The science of system theory

Copyright Graham Berrisford 2018. Last updated 13/01/2019 13:54

One of a hundred papers on the System Theory page at

Find that page for a link to the next System Theory for Architects Tutorial in London.



Preface: on business systems

The systems of interest here are islands of orderly behavior in the ever-unfolding process of the universe.

That does include the solar system, riding a bicycle and the cardio-vascular system.

But the main interest is narrower:

·         Systems in which actors respond to information encoded in messages and memories.

·         Systems in which information describes or directs entities or events of importance to the system’s actors.

·         Human activity systems in which processes depend on messages received and memories retained

·         Computer activity systems in which all the messages and memories are digital.


In business operations, human activity systems are supported and enabled by computer activity systems.

In the 1970s, business systems were often analysed and designed by people in an Operational Research department.

At the start of the Information Age, many Operational Research departments were absorbed into IT departments.

The PRISM report of 1986 divided the work of business system description into four domains.

The table below positions those four domains in the columns; each divided into three levels.







Infrastructure technology



Business roles & processes,

standardisation, integration

and road maps

Business data

standardisation, integration

and road maps

Business application portfolio

standardisation, integration

and road maps

Platform technology portfolio

standardisation, integration

and road maps



Outline design of a solution’s

required processes

Outline design of a solution’s

data architecture

Outline design of a solution’s

application(s) architecture

Outline design of a solution’s

IT production environment



Detailed design of

processes & use cases

Detailed design of

data stores and flows

Detailed design of

software architecture

Detailed design of

IT production environment


The table positions descriptions of human activity systems to the left, and computer activity systems to the right.

The two kinds of system meet wherever digital data is created and used by humans.


Business system architects are supposed to observe baseline systems, envisage target systems, and describe both.

So, you might assume they are taught about system theory and systems thinking; but this is far from the case.


Thinking about systems is often considered the domain of sociologists.

But if you are looking for discussion of social systems, you’ll have to wait for a while.

This paper (longer than the others on the web site) outlines the science and philosophy of systems.


You can’t understand systems without answering questions about the nature of description and reality.

These questions are often considered the domain of philosophers and linguists such Nietzsche and Wittgenstein.

There is some philosophy here, but the perspective is primarily scientific.


Contrary to some postmodern attacks on science and reality, as reported “A philosophical position statement”, this story respects science.

It positions systems theory in a brief history of the universe and human evolution, and as a branch of science.

The story of description and reality below is rooted in biology.

It is about humans came to communicate using languages, and describe the universe in terms of types, and systems.


The emergence of description. 3

Animal memories and messages. 3

General communication principles. 6

Human communications. 7

Human languages, natural and artificial 9

Propositional logic. 12

Types and instantiations of them.. 14

Systems as complex types. 14

Describing a human activity system.. 16

Describing a computer activity system.. 17

Conclusions. 18

The philosophy of systems theory. 19

The science of system theory. 19

Footnote on thermodynamics. 20


The emergence of description

Heinz von Foerster (1911 to 2002) was a thinker interested in the circularity of ideas.
(His contribution to systems thinking will be challenged later.)

He is reputed to have said “We live in the domain of descriptions that we invented.”


We do live in a society with laws, roles and rules invented by people.

But we don’t live in a world we have invented.

Scientists believe our universe started with a big bang about 14,000 million years ago.

The earth was formed about 4,500 million years ago.

And life on earth began at least 3,500 million years ago, possibly more.


Matter and energy exist; can be located in space and time.

A description is a physical matter/energy structure intentionally created to represent another – be it observed or envisaged.

There was no description of reality before life.

Before life emerged, there were no perceptions or memory of the universe.

There was no conceptualisation or model of structures and behaviors in the universe.

Nothing was created to represent or symbolise what exists and what happens in the real world.

There was no description of the universe before life; description is a side effect of biological evolution.

Animal memories and messages

All animals must know something of the world they live in.

An earthworm knows enough to recognise another worm of the same type – for mating purposes.

Certainly, a worm can recognise others members of the worm set, though it may not remember them, and surely cannot count them.


Even 3,500 million years ago, the earliest organisms knew enough not to eat themselves.

They could recognise their own substance and distinguish it from chemicals in their environment.


Later, through evolution, animals developed ever more sophisticated ways of knowing the world.

By about 700 million years ago, Jellyfish had nerve nets that enabled them to sense things in the world and manipulate them.

In a nerve net, intermediate neurons monitor messages from sensory neurons and react by sending messages to direct motor neurons.

Thus, animals evolved to process transient sensations – each an encoded description of a reality.


By about 550 million years ago, some animals had a central hindbrain to monitor and control homeostatic state variables.

