System stability and change

Copyright Graham Berrisford 2017. Last updated 20/02/2019 12:25

One of a hundred papers on the System Theory page at

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Heraclitus of Ephesus was a Greek philosopher known for his doctrine of change being central to the universe.

This paper explores four varieties of system change with reference to Ashby’s ideas.


Recap. 1

System stability. 2

Discrete versus continuous system state change. 2

Discrete versus continuous system mutation. 4

Conclusions. 6

Footnote 1: Why did Ashby say that?. 7

Footnote 2: On stability and change in living entities. 8



First, read these short modules.


·         Systems

·         System change

·         System regulation by circular causal loops


These modules introduced four varieties of system change.


System change

System state change

System mutation


system state change


system state change


system mutation


system mutation?


Classical cybernetics and System Dynamics are about system state change.

State variable values changes in response to events, or stock populations change in response to in/out flows.

The term adaptation is used to mean homeostatic state change – in which causal loops regulate the values of state variables.

It is an inexorable result of the system’s laws; it does not change those laws.


By contrast, second-order cybernetics is about system mutation.

Here, the term adaptation is used to mean changing the state variable types or how events change them.

It changes the very nature of the system; it changes its laws.

System stability

Plato quoted Heraclitus as saying “Everything changes and nothing stands still.

Yet history repeats itself – meaning that some conditions and reactions to them recur – which is symptomatic of a system.

And central to human existence is that some things are stable, or stable enough, for a while.


A system is an island of stability with a limited life time.

The system is shaped – by nature or design – to behave in an orderly way.

The laws of the system, the roles and rules for its actors and activities, are stable.

The trajectory of system state changes may be linear or non-linear, orderly or chaotic, but the laws are fixed.


We expect at least temporary stability in the observable behavior of:

·         banking services

·         card games

·         church services.

·         electricity supply

·         elevators

·         health care operations

·         package delivery operations

·         payroll operations

·         tennis matches

·         traffic control systems

·         voting systems.


Stable does not mean static.

All the above are dynamic activity systems whose state changes over time.

It means only that roles and rules are stable for a generation.

And stable does not mean unchanging.

Since, from one generation to the next, the roles and rules of a system may change.

Discrete versus continuous system state change

This section distinguishes discrete state change from continuous state change.


System state change: a change to the state of a system, which changes the value of at least one variable.

State changes happen during the regular processes of the system.

E.g. winning a set in a tennis match; or the changing positions of planets in their orbits.


It may turn out that state of a system

·         changes in a linear or non-linear, orderly or chaotic, manner.

·         changes continually in one direction, or oscillate back and forth.

·         settles into a steady cyclical pattern or state (as in a homeostatic system)

·         periodically moves from one steady state to another (as a weather system or solar system may do).


Steady and periodic states may be “attractive” - meaning the system, when in a nearby state, likely moves towards them.


Early system theorists were especially interested in homeostatic systems.

They studied dampening feedback loops that maintain system state variables (e.g. body temperature) in a desirable range. 

System theorists called such system state changes adaptations, meaning they adapt the entity so as to maintain homeostasis.


But not all state changes are homeostatic, or well called “adaptations”.

Some systems continually amplify or increase a variable, such as income, profit, or happiness.

And most information systems update state variable values to reflect changes in a reality of interest.


So, system state change varieties include the following.

·         Homeostasis – the process by which a system responds to internal and external state changes so as to maintain its state variables in acceptable ranges.

·         Information update – the process by which a system’s information state is changed to reflect the state of its environment.

·         Autopoiesis – the process by which a biological cell, given simple chemical inputs, sustains/replicates its own complex chemistry.


The dynamics of a system are how the state of that system changes over time.

State changes may happen in discrete steps, in response to discrete events, or continuously.


Discrete (or digital) system state change

This means a system’s state advances incrementally in response to discrete events.

The term digital is used to describe signals that are chunked into discrete units, as in a clock that displays the time as numbers. 


Continuous (or analogue) system state change

This means a system’s state advances continually in response to continuous forces or inputs.

The term analogue is used to describe signals that vary continuously, as in a clock with revolving hands.


Most business systems are driven by discrete events and experience discrete state changes.

So they are naturally modelled as what is called discrete event-driven systems (DEDS).

However, continuous systems can also be modelled as discrete event-driven systems.

