Variety (cybernetics)
Encyclopedia
In cybernetics
the term variety denotes the total number of distinct states of a system
.
. The condition for dynamic stability under perturbation (or input) was described by his Law of Requisite Variety. Ashby says:
He adds
Variety can be stated as an integer, as above, or as the logarithm to the base 2 of the number i.e. in bit
s.
(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
.
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
.
Stafford Beer defines variety as "the total number of possible states of a system, or of an element of a system", c.f. Ludwig Boltzmann
's Wahrscheinlichkeit
. Beer restates the Law of Requisite Variety as "Variety absorbs variety". Stated more simply the logarithmic measure of variety represents the minimum number of choices (by binary chop) needed to resolve uncertainty
. Beer used this to allocate the management resources necessary to maintain process viability.
with the minimum variety necessary. The mapping of input bits to output bits can then produce an estimate the minimum hardware or software components necessary to produce the desired control
behaviour; for example, in a piece of computer software
or computer hardware
.
The cybernetician Frank George discussed the variety of teams competing in games like football or rugby to produce goals or tries. A winning chess player might be said to have more variety than his losing opponent. Here a simple ordering
is implied. The attenuation
and amplification
of variety were major themes in Stafford Beer's work in management (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 of estimate 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. Small quantities, which might be overlooked, can have big effects. In his Designing Freedom Stafford Beer discusses the patient in a hospital with a temperature denoting fever. Action must be taken immediately to isolate the patient. 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
. See also State (physics) (e.g. Excited state
), State (computer science)
, State pattern
, State (controls) and Cellular automaton
. Requisite Variety can be seen in Chaitin's Algorithmic information theory
where a longer, higher variety program or finite state machine produces incompressible output with more variety or information content.
Recently James Lovelock
suggested burning and burying carbonized
agricultural waste to sequester carbon. A variety calculation requires estimates of global annual agricultural waste production, burial and pyrolysis
efficiency to estimate the mass of carbon thus sequestered from the atmosphere.
Cybernetics
Cybernetics is the interdisciplinary study of the structure of regulatory systems. Cybernetics is closely related to information theory, control theory and systems theory, at least in its first-order form...
the term variety denotes the total number of distinct states of a system
System
System is a set of interacting or interdependent components forming an integrated whole....
.
Overview
The term Variety was introduced by W. Ross Ashby to denote the count of the total number of states of a systemSystem
System is a set of interacting or interdependent components forming an integrated whole....
. The condition for dynamic stability under perturbation (or input) was described by his Law of Requisite Variety. Ashby says:
Thus, if the order of occurrence is ignored, the setc, 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 bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
s.
The Law of Requisite Variety
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 "only 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 TheoryA Mathematical Theory of Communication
"A Mathematical Theory of Communication" is an influential 1948 article by mathematician Claude E. Shannon. As of November 2011, Google Scholar has listed more than 48,000 unique citations of the article and the later-published book version...
(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
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
terms c.f. Newton's third law, Le Chatelier's principle
Le Châtelier's principle
In chemistry, Le Chatelier's principle, also called the Chatelier's principle, can be used to predict the effect of a change in conditions on a chemical equilibrium. The principle is named after Henry Louis Le Chatelier and sometimes Karl Ferdinand Braun who discovered it independently...
.
Later, in 1970, Conant working with Ashby produced the Good Regulator
Good Regulator
The Good Regulator is a theorem due to Roger C. Conant and W. Ross Ashby that is central to cybernetics. It is stated "Every Good Regulator of a system must be a model of that system"....
theorem which required autonomous systems to acquire an internal model of their environment to persist and achieve stability
Stability
-Mathematics:*Stability theory, the study of the stability of solutions to differential equations and dynamical systems**Lyapunov stability**Structural stability*Stability of a point in geometric invariant theory....
(e.g. Nyquist stability criterion
Nyquist stability criterion
When designing a feedback control system, it is generally necessary to determine whether the closed-loop system will be stable. An example of a destabilizing feedback control system would be a car steering system that overcompensates -- if the car drifts in one direction, the control system...
) or dynamic equilibrium
Dynamic equilibrium
A dynamic equilibrium exists once a reversible reaction ceases to change its ratio of reactants/products, but substances move between the chemicals at an equal rate, meaning there is no net change. It is a particular example of a system in a steady state...
.