An internal information feedback loop connected that hindbrain to the organs and motors of the body.

The hindbrain had to sense the state of the body state variables and send messages to direct actions that maintain those variables.


About 250 million years ago, the paleo-mammalian brain evolved to manage more complex emotional, sexual and fighting behaviors.

A wider information feedback loop was needed to connect that higher brain to the external world.

The higher brain had to sense the current state of food items, friends and enemies in the world, and direct appropriate actions.


Recording knowledge in memory

Animals can not only sense and react to things, but also retain descriptions of things - if only as vague sense memories.

Like all biological traits, human memory is the result of a very long history, most of it shared with other animals.

At each stage in the path from vertebrate to mammal to primate to anthropoid to human, we acquired a different kind of memory

The result, this research suggests, is that humans have seven different kinds of memory.


Animals don’t just remember static images; they can remember the sequences in which dynamic behaviors unfold.

This other research suggests even rats can replay memories in order to recognise things in sequence.

You can remember the sequence of steps in a dance, notes in a melody, or words in a story.

And of course, the sequence of words in a sentence or message is important to its meaning.


This article on how the brain works suggests we know very little about how it works.

But how brains create and use descriptions of reality doesn’t matter here; it only matters that they evidently do.


Three truth tests

The members of a social species necessarily see the world similarly.

Since their ability to perceive and communicate about the world evolved represent it.

At least well enough that they can determine their actions, cooperate socially, and survive.

How to know a description, conceptualisation or typification of reality is “true”?

There are three tests you can apply.


·         It is empirically true - supported by evidence from test cases

·         It is logically true - can be deduced from other concepts within a body of knowledge.

·         It is socially true - widely believed in your social network.


Biological evolution has favoured social animals who usually communicate what is empirically true.

And scientists take care to ensure social truth does not over-ride the first two tests above.


The need for descriptions to represent realities

To some extent, biological differences must mean people do perceive the world differently from each other, and from birds, bats and bees.

But more importantly, their conceptualisations are shaped by objectively testing them against reality.

All animal life depends on two facts:

1.      there is a real world, and

2.      only some descriptions of that reality prove accurate enough when tested.


This situation, and the philosophy here, can be represented in a triangle.




<create and use>           <symbolise>

Living entities  <sense & envisage>  Realities


We don’t need metaphysical philosophy to explain concepts, be they in minds, messages or memories.

An animal’s mental models must describe the world well enough; else the animal would not survive.

The physical world includes not only you, your food, friends and enemies, but also your concepts of those things.


Communicating via messages

Even very primitive animals signal mating intentions to each other.

By 100 million years ago, some animals cooperated in groups.

Perhaps the earliest social acts were related to marking territory, signalling danger and locating food.

E.g. Cats spray scent to mark their territory; other cats smell that scent.


Communication requires both the creation (encoding) and interpretation (decoding) of messages.

Messages are created by manipulating physical matter and energy to form symbols (smells, gestures, sounds etc.).

The symbols identify or represent things of interest, such as territorial claims, friends, enemies and food.

E.g. A honey bee can symbolise the direction and distance of a pollen source in the form of a wiggle dance.


Honey bee communication

Wiggle dances

<perform & read>        <symbolise>

Honey bees  <find & seek>  Pollen sources


Symbols can both identify things and describe their features (qualities, characteristics, attributes, properties).

E.g. Astonishingly, experiments have shown that honey bees can communicate quantities up to four.


Some system thinkers promote the “hermeneutic principle” that the hearer alone determines the meaning of an utterance.

This dreadful postmodern idea makes speakers guilty of causing offence where none was intended.

The principle for success might be called the communication principle.

Communication requires that a receiver decodes the same meaning from a message that a sender intentionally encoded in that message.


Note that biological evolution has not demanded animals communicate perfectly accurate descriptions or absolute truths.

Animals send messages that represent reality accurately enough, often enough, for message receivers to find them useful.

Communications do fail when symbols are ill-formed, lost or obscured in transit, or misread or misinterpreted on receipt.

And animals do sometimes lie to each other, as this video illustrates.

General communication principles

Many animals communicate facts to each other.

Facts can include descriptions, directions and decisions.

E.g. A bird’s alarm call may communicate the fact that a cat is near.

E.g. A honey bee’s dance communicates facts about a pollen source – its distance and direction.


Animals communicate by organising some matter and/or energy to symbolise facts of interest.

E.g. An alarm call is made by producing sound waves that can be heard.

E.g. A dance is made by moving limbs in a way that can be sensed by sight or by touch.

Our general term for such a matter and/or energy structure is a data structure.


A message contains a data structure and is conveyed (say by sight, sound or electronics) from sender to receiver.

