The bulletin of mathematical biophysics

, Volume 32, Issue 4, pp 485–498 | Cite as

The approximation method, relational biology and organismic sets

  • N. Rashevsky


It is pointed out that the approximation method for diffusion problems, developed by N. Rashevsky in 1937 and successfully used since then by many authors, was in a sense a precursor of relational biology. The connection between the approximation method, relational biology, and the theory of organismic sets, developed in a series of recent papers by N. Rashevsky, is discussed. A number of conclusions known to hold experimentally, are then derived from relational considerations and some of them are applied to organismic sets.


Binary Relation Circadian Clock Functional Relation Mathematical Biophysics Relational Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Carlson, A. J. and Johnson, V. 1953.The Machinery of the Body. Chicago: The University of Chicago Press.Google Scholar
  2. Conroy, M. F. 1969. “Estimation of Aortic Distensibility and Instantaneous Ventricular Volume in Living Man.”Bull. Math. Biophysics,31, 93–104.Google Scholar
  3. Hoagland, Hudson. 1933. “The Physiological Control of Judgments of Duration: Evidence of a Chemical Clock.”Journal Gen. Psychol. 9, 267–287.CrossRefGoogle Scholar
  4. Karreman, George. 1951. “Contribution to the Mathematical Biology of Excitation with Particular Emphasis on Changes in Membrane Permeability and on Threshold Phenomena.”Bull. Math. Biophysics,13, 189–243.Google Scholar
  5. Landahl, H. D. 1957. “Population Growth Under the Influence of Random Dispersal.”,19, 171–186.MathSciNetGoogle Scholar
  6. Legay, J. M. 1968. “Éléments D’Une Théorie Générale de la Croissance D’Une Population.”,30, 33–46.MATHGoogle Scholar
  7. Pavlidis, T. 1967a. “A Mathematical Model for the Light Affected System in the Drosophila Eclosion System.”,29, 781–791.Google Scholar
  8. Rashevsky, N. 1938.Mathematical Biophysics: Physicomathematical Foundations of Biology. Chicago: The University of Chicago Press.Google Scholar
  9. Rashevsky, N. 1948.Mathematical Biophysics. Revised Edition. Chicago: The University of Chicago Press.MATHGoogle Scholar
  10. 1954. “Topology and Life: In Search of General Mathematical Principles in Biology and Sociology.”Bull. Math. Biophysics,16, 317–348.MathSciNetGoogle Scholar
  11. 1960.Mathematical Biophysics. Physicomathematical Foundations of Biology. Third Edition, 2 Vols. New York: Dover Publications, Inc.Google Scholar
  12. 1964.Some Medical Aspects of Mathematical Biology. Springfield, Ill.: Charles C. Thomas, Publishers.Google Scholar
  13. 1967a. “Organismic Sets: Outline of a General Theory of Biological and Social Organisms.”,29, 139–152.MATHGoogle Scholar
  14. 1967b. “Organismic Sets and Biological Epimorphism.”,29, 389–393.Google Scholar
  15. 1967c. “Physics, Biology and Sociology: II. Suggestion for a Synthesis.”.29, 643–648.Google Scholar
  16. 1968a. “Organismic Sets: II. Some General Considerations.”,30, 163–174.MATHGoogle Scholar
  17. Rashevsky, N. 1968b. “Neurocybernetics as a Particular Case of General Regulatory Mechanisms in Biological and Social Organisms”.Concepts de l’age de la Science, No. 4.Google Scholar
  18. 1969a. “Outline of a Unified Approach to Physics, Biology and Sociology.”Bull. Math. Biophysics,31, 159–198.MATHGoogle Scholar
  19. 1969b. “Multiple Relational Equilibria: Polymorphism, Metamorphosis and Other Possibly Similar Phenomena.”,31, 417–427.MATHGoogle Scholar
  20. 1969c. “Some Considerations on Relational Equilibrium.”,31, 605–617.MATHGoogle Scholar
  21. 1970. “Contributions to the Theory of Organismic Sets: Leadership.”,32, 391–401.MATHGoogle Scholar
  22. Roston, S. 1959. “Mathematical Formulation of Cardiovascular Dynamics by Use of the Laplace Transform.”,21, 1–11.Google Scholar
  23. Skellam, J. G. 1951. “Random Dispersal in Theoretical Populations”.Biometrika,38, 196–218.MATHMathSciNetCrossRefGoogle Scholar
  24. Suppes, Patrik. 1957.Introduction to Logic. Princeton: van Nostrand.MATHGoogle Scholar
  25. Weinberg, A. M. 1938. “A Case of Biological Periodicity.”Growth,2, 81–92.MATHGoogle Scholar
  26. 1938. “A Case of Biological Periodicity.”Growth,2, 81–92.MATHGoogle Scholar
  27. Woodger, J. H. 1937.The Axiomatic Method in Biology. Cambridge: Cambridge University Press.MATHGoogle Scholar
  28. Young, Gaylord. 1939. “On the Mechanics of Viscous Bodies and Elongation of Ellipsoidal Cells.”Bull. Math. Biophysics,1, 31–46.MATHGoogle Scholar

Copyright information

© N. Rashevsky 1968

Authors and Affiliations

  • N. Rashevsky
    • 1
  1. 1.Central State UniversityWilberforce

Personalised recommendations