The systems thinking triad

Thinking becomes "systems thinking" with the application of a system theory. If you say an entity is a system with no reference to a system theory, then while you may be a great thinker, what you mean is unclear. Different theories, not to mention different interests, lead to different systems.

This article relates my view of Ashby’s thinking to Checkland's “soft systems thinking” about social entities. It also picks up on Kenneth Boulding's suggestion that the elements of a human activity system are roles rather than actors, which means that one actor may play roles in many systems, some of them possibly in conflict.

Contents: What Ashby said. Abstracting social systems from entities. The systems thinking triad. More on abstracting a system from a social entity. Scaling up to a large and complex social entity. Are entities also systems?

What Ashby said

These articles draw from two books by Ashby you can find on the internet "Design for a Brain" (DfaB) and "Introduction to Cybernetics" (ItC).

Ashby discussed closed systems in which state variable values change as a function of time (or discrete time events). An observer abstracts a closed system from the physical world, by selecting state variables of interest from innumerable possible variable types.

Ashby also discussed open systems in which state variable values are changed by inputs. By drawing a boundary around an open system, the observer divides variables between a) state variables inside the system and b) parameters (also variables) carried by inputs.

Aside: systems can be nested in space, so a parameter input to a small one can be a state variable inside a larger one. And nested in time, so an attribute that is an invariant in the life of a short-lived entity, may be a variable in life of a longer lived one.

When discussing variables, we tend slip between discussing variable types and variable values. We do much the same when we discusses processes or functions. But strictly, there are four concepts.

Abstracting systems from things in the physical world

In my reading, Ashby distinguished three concepts

• an "abstracted system" of variable types, defined by an observer
• a system of variable values, as may be shown to the observer on dials attached to
• a "material object", or "real machine" in the physical world.

In "Design for a Brain" Ashby made clear his system is an abstraction that describes the features of a material entity in the form of state variable values.

• DfaB 2/3. The first step is to record the behaviours of the machine's individual parts. To do this we identify any number of suitable variables [whose values might be] represented by a pointer on a dial. I shall, in fact, assume that... the experimenter is observing not the parts of the real machine directly but the dials on which the variables [values] are displayed.
• DfaB 2/4. A system is any arbitrarily selected set of variables. It is a list nominated by the experimenter, and is quite different from the real machine.
• DfaB 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.

In other words, Ashby said that since every material entity has countless describable variables, we cannot describe all of them, and we never try to. Rather, an "observer or experimenter", observes or envisages how selected state variables interact to produce a result of interest to them. And that "way of behaving" is the system of interest.”

In "An introduction to cybernetics”, Ashby's system is subset of the state variables that could be observed in a material object.

• ItC 1/3. Cybernetics stands to the real machine much as geometry stands to a real object in our terrestrial space.
• ItC 3/11 “we must be clear about how a “system” is to be defined. Our first impulse is to point at a pendulum 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 try [true?] is that we should pick out and study the facts that are relevant to some main interest that is already given.”

In short, Ashby says observers abstract systems from physical entities that he calls "real machines". Not having a word processor to help him, Ashby's vocabulary was not entirely consistent. In my reading, he distinguished concepts as shown below.

The entity-system relationship

Ross Ashby hoped that cybernetic system theory could be applied to large and complex material and social entities. In scaling up from examples of relatively simple behavior patterns to a large and complex entity, we have to confront the fact that a real-world entity is always far more complex in its countless details than any of the systems we might abstract from it.

In "Design for a Brain", Ashby said that from one large and complex entity we may abstract several different systems.

• DfaB 2/14 If we restrict our attention to the variables, we find that as every real machine provides an infinity of variables, and as from them we can form another infinity of combinations, we need some test to distinguish the natural system from the arbitrary... From now on we shall be concerned mostly with regular systems.
• We assume that preliminary investigations have been completed and that we have found a system, based on the real machine, that 1) includes the variables in which we are specially interested, and (2) includes sufficient other variables to render the whole system regular.
• DfaB 7/1 … confusion is at once removed if one ceases to think of the real physical object with its manifold properties, and selects that variable in which one happens to be interested.

In short, observers select variables and defines the rules that make the behavior of the system "regular".

In "An introduction to cybernetics”, Ashby said that from one large and complex entity we may abstract several different systems.?Given a system open to input and output, Ashby said.

