Ludwig von Bertalanffy

Karl Ludwig von Bertalanffy General System Theory and Unity of Science (September_19, 1901, Vienna, Austria - June_12, 1972, New York, USA) was a biologist who was a founder of general systems theory--which he literally translated from the mathematization of Nicolai Hartmann's Ontology as stated by himself in his seminal work. An Austrian citizen, he did much work in Canada and the United States.

The individual growth model
The individual growth model published by von Bertanlanffy in 1934 is widely used in biological models and exists in a number of permutations.

In its simplest version the so-called von Bertalanffy growth equation is expressed as a differential equation of length (L) over time (t):

$$L'(t) = r_B \left( L_\infty - L(t) \right)$$

when $$r_B$$ is the von Bertalanffy growth rate and $$L_\infty$$ the ultimate length of the individual.This model was proposed earlier by Pütter in 1920 (Arch. Gesamte Physiol. Mench. Tiere, 180: 298-340). The Dynamic Energy Budget theory provides a mechanistic explanation of this model in the case of isomorphs that experience a constant food availability. The inverse of the von Bertalanffy growth rate appears to depend linearly on the ultimate length, when different food levels are compared.The intercept relates to the maintenance costs, the slope to the rate at which reserve is mobilized for use by metabolism.The ultimate length equals the maximum length at high food availabilites.

References:
 * Bertalanffy, L. von, (1934).Untersuchungen über die Gesetzlichkeit des Wachstums. I. Allgemeine Grundlagen der Theorie; mathematische und physiologische Gesetzlichkeiten des Wachstums bei Wassertieren. Arch. Entwicklungsmech., 131:613-652.

Work
Bertanlanffy authored some 10 books


 * 1928, Kritische Theorie der Formbildung, Borntraeger. In English: Modern Theory of Development, Harper New York, 1932
 * 1930, Lebenswissenschaft und Bildung, Stenger, Erfurt 1930
 * 1937, Das Gefüge des Lebens, Teubner, Leipzig.
 * 1940, Vom Molekül zur Organismenwelt, Akademische Verlagsgesellschaft Athenaion, Potsdam.
 * 1949, Das biologische Weltbild, Europäische Rundschau, Bern. In English: Problems of Life, New York, 1952.
 * 1953, Biophysik des Fliessgleichgewichts, Vieweg, Braunschweig; 2nd rev. ed. by W. Beier and R. Laue, Akademischer Verlag, Berlin (Ost) 1977
 * 1953, Die Evolution der Organismen, in: Schöpfungsglaube und Evolutionstheorie, Alfred Kröner Verlag, Stuttgart, pp 53-66
 * 1959, Stammesgeschichte, Umwelt und Menschenbild, Schriften zur wissenschaftlichen Weltorientierung Vol 5. Lüttke, Berlin
 * 1967, Robots, Men and Minds, New York
 * 1968, General System theory: Foundations, Development, Applications, Ludwig von Bertalanffy, George Braziller New York.
 * 1968, The Organismic Psychology and Systems Theory, Worcester
 * 1975, Perspectives on General Systems Theory. Scientific-Philosophical Studies, E. Taschdjian (eds.), George Braziller New York.
 * 1981, A Systems View of Men, P. A. LaViolette, Boulder.

The first articles from Bertalanffy on General Systems Theory:
 * 1945, Zu einer allgemeinen Systemlehre, Blätter für deutsche Philosophie, 3/4. (Extract in: Biologia Generalis, 19 (1949), 139-164.
 * 1950, An Outline of General System Theory, British Journal for the Philosophy of Science 1, p.139-164
 * 1951, General system theory - A new approach to unity of science (Symposium), Human Biology, Dec 1951, Vol. 23, p. 303-361.