Feedback

Systems thinking embraces several system theories, several kinds of system and many ideas. One of the most ubiquitous concepts is that of feedback.

Feedback is important in biology, psychology, education, science, and business. And in system thinking - be it hard or soft. Every feedback loop, natural and designed, has an effect. Observers may see the effect of feedback loop as a problem to be solved - such as a "tragedy of the commons". Or else, introduce it to solve a problem - such as regulating the speed of an engine.

This article introduces quantitative feedback, qualitative feedback, and how feedback loops can be represented in flow diagrams and causal loop diagrams. The aim is not to teach you detailed techniques; it is only to introduce them well enough to help you read related articles on systems and systems thinkers.

Content: Feedback. Feedback in thermodynamic systems. Feedback in organic systems. Feedback in social systems. Feedback and regulation. Using diagrams to represent feedback loops. Feedback in cybernetics. Feedback in System Dynamics. Remarks.

Feedback

Feedback loop: a circular relationship in which an effect or output returns as, or influences, a subsequent cause or input.

The concept was known in ancient Roman times, but it did not take off until James Watt invented the centrifugal governor (1788), which sparked the creation of other control devices..

A feedback loop relates (directly or indirectly) two entities or quantities that interact, in which the actions or state of each influence the actions or state of the other. For example.

• Oceans and winds interact in hurricanes.
• Wolves and sheep interact in predator-prey ecologies.
• People and viruses interact epidemics.
• Male and female sticklebacks interact in mating rituals.
• People exchange messages in a human activity system.

All things pass, and in the end, all feedback loops are transient. Systems thinkers observe, envisage and describe feedback loops that repeat and persist long enough to be of interest.

In the relationships above, each party influences the behavior of the other. They might be seen as equal partners in the relationship. However, feedback is often regarded or used as one-way control or governance mechanism.

Feedback in thermodynamic systems

After the big bang, feedback steered the evolution of the universe. Stars and black holes shape the distribution of gas and dust clouds, thus promoting or inhibiting the formation of other stars.

Feedback loops in thermodynamic systems are mechanisms where a system's output influences its future input, regulating its behavior.

Negative/balancing feedback maintains a system in a steady state. For example. A thermostat, when the temperature drops below the set point, turns on a heater, and when the temperature reaches the desired level, turns it off again. Cruise control in a car measures the car's speed against a set point. If the speed drops, the engine is stimulated, and if the speed increases, the power to the tires is reduced.

Positive/amplifying feedback leads a system to expand or explode or crash. For example. Melting ice exposes darker surfaces, which absorb more solar radiation, causing further warming and more ice melting. Ripening fruit release hormones that trigger the production of more hormones, leading to a cascade of ripening.

In audiology, amplifying feedback occurs when a singer’s microphone sends a signal to a loudspeaker; the loudspeaker outputs a sound that enters the microphone; the microphone responds by strengthening the signal sent to the loud speaker, and so on.

Feedback loops in organic systems

Imagine a Deity gives you a barren universe of galaxies, solar systems and planets and asks to design and create a biosphere in the next 4 billion years.

First you select a planet that is the right distance from a middle-aged sun (the energy source you need), with an atmosphere containing CO2 and an ocean of H2O, which contain the chemicals you need to make bio-chemicals.

Creating an open system

After 3 billion years or so of developing life forms in the sea, and many difficult steps, you create a species of plants on land. Each plant is an open system. It uses the energy from sunlight to consume air and water, manufacture its own organic chemical structures. As a waste product, it releases oxygen. And before its gets too old, it sheds seeds to create perfect replicas in next generation.

The Deity inspects your work and says “There’s a problem. What will happen when all the CO2 has been used up?”

Creating a stable system

You hastily create a mobile animal species that consumes plants, along with the newly created oxygen, and exhales CO2. (Again, your animals reproduce perfect replicas of themselves in each new generation.)

You have now created a biosphere that gives the plants enough CO2 to survive, gives the animals enough oxygen to survive, and can maintain the atmosphere in a stable state. This causal loop diagram represents how four interrelated variables interact.