• ItC 6.1 “Every real system has an indefinitely large number of possible inputs... by which the experimenter may exert some action on the [Black Box]. Equally, it has an indefinitely large number of possible outputs... by which it may affect the experimenter... If the investigation is to be orderly, the set of inputs to be used and of outputs to be observed must be decided on, at least provisionally.”

So, Ashby's system consumes and produces only a subset of the inputs and outputs consumed and produced by a real machine. It is more like a slice, or perspective, than a part of the whole. Very much like Checklands's soft system.

Conflicting systems

Having said we must pick out the facts that are relevant to some main interest given to us, and select inputs and outputs from the large number of inputs and outputs that cross the boundary of a large entity, Ashby recognized that observers' perspectives may conflict.

• ItC 6/14 There can be no such thing as the (unique) behaviour of a very large system, apart from a given observer. For there can legitimately be as many sub-machines as observers, and therefore as many behaviours, which may actually be so different as to be incompatible if they occurred in one system.

Here, Ashby may have been thinking of incompatibilities that arise when we describe one large entity in two or more systems that are homomorphic (at different levels of granularity) or not homomorphic (addressing unrelated or possibly conflicting interests), much as the "soft systems" abstracted by Checkland from a human organization of social entity.

Abstracting social systems from social entities

As Ashby said, the starting point for systems analysis is “some interest already given”. In any human social entity, there can be conflicts between the goals or interests of actors, who may be related as superior-subordinate at two levels, or peer-to-peer at one level.

For example, there can be a conflict between the DEI goal of an HR director, and the maximise performance goal of a COO.

For example, divisions of one enterprise may compete to do the same or related work. E.g.

• our consulting division sells consultants at a high day rate, and outsources software development to India;
• our systems integration division strives to sell software project teams at a lower rate than consulting, then expands those teams if possible, and does dev ops;?and
• our managed services division sells operators at a lower rate than systems integration.

For these reasons, Checkland distinguishes a system from the social entity in which it may be observed. Similarly, one may find several of Senge's system archetypes in one organization.

Senge's system archetypes

In "The Fifth Discipline: The Art and Practice of the Learning Organization" (Doubleday, 1990), Peter Senge introduced several system archetypes, each representing a common pattern in the way people behave.

In the system archetype called "the tragedy of the commons", actors pursue actions that are beneficial to themselves in the short term, but can eventually result in exhaustion of the common resource. This diagram tells a simplified version of the story.

Increasing the number of fishers can turn the fish stock increment from positive to negative. (And whereas grass on common land can grow again, once a fish stock is exhausted, it is gone forever.)

The systems thinking triad

A dynamic system is a phenomenon that may be observed or envisaged in the behavior of some real world thing(s). In every practical school of systems thinking, the system of interest (observed or envisaged as occurring in reality) is represented in some kind of abstract model, which represents how elements of the system are related.

Axiomatic here is the idea that systems thinkers <create and use> abstract systems to <represent> real systems they <observe and envisage> in real world entities, which exist whether or not they are modeled as systems.

Abstract systems

Abstract system : a model of a real system, created and used by an observer or envisager. An observer's view of a real machine, describing its state and behavior in terms of particular state variables and rules that govern how variables change from one state to the next.

An abstract system is a model that shows how elements interact in a "holistic" way to produce effects of interest. It is typically a collection of inter-related roles and rules, which represents how actors play roles and follow rules in a real system.

An abstract system can be encoded in various ways - mental, verbal or documented in symbols of some kind. For example, a causal loop diagram of the “tragedy of the commons”, the roles and rules of the game of poker, a symphony score, or an orrery.

• "All models are wrong but some are useful" George Box

No map is a complete and perfect description of a territory. It is true in so far as it is useful, meaning, we can correlate features of interest we see on the map with features we see in the territory. Outside of mathematics and software engineering, we don’t need a model to be perfect.

So, an abstract system is a type or model that represents the structure and/or behavior of a real system - near enough. Not every abstract system we define is a good or accurate model. (Donnella Meadows noted systems thinkers rarely attempt to verify a causal loop diagram before presenting it as a model of reality.)

All models have features that can be correlated, to some degree, with features of things they model. The closer the correlation, the more useful the abstract model can be in predicting or specifying the behavior of the real system that is observed or envisaged.

