The bulletin of mathematical biophysics

, Volume 22, Issue 1, pp 73–84 | Cite as

Contributions to relational biology

  • N. Rashevsky
Article

Abstract

The principle of biotopological mapping (Rashevsky, 1954,Bull. Math. Biophysics,16, 317–48) is given a generalized formulation, as the principle of relational epimorphism in biology. The connection between this principle and Robert Rosen’s representation of organisms by means of categories (1958,Bull. Math. Biophysics,20, 317–41) is studied. Rosen’s theory of (M,R)-systems, (1958,Bull. Math. Biophysics,20, 245–60) is generalized by dropping the assumption that only terminalM i components are sending inputs into theR i components. It is shown that, if the primordial organism is an (M,R)-system, then the higher organisms, obtained by a construction well discussed previously (1958,Bull. Math. Biophysics,20, 71–93), are also (M,R)-systems. Several theorems about such derived (M,R)-systems are demonstrated.

It is shown that Rosen’s concept of an organism as a set of mappings throws light on phenomena of synesthesia and also leads to the conclusion that Gestalt phenomena must occur not only in the fields of visual and auditory perception but in perceptions of any modality.

Keywords

Rosen Directed Path High Organism Unicellular Organism Environmental Output 

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Literature

  1. Eilenberg S. and S. MacLane. 1945. “General Theory of Natural Equivalences.”Trans. Am. Math. Soc.,58, 231–94.MATHMathSciNetCrossRefGoogle Scholar
  2. Rashevsky, N. 1954. “Topology and Life: In Search of General Mathematical Principles in Biology and Sociology.”Bull. Math. Biophysics,16, 317–48.MathSciNetGoogle Scholar
  3. —. 1955. “Some Remarks on Topological Biology.”,17, 207–218.MathSciNetCrossRefGoogle Scholar
  4. —. 1956a. “Contributions to Topological Biology: Some Considerations on the Primordial Graph and Some Possible Transformation.”,18, 113–28.MathSciNetCrossRefGoogle Scholar
  5. —. 1956b. “What Type of Empirically Verifiable Predictions Can Topological Biology Make?”,18, 173–88.MathSciNetGoogle Scholar
  6. —. 1958. “A Contribution to the Search of General Mathematical Principles in Biology.”,20, 71–93.CrossRefGoogle Scholar
  7. —. 1959a. “A Set-Theoretical Approach to Biology.”,21, 101–106.CrossRefGoogle Scholar
  8. —. 1959b. “On the Nature and Origin of Life.”,21, 185–93.CrossRefGoogle Scholar
  9. Rosen, Robert. 1958a. “A Relational Theory of Biological Systems.”Bull. Math. Biophysics,20, 245–60.CrossRefGoogle Scholar
  10. —. 1958b. “The Representation of Biological Systems from the Point of View of the Theory of Categories.”,20, 317–41.CrossRefGoogle Scholar
  11. —. 1959. “A Relational Theory of Biological Systems II.”,21, 109–128.CrossRefGoogle Scholar

Copyright information

© University of Chicago 1960

Authors and Affiliations

  • N. Rashevsky
    • 1
  1. 1.Committee on Mathematical BiologyThe University of ChicagoChicagoUSA

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