International Encyclopedia of Systems and Cybernetics

"Only variety can destroy variety" (W.R. ASHBY, 1956" p.207)… or

"R's Capacity as a regulator cannot exceed its capacity as a channel for variety" (W. R. ASHBY, 1951, p.171).

In other words, the efficiency of a regulator in resisting environmental disturbances depends of the number of countervailing options it can produce.

For a system, this means that its regulators are able to maintain the system organization only to the extend that they can produce alternative states for any perturbation imposed by environmental noise.

Explain H. ATLAN: "This law is important… to understand the minimal conditions of structure needed for the survival of any system depending on an environmental source of aggressions and random perturbations.

"Let us consider a system exposed to a number of different possible perturbations. It has at is disposal a number of responses. Among the multiple possible states, only some are "acceptable" in view of the finality (at least apparent) of the system, which may be its sheer survival or the accomplishment of some function. The regulation is meant as choosing among the possible responses, those that will place the system in an acceptable state. ASHBY's law states a relation between the variety of perturbations, the one of responses and the one of acceptable states. Variety of responses must be bigger if variety of perturbations is big and the one of acceptable states small. In other words, a great variety of available responses is needed in order to insure a regulation in a system such as to maintain it in a very limited number of states while submitted to a great variety of aggressions. Still more, in any environment being a source of variable and unforeseable aggressions, variety in the structures and functions of the system is an requisite factor of autonomy" (1972, p.25).

This celebrated law was proposed by W.R. ASHBY in 1956. R. VALLÉE comments it in the following way: "Schematically, this principle, which is still controversial, as restated by R. CONANT (1969, p.334-6), says that the ability of a feedback device (for example a regulator) to resist successfully to a perturbing noise, increases with its capacity to transmit a greater quantity of information, per time unit, through its feedback chain. We have here a concept derived from SHANNON's theory (the capacity to transmit information) and an idea coming from games theory (the ability to resist to an opponent), the variety requisite for achieving the chosen purpose, being the variety of informations transmitted per time unit" (1993a, p.88).

In very complex interrelations between a system and its environment, it is not possible for the system to obtain absolute control over its environment because there is an upper limit to the variety that the system may contain.