The sender encodes some intended meaning in a data structure. E.g. one bird makes an alarm call.

A receiver decodes some meaning from a data structure. E.g. another bird hears the call and takes flight.


Information is meaning created or found in a data structure – at the point it is created or found.

To find an intended meaning in a message, the receiver must decode it using the same language the sender used to encode it.


Nothing above depends on humans or human-invented technologies.

But the same general communication principles apply to communication between humans and computers.

Human communications

The earliest human brain, though larger than other mammals, was about the same size as a chimpanzee’s brain.

Over the last six or seven million years, the human brain tripled in size.

By two million years ago, homo erectus brains averaged a little more than 600 ml.

And by 300 thousand years ago, early homo sapiens brains averaged 1,200 ml, not far from the average today.


Why this growth?

Three million years ago, human-like primates learnt to make tools with a cutting edge or point.

Humans needed a bigger brain to make and use increasingly complex tools to hunt and cultivate food.

At the same time, intelligence was needed for the increasingly complex language humans used to cooperate.


Neither conceptualisation nor cooperation by communication is unique to humans.

But only humans communicate by inventing words to symbolise things and their qualities.


The spoken word – transient messages

Many non-human animals use sounds to communicate information about things of interest to them.

But they use sounds instinctively, with fixed meanings.

Between 150 and 300 thousand years ago, humans started inventing sounds (words) to convey meanings.

This emergence of speech may well have reflected changes in human society.

Notably, the change from a gorilla-style dominance hierarchy to the more cooperative and egalitarian lifestyle of hunter-gatherers.

Increasingly, humans used words to express descriptions, directions and decisions, and share them with each other.


The ability to create words and assign meanings to them had a profound effect on thinking.

In describing pollen sources, honey bees describe things that resemble each other, but they don’t discuss what those resemblances are.

Words enable humans to discuss the resemblances between things; inventing words such as “pollen source” to label all similar things.


To idealise a thing means to abstract some features or qualities of the thing, and represent them in a symbolic form – such as words.

We observe and envisage realities; we create and use descriptions; our descriptions idealise or symbolise realities.

These three relations can be shown in a triangle.


Human communication

Verbal descriptions

<create and use>         <symbolise>

Humans  <observe & envisage>  Realities


The ability to describe realities in words makes humans unique.

We don’t inherit words with particular meanings; we imitate and invent words.

We can invent words to symbolise infinite concepts – not only realistic ones but also impossible ones, like a flying elephant.

This freedom to invent words and sentences enables creative thinking and scientific postulations.


Words are unreliable; we not only abuse words, we also change their meanings.

The popular meaning of a word can evolve rapidly and change dramatically.

In every oral communication, a word has a meaning when spoken to its creator, and a meaning when heard to a receiver.

There is no guarantee that the two meanings are the same.


Note again: biological evolution has not demanded that words express perfectly accurate descriptions or absolute truths.

It requires only that spoken words are understood well enough, often enough.


How to separate the signal from the noise?

What if the message we send may lose some data in transit?

We may repeat the whole message.


What if the reader of a message use words a little differently from the sender?

As senders, we commonly overload communications with redundant information.

Describing one thing in several different ways reduces the chances of miss-communication.


What if a message may gain some meaningless noise in transit?

How to separate the signal from the noise? It depends what you mean..

Because the phrase “signal-to-noise ratio” has one scientific meaning and one or two metaphorical meanings.


In engineering, signal-to-noise ratio = The strength of an electrical or other signal carrying information, compared to that of unwanted interference.

Here, the signal is the data encoded by a sender within a message.

The reader wants to remove or ignore any interference, in order to find the original signal/data.


In sociology, signal-to-noise ratio = The ratio of useful information to false or irrelevant data in a message or series of messages.

Here the signal is the message(s) that readers are interested in.

The reader wants to remove or ignore data that they regard as misleading, mistaken or irrelevant to their particular interest.


In data analysis, signal-to-noise ratio = A conclusion to be drawn from examining a sample of data values.

The reader want to ignore small, random or statistically insignificant variations, and focusing on the largest variations.


The written word – persistent memories

5 or 6 thousand years ago, people found ways to persist spoken words using written symbols.

Scholars suggest this may have happened separately in Sumeria/Egypt, the Indus River, the Yellow River, the Central Andes and Mesoamerica.

Writing made one person’s thoughts available for inspection and use by others in different places and times.


The invention of writing enabled the development of civilization.

First, people could do business and conduct trade on the basis of facts recorded on clay tablets or papyrus.

Second, translating spoken words into and out of written words helped people clarify their thoughts and communicate over distance and time.

The written record revolutionised humans’ ability to think deeply, think straight, remember things and communicate.

