Abstracting systems from phenomena

Copyright 2021 Graham Berrisford. A chapter in the book https://bit.ly/2yXGImr. Updated 23/08/2021 14:42


Reading online? If your screen is wide, shrink the width for easier reading.


This chapter helps you avoid confusion by disentangling descriptions of activity systems from reality the of physical entities and phenomena. Don’t worry if you don’t get all the ideas first time through. When they reappear in later chapters, you may find it helps to return here.


Introduction. 1

Abstracting activity systems from physical entities. 2

Relating abstract activity systems to physical entities. 4

The realization of an abstract activity system in reality. 5

Dependencies in reality between independent systems. 5

Abstracting activity systems from social entities. 6

An epistemological triangle. 8

Conclusions and remarks. 10



“Systems theory is the interdisciplinary study of systems in general, with the goal of elucidating principles that can be applied to all types of systems at all nesting levels in all fields of research. The term does not yet have a well-established, precise meaning,”  Wikipedia


What people call “systems thinking” ranges from the softest of sociology to the hardest of physics and mathematics. Some generalize across these different domains of knowledge by defining a system as a whole made of parts. The trouble is that every individual entity you can see or name is divisible into separately describable parts. If the term system is to be useful, more than a vacuous noise word, more than a synonym for entity, then it must have some more particular meaning.

Abstraction of structures and behaviors (repeat)

The universe is an ever-unfolding process from the big bang onwards. We observe, envisage and describe the universe by carving up space and time.


From the continuous expanse of space, we carve out discrete structures - entities and actors. And from the continuous flow of change over time, we carve out discrete behaviors - events and activities.


Structure examples

Behavior examples

Solar system







Heart beat, life

Motor cycle

Two-stroke cylinder cycle


Billing process


Every structure has a life time over which it changes – whether cyclically or progressively. An aggregate entity is a collection of elementary entities that interact – whether cyclically or progressively.


Every behavior, be it cyclic or progressive, is constrained by the laws of nature or other rules. An activity system is a pattern of behavior we observe or envisage in what one or more entities do over time – as in cybernetics, system dynamics and soft systems methodology.


The first big cause of confusion is the use of the word “system” for both aggregate entities and activity systems. The second is the presumption that one aggregate entity corresponds to one activity system. In general, the relationship is between them is many-to-many.

Abstracting activity systems from physical entities

“It is important to stress Ashby defined a system not as something that exists in nature. A system consisted of a set of variables chosen for attention and relationships between these variables, established by observation, experimentation, or design." Ashby’s student Krippendorff writing in 2009 on Ashby’s Information Theory


Every activity system in the real world is “soft” in the sense its boundary is determined by its observer/describer/designer. In operation, it is dynamic in the sense it changes from state to state and/or produces outputs from inputs in a way that is regular or repeatable enough to be modelled by an observer/describer/designer.


Ashby distinguished reality from description. He distinguished a physical entity (which he sometimes called the real 'machine') that is observable as changing over time from the countless regular systems we might abstract from observing that entity.


2/5. It will be appreciated that every real 'machine' embodies no less than an infinite number of variables, most of which must of necessity be ignored. Ashby’s “Design for a Brain”


3/11 “At this point we must be clear about how a “system” is to be defined. Our first impulse is to point at a [physical 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. [We must] pick out and study the facts that are relevant to some main interest that is already given.” (Ashby’s “Introduction to Cybernetics”)


Ashby’s wording was not entirely consistent between, and even within, his books. It seems fair to say however that his real 'machine' is some material object(s) that can be observed as behaving in the way described by an abstract system.


In both cybernetic and in system dynamics, the abstract system is a set of state variable types, and rules for activities that change the values of those state variables over time. Then, a real 'machine' is a physical entity that can realize an abstract system – near enough.


The larger and more complex the physical entity, the less of its behavior an observer can abstract into a system description. Consider how five observers may see the same card school.



The system they abstract from a card school

A card player

a poker game

An economist

a system to transfer money from less skilled to more skilled.

A psychologist

a system in which players are conditioned by occasional and near random rewards to repeat a behavior.

A sociologist

a system in which players swap anecdotes and bond socially

A heating engineer

a system that generates heat and so reduces the host’s heating bill


The system an observer abstracts from the phenomena depends on the interest they bring to their observation. The graphic below shows how different observers/describers observe or envisage different activity systems in one physical entity, and create or use abstract descriptions of those systems.