An abstract system is itself real. It is abstract only in relation to whatever real system it is created or used to model. And it only plays the role of being a model in the processes of being created or used in that way.

Real systems

Real system: an instantiation of an abstract system by a real world entity; an instance of a potentially describable abstract system (whether or not the real system has been observed or envisaged).

A real system is a phenomenon or behavior that may conform to an abstract system. If it does, then it is a performance of defined activities, which gives values to variables. and correlates, well enough, with an abstract system. For example: over fishing of a herring stock, a game of poker, a symphony performance, or solar system orbits.

Natural systems exist in reality before they are observed and described. By contrast, designed systems exist in reality only after they have been envisaged and described.

For example, a card school cannot play a card game until the rules are written, and an orchestra cannot perform a symphony until there is a score. There is no Platonic ideal of a card game or symphony. And if all copies of a card game's rules or a symphony score (in memories and messages) were destroyed, then it would no longer exist.

A real system may instantiate an abstract system imperfectly, yet near enough to be useful. Outside of mathematics, many abstract types are imperfectly instantiated in the real world. E.g. every symphony performance is different, but near enough is good enough.

Real-world entities

Real world entity: a stateful material object that behaves regardless of any observers; a collection of actors or components that may realize a real system.

An entity is a material or social entity that may participate in one or more real systems. For example: a fishing community, a card school, an orchestra, and the material bodies that make up the solar system.

What a real world entity does outside of what is defined in an abstract system lies outside of the real system of interest. The same entity may realize different abstract systems, following different sets of rules.

Rules

Newton’s first law of motion is an abstraction from the movement of physical objects, and is expressed in an equation: F = M * A. We may observe real world objects move as the law predicts (near enough to satisfy NASA they can put a man on the moon) but the law is violated near the speed of light.

The rules of poker are an abstraction from the game played by poker players, and are expressed in a rule book. Real world poker players may behave as the rules predict (near enough to satisfy the poker players), or violate the rules.

Senge’s system archetype “the tragedy of the commons” is an abstraction from the behavior of actors in a social entity (competing for a share resource) and is expressed as rules in a causal loop diagram. Real world actors may behave as the rules predict, or violate the rules.

Generally, a social system is an abstraction from the behavior of actors in a social entity and is expressed as rules. Real world actors may behave as the rules predict, or violate the rules.

FAQS

To answer some questions asked by readers.

Is an abstract system a system description? Yes, and the description or model contains variables (be they quantitative and/or qualitative) that characterize the system.

Do real systems exist in the real world? Yes, real systems exist when elements interact to give values to variables defined in abstract systems. Any number of real systems may exist in a large and complex material entity, whether they are observed or not.

Can a real system's behavior be measured by instruments? Yes. And since any material entity is and does more than any real system we can describe, probing it may reveal variables we haven’t thought of.

What do you mean by observation of a real system? An observer receives outputs from the system of interest, and so, can observe variable values inside them. The observer may also use their senses to observe the parts of a system and how they interact.

Where does system evolution appear in the triad? Change the equation for Newton’s law and it is no longer his law. Change the rules of poker and it is no longer the same game, but we might still call it “poker”. Change the rules of a system and it is no longer the same system, but we might call it system version 2.

The evolution of organic systems requires an ever-continuing cycle on which an older generation replaces itself by a slightly different younger generation.

The evolution of a designed system requires an observer to design the replacement. The <observe and envisage> relationship covers monitoring the state of a real, baseline, system. The <create and use> relationship covers changing the abstract system that represents a real, target system (a necessary precursor to instantiating a new generation).

An important question for systems theorists arises here.

Is a new system generation a different system ? Yes, it is a different system. But paradoxically, if you widen the system boundary to include the system or process by which the new system generation is generated, then that wider system remains unchanged. (See the discussion of second order cybernetics in the next article.)

Is this systems theory or system philosophy? Both. Since one material object may realize many systems, I depart from Ashby a little by separating his "material object" from his "real machine". And since abstractions are created and used by actors, I promote a kind of nominalist philosophy, and challenge some other sociological and philosophical positions.