Stafford Beer defines variety as "the total number of possible states of a system, or of an element of a system", c.f. Ludwig Boltzmann
Ludwig Boltzmann
Ludwig Eduard Boltzmann was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics...
's Wahrscheinlichkeit
Boltzmann's entropy formula
In statistical thermodynamics, Boltzmann's equation is a probability equation relating the entropy S of an ideal gas to the quantity W, which is the number of microstates corresponding to a given macrostate:...
. Beer restates the Law of Requisite Variety as "Variety absorbs variety". Stated more simply the logarithmic measure of variety represents the minimum number of choices (by binary chop) needed to resolve uncertainty
Uncertainty
Uncertainty is a term used in subtly different ways in a number of fields, including physics, philosophy, statistics, economics, finance, insurance, psychology, sociology, engineering, and information science...
. Beer used this to allocate the management resources necessary to maintain process viability.
Applications
In general a description of the required inputs and outputs is established then encodedEncoder
An encoder is a device, circuit, transducer, software program, algorithm or person that converts information from one format or code to another, for the purposes of standardization, speed, secrecy, security, or saving space by shrinking size.-Media:...
with the minimum variety necessary. The mapping of input bits to output bits can then produce an estimate the minimum hardware or software components necessary to produce the desired control
Control system
A control system is a device, or set of devices to manage, command, direct or regulate the behavior of other devices or system.There are two common classes of control systems, with many variations and combinations: logic or sequential controls, and feedback or linear controls...
behaviour; for example, in a piece of computer software
Computer software
Computer software, or just software, is a collection of computer programs and related data that provide the instructions for telling a computer what to do and how to do it....
or computer hardware
Computer hardware
Personal computer hardware are component devices which are typically installed into or peripheral to a computer case to create a personal computer upon which system software is installed including a firmware interface such as a BIOS and an operating system which supports application software that...
.
The cybernetician Frank George discussed the variety of teams competing in games like football or rugby to produce goals or tries. A winning chess player might be said to have more variety than his losing opponent. Here a simple ordering
Order (group theory)
In group theory, a branch of mathematics, the term order is used in two closely related senses:* The order of a group is its cardinality, i.e., the number of its elements....
is implied. The attenuation
Attenuation
In physics, attenuation is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, X-rays are attenuated by lead, and light and sound are attenuated by water.In electrical engineering and telecommunications, attenuation affects the...
and amplification
Amplifier
Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...
of variety were major themes in Stafford Beer's work in management (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 of estimate Ashby's "powers of discrimination" (see above quote). Given the butterfly effect
Butterfly effect
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions; where a small change at one place in a nonlinear system can result in large differences to a later state...
of dynamical systems care must be taken before quantitative measures can be produced. Small quantities, which might be overlooked, can have big effects. In his Designing Freedom Stafford Beer discusses the patient in a hospital with a temperature denoting fever. Action must be taken immediately to isolate the patient. 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
Viable System Model
The viable systems model, or VSM is a model of the organisational structure of any viable or autonomous system. A viable system is any system organised in such a way as to meet the demands of surviving in the changing environment. One of the prime features of systems that survive is that they are...
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
Bandwidth (computing)
In computer networking and computer science, bandwidth, network bandwidth, data bandwidth, or digital bandwidth is a measure of available or consumed data communication resources expressed in bits/second or multiples of it .Note that in textbooks on wireless communications, modem data transmission,...
requirements, redundancy
Redundant code
Redundant code is a computer programming term for code, which may be source code or compiled code in a computer program, that has any form of redundancy, such as recomputing a value that has previously been calculated and is still available, code that is never executed , or code which is executed...
and software bloat
Software bloat
Software bloat is a process whereby successive versions of a computer program include an increasing proportion of unnecessary features that are not used by end users, or generally use more system resources than necessary, while offering little or no benefit to its users.-Causes:Software developers...
, the bit representation of data types and indexes
B-tree
In computer science, a B-tree is a tree data structure that keeps data sorted and allows searches, sequential access, insertions, and deletions in logarithmic time. The B-tree is a generalization of a binary search tree in that a node can have more than two children...
, analogue to digital conversion
Analog-to-digital converter
An analog-to-digital converter is a device that converts a continuous quantity to a discrete time digital representation. An ADC may also provide an isolated measurement...
, the bounds on finite state machines and data compression
Data compression
In computer science and information theory, data compression, source coding or bit-rate reduction is the process of encoding information using fewer bits than the original representation would use....
