Variety (cybernetics)
In cybernetics, the term variety denotes the total number of distinguishable elements of a set, most often the set of states, inputs, or outputs of a finite-state machine or transformation, or the binary logarithm of the same quantity.
[1] Variety is used in cybernetics as an information theory that is easily related to deterministic finite automata, and less formally as a conceptual tool for thinking about organization, regulation, and stability.
[2] The term "variety" was introduced by W. Ross Ashby to extend his analysis of machines to their set of possible behaviors.
The reference frame consists of a state space and the set of measurements available to the observer, which have total variety
, which is reduced as the observer loses uncertainty about the state by learning to predict the system.
The law of experience holds that machines under input tend to lose information about their original state, and the law of requisite variety states a necessary, though not sufficient, condition for a regulator to exert anticipatory control by responding to its current input (rather than the previous output as in error-controlled regulation).
The law of experience refers to the observation that the variety of states exhibited by a deterministic machine in isolation cannot increase, and a set of identical machines fed the same inputs cannot exhibit increasing variety of states, and tend to synchronize instead.
As a result, an observer's uncertainty about the state of the machine either remains constant or decreases with time.
the machines' states move toward any attractors that exist in the corresponding transformation and some may synchronize at these points.
and the machines' behavior enacts a different transformation, more than one of these attractors may sit in the same basin of attraction under
"In other words," Ashby says, "changes at the input of a transducer tend to make the system's state (at a given moment) less dependent on the transducer's individual initial state and more dependent on the particular sequence of parameter-values used as input.
Ashby used variety to analyze the problem of regulation by considering a two-player game, where one player,
, the table is chosen so that no outcome is repeated in any column, which ensures that in the corresponding game any change in
[1]: 207–208 Ashby described the law of requisite variety as related to the tenth theorem in Shannon's Mathematical Theory of Communication (1948):[6] This law (of which Shannon's theorem 10 relating to the suppression of noise is a special case) says that if a certain quantity of disturbance is prevented by a regulator from reaching some essential variables, then that regulator must be capable of exerting at least that quantity of selection.
[1]: 209 Ashby saw this law as relevant to problems in biology such as homeostasis, and a "wealth of possible applications".
Later, in 1970, Conant working with Ashby produced the good regulator theorem[7] 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.
A further practical application of this law is the view that information systems (IS) alignment is a continuous coevolutionary process that reconciles top-down ‘rational designs’ and bottom-up ‘emergent processes’ of consciously and coherently interrelating all components of the Business/IS relationships in order to contribute to an organization’s performance over time.
"[11] Stated more simply, the logarithmic measure of variety represents the minimum number of choices (by binary chop) needed to resolve uncertainty.
The cybernetician Frank George discussed the variety of teams competing in games like football or rugby to produce goals or tries.
The attenuation and amplification of variety were major themes in Stafford Beer's work in management [10] (the profession of control, as he called it).
The number of staff needed to answer telephones, control crowds or tend to patients are clear examples.
The application of natural and analogue signals to variety analysis require an estimate of Ashby's "powers of discrimination" (see above quote).
Given the butterfly effect of dynamical systems care must be taken before quantitative measures can be produced.
In his Designing Freedom Stafford Beer discusses the patient in a hospital with a temperature denoting fever.
Here no amount of variety recording the patients' average temperature would detect this small signal which might have a big effect.
Monitoring is required on individuals thus amplifying variety (see Algedonic alerts in the viable system model or VSM).
Beer's work in management cybernetics and VSM is largely based on variety engineering.
Further applications involving Ashby's view of state counting include the analysis of digital bandwidth requirements, redundancy and software bloat, the bit representation of data types and indexes, analogue to digital conversion, the bounds on finite-state machines and data compression.
In general a description of the required inputs and outputs is established then encoded with the minimum variety necessary.
The mapping of input bits to output bits can then produce an estimate of the minimum hardware or software components necessary to produce the desired control behaviour; for example, in a piece of computer software or computer hardware.