The animals you have designed are complex machines and very sensitive to conditions, external and internal. Feedback is what enables an animal's nervous system to maintain the body in a steady state, by monitoring and regulating quantitative state variables such as temperature, salinity, acidity and vertical stance. The animal’s nervous system and body are connected in a number of internal feedback loops.

The Deity directs you: “I see your single plant species and animal species are restricted to a very narrow range of conditions on the planet’s surface. Now cover the rest of the planet, as far as you can.”

So, you create a hundred species of plants to occupy every habitable space on the planet’s surface and hundred animal species to occupy every niche that those plants create.

Creating a meta stable system

A metastable system stays in a stable state (in a basin of attraction) under normal conditions, but when a disturbance occurs, may transition to a new stable state.

The Deity says: “Your biosphere is stable now, but the planet's surface environment is unstable. Not only do conditions very from hot to very cold, from very wet to very dry, but the climate swings from ice age to ice age, the composition of the atmosphere may vary somewhat, and continental drift may carry a species on land into a different climate. So, can you ensure the plants and animals in your defined species will survive when conditions change?”

After some thought, you conclude the answer is to increase the number and variety of species and individuals.

First you design and create half a million species of plants to occupy every habitable space on the planet’s surface. You create several million animal species to occupy every niche for life that those plants create. If conditions change, one species will be surely better than another at handling it.

Then you have a brain wave. You introduce variation into the reproduction process. Instead of creating replicas, each individual will mix their genes with another of the same species to produce a unique individual. And in addition, you allow small number of genes to change at random. Thus you ensure there is continual generation of slightly different plants and animals. By chance, when conditions change, some will be better adapted to them, and so better able to survive and reproduce. In fact, whole new species can evolve of their own accord.

You job is done! The Deity says: “Good work. Let us hope at least one animal species will evolve with enough intelligence to find a new planet when this one become inhabitable.”

Feedback in human life

Your life depends on countless feedback loops - conscious and autonomous, internal and external. You could not survive, learn, navigate the world, or enjoy a social life without feedback. To ride a bicycle requires astonishing sensitivity in the feedback loop between the movements of the rider and the bicycle. You play roles in social, economic and political systems that are driven by feedback.

Feedback in social systems

Let me say a little about systems thinking in a management science context.

Churchman, a founder of management science and a "soft systems" thinker, was concerned with the behavior of an organized social entity such as an industrial or commercial business, or an institution, which he questionably called "a system". He drew this concept graph of a managed human organization.

This concept graph does not represent the structure or behavior of a system. Rather, each arrow represents the grammatical order (subject > verb > object) of a statement that is true in the domain of knowledge that is management science. But note the "model" element to the right of the diagram above.

On the "purpose" of a human activity system

Philosophers of the pragmatic school say: “A thing is what it does.” Churchman said: "A system is what it does". Stafford Beer said something rather different: “The Purpose Of a System is What it Does” (POSIWID).

Like Russell Ackoff, Beer noted that human organizations often fail to meet their ostensible aims. Employee’s actions depart from the aims of the organization’s owners. Government initiatives have unintended consequences, resulting in the opposite of that which was intended. The implication is that real-world systems in operation differ from systems envisaged by organization owners or directors.

The word purpose is open to interpretation. Is the purpose of a pen to make marks on paper? Or to get wax out of your ear? It is important to distinguish between the aims and outcomes of a system.

Outcome: an effect or result of some action(s). It may be declared or not, desired or not, observed or not, and beneficial, harmful or neutral to some stakeholder.

An open system has two kinds of outcome: internal state changes, and external outputs or effects. Those outcomes may or may not correspond to aims of stakeholders in the system of interest.

Aim: a desired outcome, a target, an intent held by some actor(s) with foresight. An actor may be a stakeholder such as a designer or user of a system, or an actor playing a role in it.

Does a bicycle have an aim? A bicycle and its rider interact in a feedback loop. The outcome of their interaction may be to win or lose a race. The aim of the rider may be to win the race. The bicycle doesn't care; it has no foresight, intent or aim.

