International Encyclopedia of Systems and Cybernetics

Variety, in ASHBY's sense, is the condition for complexity.

J.de ROSNAY explains it in the following way: "The growth of a complex system – in volume, size, or number of elements – depends on positive feedbacks and storage of energy. Indeed, a positive feedback, when always working in the same way, results in the accelerated growth of some specific magnitude. It may be the number (growth of a population), diversity (variety of the elements and of their interactions), energy (surplus of energy, profits accumulation, capital growth).

"The positive feedback is equivalent to a random variety generator. It enlarges the slightest difference. It increases the possibilities for choice; accentuates differentiation and generates complexity by multiplying interactions possibilities.

"Variety and complexity are strongly related. But variety is at the same time one of the conditions of stability of any system. Indeed, homeostasis can appear and subsist only through a very great variety of regulations. The more complex the system, the more complex the control subsystem must be, in order to match the multiple perturbations coming from the environment. This is what the Law of Requisite Variety (proposed by W Ross ASHBY in 1958) expresses. This Law, extremely general, establishes in a mathematical form that a system's regulation is efficient only if it relies on a control system as complex as the system itself. In other words, control actions must have a variety equivalent to the variety of the system. In ecology, for example, it is the variety of species; the number of ecological "niches", the wealth of interactions between species and between community and environment, which guarantees the stability and permanence of this community. Variety allows for a very extended supply of responses to the possible forms of aggressions from the environment".

Variety is thus clearly correlated to size.

de ROSNAY still adds: "Variety generation may thus lead to adaptations by increasing complexity. But by confrontation with environment's randomness, it generates also the unexpected, which is the source of change. Growth is thus at the same time the prime mover of change, and the way to adapt to the environment's modifications. One glimpses the way through which a homeostatic system may evolve, while constructed to resist change. It evolves through a complementary process of desorganization (partial or total) and of reorganization. This happens either during the clash of the system with random perturbations from the environment (mutations, events, noise), or during the readjustement of some desequilibrium resulting, for example, of too fast a growth" (1990, p.120).