[jpg missing from on-line display]



The graphic is a description in which the phrase “a game or tennis” or “a beating heart” is a proxy for a real-world system in operation.


Suppose a heart surgeon’s abstract system is this a model of a heart beat.


1.     The atria walls contract and force blood into the ventricles.

2.     The ventricles walls contract and force blood from the heart into the lungs and body.

3.     The atria fills with blood (and the cycle begins again).


The model above represents a physical system (an actual heart beat) performed by a physical entity (a heart). The physical activity system, though inseparable from the physical entity, is only that part or aspect of the entity that is correlatable with the abstract system description.


The graphic is a little too neat. It shows observers abstracting distinct systems. In practice, the systems abstracted by observers may be independent, nested or overlapping. For example, from the body of an animal, specialists might model several overlapping, systems related to digestion.

Relating abstract activity systems to physical entities

Abstract systems are descriptions that typify some behavior. Physical entities are individuals. The relationship between them is many to many.


Admittedly, in conversation, we do often correlate one physical entity with one system. For example, we might speak of a physical machine (like a steam engine, or an organism like you or me) as being a system. By way of contrast consider the entity that so many “system thinkers” focus on - a human society. This is very different in character.


About the entity of interest

Steam engine


Human society

Is it a bounded solid entity, locatable in space?




It is a network of parts distributed in space.

Does its boundary enclose its parts, visibly and tangibly?




It has no visible or tangible boundary.

Does it realize a specification encoded in a design or genotype?




Its structures and behaviors are fluid, not determined by a specification.

Does it have a single main purpose?


Moving things.


Gene propagation.


It continually evolves to meet the disparate purposes of disparate stakeholders.

Are its parts primarily dedicated to its purpose?




Each actor is agent with their own aims who divides their time between different social entities, some in competition or conflict.


The trouble for coherent systems thinking is this: the relationship between abstract activity systems and physical entities is many to many. First one physical entity may realize or participate in several abstract systems.


One physical entity

may realize many abstract systems

One rain forest

may capture carbon in tree trunks, and feed squirrels

One card school

may play many games (poker, whist and pizza sharing)

One orchestra

may perform many different musical scores

One computer

may execute many different programs, or be used as a doorstop

One human being

exhibits heart beat, digestion and breathing systems


And conversely, one abstract activity system may be realized by many physical entities.


One abstract system

may be realized by many physical entities

“Carbon capture”

realized by photosynthesis in countless rain forests


followed in the playing of games by many card schools

One musical score

performed by many orchestras

One program

executed by many computers


exhibited by many human beings


Generally speaking, one abstract system may represent (idealize, typify, codify, defined the behavior of) several physical entities. One physical entity may realize (embody, exemplify, manifest, behave as defined by) several abstract systems.


In a sociological context, one social entity can realize several social activity systems. And conversely, one social activity system can be realized by several social entities.

The realization of an abstract activity system in reality

Some go as far as to say activity systems are purely abstractions; they exist only in models; don’t exist in the natural world, which is misleading, because a physical activity system exists whenever a physical entity – near enough - realizes an abstract system.


Below, Ashby’s real 'machine' is divided into two aspects. There is a physical activity system - a performance of the defined activities, giving values to the defined variables. And there is a physical entity - some actor(s) able to perform the activities in the system (and possibly activities in many other systems).


Realizations can be imperfect. We can model the way a pendulum behaves – near enough. However, when operating out of doors, buffeted by a wind, the behavior of the real machine will depart from that of our ideal machine.


Realizations can change. The genome of an organism can be seen as codifying the structures and behaviors of a biological system. So, when a bacterium acquires some genetic material from another bacterium, from then on, it will realize a different system.


A physical entity (be it a machine, animal or social entity) is always more than any activity system realizes. And when we model a system, we do so at one level of the hierarchy of sciences introduced in the previous chapter.


A social entity behaves in ways above and beyond the biology of its individual members. It has been suggested that the nature/nature influence on human abilities is 70/30. Whatever the true proportion, much of what a human actor does is not defined in its genome. Some behavior is shaped by the actor’s experience, education and roles in social interactions that are constructed to meet some goals.

Dependencies in reality between independent systems

Observers may abstract countless independent systems from observation of one physical entity, such as a human being. The three systems in the table below are independent in that their models do not overlap or connect.






