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TB872: Regression and recursion

Note: this is a post reflecting on one of the modules of my MSc in Systems Thinking in Practice. You can see all of the related posts in this category.


The image depicts a scene with three individuals, each with a thought bubble. Person 1 (P1) on the left, Person 2 (P2) on the right, and Person 3 (P3) in the center. P1 and P2 are standing while P3 is in a thoughtful pose, possibly crouching or sitting.

P1's thought bubble shows a "Hierarchical model" consisting of a typical organizational chart with boxes connected in a tree structure. This represents a traditional approach to organization, where each box likely represents different roles or departments in a hierarchy.

P2's thought bubble displays a "Recursive model," which contains circles within a larger circle, each with arrows pointing clockwise. This suggests a system where components are nested within each other, continuously influencing one another in a cycle.

The central figure (P3) is surrounded by thought bubbles from both P1 and P2, indicating that they are considering both hierarchical and recursive models. This may suggest that P3 is in the process of synthesizing these two perspectives or models.

The overall scene suggests a discussion or contemplation of different models or systems of organization, with each person contributing a distinct viewpoint. The circular boundary that encapsulates P1, P2, and P3 suggests a boundary of a system or a domain where these interactions and thought processes are taking place.

One of my favourite artists is Will Holland, aka Quantic. Here are the lyrics for his track ‘Infinite Regression’ from the album The Fifth Exotic, which quotes Dr Hasslein in Escape From The Planet of the Apes:

Here is the painting of a landscape
But the artist who painted that picture says
– Something is missing. What is it?
It is I myself who was a part of the landscape I painted
So he mentally takes a step backward
– or ‘regresses’ — and paints…

…a picture of the artist painting
A picture of the landscape
And still something is missing. And that
Something is still his real self
Painting the second picture. So he
‘regresses’ further and paints a third…

…a picture of the artist painting a
Picture of the artist painting a
Picture of the landscape. And because
Something is still missing, he paints a
Fourth and fifth picture…

…until there is a picture of
The artist painting a picture of the
Artist painting a picture of the
Artist painting a picture of the
Artist painting the landscape

So infinite regression is–

–It is the moment when our artist
Having regressed to the point of
Infinity, himself becomes a part
Of the picture he has painted and
Is both the Observer and the observed

Regression and recursion are two related, but distinct concepts. They have defined meanings in mathematics, but for the sake of my purposes here, in a systems thinking context, I’m going to define them in the following way:

  • Regression — used to analyse relationships within a system for the purposes of identifying how variables influence each other. Regression can imply a system’s reversion to a prior state, often viewed as a (strategic) retreat to stability. It’s also possible to use regression techniques to examine historical patterns to predict future system states.
  • Recursion — a process where the system’s outputs loop back as inputs, creating continuous feedback cycles. Recursion helps us understand the dynamic nature of systems: learning and adaptation occur through iterative feedback loops that shape and are shaped by the system itself.

So while regression in systems thinking looks for relationships and patterns to predict or explain, recursion involves a process where the system’s past or current output becomes an input in a self-referential manner.

The image at the top of this post from the TB872 course materials shows how different practitioners can have different frameworks and models that affect how they understand situations. This reminds me a bit of the book Images of Organization by Gareth Morgan, which I studied as part of my Ed.D. I’ve often used that as a touchstone when consulting, as it’s a useful reminder that people can conceptualise of the organisation within which they work in very different ways.

For example, I remember being told by someone that a new Principal that came into the Academy in which I was working was “very hierarchical”. I saw that as a massive red flag, as it seemed anathema to a learning organisation. That’s not to say that double-loop and triple-loop learning can’t happen within hierarchical organisations, it’s just that it’s the exception rather than the norm.

By reflecting on what we are doing as practitioners, we can achieve higher-order thinking, abstracting away from the specifics of the situation to understand what it is that we do when we do what we do.