Does a pen have an aim? A pen and a writer interact, via hand and eye, in a feedback loop. The immediate outcomes of their interaction are to reduce the pen's internal stock of ink, and output ink onto a surface. The wider aim of the writer may be to transform words encoded in their neural system into words encoded on paper and read by others. The narrower outcomes may or may not result in the wider outcome, corresponding to the writer's aim. The pen doesn't care; it has no foresight, intent or aim.

In short, POSIWID confuses aims and outcomes. All actions, feedback loops and dynamic system have outcomes, effects or results. Any inanimate object like a baseball bat, or natural system like the solar system, or designed system like a bicycle, can behave or be used to produce observable outcomes. But to have an aim, or ascribe an aim to a thing, you must have intent or foresight. No bat, solar system or bicycle has intent or foresight.

Aside: Ackoff and Beer both distinguished "purposive" and "purposeful" systems, but in different ways. The trouble is that aims are found in so many places. A system has aims given to it, by directors or by agreement. Each system role, played by actors, has aims. Each individual actor has their own aims. External observers may ascribe different aims to the same system, its roles and actors. Moreover, actors can play roles in several systems, potentially in conflict - a topic for another article.

Quantitative feedback

The phrase "If you cannot measure it, you cannot improve it" is often attributed to Lord Kelvin, also known as William Thomson. He maintained that until you know how measure a quality and express it in numbers, your understanding of the concept is incomplete and less than satisfactory. Even a quantity such as facial beauty can be measured in terms of shapes and their positions.

Feedback is often taught as a mathematical concept, as a relationship between quantitative state variables - as in cybernetics and System Dynamics, discussed later in this article. Nevertheless, feedback can also be discussed in terms of qualitative effects or results, without quantification.

Qualitative feedback

In biology, feedback occurs in a progressive dialogue when male and female sticklebacks communicate by sending and receiving information in visual signals that inform and direct each other's actions.

In psychology, feedback enables us to learn by trial and error, and helps us control the state of things in our environment that we need to survive.

In sociology, feedback from others helps us verify perceptions and ideas, and is a basis of peer review in science. (See the article "How we assess truth") Feedback between voters and politicians is a basis of democratic government. Feedback between customers and suppliers is the basis of a market economy.

Aside: the importance of feedback to education, science, business, politics and economics, to learning, growth and success, is a reason to maintain the principle of free speech.

In business, feedback between communicating parties often takes the form a progressive dialogue in which parties alternately act to advance the state of a business process. The output from one party stimulates the other party to feedback an input, in a circular fashion.

Although this standard BPMN example shows two control flows, one in each swim lane, there is in fact one process flow; in which control alternates between the two parties.

Such progressive dialogues are commonplace in human systems, in formal protocols, and in the user interfaces (or use cases) of software applications.

Weak or partial feedback

Every business information system is connected in a feedback loop with the external entities that it monitors and directs. However, the feedback may be partial or ineffective.

A business activity system is divided in the flow diagram below into subsystems. The arrows represent flows of material goods or information. There might be a circular feedback loop in which new Supply Orders are amplified by customers’ appreciation of past Products Shipped.

The feedback loop in the flow diagram may be weakly related to a relationship between the values of the quantitative state variables “Ingredients-in-stock” and “Products-to-be-shipped”, (variables of the kind you may see in a causal loop diagram). However, the relationship between those two variables is obscure in the flow diagram, and surely not algorithmic. Flow rates in this system depend on decisions made by customers, suppliers and system managers, who may all decide to increase or decrease their activity unpredictably.

Using diagrams to model systems

A variety of diagram types are used to model the operations or behavior of a system. Many are "directed graphs" in which nodes are connected by arrows. Each arrow relates a source concept A to a target concept B in a very particular way.

• An activity diagram arrow shows the sequence in which action A is followed by action B.
• A state chart arrow shows the change from state A to state B over time.
• A flow diagram arrow shows the movement of a thing from place A to place B
• A causal diagram arrow shows that A affects or has an effect on B.

This article goes on to illustrate feedback loops using flow diagrams and causal loop diagrams.

