Complexity explained? Part 2

Copyright 2014-17 Graham Berrisford. One of more than 100 papers on the System Theory page at Last updated 20/05/2019 13:54


To master complexity implies knowing how to define, describe and design it.

Part 1 discusses some views of complexity, including state variety, chaos, unpredictability and self-organising.

Part 2 discusses more views: complication, complex adaptive systems and relative complexity.


Complication. 1

Complex adaptive systems. 2

Relative complexity?. 3

Conclusions and remarks. 4

Links. 6



Some systems thinkers use the terms complex and complicated as though the latter is simpler.

Mostly, it seems, they are really contrasting concrete realities (complex) with abstract descriptions (merely complicated).



The Solar System

A Beethoven symphony




Abstract system

The “Solar System”

as described by an astronomer

The musical score by Beethoven

Exchange of Birthday cards

Order > Invoice > Payment


Concrete system

Several large physical

bodies orbiting the sun

Performances that instantiate the

symphony in physical sound waves

A network of friends

IBM finance department



Every discrete chunk of reality has

·         as many different complexities as there are different descriptions of it

·         multiplied by the number of different complexity measures applicabe to the description.


Differentiating abstract systems from physical realities

Sitting at your lap top, sending an email seems a simple one step action.

None of us can begin to imagine the full sequence of actions involved, as the message bounces from node to node across the internet.

It could well be that millions of software actions are performed between sender and receiver.

And perhaps billions of detectable physical events at the level of electrons and radio waves?


The same physical reality (atomic particles and energy waves) underpins mechanical, biological and sociological systems.

And the physical reality of any machine, organism or society is well-nigh infinitely complex.

But systems are abstractions from physical realities.


“At this point we must be clear about how a "system" is to be defined.

Our first impulse is to point at [some entity] and to say "the system is that thing there".

This method, however, has a fundamental disadvantage:

every material object contains no less than an infinity of variables and therefore of possible systems.

Any suggestion that we should study "all" the facts is unrealistic, and actually the attempt is never made.

What is necessary is that we should pick out and study the facts that are relevant to some main interest that is already given.” (1956)


Differentiating social systems from social networks

Let us say a social system is – in the abstract - a set of roles and rules

And a social network is a physical group of actors who communicate with each other, and may realise a system by performing activities.

To paraphrase Ashby:


Our first impulse is to point at social network and to say "the system is that group of people there".

This method, however, has a fundamental disadvantage: every social network can act as several social systems

Its actors can play unrelated roles in (say) a football team and a choir.

Any suggestion that we can measure all the characteristics of a social network is unrealistic, and actually the attempt is never made.

Instead, we pick out and study roles and rules that are relevant to some interest already given.

Complex adaptive systems

Many terms in systems thinking discussion are ambiguous or undefined

E.g. some speak of Complex Adaptive Systems (CAS).

Notably, where human actors organise themselves to achieve something.

Often there is a leaning towards anarchy or “participatory democracy” rather than hierarchic decision making

And a rejection of “external intervention, central authorities or leaders”.


There are profound terminology clashes between classical cybernetics and social systems thinking.



In cybernetics, a system is complex if the system description is complex; the roles and rules are complex

To social systems thinkers, a system is complex if the reality is complex, the actors are complex; their roles and rules may be lightly prescribed, if at all.



In cybernetics, a system adapts to feedback from its environment by changing state – which may be called self-regulating.

To social systems thinkers, a system mutates as actors change its roles, rules or aims - which may be called self-organising.



In cybernetics and system dynamics, a system is a collection of repeated or repeatable activities.

In social systems thinking, a system is a collection of actors, who interact as they choose.


One source pitches a complex adaptive system half way between chaos and order

·         Ordered system: actors are fully constrained to follow the rules of the system

·         Complex adaptive system: a “self-organising system” that is lightly constrained by roles and rules, and actors behave outside those.

·         Chaotic system: unconstrained; there are no roles or rules.


This seems odd to those of us who would see the fully ordered system to be the most complex.

If the aims, rules and roles of social network are in flux, then there is little or no system to speak of.

At the extreme, a social network is merely a group of actors who do whatever they like – which is chaos rather than a system.


For a wider analysis read Complex Adaptive Systems.

Relative complexity?

How to objectively compare the relative complexity of two real entities, machines, societies or businesses?

You could do as follows.

1.      Choose your measure of complexity

2.      Identify the elements to be described (roles, actors, processes, variables, whatever)

3.      Describe two real world entities in terms of those elements

4.      Demonstrate your two descriptions have been made to the same level of abstraction.

5.      Demonstrate by testing that the two real world entities behave according to your two descriptions.

6.      Then apply the complexity measure and compare.


However the process looks fanciful and impractical, leaving us with complexity as a subjective assessment.


