## TRANSFORMATION (Principle of nonproportional)
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"As any structure grows, the proportions of its parts and of its significant variables cannot remain constant" (K. BOULDING, 1956, p.71).

BOULDING explains this principle in the following way: "It is impossible… to reproduce all the characteristics of a structure in a scale model of different size. This is because a uniform increase in the linear dimensions of a structure will increase all its areas as the square, and its volumes as the cube, of the increase in the linear dimension. Thus a twofold increase in all the lengths of a structure increases its areas by four times and its volumes by eight times. As some of the essential functions and variables of structure depend on its linear dimensions, some on its areal dimensions, and some on its volumetric dimensions, it is impossible to keep the same proportions between all the significant variables and functions as the structure grows" (Ibid).

d'Arcy Wentworth THOMPSON in his fascinating work "On Growth and Form", first published in 1916, scrutinizes a considerable number of consequences of this principle, mainly in biology and engineering. His concept of transformation is basically geometrical: New biological forms, for example, are obtained by the deformations of a geometrical grid. But it is clear that the transformation model can be adapted and extended to animal and human social organizations and explain generally numerous problems linked with gigantism. BOULDING gives some striking examples.

### Categories

- 1) General information
- 2) Methodology or model
- 3) Epistemology, ontology and semantics
- 4) Human sciences
- 5) Discipline oriented

### Publisher

Bertalanffy Center for the Study of Systems Science(2020).

To cite this page, please use the following information:

* Bertalanffy Center for the Study of Systems Science (2020).* Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]

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