Flow diagram: the nodes represent components or subsystems connected by flows. A flow may contain material, energy or information, depending on domain of knowledge in which the system is defined.

This flow diagram illustrates a system with a number of feedback loops. The higher brain, lower brain and thermostat each act as a regulator of what they monitor and direct.

The top-right corner includes the sensor (thermometer) and actuator (radiator) of a mechanical regulatory system.

Causal loop diagram (CLD): The nodes are quantitative state variables connected by cause-effect relationships. An arrow says the destination variable increases and decreases in the same or opposite direction as source variable.

The CLD below represents the same system as the flow diagram above. The top-right corner includes variable attributes of the sensor (thermometer) and actuator (radiator) of the mechanical regulatory system. (The aim here is to facilitate comparison, not to claim this is the best or only CLD that could be drawn.)

The steps for drawing a CLD like the one above are listed below.

1. Name nodes as quantities of interest that vary over time.
2. Identify where each variable directly influences another.
3. Draw an arrow to indicate the source-to-target influence.
4. If increasing/decreasing the source increases/decreases the target, annotate the arrow with + or same.
5. If increasing/decreasing the source decreases/increases the target, annotate the arrow with - or opposite.
6. Identify and annotate where a cause-to-effect is delayed.

Further steps are discussed below.

Identify reinforcing/amplifying loops

A loop with an even number of negative/opposite arrows is reinforcing. It has an amplifying effect, so the two related variables either grow exponentially or shrink to nothing.

Consider how wind speed and sea water evaporation interact in a loop that represents how increasing or decreasing one causes the other to increase or decrease in the same direction.

In the notation used here: + same means changing the source causes the target to change in the same direction, and - opposite means changing the source causes the target to change in the opposite direction.

The two abstract system models described above, once set in motion, would either expand to infinity, or crash to zero. In reality, the growth or shrinkage of the quantities or stocks is limited by the available supply of materials, energy, or by another variable not yet included in model.

Identify balancing/dampening loops

A loop with an odd number negative causal link is balancing. It has a dampening effect, enabling the two related variables to oscillate around an attractor or equilibrium state.

Consider how wolf and sheep populations interact in a loop that represents discrete birth and death events in the lives of individual wolves and sheep.

Follow each loop to test the story it depicts.

Walk around a feedback loop - does it make sense? Does it match your observation of what happens in the world? Bear in mind a causal flow at the abstract level of aggregate quantities (such as wolf and sheep populations) reflects cause-effect relationships at the concrete level of discrete events (such as births, deaths and predation events) that incrementally increase and decrease those quantities one unit at a time.

Finally, verify the story against available evidence.

Feedback in cybernetics

Norbert Wiener defined cybernetics as "the science of control and communication in both animals and machines". He defined feedback as "a method of controlling a system by reinserting into it the results of its past performance".

Cybernetics gives us a way to model and understand adaptive systems in which regulators regulate the state of regulated entities/systems. Generally, a regulator is coupled to a regulated entity in feedback loop, by consuming inputs from it and providing outputs.

In his introduction to cybernetics, Ashby wrote “Co-ordination, regulation and control are themes, for these are of the greatest biological and practical interest.” He introduced feedback in a biological context thus: "The organism affects the environment, and the environment affects the organism, such a system is said to have feedback."

Remarks on CLDs

People draw CLDs to tell a story, to persuade people to take a position, or simply to express the complexity of a cause-effect network.

Must a CLD contain a feedback loop?

Some say a CLD must contain at least one loop that connects a variable to itself - in both source and target roles. Some say more, that a CLD must be loopful - with no cause-only variables or effect-only “sink” variables.

Some allow that CLD can represent a linear system that includes a cause-only source variable not changed by others, and a sink variable that does not affect other variables.

If it were animated, this process would run for only one time cycle. However, you could manually reset the first variable and re-run the process, or else connect the variable to itself in a loop that successively changes its value (say, incrementally increases it).

Limiting a CLD to closed loops can undermine its usefulness by encouraging the diagram drawer to draw tenuous connections between variables in the diagram, and ignore important cause-only variables, whose variation over time is critical to the system's behavior.