Abstract system

Heartbeat model

Digestive system model

Contract signing model

Physical system

A beating heart

The digestion of food

The signing of a contract

Physical entity

A heart

Teeth, stomach, intestines etc.

Brain, eyes, hand etc.


However, in reality, S3 depends on the successful operation of S1 and S2. Moreover, all three systems depend on a body’s nervous system. Similarly, on your computer, your spreadsheet and browser applications are independent systems, yet both depend on your computer’s operating system. And more generally, any two systems may be related indirectly by their dependence on another (server, platform or infrastructure) system.


Despite the dependencies in reality between what is described as independent systems, there is no prospect of modelling the whole of a human being (all its physical, biological, psychological, social behaviors) in one abstract system. We can only study and define tiny aspects of the whole as a system.

Abstracting activity systems from social entities

4/16. “Up till now, the systems considered have all seemed fairly simple, and it has been assumed that at all times we have understood them in all detail. Cybernetics, however, looks forward to being able to handle systems of vastly greater complexity: computing machines, nervous systems, societies.” (Ashby’s “Introduction to Cybernetics”.)


If cybernetics is to be applied to a computer, not only must the material reality of that computer be massively simplified, but also, the physical components of the computer must be distinguished from the countless applications systems the computer may offer its users.


Similarly, if cybernetics is to be applied to a society (a set of communicating actors), not only must that social entity be massively simplified, but also, its physical components (the actors) must be distinguished from the roles they play in completing actions.


"The first decision is what to treat as the basic elements of the social system. The sociological tradition suggests two alternatives: either persons or actions." David Seidl 2001


Person-centric social entity thinking is one thing; action-centric activity systems thinking is another. Both are useful views, but the “system” in one is not the “system” in the other. It is unfortunate that even highly respected systems thinkers have flipped from one to the other, in speaking or writing. If systems thinking is to advance, thinking about a social entity must be distinguished from thinking about an activity system it may perform or participate in.


A first social activity system

Think of a card school. The quantity of money in front of each player is a variable that is increased and decreased by playing hands in a game of poker. The card school is a social entity that can be seen as a physical system when and where it plays a game of poker.



A game of poker

Abstract system

The rules of the game and roles for players

Physical system

A game of poker, in which defined variables change value

Physical entity

A card school, whose members are able to play the game


Again, the relationship is many to many. One activity system can be realized by several social entities (the game of poker can be realized by many card schools). Conversely, one social entity can realize several activity systems (the card school can play whist, or share a pizza). There is much more to know about a card school than its playing of games. Its members can act in many other social entities, some of which may conflict or compete with each other.


A second social activity system

A composer conceives and organizes the musical notes an orchestra (a social entity) should  play in a symphony (an activity system).



A symphony

Abstract system

A symphony score: musical notes and how they relate to each other.

Physical system

Symphony performance: outputs notes as sounds in a venue.

Physical entity

Orchestra members employed to play roles in a performance.


The symphony score does not address the whole of the social entity that is an orchestra. The composer addresses only the roles that orchestra members play in sounding musical notes, and the kinds of instrument they need to play their roles. The description of roles, notes and resources add up to the complex type that is a symphony score. At run time, in a performance supervised by a conductor who keeps things in order, orchestra members cooperate to realize the abstract symphony score in a performance.


Composers <observe & envisage> Symphony performances

Describers <create and use> Symphony scores

Symphony scores <represent> Symphony performances


A third social activity system

A business architect describes or designs the activities a business (a social entity) is to play regular business operations (an activity system).



A business

Abstract system

Business activity model (as in soft systems methodology)

Physical system

Business operations that realize the model above

Physical entity

Actors employed to play roles in business operations.


An enterprise typically realizes a mess of countless different activity systems, some duplicated, some uncoordinated and some in conflict (which is the problem that enterprise architecture was invented to address). At run time, in operations supervised by managers who keeps things in order, human actors cooperate to realize the abstract system in the everyday performance of their roles and processes


Business architects <observe & envisage> Business operations

Business architects <create and use> Business activity models

Business activity models <represent> Business operations


Abstraction in system dynamics

The same layering can be seen in a closed system of feedback loops, as may be modelled using system dynamics.