More on abstracting systems from social entities

Kenneth Boulding (in his 1956 essay) may have been the first to try to apply system theory to management science (as it was called then). In what might appear to be a throwaway remark, he suggested the element of a human system might be “role” rather than “actor”. Ever since, it seems to me that much “systems thinking” discussion has confused

• actors with the roles they play, and
• entities with the systems they realize.

In sociological systems thinking we may distinguish

• a social entity, which realizes any number of social systems, from
• a social system, which may be realized by any number of social entities.

The concept graph to the left illustrates social systems thinking. The concept graph to the right applies the same ideas to Senges's creation and use of system archetypes.

A real system (such as a game of poker) is a real-world instantiation of an abstract system (as defined in a "poker" rule book) by a real world entity (such as a card school).

A card school is a social entity. What a card school does outside the abstract rules of a card game lies outside of the corresponding real system. The card school may decide to play a different card game - switch from poker to bridge - following a different set of rules.

Scaling up to a large and complex social entity

Ashby had hoped that cybernetics could be scaled up to illuminate thinking about very large and complex biological and social systems. In practice, it can illuminate only some aspect (some particular system of interest) that a large organic or social entity contains or participates in.

A systems thinker observes patterns of behavior in real systems, creates and uses patterns in abstract systems, and envisages where abstract systems can be instantiated. A systems thinker cannot address the whole of a material or social entity, but can address how it instantiates an abstract system.

Systems thinking involves or addresses

• analysis (dividing things into parts) and synthesis (relating parts in wholes)
• simple systems and complex systems (whatever you mean by "complex")
• desirable systems and undesirable systems (as in Senge's archetypes)
• physical interactions and logical nteractions (information exchanges).

Senge's approach to analyzing a large and complex business involves looking for instances of system archetypes he defined. Several different system archetypes may be found in one business.

Checkland complained that students struggle to understand what he meant by a system: "they get it one day and lose it the next". His soft system is not a comprehensive description of a named business entity (or other social entity). His approach to analyzing a large and complex business assumes different stakeholders may find different systems in it.

A soft system is an observer’s view of what a real world entity does; it is only a perspective (a Weltanschauung, Checkland called it) of that entity. In essence, he defines a soft system by establishing an observer's interests, identifying features relevant to those interests, and the finding or defining an I/O transformation to address those interests.

Having said that, are entities also systems?

We should be cautious about speaking of a large and complex entity as a system.

Any business that instantiates a system you specify will have very many more features than you have thought of. It will likely implement other systems, specified by others, some of which may conflict with yours. Moreover, the employees may act in ad hoc ways, outside any describable system.

Suppose you casually speak of a human being as a system. I do not know how you bound it, what inputs and outputs, or variables and rules you have in mind. Are you thinking of

• A collection of cells that follows instructions encoded in DNA?
• An engine that transforms oxygen into carbon dioxide?
• A vehicle for propagating your genes in the next generation?
• A sender and a receiver of messages in a social communication system?

Does it make sense to say these views add up to one system? Or is it clearer to say that one biological entity may instantiate different systems?

Suppose you casually speak of a social entity as a system. I do not know how you bound it, what inputs and outputs, or variables and rules you have in mind. Are you thinking of

• A collection of messages about a theme (Luhmann)?
• A collection of social actors that cooperate to reach some goal?
• A collection of selfish actors that each act to maximise the pay off to themselves?
• A collection of actors that maximise the presence of their genes in the next generation?
• A collection of genes that direct actors to behave in ways that propagate the genes?

Does it make sense to say these views add up to one system? Or is it clearer to say that one social entity may instantiate different systems?

So, when is an entity not well-called a system?

There are several system theories. Until and unless we apply a system theory to an entity, we have no description of it as a system, no model of it and no prospect of completing one. So, to speak of it as system leaves the listener none the wiser.

Moreover, we have to address the challenge that in the real world there are many-to-many relationships.

• One material or social entity may realize many systems.
• One abstract system may be realized by many material or social entitties.

A large and complex organism or social entity might in theory be modeled as a system, but the entity is so massively large and complex that we will never be able to model more than a perspective of it as a system, and some of those perspectives, those systems, may have conflicting goals.

So, I distinguish a social system, in which human activities conform to the pattern or rules of a system we can describe, from a social entity, which may realize any number of such systems.

Related articles

If you want to read this article in the context of a book, watch this space.