Ashby’s law of requisite variety

Copyright 2017 Graham Berrisford. One of several hundred papers at http://avancier.website. Last updated 08/03/2019 13:18

 

W. Ross Ashby (1903-1972) was a psychologist and systems theorist.

“Despite being widely influential within cybernetics, systems theory… Ashby is not as well known as many of the notable scientists his work influenced.”

Understanding Ashby’s ideas helps you to understand much else in the field of systems thinking.

This paper explores his particular ideas about the variety a regulator needs to control a system.

Unless otherwise stated, quotes below are from Introduction to Cybernetics” (1956) W. Ross Ashby.

Contents

The brain as a control system.. 1

Variety as a measure of complexity. 1

Variety absorbs variety - the law of requisite variety. 2

Ashby’s law reviewed and revisited. 2

Ashby’s law elaborated. 3

 

The brain as a control system

In “Design for a Brain” (1952), Ashby presented the brain as a control system.

“The book dealt primarily with homeostatic processes within living organisms, rather than in an engineering or electronic context.” Wikipedia 2017

 

In cybernetic regulation, a control system directs a target system to maintain its state variables in a desired range.

A thermostat (control system) directs the actions of a heating system (target system).

In Ashby’s view, the brain (control system) directs the actions of a body (target system).

He saw the brain as a regulator that maintains a body’s state variables in the ranges suited to life

The aim is homeostasis – to maintain the state of the body - and so help it achieve other desired outcomes.

 

He selected variables relevant to his interest in the brain as a control system,

Setting aside other things you might consider important to being human, such as consciousness.

The basic idea might be distilled into one sentence thus.

 

Generic system description

Ashby’s design for a brain

A collection of active structures

that interact in regular behaviors

that maintain system state and/or

consume/deliver inputs/outputs

from/to the wider environment.

A collection of brain cells that

interact in processes to

maintain body state variables by

receiving/sending information

from/to bodily sensors/motors.

 

Ashby’s book holds an abstract description of a brain, which in turn holds an abstract description of a body’s physical variables.

Much as an engineer’s specification holds an abstract description of a control system, which in turn holds an abstract description of the physical variables it controls in a target system.

 

Ashby’s book holds an abstract description of a brain, which in turn holds an abstract description of a body’s physical variables.

Much as an engineer’s specification holds an abstract description of a control system, which in turn holds an abstract description of the physical variables it controls in a target system.

The graphic below separates a control system (the brain) from its target system (the remainder of the body).

 

Control system

Target system

“Design for a brain”

<wrote>                  <realised in>

Ashby                 <envisaged>               Brains

 

 

<monitor> Body state variables

<control>  Muscles and organs

 

Information flows are central to cybernetics.

 

Brains and businesses

Cybernetics has influenced systems thinking in general, and business system thinking in particular.

Businesses can be seen as successfully applying the principles of general system theory and cybernetics.

A brain maintains mental models of things (food, friends, enemies, etc.) it perceives to be out there.

A business (in its information systems) maintains documented models of actors and activities it monitors and directs through information feedback loops.

 

A business system is connected to its wider environment by feedback loops.

It receives information about the state of entities and activities in its environment, and records that information in memory.

The state information it receives and stores must model reality well enough, else the system will fail.

It outputs information to inform and direct entities and activities as need be.

Variety as a measure of complexity

Ashby wrote:

“a system is any set of variables which he [the observer] selects”. 

“A system's variety V measures the number of possible states it can exhibit, and corresponds to the number of independent binary variables.

But in general, the variables used to describe a system are neither binary nor independent.”

 

In short, complexity = variety = the number of possible states a system can exhibit.

There are many difficulties with this definition of complexity.

 

First, the measure is incalculably large for any system with a non-trivial state.

 

Second, there is no widely agreed measure of complexity.

There is complexity in system state/structure - as in Ashby’s measure of “variety”.

Also complexity in behavior - as in Mcabe’s measure of procedural complexity.

And complexity in the trajectory of system state change – an interest in System Dynamics.

(Here, I propose: complexity = the number of event/state combinations * the average procedural complexity of the rules applied to them.)

 

Third, what is measured - the control system, the target system, or the real world entity?

Consider the complexity of a tennis match in real world.

Consider the thought processes of its players, and the molecular structures and movements in the players, court surface and tennis balls.

Obviously, you can never measure the complexity of real world entity or behavior per se.

You can only measure it with respect to your chosen description of its elements (roles, actors, processes, variables, whatever).

And then, only measure it at the level of abstraction at which you choose to describe those elements and their inter-relationships.

 

From the viewpoint of a describer, a system is only as complex as its description.

From the viewpoint of a control system, a target system is only as complex as those variables the control system monitors and controls.

Read “Complexity” for more on that topic.

Variety absorbs variety - the law of requisite variety

Ashby’s ideas about regulatory systems include:

·         Variety: the number of possible states a system can exhibit

·         Attenuator: a device that reduces variety.

·         Amplifier: a device that increases variety.

 

Ashby's law of requisite variety applies to how a control system controls selected or essential variables of a target system.

"The larger the variety of actions available to a control system, the larger the variety of perturbations [in values of target system variables] it is able to compensate".

 

The law defines the minimum number of states necessary for a control system to control a target system with a given number of states.

