Variety (cybernetics)

In cybernetics, the term variety denotes the total number of distinct states of a system.

The term Variety was introduced by W. Ross Ashby to denote the count of the total number of states of a system. The condition for dynamic stability under (or input) was described by his Law of Requisite Variety. Ashby says:

Thus, if the order of occurrence is ignored, the collection
c, b, c, a, c, c, a, b, c, b, b, a
which contains twelve elements, contains only three distinct elements- a, b, c. Such a set will be said to have a variety of three elements.

He adds

The observer and his powers of discrimination may have to be specified if the variety is to be well defined.

Variety can be stated as an integer, as above, or as the logarithm to the base 2 of the number i.e. in bits.

If a system is to be stable, the number of states of its control mechanism must be greater than or equal to the number of states in the system being controlled. Ashby states the Law as "variety can destroy variety". He sees this as aiding the study of problems in biology and a "wealth of possible applications" . He sees his approach as introductory to Shannon Information Theory (1948) which deals with the case of "incessant fluctuations" or noise. The Requisite Variety condition can be seen as a simple statement of a necessary dynamic equilibrium condition in information theory terms c.f. Newton's third law, Le Chatelier's principle.

[ A system has good Control if and only if the dependent variables remain the same even when the independent variables or the State Function have changed. In a real system this implies that the State Function is a composition of two functions, such that the second is the inverse of ( the possible changes of ) the first:

y = F(G(x)) where

F = controller system's function of state

G = controlled system's function of state

x = inputs, OR, independent variables

y = outputs, OR, dependent variables.]

Later, in 1970, Conant working with Ashby produced the good regulator theorem which required autonomous systems to acquire an internal model of their environment to persist and achieve stability (e.g. Nyquist stability criterion) or dynamic equilibrium.

...
Wikipedia