Third, people could record ideas for inspection by future generations.


"The metaphor of dwarfs standing on the shoulders of giants expresses the meaning of "discovering truth by building on previous discoveries".

This concept has been traced to the 12th century, attributed to Bernard of Chartres.

Its most familiar expression in English is by Isaac Newton in 1675: "If I have seen further it is by standing on the shoulders of Giants." Wikipeda December 2018


One “landmark in the triumph of the centralised written record” recorded the enterprise architecture of a nation state.

After the Norman Conquest of England (1066), King William ordered an audit of locations in England and parts of Wales

The aim was to record who held what land, provide proof of rights to land and obligations to tax and military service.

This survey resulted in The Domesday Book, which classifies towns, industries, resources and people into various types.

Human languages, natural and artificial

Language is not the basis of thinking.

Eons before animals had languages to communicate, they could think.

They could a recognise a thing they had perceived before, even if that thing had changed a little

And so, they could recognise “family resemblances” between any two things they perceive to be similar.

In effect, they could classify things they perceive into fuzzy, informal, overlapping classes or types


Only we humans invent words to describe things, and to describe a thing is to typify it.

The fluidity and fuzziness of a type defined in natural language assists survival and creativity in an ever-changing world.

But to specify the regular or repeatable behaviors of an activity system, we have to be more formal.

We have describe/typify the roles of actors, the messages they exchange, and the rules they follow, more formally.

And to do this in an unambiguous and testable way, we need an artificial, logically consistent, language.


Family resemblances and natural languages

The philosopher Ludwig Wittgenstein (1889-1951) initially presumed language is precise.

So, words can be seen as type names that define the members of a set.

To describe something as the game is to say it is the only one of that named type.

To describe something as a game is to say it is one of a set containing many things of that named type.

Later, he changed his mind, and turned his focus to the fluidity of language.

He considered games as a set that includes activities as varied as chess, archery and Super Mario.

He argued the set members have overlapping lists of features, but no single feature in common.

He used “game” as an example to tell us that words (in natural language) are not type names.

Rather, games exhibit family resemblances.


This is disappointing if you are a mathematician who had hoped that a word defines the members of a set.

But it is no surprise to a biologist or psychologist coming at this from a different direction.

Natural language is a biological phenomenon rather than a mathematical one.

We use words to indicate one thing resemble another in a loose and informal way.

No word, description or message has a universally-agreed meaning.

And since the words and grammar we use are so flexible, there is ambiguity and fuzziness in natural language

There are degrees of truth in how well a reality matches a description we make of it.


The marvel is not that words are used so loosely in natural language.

The marvel is that we can force them to act as the names of types that do have one or more features in common.

E.g. A biologist might define a game as “an activity that serves as a direct or indirect rehearsal of skills useful to survival.”

And to create a holistic, unambiguous and testable description of a system, we must do this.

We have to create an artificial domain-specific language in which words do act as type names.


Types and artificial domain-specific languages

A. J. Ayer (1910 to 1989) was a philosopher who wrote about language, truth, logic and knowledge.

He rejected metaphysics and much philosophical discussion as meaningless, that is, not provable or disprovable by experience

He pointed out that every coherent description of an individual thing or situation is a type definition.

“In describing a situation, one is not merely registering a [perception], one is classifying it in some way,

and this means going beyond what is immediately given.” Chapter 5 of “Language, truth and logic”


As Wittgenstein indicated, the set of things people call a game is elastic, and it is difficult to agree a type that defines every set member.

However, words do give humans the ability to classify or typify things more formally and rigidly.

Within a bounded context, or domain of knowledge, we can determinedly fix the meanings of words.

A domain-specific language is an island of inter-related words with stable meanings, in the ever-unfolding evolution of natural language.

Words are treated as type names, and each type is defined by statements relating it to other types.

A type defines features (qualities, characteristics, attributes, properties) shared by things that instantiate or realise that type.



Did types and numbers exist before life?

As soon as humans have a group or type in mind, we can count the members of the group or type.

And soon as we can count, we find many groups and types have something in common.

That is, the total number of members, whatever they are.


We use numbers as types, to describe what groups of the same size have in common.

The human ability to generalise across groups and types of different things led to numbers.

And numbers are the basis of mathematics, hard science and the types used in software.


In the domain of mathematics, more abstract type names include: “number”, “division” and “remainder”.

Type definitions include: “An even number is a number that is divisible by two with no remainder.”


In the domain of physics, type names include “Force,” “Mass” and “Acceleration”.

Type definitions include: Force = Mass * Acceleration.

By contrast, in the language of management science, a force is a pressure acting on a business, such as competition or regulations.


