Advertisement

The bulletin of mathematical biophysics

, Volume 30, Issue 1, pp 135–151 | Cite as

A contribution to Rashevsky’s mathematical theory of development

  • Edward G. Butz
Article

Abstract

The application of Rashevsky’s transformationT to a primordial graph yields a set of graphs corresponding to different stages in the development of the organism. However, sinceT is multiple-valued the graphs obtained are not ordered. To obtain an ordering, it is first shown that the set of graphs under consideration is equivalent to a well defined setO (for “organism”) ofn-tuples. A metric is then introduced which is based on a biological consideration discussed by Rashevsky (Bull. Math. Biophysics,16, 317–348, 1954). Since a metric implies an ordering of the setO, with a knowledge of the structure of the primordial, one can obtain the developmental sequence. Unfortunately, at present, the structure of the primordial graph is unknown which makes the direct application of the above principle impossible. Consequently, an indirect approach which makes use of more accessible biological phenomena is discussed as well. The hypothesis thatrate of development decreases exponentially and the implications this has with regard to the metric onO are discussed. It is shown that if the hypothesis is accepted the search for the developmental sequence is narrowed.

Keywords

Transformation Rule Developmental Sequence Specializable Vertex Numerical Weight Biological Consideration 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. Balinsky, B. I. 1960.An Introduction to Embryology. Philadelphia: W. B. Saunders.Google Scholar
  2. Motzkin, T. S. 1952. “Systems of Inequalities.” U.S. Air Force Project, Rand Publication T-22.Google Scholar
  3. Rashevsky, N. 1954. “Topology and Life: In Search of General Mathematical Principles in Biology and Sociology.”Bull. Math. Biophysics,16, 317–348.MathSciNetGoogle Scholar
  4. 1955a. “Note on a Combinatorial Problem in Topological Biology.”,17, 45–50.MathSciNetGoogle Scholar
  5. 1955b. “Life Information Theory, and Topology.”17, 229–235.MathSciNetGoogle Scholar
  6. 1961. “Abstract Mathematical Molecular Biology.”23, 237–260.MATHMathSciNetGoogle Scholar
  7. Saaty, T. L. 1959.Mathematical Methods of Operations Research. New York: McGraw-Hill.MATHGoogle Scholar
  8. Trucco, E. 1956. “On the Information Content of Graphs: Compound Symbols; Different States For Each Point.”Bull. Math. Biophysics,18, 237–253.MathSciNetGoogle Scholar

Copyright information

© N. Rashevsky 1968

Authors and Affiliations

  • Edward G. Butz
    • 1
  1. 1.Department of MathematicsUniversity of WaterlooWaterloo

Personalised recommendations