system and the environment maintains and periodically increases the variety of the system.

    1. J. Cairns, J. Overbough, S. Miller, Nature 335:142 (1988).
    2. E. D. Schulze, H. A. Mooney (eds), "Biodiversity and Ecosystem Function", (1993).
    3. M. H. Mitias, "Toward a Concept of Universal Justice", Dialog and Humanism 3-4 (1992).
    4. P. K. Feyerabend, "Science in a free society", (1979).
    5. P. Bak, Ch. Tang, K. Wiesenfeld, Phys. Rev. A 38:1
    6. A. A. Davidov, "Module Analysis and Construction of Society" (in Russian, 1994).
    7. B. A. Trubnikov, "The Law of Distribution of Competitors //Priroda (in Russian, 1993).