In any business domain, people define the rules of their specific business in terms of relations connecting types.

“An employee has a salary and may be assigned to a project.”

“An order is placed by a customer; a customer can place several orders.”


The logical syntax of language

Rudolf Carnap (1891 – 1970) was a member the Vienna circle who contributed to the philosophy of science and of language.

Carnap has been called a logical positivist, but he disagreed with Wittgenstein.

He considered philosophy must be committed to the primacy of science and logic, rather than verbal language.


Carnap’s first major work, Logical Syntax of Language can be regarded as a response to Wittgenstein 's Tractatus.

the sentences of metaphysics are pseudo-sentences which on logical analysis are proved to be either empty phrases or phrases which violate the rules of syntax.

Of the so-called philosophical problems, the only questions which have any meaning are those of the logic of science.

To share this view is to substitute logical syntax for philosophy.”

— Carnap, Page 8, Logical Syntax of Language, quoted in Wikipedia.


He defined the purpose of logical syntax thus:

to provide a system of concepts, a language, by the help of which the results of logical analysis will be exactly formulable.”

“Philosophy is to be replaced by the logic of science – that is to say, by the logical analysis of the concepts and sentences of the sciences...”

Foreword, Logical Syntax of Language, quoted in Wikipedia.


He defined the logical syntax of a language thus:

the systematic statement of the formal rules which govern [the language] together with the development of the consequences which follow from these rules.

Page 1, Logical Syntax of Language, quoted in Wikipedia.


Carnap’s second major work, Pseudoproblems in Philosophy asserted that many metaphysical philosophical questions were meaningless.

His Principle of Tolerance says there is no such thing as a "true" or "correct" logic or language.

His concept of logical syntax is important in formalising the storage and communication of information/descriptions.

Computers require that logical data structures are defined using a formal grammar called a regular expression.

It is said that Carnap’s ideas helped the development of natural language processing and compiler design.


As I understand it, Carnap said:

A statement is only meaningful with respect to a given theory - a set of inter-related domain-specific predicate statements.

And only true to the extent it can be supported by experience or testing.

Propositional logic

Again, to create a holistic, unambiguous and testable description of a system, we need an artificial domain-specific language.

A natural language can contain several popular and alternative meanings for the same word.

By contrast, in a domain-specific language, terms are fixed to meanings and defined with reference to each other.


To define a domain-specific vocabulary, we make statements in a disciplined manner.

The basic logic of statements is called propositional logic (or calculus).


A proposition is a statement that asserts a fact that may be true or false.

In natural language it takes the form of a sentence: e.g. the sun is shining.

A predicate is a verbal phrase, with or without an object, which declares a feature of a subject.


Proposition (in the form of a predicate statement)



Verb phrase


A particular thing

or instance of a general type

A verb or verbal phrase

that either stands alone or

relates the subject to the object

A particular thing or a general type

related to the subject by the predicate.

The sun

is shining

A game of monopoly

results in

a winner with the largest credit amount

A game

is kind of


A game

is played by

one or more animate players

A game

results in

a measure of achievement

An order

is placed by

a customer

A customer

has placed

one or more orders


A subject or object above might be read as one instance in a set.

E.g. “An instance of the customer type has placed one or more instances of the order type”.


Compound propositions

Connectives (e.g. and, or, not and if) express logical relationships between predicates in a compound proposition.

E.g. pigeons fly <and> eat corn.


Predicate logic

Propositional logic is the foundation of first-order or predicate logic.

Here, a predicate is a statement that contains variables; it  may be true or false depending on the values of these variables.

For more on predicate logic, try

Types and instantiations of them

To paraphrase von Foerster: “We live in the domain of types that we invented.”

The types idealise and symbolise the realities we observe and envisage.

These relations can be shown in the triangle you may now becoming familiar with.




<invent>                 <symbolise>

Human intelligences <observe & envisage> Realities


A type can be presented as a proposition with a compound predicate.

E.g. “A game is a kind of activity <and> is played by one or more animate players <and> results in a measure of achievement>.”


The words in a domain-specific language serve as type names.

A predicate statement defines (or partly defines) a type by relating it to other types in the same language. 7

Generally: “An instance of type A is related by a verb phrase to one or more instances of type B.”

E.g. “An instance of the customer type has placed one or more instances of the order type”.


A type is a description; moreover, a description may be viewed as a type.

Any coherent description, even a long and complex one, can serve as a type definition.

E.g. To describe the Statue of Liberty is to describe something of which many instances could be made.


Fuzziness in the instantiation of a type

The matching of a thing to a type can be incomplete.

Given a monothetic type like “even number”, every instance must have all its features.

Given a polythetic type like “game”, an instance need not have all its features.