It is interpreted here as meaning:

·         A control system’s information state models only those variables in the target system’s concrete state that are monitored and controlled.

·         For a homeostatic system to be stable, the number of states of the control system must be at least equal to the number of states in the target system.

·         The more ways that a homeostatic system can deviate from its ideal state, the more control actions a control system will need.

 

In response, Conant (1970) produced his so-called "Good Regulator theorem" stating that

"every Good Regulator of a System Must be a Model of that System".

 

Observation:

The Good Regulator theorem was proved by biological evolution long before Conant articulated it.

Animal brains maintain mental models of things (food, friends, enemies etc.) they care about in their environment.

These mental models must be accurate enough to enable the animals to monitor and manipulate those things.

Read Knowledge and Truth for more on the fuzziness of truth.

 

Ashby’s law reviewed and revisited

The law says having enough variety is a necessary precondition to control selected variables in a target system.

 

The law does not say variety is all you need

The law does not say having enough variety is a sufficient precondition to control selected variables.

 

The law does not mean maximising variety

The law does not say having more than enough variety is a good idea.

Ashby emphasised the need to be selective.

“we should pick out and study the facts that are relevant to some main interest that is already given.”

 

Which is contrary to the following “maximize internal variety” principle,

"Since the variety of perturbations a [control] system can potentially be confronted with is unlimited, we should always try maximize its internal variety (or diversity),

so as to be optimally prepared for any foreseeable or unforeseeable contingency." Principia Cybernetica.

This suggests redundant design effort, inefficient system operation and may result in data quality issues.

 

One real world entity may be subject to many control systems

Ashby’s view of a human being had something of Cartesian dualism about it.

He treated the body as the target system and the brain/central nervous system as the control system.

 

Today, psychobiology tends to the view that mental states and activities are bodily states.

This view, that the mind is inseparable from the body, is called “cognitive embodiment”.

And it appears we do not maintain homeostasis purely by control from the higher brain..

Rather, our many state variables are maintained by different control systems, which operate in parallel.

These control systems are distributed through the body and not in direct communication with each other.

 

The law does not mean matching the variety of the whole target system

The law does not mean the control system must be as complex as the concrete reality of the entity controlled

A control system is usually much simpler than any real world entity it controls.

 

E.g. a thermostat models only as much variety (colder or hotter than a given temperature) as the behavior (heating system on or off) it controls.

To the control system, the target system is no more complex than the variables it controls.

 

Control system

Target system

Control system designs

<create and use>                  <realised by>

Engineers      <observe and envisage> Control systems

 

 

<monitor and control>   Heating systems

 

E.g. a tennis a score board models only a few essential variables of a tennis match.

To umpires, what matters are the rules that determine the score, not the length or complexity of the rallies.

 

Control system

Target system

Laws of tennis

<create and use>             <realised by>

LTA      <observe and envisage > Umpires

 

 

<monitor and control> Real tennis matches

 

An implication is that the system describer must be experienced, expert and trained enough to “pick out and study the facts that are relevant”.

System architects must know what is architecturally significant to their and stakeholders’ interests in the target system.

 

The universe is a mess of more or less related systems

In nature and in business, control systems may be distributed, and act independently of each other.

An oyster manages to maintain homeostasis this way, without a central brain and nervous system.

In a large business, parallel divisions may compete for customers, or resources, or have conflicting goals.

 

From the perspective of two different control systems, one real world entity can be two different target systems.

Two control systems may simultaneously compete with and complement each other in controlling the state of one real world entity.

Surely, this is the very stuff of relationships between people in a social group?

 

The wider universe is divisible into infinite systems, separate, nested and overlapping.

Two systems may be described as related as:

·         Control (regulatory) and target systems

·         Cooperating (symbiotic) systems

·         Competing systems

 

But which labels you use may depend on your perspective.

Surely, a heating system controls the behavior of its thermostat?

Ashby’s law elaborated

Ashby’s law might be interpreted for a business thus:

·         A business system’s information state models only those variables of actors and activities that the business monitors and directs.

·         For directions to be effective, the information state must model those variables accurately enough.

·         The more variegated the actors and activities to be monitored and directed, the more complex a business system must be.

 

To direct an actor or activity in its environment, a brain or a business must be able to:

·         maintain or obtain a model of the state of that actor or activity (the model must be accurate enough).

·         gather inputs: detect events that reveal a significant state change (in an acceptably reliable and timely fashion).

·         produce outputs: respond to events or state changes by sending directives to actors to perform activities (in an acceptably reliable and timely fashion).

·         adapt if the actor does not respond to a directive as expected, in an acceptably reliable and timely fashion.

 

To generalise, a control system

·         must know just enough about the state of target system it monitors and directs

·         must detect events that reveal significant state changes in the target system - in an acceptably reliable and timely fashion.

·         must respond to those events by sending appropriate directives to the target system - in an acceptably reliable and timely fashion.

 

A control system can expect a target system to respond appropriately provided that:

·         monitor and control signals cannot go missing or be corrupted

·         time/speed, capacity/throughput, availability and any other non-functional requirements are met

·         the target system has no other (competing/interfering) control system

·         the target system is not capable of self-determination, of choosing an inappropriate response to a control message.

 

 

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