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Some considerations on relational equilibria

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Abstract

A previous study (Bull. Math. Biophysics,31, 417–427, 1969) on the definitions of stability of equilibria in organismic sets determined byQ relations is continued. An attempt is made to bring this definition into a form as similar as possible to that used in physical systems determined byF-relations. With examples taken from physics, biology and sociology, it is shown that a definition of equilibria forQ-relational systems similar to the definitions used in physics can be obtained, provided the concept of stable or unstable structures of a system determined byQ-relations is considered in a probabilistic manner. This offers an illustration of “fuzzy categories,” a notion introduced by I. Bąianu and M. Marinescu (Bull. Math. Biophysics,30, 625–635, 1968), in their paper on organismic supercategories, which is designed to provide a mathematical formalism for Rashevsky's theory of Organismic Sets (Bull. Math. Biophysics,29, 389–393, 1967;30, 163–174, 1968;31, 159–198, 1969). A suggestion is made for a method of mapping the abstract discrete space ofQ-relations on a continuum of variables ofF-relations. Problems of polymorphism and metamorphosis, both in biological and social organisms, are discussed in the light of the theory.

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Literature

  • Baianu, I. and M. Marinescu. 1968. “Organismic Supercategories: I. Proposals for a General Unitary Theory of Systems.”Bull. Math. Biophysics,30, 625–635.

    MATH  MathSciNet  Google Scholar 

  • Jacob, F. and J. Monod. 1961. “On the Regulation of Gene Activity.”Cold Spring Harbor Symposium on Quantitative Biology,26, 193–209.

    Google Scholar 

  • Kauzman, W. 1957.Quantum Chemistry. New York: Academic Press.

    Google Scholar 

  • Lwoff, A. 1962.Biological Order. Cambridge, Massachusetts: M.I.T. Press.

    Google Scholar 

  • Martinez, H. 1964. “Toward an Optimal Design Principle in Relational Biology.”Bull. Math. Biophysics,26, 351–365.

    MATH  Google Scholar 

  • Monod, J. and F. Jacobs, 1961. “General Conclusions, Teleonomic Mechanisms in Cellular Metabolism.”Cold Spring Harbor Symposium on Quantitative Biology,26, 289–400.

    Google Scholar 

  • Prosser, C. L. and F. A. Brown, Jr. 1961.Comparative Animal Physiology. pp. 560–561. Philadelphia: W. B. Saunders, Co.

    Google Scholar 

  • Rashevsky, N. 1955. “Some Remarks on Topological Biology.”Bull. Math. Biophysics,17, 207–218.

    MathSciNet  Google Scholar 

  • — 1960.Mathematical Biophysics. The Physico-Mathematical Foundations of Biology. Third and Revised Edition. New York: Dover Publications, Inc.

    Google Scholar 

  • — 1965. “The Representation of Organisms in Terms of Predicates.”Bull. Math. Biophysics,27, 477–491.

    Google Scholar 

  • — 1966. “Physics, Biology, and Sociology: A Reappraisal.” —Ibid.,28, 283–308.

    MathSciNet  Google Scholar 

  • Rashevsky, N. 1967a. “Organismic Sets: Outline of a General Theory of Biological and Social Organisms.”Bull. Math. Biophysics,29, 139–152.

    MATH  Google Scholar 

  • — 1967b. “Organismic Sets and Biological Epimorphism.” —Ibid.,29, 389–393.

    Google Scholar 

  • — 1967c. “Physics, Biology and Sociology: II. Suggestion for a Synthesis.” —Ibid.,29, 643–648.

    Google Scholar 

  • — 1968. “Organismic Sets: II. Some General Considerations.” —Ibid.,30, 163–174.

    MATH  Google Scholar 

  • — 1969a. “Outline of a Unified Approach to Physics, Biology and Sociology.” —Ibid.,31, 159–198.

    MATH  Google Scholar 

  • — 1969b. “Multiple Relational Equilibria: Polymorphism, Metamorphosis and Other Possible Similar Phenomena.” —Ibid.,31, 417–427.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Mental Health Research Institute, University of Michigan, Ann Arbor, Michigan

    N. Rashevsky

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  1. N. Rashevsky
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Rashevsky, N. Some considerations on relational equilibria. Bulletin of Mathematical Biophysics 31, 605–617 (1969). https://doi.org/10.1007/BF02476641

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  • DOI: https://doi.org/10.1007/BF02476641

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