System change varieties

Copyright 2019 Graham Berrisford. One of about 100 papers on the System Theory page at Last updated 23/05/2019 17:05


Basic system change distinctions. 1

Contrasting state change and mutation. 2

More on system state change. 3

System state regulation. 3

Modelling continuous system change as discrete. 5

Modelling continuous system state change as discrete. 5

Modelling continuous system mutation as discrete. 5

Conclusions and remarks. 6


Basic system change distinctions

To discuss system change we need to make at least three distinctions.

First, we must distinguish between system state changes (be they linear or chaotic) and system mutations (be they small or large).


In system state change, a system’s property values change.

·         A bicycle + rider change state by accelerating, or steering to the left.

·         A crystal changes state by growing in a liquid.

·         A heater changes state in response to messages from thermostat.

It turns out that the simplest of systems can change state in chaotic and unpredictable ways.

Whatever the state change trajectory looks like, it is an inexorable result of actors behaving according to given rules.

While the state of a weather system may change in non-linear way, the laws of physics do not change.


In system mutation, a system’s property types change, it becomes a different system.

·         A bicycle is converted into monocycle.

·         A car is converted into a boat.

·         An entity is replaced by another (as a parent is replaced by a child).

The simplest of systems can mutate, or be replaced by a new generation.

Mutation is creative in the sense that it changes the very nature of a system, from one generation to the next.


Second, we must distinguish between continuous and discrete mutation.

A game of cards is a system in which there are regular, determinate and repeatable processes.

People can’t play a game of cards unless the players agree the rules, at least for the duration of one round.

Provided actors change the system incrementally, and all together, the classical concept of a system is upheld.

Continuous mutation undermines the very concept of a system, since it is disorganising rather than organising.

Instead of seeing an island of stability or order, we see an ever mutating entity that is never describable and testable.


Third, we must distinguish a system from what (be it an actor or a process) causes it to mutate.
Ashby and Maturana said the change agent must sit outside the system of interest; a machine cannot change itself.

For them, “re-organisation” requires the intervention of a higher level process or actor.

E.g. The process of biological evolution runs over and above any individual organism.

And to modify the car + driver system, you play a role in a different system, which may be called car design or psycho-therapy.

Contrasting state change and mutation

Imagine, while watching some actors playing a game of cards, you observe two kinds of change.

You notice state changing actions: when actors play their roles according to the rules, they win “tricks” that advance the state of the game.

You also notice game changing actions: actors stop the game, agree a change to the rules, then play on; this creative act changes the game itself.


Consider a system modelled using Meadow’s System Dynamics.

System Dynamics is about system state change; about stock populations changing in response to in/out flows.

These changes are an inexorable result of the system’s laws; they do not change those laws.

An observer sets the system in motion, then observes how inter-stock flows change the volumes of stocks over time.

But the system cannot change its very nature.


By contrast, the system modeller can change the inter-stock flows, add or remove stock types.

To change the rules thus is to change the system itself, from one generation to the next.

"Change the rules from those of football to those of basketball, and you’ve got, as they say, a whole new ball game.” Meadows


Consider a system modelled using Ashby’s classical cybernetics.

Here, the term adaptation usually means system state change - changing state variable values in response to events.

It often means homeostasis - maintaining given variable values in a desirable range.


By contrast, second-order cybernetics emerged out of thinking about social organisations.

Here, the term adaptation often means system mutation - changing state variable types or the rules for responding to events.

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


One more kind of system change should be mentioned.


System reconfiguration

This means changing behaviour in a pre-ordained way.

Consider for example the re-configuration of a caterpillar (via a pupae) into a butterfly, which is pre-ordained in the DNA of the caterpillar.


Consider as a system, a machine that is coupled to a lever.

“Many a machine has a switch or lever on it that can be set at any one of three positions, and the setting determines which of three ways of behaving will occur.” (1956)

This flexible machine is more complex than a rigid one.

But still, the ways of behaving are constrained, and we know what pulling the lever will do.

So reconfiguring the machine, switching it from one mode to another, does not change what it has the potential to do.

More on system state change

Classical cybernetics is about system state change; about state variable values that change in response to input or events

System Dynamics is also about system state change; about stock populations that change in response to inter-stock flows.

In both, the state changes are an inexorable result of the system’s laws; they do not change those laws.


Setting a System Dynamics model in motion reveals the trajectory of state changes over time.

It may reveal that the quantitative values of state variable or stock population:

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

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

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

·         periodically move 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.

Some say such a system appears is “self-organising”, but it might better be called “self-regulating”.

System state regulation

System Dynamics features causal or feedback loops.

A causal loop is formed when two stocks are connected by flows in both directions.

A causal loop may have a reinforcing/amplifying or balancing/dampening effect on the populations of the stocks.


Reinforcing (amplifying) loops

The two flows in a causal loop may reinforce each other.

Two stocks can continually expand or grow.



sales income




sales income


Sometimes the long-term result of a causal loop can be chaotic.

Or a stock may exhaust a resource it needs.

But our main interest here is in causal loops of the kind found in homeostatic systems.


Balancing (dampening, self regulating) loops

In a homeostatic system, two subsystems or stocks may interact so as to regulate system state change.

Each keeps the state of the other within certain bounds.

This kind of adaptation or self-regulation has been recognised in biology for c200 years.

It can happen also, for example, in a solar system or a weather system.


A predator-prey system

A flock of sheep and a pack of wolves can be represented by two variables: the quantity of sheep and the quantity of wolves.

A System Dynamics model can help to explain how these stocks interact.