Moreover, there can be degrees of truth in a predicate statement.

Newton’s laws describe the motion of things in the reality we normally experience.

The laws are true to the degree of accuracy we need, but only approximations, neither wholly true nor wholly false.

For more on fuzzy logic and fuzzy sets, try this link.

Systems as complex types

Humans have long classified people according to roles they play – a role is a type.

The Greeks divided dramatic roles into types: hero, ingénue, jester and wise man.

In the 11th century, The Domesday Book classified people into types according to their rank and role in a feudal society.

Nowadays, we classify regular patterns of behavior as systems – a system is a type.



In his introduction to cybernetics (1956), Ashby said a system is characterised by exhibiting regular or repeatable behaviors.

Ashby defined a system as an abstraction from the infinite complexity of any entity that realises it.

A system may be characterised as a set of roles and rules (e.g. the mating ritual of a pair of sticklebacks).

When those abstract roles and rules are realised by a concrete entity, which behaves as described, we have a concrete system.


Abstract system

A set of roles and rules (the logic or laws actors follow)

Concrete entity

Actors playing the roles and acting according to the rules


There is a many-to-many relationship between abstract systems and concrete entities.

One abstract system may be realised many times.

E.g. the roles and rules of tennis may be realised in many concrete tennis matches.

Conversely, a concrete entity may realise any number of abstract systems.

E.g. a pair of people may realise many tennis matches and many games of chess.


Note that a social group in the real world is distinct from any abstract social system it realises.

A social system description hides the infinite complexity of the actors and activities in a social group.

To be scientific, we must describe a system in a way that enables us to test whether a social group instantiates it or not.


In short, classical cybernetics describes a system by

·         typifying actors in terms of roles they play

·         typifying activities in terms rules that actors follow.

·         typifying acted-on things in terms of variable qualities or values.


The types range all the way from loosely-defined human roles to rigid software classes and data types.



Roles, Rules & Variables

<create and use>                   <idealise>

Systems thinkers <observe & envisage> Actors, Activities & Values


The science of cybernetics was quickly embraced within a broader system theory movement.


General system theory

General system theory incorporates cybernetic concepts such as:

·         System environment: the world outside the system of interest.

·         System boundary: a line (physical or logical) that separates a system from is environment.

·         System interface: a description of inputs and outputs that cross the system boundary.

·         System state: the current structure or variables of a system, which changes over time.


System theorists distinguish abstract system descriptions from concrete entities that instantiate (realise) them.

Again, a system description is a complex type; it symbolises both the structures and the behaviors of each entity that realises the system.


General system theory

Abstract / theoretical systems

<create and use>                    <symbolise>

System theorists <observe & envisage>  Concrete / empirical systems

Describing a human activity system

The systems of interest here are islands of orderly behavior in the ever-unfolding process of the universe.

Especially human activity systems in which processes depend on messages received and memories retained

And computer activity systems in which all the messages and memories are digital.

Both kinds of activity system are specifiable using the same general tools and an artificial domain-specific language.


How to specify a message or memory?

We use a domain-specific language to specify the data types contained in messages and memories.

We define each data type in terms of a generic data type (number, text, date etc.) plus a domain-specific meaning.

We relate the data types in larger structures

We define the structure of a message using the grammar of a regular expression (as in a structure of sequences, selections and iterations.

We define the structure of a memory using the grammar of predicate logic (as in an entity-attribute-relationship model.


How to specify a system actor?

We define the role of the actor in terms of the activities they are expected to perform.


How to specify a system activity?

We define the inputs and outputs of the activity and the rules that apply to it

A rule definition states a precondition or post condition of an activity.

Each rule refers to the particular values of data types created and used by the activity.


Charles Antony Richard Hoare (1934 - ) is a British computer scientist.

Few have taken up his work on formal specification languages such as CSP and Z.

But many use Hoare logic to describe how an activity changes the state of a system.

The logic is based on the Hoare triple, which may be expressed as: {Precondition} Activity {Post condition}.

The meaning is: If the precondition is true AND the activity proceeds to completion THEN the post condition will be true.


Hoare logic underpins many ways to analyse requirements and define business activities.

It can be seen in definitions of “value streams”, “business scenarios”, “use cases” and “service contracts”.


How to specify a process that connects activities in a logical flow?

We use the concept of an algorithm, which was known to Greek mathematicians and was formalized in the 1930s.

(See Wikipedia for references to Gödel–HerbrandKleene, Alonzo Church, Emil Post and Alan Turing.)

We often specify an algorithm using a process flow chart.


Types and meta types

Descriptive types generalise qualities or properties of individual structure and behaviors in natural systems and artificial designed systems.