“We shall assume that the change occurs by a measurable jump, as the money in a bank account changes by at least a penny.

consideration of the case in which all differences are finite loses nothing; it gives a clear and simple foundation;

and it can always be converted to the continuous form if that is desired.” Ashby 1956

Discrete versus continuous system mutation

This section distinguishes discrete state mutation from continuous system mutation.


System mutation: a change to the nature of a system, which changes the type of at least one variable or behavior.

Mutations happen when the processes of the system are changed

E.g. The Lawn Tennis Association publishes changes to the laws of tennis.

Or an asteroid knocks a planet out of its orbit.


System mutation varieties include the following.

·         Reproduction with modification - the process that creates a new, different, descendant system (generation N + 1).

·         Maturation – the process by which seeds or eggs develop into adult forms.

·         Learning – the process by which intelligent actors (animal or machine) respond differently to a new input after recognising its resemblance to past inputs (implies fuzzy logic).


Reproduction with modification happens in clearly identifiable discrete steps, each system generation replacing the last.

By contrast, maturation and learning may happen continuously, or in such small steps it is regarded as continuous.


Discrete system mutation: a step change from one system generation to the next.


To change a biological organism is to change its DNA.

Discrete-step generational system change is the natural course of events in biology.


To change a System Dynamics model is to change its stocks and flows.

Discrete-step generational system changes are made by the system modellers to improve the model.


To change a business system is to change its roles and rules.

Change requests may come from owners, sponsors, observers, designers and actors in the system.

In business, so-called “continuous improvement” is typically managed in discrete cycles

The cycle is sometimes called PDCA (plan–do–check–act/adjust), the Deming circle/cycle/wheel, the Shewhart cycle, or the control circle/cycle.


The purpose of an enterprise architecture function is to design and plan discrete-step mutations to business systems.

The enterprise function is a meta system to the business systems it observes and envisages.


How to distinguish descendants from ancestors?

Most parents give children different names; however, the veteran golfer Davis Love III is now a caddy for Davis Love IV.

Version numbering usually implies ancestors will eventually be replaced by descendants.


If an ancestor

the descendant may be named

or else

is replaced by a descendant

using the same name

the same name with a new generation or version number

continues in parallel with a descendant

using a new name


Evolution by discrete step mutation

The process of Darwinian evolution can be separated from biology, and from the processes that sustain a system during its life time.

It is an inter-generational process that reproduces system version N with small modifications in system version N+1.

The better that system N+1 is fitted to its environment, the more likely it will be reproduced again.


One ancestor system may give rise to two or more descendent systems at generation N+1.

The two descendant systems will likely be regarded as relatives or members of the same species.

Successive generation changes will likely lead to increasingly diverse descendant systems.

Eventually the descendant systems will likely diverge so far that they can no longer be recognised as relatives or members of the same species.


“Since offspring tend to vary slightly from their parents,

mutations which make an organism better adapted to its environment will be encouraged and developed by the pressures of natural selection,

leading to the evolution of new species [eventually] differing widely from one another and from their common ancestors.”


Note that evolutionary biology plays two roles in these papers.

It explains why animals retain mental models of the world, which helps us to answer questions about the description-reality dichotomy.

It also helps us distinguish system state changes from system mutations.

Individual organisms experience system stage changes – as discussed in cybernetics and general system theory.

A species undergoes system mutations - via reproduction and evolution.


Continuous system mutation = disorderly situation or disorganised entity.

Imagine that the rules of a game could change in a continuous and unpredictable manner.

This undermines the very concept of a game.

When the rules change - how do all players get to hear of them? Who tells them to start using the new rules?

Can some players use the new rules while others are still using the old rules?

Down this road you have a disorderly situation or disorganised entity, not a system at all.


Certainly, the actors in a social group can change the roles of a system they play roles in.

But you cannot change the laws of tennis while you are playing a rally.

You have to stop the game, agree new laws, and restart the game.

To maintain the integrity of the system concept we must insist its rules are changed incrementally – generation by generation.

Because if the rules change continually, there is never any describable or testable system, and to call the entity a system is meaningless.

There is instead a disorderly situation or disorganised entity.


It is commonly said that “enterprise architecture views the enterprise as a system, or system of systems”.

But there are misunderstandings of what this means.

To call every problem, situation or business “a system” is unhelpful.

The misleading equation “entity = system” runs though much systems thinking discussion.

How to restore the system concept to systems thinking?

The conclusions below are in part repeated and in part extended from Social networks versus social systems.


1: The state of an activity system may change

In biology, the values of state variables (temperature, salinity, etc) of an organism vary over time.