It employs the idea of causal loop between what Marx and Engels might call opposites.









In "Thinking in Systems – A Primer" Donella H. Meadows wrote that a system generally "goes on being itself... even with complete substitutions of its elements."

In our example, this means that individual sheep and wolves come and go.
What remains stable is only the roles that sheep and wolves play in the described system’s behaviours.


Of course, a System Dynamics model does not contain any wolves or sheep.

It models entity stocks (wolf pack, sheep flock), not individual entities (a wolf, a sheep), unless you count each “1” in a stock total as a model.

It models events batches (sheep killed per time unit), not individual events (a single birth or death), unless you count each “1” in a number of events as a model.


Real wolves and sheep realises the abstract system only in so far they demonstrably play their roles.

Almost everything real sheep and wolves do lies outside the described system.
The wolves can act contrary to the system; say find another flock on which to predate.
The sheep may play unrelated roles in other systems, both natural system (eating grass) and designed (sheep shearing).


The biomass system

We all depend on the fact that plants and animals balance the stock of oxygen.

System Dynamics helps to explain how these stocks interact so as to reach a balance.

A model might include these flows (and others).



plant material


atmospheric oxygen


animal material


animal material


atmospheric oxygen


plant material


Every model of the world is a selective abstraction.

E.g. this one excludes carbon dioxide, others consumers of oxygen, water, and global warming.

So the real world is likely to behave differently from a model, to some extent.

Modelling continuous system change as discrete

The state of a system is dynamic - it changes over time.

Change can occur in one or other of two ways – discrete and continuous.

For reasons to be explained, most system theorists model discrete rather than continuous change.

Modelling continuous system state change as discrete


Continuous state change

A system’s state may change continuously.

Consider the positions of planets in their orbits, and analogue signals such the revolving hands of a clock,


Discrete state change

The state of a discrete event-driven system advances incrementally in response to discrete events.

Consider digital signals, such as a time displayed as numbers, which advances in discrete steps.


It is possible to model continuous state change mathematically, but we have no need to do so.

Because as Ashby pointed out, we can model any continuous state change as a discrete event-driven change.


“Often a change occurs continuously, that is, by infinitesimal steps, as when the earth moves through space, or a sunbather's skin darkens under exposure.

The consideration of steps that are infinitesimal, however, raises a number of purely mathematical difficulties, so we shall avoid their consideration entirely.

Instead, we shall assume in all cases that the changes occur by finite steps in time and that any difference is also finite.

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

Modelling continuous system mutation as discrete

A system is, by definition, organised or orderly in some way.

A disorganised, disorderly, situation or entity is not a system.

A system must exhibit some repeated or repeatable behaviour that we can describe and test.


Continuous system mutation (impossible)

The concept of a continuously mutating system negates the very concept of a system.

Because we can never describe it, let alone test it as conforming to a system description.


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.


Discrete system mutation

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.


In short, by definition, system mutation is discrete, it changes a system from one (orderly) generation to the next.

You might however, be able to systematise the migration from one generation to the next.

Conclusions and remarks

This paper discusses some varieties of system change.

Further analysis in this Second Order Cybernetics paper resulted in this (tentative) classification.


·         State change: changing the values of given state variables (typically triggered by inputs).

·         Update: changing the values of variables in response to inputs.

·         Accretion: as in the expansion of a city, or the inexorable growth of a crystal in a super-saturated liquid

·         Flocking: as in the flocking of starlings, or the shoaling behavior of fish

·         Self-regulation: as in the maintenance of homeostasis during the life of an entity

·         Self-sustaining: in which autopoietic processes make and maintain the structures that perform the processes.

·         System change: changing the variables or the rules that update their values.

·         Reconfiguration: changing behaviour in a pre-ordained way.

·         Leverage: switching a system from one given configuration to another.

·         Morphogenesis: as in the inexorable growth an embryo into an adult

·         Evolution: changing behaviour in a random or creative way.

·         Discrete mutation: replacement of one system generation by the next.

·         Mutation with random change: as in biological evolution.

·         Mutation with designed change

·         External: redesign by external observers

·         Internal: redesign by self-aware actors who observe and change the system they play roles in.

·         Continuous mutation: n/a. Impossible here, since it is contrary to the notion of a system.


Some speak of Complex Adaptive Systems (CAS).

Note that a system that adapts by changing state might be a SAS (simple adaptive system) rather than a CAS.

And a system that adapts by mutating (or a “learning organisation”) might be called an EME (ever evolving entity) rather than a CAS.

A continuously mutating entity (or ever unfolding process) - in which no behavior is regular, or determinate, or reproducible – is not a system in the ordinary sense of the term.


System designers apply the principles of general system theory and cybernetics to design role-and-rule-bound systems

But the social network (aka social system) that designs those systems is radically different.

·         It is more goal-bound than role-and-rule-bound.

·         Its roles and rules are more natural or self-defined than given.


Finally, can system mutation be by self-organisation?

Does it mean the system adapts itself, rather than is adapted by an external designer?

The actors who play roles in the system can also change its roles and rules?

This is a basis of “second-order cybernetics”, the recursive application of cybernetics to itself.

It allows systems actors to be system thinkers, who study the system the work in an re-organise themselves.

Actors not only play roles in a system, but also observe it, and change its roles, rules and state variables.


System theory gurus Ashby and Maturana rejected the concept of a self-organising system; said it makes no sense, it is impossible.

How to extend general system theory to embrace “self-organisation”?

Read second order cybernetics for the start of an answer to that question.


If your interest is the application of these ideas to agile architecture, try