Consider system state changes and mutations in playing a game of cards.
There are state changes: In playing their cards, according to defined rules, players win “tricks” which advance the state of the game.
There can be mutations: The players can stop the game, agree a change to the rules, then play on; this is a creative act that changes the game itself.
System change may be divided into two broad types:
· system state change: changing the values of given state variables (whether triggered by input or not)
· system behaviour change: changing the variable types or the rules that update their values.
The second kind of change may be further subdivided into reconfiguration and mutation.
System reconfiguration: changing behaviour in a pre-ordained way.
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)
Notice that more flexible machine is more complex than a rigid one (this is a universal trade off).
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.
Consider the re-configuration of a caterpillar, via a pupae, into a butterfly.
This change is pre-ordained in the DNA of the caterpillar.
System mutation: changing behaviour in a random or creative way.
A mutation can happen at random (as in biological evolution) or by intention (as in re-engineering a machine).
Ashby argued a machine cannot change itself in this way.
This “re-organisation” requires the intervention of a higher level process or machine.
It is creative in that it changes the very nature of the machine, from one generation to the next.
And it is the kind of change of most interest in social and business systems thinking.
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 - or evolution - changing state variable types or the rules for responding to events.
This changes the very nature of the system; it changes its laws.
The two kinds of change can occur in one or other two ways – discrete and continuous.
In practice, most system theorists presume or model discrete rather than continuous change.
Modelling continuous state change as discrete
Analogue signals, such the revolving hands of a clock, vary continuously.
A system’s state, such as the position of a planet in its orbit, may change continuously.
By contrast, digital signals, such as a time displayed as numbers, advance in discrete steps.
The state of a discrete event-driven system advances incrementally in response to discrete events.
The state of a system is dynamic - it changes over time – either continuously or 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 disorganised, disorderly, situation or entity is not a system.
A system is, by definition, organised or orderly in some way.
A system exhibits some repeated or repeatable behavior that we can describe and test.
So, 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.
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.
This second paper reconciles classical and second order cybernetics.