Editing Ludwig von Bertalanffy (section)

== Work ==
Today, Bertalanffy is considered to be a founder and one of the principal authors of the interdisciplinary school of thought known as [[general systems theory]], which was pioneered by [[Alexander Bogdanov]].<ref name=":0">{{Cite journal |last=Gare |first=Arran |date=2000-11-01 |title=Aleksandr Bogdanov and Systems Theory |url=https://doi.org/10.1080/10855660020020230 |journal=Democracy & Nature |volume=6 |issue=3 |pages=341–359 |doi=10.1080/10855660020020230 |issn=1085-5661|hdl=1959.3/751 |hdl-access=free }}</ref> According to [[Thaddus E. Weckowicz|Weckowicz]] (1989), he "occupies an important position in the intellectual history of the twentieth century. His contributions went beyond [[biology]], and extended into [[cybernetics]], [[education]], [[history]], [[philosophy]], [[psychiatry]], [[psychology]] and [[sociology]]. Some of his admirers even believe that this theory will one day provide a conceptual framework for all these disciplines".<ref name="TEW89"/>

=== Individual growth model ===
The [[cell growth|individual growth]] [[model (abstract)|model]] published by Ludwig von Bertalanffy in 1934 is widely used in biological models and exists in a number of permutations.

In its simplest version the so-called Bertalanffy growth equation is expressed as a [[differential equation]] of length (''L'') over time (''t''):

<math>L'(t) = r_B \left( L_\infty - L(t) \right)</math>

when <math>r_B</math> is the Bertalanffy growth rate and <math>L_\infty</math> the ultimate length of the individual. This model was proposed earlier by August Friedrich Robert Pūtter (1879-1929), writing in 1920.<ref>August Friedrich Robert Pūtter (6 April 1879 - 11 March 1929) wrote a textbook on comparative physiology entitled ''Vergleichende Physiologie'' (Jena: G. Fischer, 1911) and many other notable works. For a translation of his "Studien ūber physiologische Ähnlichkeit. VI. Wachstumsähnlichkeiten" ("Studies on Physiological Similarity. VI. Analogies of Growth") in ''Pflūgers Archiv fūr die gesamte Physiologie des Menschen und der Tiere'', '''180''': 298-340, see http://www.dfo-mpo.gc.ca/Library/147555.pdf</ref>

The [[dynamic energy budget theory]] provides a mechanistic explanation of this model in the case of [[isomorph]]s that experience a constant food availability. The inverse of the 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 availabilities.<ref name=ber1934>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.</ref>

[[Image:PassiveAnalog.jpg|thumb|right|Passive electrical schematic of the Bertalanffy module together with equivalent expression in the [[Energy Systems Language]]]]

=== Bertalanffy equation ===
The Bertalanffy equation describes the growth of a biological organism. It was presented by Ludwig von Bertalanffy in 1969.<ref>Bertalanffy, L. von, (1969). ''General System Theory''. New York: George Braziller, pp. 136</ref>

<math>
 \frac{dW}{dt}= \eta S- k V
</math>

Here W is organism weight, t is the time, S is the area of organism surface, and V is a physical volume of the organism.

The coefficients <math>\eta</math> and <math> k </math> are (by Bertalanffy's definition) the "coefficient of anabolism" and "coefficient of catabolism" respectively.

The solution of the Bertalanffy equation is the function:

<math>
W(t)=\Big(\eta\,c_1 -c_2\,e^{-\tfrac{k}{3}t}\Big)^3\,, 
</math>

where <math>c_1</math> and <math>c_2</math> are constants.

Bertalanffy couldn't explain the meaning of the parameters <math>\eta </math> (the coefficient of anabolism) and <math> k </math> (coefficient of catabolism) in his works, which prompted criticism from biologists.  However, the Bertalanffy equation is a special case of the Tetearing equation,<ref name=Tetearing2012>{{cite book 
|author1=Alexandr N. Tetearing
 |title=Theory of populations |year=2012 |page=607 |isbn=978-1-365-56080-4 |publisher=SSO Foundation |location=Moscow}}</ref> that is a more general equation of the growth of a biological organism. The Tetearing equation does provide a physical meaning of the coefficients <math>\eta </math> and <math> k </math>.

===Bertalanffy module===
To honour Bertalanffy, ecological systems engineer and scientist [[Howard T. Odum]] named the storage symbol of his [[Energy Systems Language|General Systems Language]] as the Bertalanffy module (see image right).<ref>Nicholas D. Rizzo William Gray (Editor), Nicholas D. Rizzo (Editor), (1973) ''Unity Through Diversity. A Festschrift for Ludwig von Bertalanffy''. Gordon & Breach Science Pub</ref>

=== General system theory ===
In the late 1920s, the Soviet philosopher [[Alexander Bogdanov]] pioneered "''Tektology''", whom [[Johann Plenge]] referred to as the theory of "general systems".<ref name=":0" /><ref>{{Cite journal |last=Plenge |first=Johann |date=1927 |title=Um die Allgemeine Organisationslehre |url=https://ia802808.us.archive.org/1/items/PlengeReviewOfTektology/Plenge%20Review%20of%20Tektology.pdf |journal=Weltwirtschaftliches Archiv Review of World Economics |volume=25 |pages=18–29 |via=[[Internet Archive]]}}</ref> However, in the West, Bertalanffy is widely recognized for the development of a theory known as [[Systems theory|general system theory]] (GST). The theory attempted to provide alternatives to conventional models of [[organization]]. GST defined new foundations and developments as a generalized theory of systems with applications to numerous areas of study, emphasizing [[holism]] over reductionism, [[organism]] over mechanism.

Foundational to GST are the inter-relationships between elements which all together form the whole.