Individual Insurance Claim processes can only be regarded as instances of a descriptive type when then that type exists in reality.

There can be many copies of that descriptive type, in people’s minds, in diagrams drawn using ArchiMate, BMPMN and UML symbols

But there is no more ethereal Insurance Claim process type or concept – outside or above those copies of it.

There is however a more generic meta type – Business Process.


Idealisation from run-time

Generalisation description

System description element


Design time description

Meta meta model

Behavior type


Meta model

Business Process type

Subtype of Behavior


Insurance Claim Process type

Subtype of Business Process

Run-time behavior

Operation in the real world

Insurance Claim 999999

Instance of Insurance Claim Process type


Describing a computer activity system

By accident or intent, humans rarely realise an activity system perfectly in accord with its general description.

That fuzziness in instantiating a system type is surely vital to success of human society.


But computers can and do realise an activity system perfectly in accord with its general description.

A software system can be seen as an exceptionally perfect example the systems discussed in “Introduction to Cybernetics” (1956) by W Ross Ashby.


Software engineering exemplifies the scientific method

Scientists develop a theory that typifies how structures in the universe behave.

Then run experiments to test that the structures do behave that way.

Similarly, software developers write code that describes process types (behaviors) that create and use data types (structures).

Then runs test to show that data is processed as expected.


Software engineering exemplifies a philosophy of description and reality

Software engineering illustrates the philosophy expressed in this triangular graphic.




<create and use>           <symbolise>

Living entities  <sense & envisage>  Realities


In general, a description of real world behavior is more or less accurately performed by actors.

Moreover, the actors may do more or less than is described.


Software is strange and wonderful in that it perfectly aligns description and reality.

The software is a description of system behavior that can and will be perfectly performed.

The computer actor can only behave as described in the software.


There may be a perfect correspondence between description and reality.

But don’t confuse the software with the run-time operation of the system.

The software version of the triangle is this.



Software system code

<creates>                     <symbolises>

Programmer <envisages> Run-time system operation


The software code is a relatively simple abstract description

The run-time system operation a very complex, electrically powered machine that reads the software and performs to the instructions in it.



The philosophy of systems theory

In so far as philosophy is about language, knowledge and truth, it seems to have been overtaken by biological and software sciences.

This new attempt at a “tractacus” is written from the perspective of a psycho-biologist rather than a linguist or mathematician.


1.      Reality is what exists in matter and energy, in space and time.

2.      A description is created by an actor (internally or externally) to represent a reality that is observed or envisaged.

3.      A description is also a part of reality - it is not ethereal.

4.      The truth of a description is subjective, there can be degrees of truth in its creation and in its use.

5.      A description (e.g. standing on that railway track is dangerous) is:

·         True to an actor who creates the description with the intent to represent a reality - well enough to be useful.

·         True to an actor who finds (in empirical or logical tests) that it does represent a reality - well enough to be useful.

6.      A description (e.g. this horse has five legs) is:

·         False to an actor who creates the description with the intent to misrepresent a reality.

·         False to an actor who finds (in empirical or logical tests) that it does misrepresent a reality.

7.      A description (e.g. of a unicorn) is fanciful to an actor who believes it represents an imaginary reality (though it might turn out to true).

8.      Communication succeeds when the meanings/information in a description are the same when encoded and decoded - near enough.

9.      Communication requires that speakers and listeners share the same language for encoding and decoding a description.

10.  To share a language, human speakers and listeners must also largely share the same biology, psychology, experience of the world and education.

11.  A description typifies what is described; descriptions attribute general properties or qualities to particular things.

12.  A description may be a singular type (e.g. tasty) or a compound type (extending to large and complex system description).

13.  Unlike basic mathematical types, natural language types are loose, fuzzy and flexible.

14.  A singular description/type is explained in a circular fashion in terms of other descriptive types. E.g. A “rock” might be described/typified as “dry”, “perceptibly discrete entity”, “solid body” and “mineral material”.

15.  To create a consistent and coherent domain-specific language we break the circularity by agreeing some basic axioms or base types.

16.  In languages for describing systems, the base types divide along the lines of space and time (actors and activities, entities and events, objects and operations, products and processes, or structures and behaviors).


Read “The philosophy of system theory” for discussion of this tractacus from a philosophical view point

The science of system theory

System architects observe baseline systems, envisage target systems, and describe both.

This paper traces the pre-history of systems thinking and concludes with a few modern ideas.

It discusses the relationship of real world actors and activities to descriptions of them (as in data structures).

And the specification of rules as pre and post conditions of activities (as in business processes).

Below are some of the points made above.


Reality and descriptions of it

·         The systems of interest here are islands of orderly behavior in the ever-unfolding process of the universe.