A CLD notation variant

In drawing CLDs to represent organizational behavior patterns, Peter Senge used the flow labels ambiguously. Same means changing the source either:

• causes the target to change in the same direction, or else
• adds the source to the target.

Opposite means changing the source either:

• causes the target to change in the opposite direction, or else,
• subtracts the source from the target.

Would it not be better to distinguish the two meanings by different annotations?

Feedback in System Dynamics

Click here for Stock and Flow diagram examples and some methodology. A stock and flow diagram can be animated to simulate the system that it models, and its state change trajectory can be plotted on a graph.

The usual starting point for build stock and flow diagram is a causal loop diagram. For a CLD to be useful as a stepping to building a stock and flow diagram, the variables must be well-defined quantities, and changes to them must be expressible in mathematical flow rates.

To model the system’s dynamics you must define the rules (equations) for each flow. To animate the model, you must initialize the model's variables before you run the model. Then, you should review the results, verify and refine the model.

Regulation

There is no universal agreement about the difference between control and regulation. However, in systems thinking, the difference may be drawn thus.

A controller directs an entity or system to act in a way that leads it to a desired state, whether homeostatic or terminal.

A regulator is controller that directs an entity or system to act in a way that maintains it in a viable state, a homeostatic state, a range of state variable values that enables it to survive.

Regulation and adaptation

Ashby was concerned to explain how feedback enables an animal or machine to adapt by maintaining a homeostatic state, and learning from trial and error.

In cybernetics, a regulator monitors and directs the state of a regulated entity. To do this, a regulator must:

• sense/obtain information about the state of the entity of interest,
• detect or predict when the value of a state variable deviates from a desired state, and
• act to restore or maintain the state by activating the necessary actuators/effectors.

Ashby's law of requisite variety

A regulator must be complex enough to do its job, yet may be simpler than what it regulates.

Ashby's law says a regulator must be as variegated as those states or conditions of that entity that it regulates. And to that extent, it is a model of the regulated entity.

However, holism is not wholeism. A regulator typically regulates only a small subset of an entity's state variables. Moreover, since the environment has infinite variety, a regulator must limit the events or states it detects. It should be “information tight”. It needs just enough information to detect or predict state changes that require regulation. To monitor more would be redundant and inefficient, and biological evolution tends to weed inefficient processes in an animal.

Regulating a social entity

To explain cybernetic principles, people use simple examples where one regulator regulates the state of one variable or target entity. A governor that regulates the speed of an engine connects the two in simple 1-1 relationship. Many situations are more complex.

The air in a room may be governed by several regulators: a radiator, a ventilator and a humidifier - along with sensors/processors/actuators. A child's behavior may be regulated by parents, teachers and other authority figures. The N-N relationships between people in a social entity, and customers and suppliers in an economy, are more complex again.

In the example above three regulators (higher brain, lower brain and thermostat) all play a role in regulating a body temperature. Since all three have the same aim, if one overrides another, it may not matter.

In a regulation relationship, one party is seen as regulating the state or behavior of the other, regulated, party (in what sociologists might call a power relationship). In a designed machine, it may be that one party has no other responsibility than to regulate or govern the other party, but human social relationships are rarely so simple or one-sided.

Difficulties arise when different observers try to regulate the same variable to produce desired effects that are in conflict. For example, one director wants to speed up product delivery by reducing quality assurance; another director wants to increase product quality by spending longer on quality assurance.

So, having requisite variety is not sufficient for a regulator to be effective, especially in a social entity in which actors are related in complex many-to-many relationships. Actors seeking to regulate the same variable may undermine each other. Actors being regulated may favor one regulator, or ignore all of them.

Reliable regulation in a business requires that it has a stable management hierarchy, in which regulatory roles and responsibilities are clearly defined, delineated and exercised. This can run counter to delegating responsibility. Abstracting regulated variables to profit/loss or such like allows more freedom to the regulated entity.

Related articles

This article introduces the idea of feedback, so that it can be referred to without explanation in related articles.