Knowing that Ashby’s measure of complexity is incalculable in all business systems of interest, Beer said that relative statements are valid.

OK, so which is more complex out of communism or capitalism?

Too difficult to answer?

OK, which is more complex out of IBM, Microsoft, a chicken and a hen’s egg?

A description of IBM as a receiver of money from customers and sender of money to suppliers is simple.

A description of IBM that included every activity of every employee would be complex beyond imagination.

But then, a description of a hen’s egg that included every sub-atomic particle would be even more complex.


Some say the human brain is the most complex thing in the universe.

Yet a brain has a simple structure (forebrain, midbrain and hindbrain) at the highest level of description.

Some attribute the complexity of human intelligence to the brain structure having 100 billion cells and 100 trillion connections.

But elephants have two or three times more neurons:

Surely what makes the human brain complex is the variety of thoughts that those cells and connections make possible?

And that is magnified by the ability to communicate and remember concepts encoded in words?


Measuring the structure of the brain is one thing; what about its behavior?

Perhaps we should measure a brain’s complexity by the variety and success of the mental models it makes?

Conclusions and remarks

To master complexity implies knowing how to define, describe and design it.

It seems we are far from mastering complexity, not least because we don’t agree what it is.


For more detailed discussion of measures, read complexity measures.


Some complexity measurement principles


A complexity measure must assume a system is bounded.

You must exclude entities and activities outside the system, in its environment.

E.g. in measuring the complexity of a retail shop, you ought to ignore the remote payment card systems that enable payment card transactions.

A complexity measure must define the atomicity of components.

You must exclude the internals of components you consider to be atomic.

E.g. to measure the complexity of a human organisation, you ignore the internal biochemistry of the humans.

Given a railway network, you ignore the internal complexity of switching systems, and railway carriages.

A complexity measure likely excludes pre-defined components.

You probably ought to exclude the internals of generic components you can plug in.

E.g. to measure the complexity of clock, you’ll probably ignore the internal complexity of the replaceable battery.

A measure of one view’s complexity may hide complexity in another view.

You have to consider what kinds of complexity matter to you.
Since there are infinite ways to juggle internal design elements and trade complexity in one area for simplicity in another.


Reducing the complexity of

May increase the complexity of

Individual components

Inter-component processes

Inter component communication

Individual components


Data structures


Internal complication and external complexity

The internal complication of variables and rules is one thing.

Ignoring these, you might measure the amount and complexity of input-output transformations made.

This involves counting and assessing the atomic inputs and outputs.

A technique called function point analysis considers individual data movements made by information systems.

Is there any similar technique for other kinds of system?


The more abstract the description, the simpler the system

EA frameworks propose describing an enterprise in a hierarchical business function/capability structure.

So, the enterprise can be seen as simple or complex, depending on how many levels you describe, and which level of description you look at.

And then, how to measure the abstraction gap between the description and the operational system?


On the description-reality gap

Not only do people not agree what "complexity" means, they confuse systems with things that realise systems

There are two completely different and irreconcilable views of complexity

·         The complexity of what is in an abstract system description – with no reference to an operational system

·         The complexity of what is in a concrete operational system - with reference to a particular system description


Systems thinking deliberately hides the full complexity of whatever realises the “system of interest”.

And it is impossible to answer questions about complexity without answering questions about abstraction.

From the viewpoint of an observer/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.


Technological systems

Software systems are surely - by some distance - the most complex systems we make.

They are complex both in description and in operation.

Even so, there is a description-reality gap.

In observing a computer system, you see nothing of the software or network complexity.

Programmers never consider the internal complexity of the operating system or other platform technologies.


Human systems

Boulding regarded social systems as the most complex kind of system.

People consider human systems to be complex - because they include humans.

Yet in description, a social system can be very simple. E.g. “you scratch my back, I scratch yours”.


In observing a any social system, you completely ignore the staggeringly complex internal biochemistry of the participants.

On top of that, human actors do much (relevant to system goals) that is not mentioned any system description

Since this behavior is outside the "system", its complexity cannot be measured.


One difference between technological and human machines is in the size of the description- reality gap.

The gap is larger in social systems.



Technological systems

Human systems

Abstract system description

Tend to be complex

Tend to be simple

Description-reality gap



Concrete system reality

Very complex

Impossibly complex


The architects of human systems can get away with high level abstraction and sloppy system description.

The human actors will compensate by making intelligent judgements about the right thing to do, or indeed by changing the system’s rules on the fly.

The architects of technological systems cannot get away with it.

And the architects of socio-technical systems have the most challenging task of all?



All said above is explored on the "System Theory" page at

For more on complexity, read Complexity explained part 1.

For discussion of particular points made, readSystem coupling concepts”,  Second order cybernetics”, “Third order cyberneticsand Complex adaptive systems”.


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