In System Dynamics, the population of a stock may grow, shrink or be exhausted.

Classical cybernetics is about system state change of this kind.

The term adaptation is used to mean homeostatic state change – regulating the values of state variables.


2: The roles and rules of a system are fixed for a system generation

In biology, the roles and rules of the cells are encoded for a generation in an organism’s DNA..

In System Dynamics, the rules governing flows between stocks are fixed for a generation.


3: One social network can realise several systems

It is important to distinguish:

·         a social network in which people communicate

·         a social system in which people realise role and rules.


An enterprise is one social network that realises many social and technological systems.

These systems may overlap, duplicate or even conflict with each other.


4: Changing the roles and rules makes a new system or system version.

Changing roles and rules makes a different system - or at least, a new system version or generation.

In System Dynamics, the model of stocks and flows can be changed, and the model rerun to see how its outcomes differ.

In Darwin's theory of evolution, the form and functions of a species changes as its DNA changes from generation to generation.

Second-order cybernetics is about system mutation of this kind

The term adaptation is used to mean changing the state variable types, or the rules that update their values.

Moreover, the system is self-organising.


5: A system that changes the rules of another system is a meta system

Ashby insisted we distinguish two kinds of system change, which need different names here.

1.      System state change: e.g. increasing turnover, decreasing profit.

2.      System mutation: e.g. reorganising to offer new services, or offer old ones differently


This paper points towards a “third order cybernetics.”

Whereas second order cybernetics tends to undermine classical cybernetics, third order cybernetics preserves it.

It treats the description of one (base) system as the state of a meta system.

In a base system, actors advance the state of the system according to roles and rules.

In a meta system, actors define or change the roles and rules of the base system.


6: The actors in a social network can play roles in systems at the same and different levels

Importantly, one actor may alternate between a role in a base system and a role in a meta system.

But one action is in one or the other system – not in both.


See the next paper on self-organisation for some consequences of these conclusions.

Footnote 1: Why did Ashby say that?

At run time, actors can trigger behaviors and state changes in system X - according to rules that can be modelled.

At design time, actors can change the behavior and state variable types in the description of system X - which is a creative act.


Why did Ashby say the distinction is fundamental and must on no account be slighted?

First, he wanted us to recognise descriptions are distinct from the reality described.

A system is not the world, it is an abstraction, a way of looking at the world.

It is found when looking for some orderly and stable pattern in the world.

A system with no order, no stability, no pattern is a contradiction in terms.


Second, he wanted us to recognise that to change a designed entity is to imply an intent, a motivation (“the whim of the experimenter”).

For sure, the human actors playing roles in a system may want to change it.

But you can’t change the rules of tennis while you are playing a rally.

To change the rules you have to stop the game, agree some rule changes, then restart.

We cannot conceive of, let alone model, all the rules that might be invented, and the reasons for doing so.


Finally, an entity that changes its nature while being described cannot be regarded as a system.

Its dynamics (stocks and flows if you like) cannot be modelled.

We cannot simulate its operation and study the trajectory of how its state changes over time.

Because we do not know what those state variables are, let alone how they will change.


Having said that last, Ashby would have no problem with computer programs that rewrite their own code.

Or with machines which reproduce themselves with some alteration or mutation.

Because in these cases, the change is controlled rather than continuous.

First, a named entity realises one system (generation 1); later, it realises another system (generation N+1).

Each generation is orderly and stable, each can be described and tested.

Footnote 2: On stability and change in living entities

Following the principles above, we may distinguish:

·         a biological organism: a social network of cells

·         a biological system: the roles played by cells and the rules they follow.


And distinguish two kinds of system change:

·         biological system state change, which occurs by homeostasis (as in classical cybernetics and general system theory).

·         biological system mutation, which occurs by reproduction and evolution.


The biologists Maturana and Varela characterised living entities as autopoietic (think, self sustaining).

An autopoietic organism manufactures its own body parts from primitive edible chemicals.

The processes make the structures, which perform the processes, which make the structures, which perform the processes, and so on.


There is no one definitive list of what characterises a life form, but there are similarities between lists in different sources.

And various system theory concepts can be found in the lists from two sources below.


System Theory concepts

In this source

living entities have

7 characteristics

In this source

living entities have

8 characteristics

System description/definition



System mutation


Adaptation through evolution



System state change


Growth and development

System composition


Cellular organization

System processing




Response to stimuli



System input (material and information)



System output (material)




Neither source mentions decay and death as characteristics that define a living entity.



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