System dynamics in general

Abstract system

Quantitative variables connected by flows (rules for change)

Physical system

Real-world interactions between things or qualities below

Physical entity

A selection of related material entities and/or qualities of them

An epistemological triangle

In philosophy, ontology is about what things are, independent of observation. By contrast, epistemology is about what we know of things, and empiricism is about what we can know by observation. Science is empirical; it does say what a physical entity “really is”; only that it matches (near enough) some theory or model we have. 


Cartography is empirical; it does say what a territory “really is”; only that it matches (near enough) some map we have. It involves three relations of the kind we have seen above.


Mappers <observe and envisage> Territories.

Mappers <create and use> Maps.

Maps <represent> Territories.


In some later chapters, this book represents such relations using a triangular graphic. For example, read the graphic below from left to right.




<create and use>          <represent>

Mappers    <observe & envisage>   Territories


The map is not the territory, but the two must be correlated well enough to help map users find things. Bear in mind however that one phenomenon can be described in several ways. Different maps, showing different features, may be drawn of one territory. You may use different maps for country walks, planning journeys, driving, studying geographic features, studying demographic features. And you may need to find or buy a new map now and then.


Bear in mind also that no description is complete. A territory is infinitely complex; a map cannot be a complete or perfect representation of it. A map is an abstraction that shows only enough that we can find or learn what we need to.

Musical composition

Composers (describers) define the notes and instruments required for symphony performances (described things) in symphony scores (descriptions).


Composers <envisage> Performances

Composers <create> Symphony scores

Symphony scores <represent> Performances


The composer does not address the whole of the social entity that is an orchestra. The composer addresses only the roles that orchestra members play in sounding musical notes, and the kinds of instrument they need to play their roles. All the documented role, note and resource types add up to a complex type we call the symphony score.



Symphony scores

<create and use>                          <represent>

Classical composers <observe and envisage> Symphony performances


At run time, conductors use a score to drive an orchestra, beat by beat, to perform the symphony in a discrete event-driven way. Thus, supervised by a conductor who keeps things in order, an orchestra realizes the abstract symphony score in a performance.

Business activity systems

Systems thinking is empirical; it does not insist a physical entity is a system, only that its behaviour (near enough) matches some system model we have.


The designer of a business activity system cannot address the whole of the social entity that is a business. The designer addresses the roles that business actors play in a performance of the business system, and the kinds of resource they need to play those roles.


The designer describes entity types like customer, event types like order and payment, process types like billing, and rule types like order value = order amount * unit price. All these entity, event, process, data and rule types add up to a complex type we may call an abstract activity system.


Business activity systems

Abstract activity systems

<create and use>                     <represent>

Business architects <observe and envisage> Physical operations


At run time, supervised by managers who keep thing in order, business actors realize the abstract activity system in a physical activity system that consumes inputs, creates business data and uses it to decide how to respond to events.


In cybernetic terms, a business activity system of this kind can be seen as a machine that imitates what comes naturally to animals. It detects events, interprets their significance in the light of memories retained, and responds by acting in a way that serves the interests or aims of the business, machine or animal.


The more general triangle below relates describers to descriptions and phenomena. Note that a description in the mind is at the top of this triangle, not the left.




<create and use>              <represent>

Describers <observe and envisage> Phenomena


In the first three parts of this book, don’t worry about the triangles. Treat them as informal graphics that illuminate the text. In the fourth part, the semantics of the triangle are more important, because it turns out there is an essential difference between our triangle and comparable triangles you can find in semiotics and philosophy.

Conclusions and remarks

My education (in psychology, biology and the philosophy of science) leads me to the conclusion that a government institution, or a university, is not a system. Rather, it is a social entity (in which the basic elements are actors) that employs and participates in several human activity systems (in which the basic elements are actions). Accordingly, this chapter has distinguished abstract systems from physical or social entities that realize them. Later, this will be important to how we think of systems in practical enterprise architecture.


This final section includes a few more remarks on description and reality.

Description and design: analysis and synthesis

Analytical and synthetic thinking are often contrasted as though people do one or the other. In practice, we interleave the two processes. Analysis is what we do in reverse-engineering, when we observe and describe an existing thing by dividing it into parts and then drawing a map, or studying how parts interact to produce so-called “emergent properties”.


Synthesis is what we do in forward engineering, when we envisage and design a new thing by relating parts so as to produce some desired or required emergent properties. Synthetic design involves not only creating connections between things but also describing them. This book does not say much about the design process, but it does discuss the product - a description of what is designed.