·         Especially systems in which entities act (systematically) in response to information encoded in messages and memories.

·         And usually, systems in which that information describes or directs some entities or events in reality.

·         Our descriptions of reality are digital in the sense that we divide reality into discrete entities (structures) and events (behaviors). 2


Animal memories and messages

·         Only some descriptions of reality prove useful when tested.

·         Communication requires that a receiver decodes the same meaning from a message that a sender intentionally encodes in that message. 3


Human communications

·         Only humans invent words to symbolise things and their qualities.

·         The written record revolutionised our ability to think deeply, think straight, remember things and communicate. 5


Human languages, natural and artificial

·         The fluidity and imprecision of natural language enables human creativity and assists survival in a changing world.

·         For a system description to be holistic, unambiguous and testable, an artificial domain-specific language is needed.

·         A domain-specific language is an island of inter-related words with stable meanings, in the ever-unfolding evolution of natural language.


Thinking about systems  9

·         A system description is a complex type that symbolises the structures and the behaviors of each entity that realises the system.

·         To make testable assertions about a system’s behavior, we specify processes by their pre and post conditions.

·         A concrete system is composed of actors performing activities.

·         An abstract system typifies actors in role descriptions and activities in rule descriptions.

·         A role is a list of activities performable by an actor.

·         A rule is a precondition or post condition of an activity.


By the way, some systems thinkers speak of systems maintaining order, or “negative entropy”.

It turns out that thermodynamics is tangential to most practical applications of general system theory.

Having said that, a few notes on thermodynamics are included in the footnotes below.

Footnote on thermodynamics

Some systems thinkers speak of systems maintaining order, or “negative entropy”.

It turns out that thermodynamics is tangential to most practical applications of general system theory.

“Cybernetics depends in no essential way on the laws of physics.”

“In this discussion, questions of energy play almost no part; the energy is simply taken for granted.” Ashby

Having said that, a few notes on thermodynamics are included below.


The need for energy to maintain order

Generally, a system is an island of orderly behavior in the ever-unfolding process of the universe.

To maintain order (or negative entropy) in its structures and behaviors, a system must consume energy.


Ludwig von Bertalanffy (1901-1972) considered an organism as a thermodynamic system in which homeostatic processes keep entropy at bay.

“By importing complex molecules high in free energy, an organism can maintain its state, avoid increasing entropy…."


Observation: while homeostasis was a focus of many early system theorists, it is not a property of all systems.

The fact is that social and business systems can grow, shrink, die and produce chaotic outcomes.


Information as a subtype of order

Erwin Schrödinger (1887 –1961) also discussed the thermodynamic processes by which organisms maintains themselves in an orderly state.

 “Living matter evades the decay to thermodynamical equilibrium by homeostatically maintaining negative entropy (today this quantity is called information) in an open system.”

“The increase of order inside an organism is more than paid for by an increase in disorder outside this organism by the loss of heat into the environment.” Cornell University web site.


Observation: In 2009, Mahulikar & Herwig re-defined the negative entropy (negentropy) of a dynamically ordered sub-system.

Negentropy = the entropy deficit of an ordered system relative to its surrounding chaos.

Negentropy might be equated with “free energy” in physics or with “order”; some equate it with "information".

But in cybernetics and systems thinking "information" usually has a more specific meaning.

Information is the meaning created or found by an actor in a description of a reality.

To encode meaning in a description (or data structure) is to use some energy to create a very specific kind of order.


The tendency of systems in competition to optimise their use of energy

“Nature's many complex systems--physical, biological, and cultural--are islands of low-entropy order within increasingly disordered seas of surrounding, high-entropy chaos.

Energy is a principal facilitator of the rising complexity of all such systems in the expanding Universe, including galaxies, stars, planets, life, society, and machines.

Energy flows are as centrally important to life and society as they are to stars and galaxies.

Operationally, those systems able to utilize optimal amounts of energy tend to survive and those that cannot are non-randomly eliminated.” Cornell University web site.


Observation: this “optimal use of energy” principle has been at work in the evolution of biological systems.

But where minimising energy consumption is of little or no advantage, evolution proceeds in a suboptimal way.


The tendency of systems, where resources are cheap, to sub-optimise use of energy

The highest energy consumption per head is not found in countries that are especially orderly.

Energy consumption is highest in countries that are:

·         Too cold: Iceland, Canada,

·         Too hot: Trinidad and Tobago, Qatar, Kuwait, Brunei Darussalam, United Arab Emirates, Bahrain, Oman, or

·         Too rich to care about the cost: Luxembourg, and the United States.


Many modern software systems are over complex and suboptimal, because we give them as much memory space and electricity as they need.