International Encyclopedia of Systems and Cybernetics

"It is impossible for models of different sizes to possess identical characteristics"

The principle has been enunciated by K. BOULDING (1956, p.66-75), who comments: "As any structure grows, the proportions of its parts and of its significant variables cannot remain constant. 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… 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 system grows.

"This principle has two important corollaries. The first is that growth of a structure always involves a compensatory change in the relative sizes of its various parts to compensate for the fact that those functions and properties which depend on volume tend increasingly to dominate those depending on length. Large structures therefore tend to be "longer" and more convoluted than small structures in the attempt to increase the proportion of linear and areal dimensions to volumes" (p.71).

BOULDING gives interesting examples from biology to insect and human architecture.

"The second corollary follows immediately from the first: If the process of compensation for structural disproportion has limits, as it seems to be the case, the size of the structure itself is limited by its ultimate inability to compensate for the non-proportional changes. This is the basic principle for the "law of eventually diminishing returns to scale" familiar to economists" (p.72).

This corollary shows that the analogy between dinosaurs, business conglomerates and bloated bureaucracies is quite more than a metaphor. It also shows how much any type of organization would benefit from a better understanding of global isomorphisms.

BOULDING still adds: "It is interesting to note that the principle of compensation may operate in two very distinct ways – in the direction of attempt to solve the problems posed by large scale or in the direction of an attempt to avoid these problems" (p.72).

Of course, the second way is generally much more economical than the first one, since the reduction of an overgrown structure is much more costly – when still possible! – than the means usable to avoid its excessive growth.