Aside: when we speak of the design of a natural system, we refer to a structure and/or behavior that is an outcome of evolution. You might think of evolution as an opportunistic kind of design process, and a genome as a special kind of description.

Description at individual and statistical levels

The system defined in an event-driven model of a dynamic system is a model of individual entities and events. Below are four related entity types, documented in the style of relational data analysis. The identifiers are underlined. The relationships are indicated by asterisks.


Housing market: entity types





City Name

Total Houses

Houses For Sale

City Name*


Owner Person id *

For Sale Status

For Sale Price

Person id *

Address *

Person Id

Person Name


To complete an entity-event model, one defines the events that create entities, update the values their of attributes and remove them. Key events here may include Put House On Market, Buy House, and Remove House From Market, along with discrete events to register and remove an entity of each type.


By contrast, a system dynamics model is a model of aggregate quantities at a statistical level.


Housing market: system dynamics model

Growth in

Feedback loop

Growth in

Houses for Sale



Average House Price


However, models of individuals and aggregates are naturally entangled. First, an individual entity can have an aggregate property, such as a bank account level, or a number of children. Second, we may be able to describe a stock, population or aggregate not just in terms of its quantity, but also as an individual entity with attributes like name, weight, volume, average size, unit price, whatever. And using agent-based modelling software, we can represent the individuals in a statistical model, such as the fish in a shoal, as dots on a screen.


The chapter on dynamics discusses abstracting from the individual to the aggregate level.

Homomorphic and isomorphic descriptions and realities

Ashby wrote that a regulator’s model of a target must be isomorphic with the target that is regulated, meaning, the elements and relationships in the model must be correlatable with elements and relationships in the reality. This isomorphism is logical rather than physical.


Two models or descriptions are homomorphic when one is an abstraction or elaboration of the other. A higher-level description may be more abstract (by composition or generalisation); a lower-level description may be more elaborate (extended by decomposition or specialization). Homomorphism may be seen as a special case of isomorphism.


Two things are said to be isomorphic when they are similar in shape or pattern, such that the elements of one can be correlated with the elements of the other. Systems thinkers use the term with various meanings that bear closer examination, because some are more useful than others. The classification below elaborates on the one in Ashby’s Introduction to Cybernetics (6/8).


Passive structure isomorphism

This occurs when two passive structures resemble each other in shape. At least three varieties may be distinguished.


Natural isomorphism occurs when passive structures are paired by the laws of nature, like an image to its reflection in a mirror, or a photograph to its negative


Description-to-reality isomorphism occurs when icons or symbols correspond (by design) to reality, like a statue to a person, or a map to a territory.


Symbol-only isomorphism has no significance. For example;

·       This sentence’s words are structurally isomorphic to the words below.

·       John Kennedy was the thirty-fifth president of the United States.


Activity system isomorphism

This occurs when two activity systems resemble each other in structure and/or behavior. Again, at least three varieties may be distinguished.


Behavior-only isomorphism. Ashby called this the “strictest” kind of isomorphism. Two “black box” systems may behave the same, regardless of their internal structure. So, interchanging them cannot be detected by testing their input-to-output behavior. Such encapsulation of systems and components has been a basic principle of every software design fashion since 1970 (modular programming, object-oriented design, component-based design, service-oriented architecture, microservices, etc).


Full isomorphism. Two systems may not only behave in a similar way, but also have similar internal structures, like the mechanical and electrical machines in Ashby’s figure 6/8/1. The output display dials show measures of different qualities.


Ashby’s isomorphic systems


Mechanical system

Electrical system

Input parameter

First shaft: degree of rotation

Potentiometer: voltage


Spring: stiffness

Inductor: inductance

Fly wheel: inertia

Resistor: resistance

Liquid trough: friction

Capacitor: capacitance

Output variable

Second shaft: degree of rotation

Current meter: sum of currents


[jpg missing from on-line display]


Structure-only isomorphism. Lastly, two systems may have the same structure, but behave differently, as in the correlation drawn by Stafford Beer between the structure of the human nervous system and the management structure of a business. This is the weakest kind of isomorphism. At best, it provides a teacher with an analogy for use in education.


The later chapter on Beer’s ideas suggests this last kind of isomorphism can mislead people about the nature of one or other of the two things compared.