. See also State (physics) (e.g. Excited state
Excited state
Excitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being excited to an excited state....
), State (computer science)
State (computer science)
In computer science and automata theory, a state is a unique configuration of information in a program or machine. It is a concept that occasionally extends into some forms of systems programming such as lexers and parsers....
, State pattern
State pattern
The state pattern, which closely resembles Strategy Pattern, is a behavioral software design pattern, also known as the objects for states pattern. This pattern is used in computer programming to represent the state of an object. This is a clean way for an object to partially change its type at...
, State (controls) and Cellular automaton
Cellular automaton
A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. It consists of a regular grid of cells, each in one of a finite number of states, such as "On" and "Off"...
. Requisite Variety can be seen in Chaitin's Algorithmic information theory
Algorithmic information theory
Algorithmic information theory is a subfield of information theory and computer science that concerns itself with the relationship between computation and information...
where a longer, higher variety program or finite state machine produces incompressible output with more variety or information content.
Recently James Lovelock
James Lovelock
James Lovelock, CH, CBE, FRS is an independent scientist, environmentalist and futurologist who lives in Devon, England. He is best known for proposing the Gaia hypothesis, which postulates that the biosphere is a self-regulating entity with the capacity to keep our planet healthy by controlling...
suggested burning and burying carbonized
Carbonization
Carbonization or carbonisation is the term for the conversion of an organic substance into carbon or a carbon-containing residue through pyrolysis or destructive distillation. It is often used in organic chemistry with reference to the generation of coal gas and coal tar from raw coal...
agricultural waste to sequester carbon. A variety calculation requires estimates of global annual agricultural waste production, burial and pyrolysis
Biochar
Biochar or terra preta is charcoal created by pyrolysis of biomass. Biochar is under investigation as an approach to carbon sequestration via bio-energy with carbon capture and storage. Biochar thus has the potential to help mitigate climate change, via carbon sequestration...
efficiency to estimate the mass of carbon thus sequestered from the atmosphere.
See also
- Cardinality
- ComplexityComplexityIn general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. The study of these complex linkages is the main goal of complex systems theory. In science there are at this time a number of approaches to characterizing complexity, many of which are...
- Degrees of freedomDegrees of freedom (physics and chemistry)A degree of freedom is an independent physical parameter, often called a dimension, in the formal description of the state of a physical system...
- Power set
Further reading
- Ashby, W.R. 1956, An Introduction to Cybernetics, Chapman & Hall, 1956, ISBN 0-416-68300-2 (also available in electronic form as a PDF from Principia Cybernetica)
- Ashby, W.R. 1958, Requisite Variety and its implications for the control of complex systems, Cybernetica (Namur) Vo1 1, No 2, 1958.
- Beer, S. 1974, Designing Freedom, CBC Learning Systems, Toronto, 1974; and John Wiley, London and New York, 1975. Translated into Spanish and Japanese.
- Beer, S. 1975, Platform for Change, John Wiley, London and New York. Reprinted with corrections 1978.
- Beer, S. 1979, The Heart of Enterprise, John Wiley, London and New York. Reprinted with corrections 1988.
- Beer, S. 1981, Brain of the Firm; Second Edition (much extended), John Wiley, London and New York. Reprinted 1986, 1988. Translated into Russian.
- Beer, S. 1985, Diagnosing the System for Organisations; John Wiley, London and New York. Translated into Italian and Japanese. Reprinted 1988, 1990, 1991.
- Conant, R. 1981 Mechanisms of Intelligence: Ross Ashby's papers and writings Intersystems Publications ISBN 1127197703
External links
- The Law of Requisite Variety in the Principia Cybernetica Web, 2001.
- Systems concepts and 9/11 Allenna LeonardAllenna LeonardAllenna Leonard is an American cyberneticist, consultant and Director of Team Syntegrity Inc. of Toronto, Canada, internationally, specializing in the application of Stafford Beer's Viable System Model and Syntegration.- Biography :...
on Requisite Variety - All references to The Law of Requisite Variety in Ross Ashby's journal 1953-1961.
- Management Cybernetics: The Law of Requisite Variety Livas short introductory videos on YouTubeYouTubeYouTube is a video-sharing website, created by three former PayPal employees in February 2005, on which users can upload, view and share videos....