Four ways to understand organizational change

River and Forest

cc-nc-nd by *wb-skinner

You cannot step twice into the same river. (Heraclitus)

The above quotation was on the wall of my classroom at my previous school. Heraclitus is also attributed as saying, “The road up and the road down is one and the same” (also on my wall). Heraclitus recognised that whilst there is nothing fundamentally new under the sun, nevertheless the whole universe is in a constant state of flux with nothing fixed. Heraclitus believed the secrets of the unvierse could be found in finding patterns in the changes that take place.

David Bohm was a quantum physicist who, in the 20th century, developed a theory that ‘invites us to understand the universe as a flowing and unbroken wholeness.’ (Morgan, 1998:214) A useful metaphor that Morgan uses pace Bohm is that of the whirlpool in a river. Whilst such a whirlpool has a relatively constant form, it does not exist separately from the movement of the river.

Four ‘logics of change’

Morgan addresses four ‘logics of change’ in his chapter Unfolding Logics of Change, namely:

  1. Autopoiesis
  2. Chaos & complexity
  3. Mutual causality
  4. Dialectical change

1. Autopoiesis

Traditional organization theories frame organizations in reference to their external environment. A new approach to systems theory was developed by Maturana and Varela which they termed Autopoiesis (from the Greek auto – for self- and poiesis for creation or production, literally ‘auto self production’). They argue that all living systems are ‘organizationally closed’ and make reference only to themselves. The idea, therefore, that such a system is open to an environment is the product of an external observer trying to make sense of it.

Maturana and Varela believe living systems to be characterized by autonomy, circularity and self-reference. These three features allow the system to self-create or self-renew. The aim of autopoietic systems is to produce themselves and therefore their own organization and identity is paramount.

Artificial BrainIn order to back up their theory, Maturana and Varela point to the brain as a ‘living system’. The brain, they contend, is ‘closed, autonomous, circular and self-referential.’ (Morgan, 1998:216) Although it seems obvious to us that the brain processes information from the external environment, Maturana and Varela point to the impossibility of the brain having an external point of reference:

If one thinks about it, the idea that the brain can make true representations of its environment presumes some external point of reference form which it is possible to judge the degree of correspondence between the representation and reality. This implicitly presumes that the brain must have a capacity to see and understand its world from a point outside itself. Clearly, this cannot be so. (Morgan, 1998:216)

Taken as a metaphor for organizations, the theory of Autopoiesis has three main implications:

  • Organizations are always attempting to achieve ‘self-referential closure… enacting their environments as extensions of their own identity.’
  • Many of the problems that organizations encounter are a result of their attempt to maintain a particular identity.
  • Explanations of organizational evolution, change and development must give attention to the factors that shape patterns affecting organizations.

Morgan contrasts what he calls ‘egocentric organizations’ with ‘systemic wisdom’. The former have a fixed notion of who or what they are and are determined to sustain this at all costs. ‘This leads them to overemphasize the importance of themselves while underplaying the significance of the wider system of relations in which they exist.’ (Morgan, 1998:219) The example Morgan gives is of ‘watchmakers’ and ‘typewriter firms’ failing to take account of developments in microprocessing and digital technologies. Their identity as producing a certain kind of equipment led to their downfall.

Contrasted with this is the idea of ‘systemic wisdom’ where organizations have an ‘evolving identity.’ Morgan believes that organizations can never survive being against their environment:

In the long run, survival can only be survival with, never survival against, the environment or context in which one is operating. (Morgan, 1998:221)

To be successful, therefore, organizations must be willing and able to transform themselves along with their environment in an evolutionary manner.

2. Chaos & complexity

complexityAlthough it is usual to draw a clear distinction between ‘chaos’ and ‘complexity,’ Morgan (1998:222) states, it makes more sense in terms of organizations and their environments to consider them to be parts of the same interconnected (evolving) pattern. Using evolutionary theory as a touchstone, Morgan talks about the ‘random disturbances [that] can produce unpredictable events and relationships.’ However, ‘coherent order always emerges out of the randomness and surface chaos.’ (ibid.)

Rather than internal complexity, randomness and diversity being organizationally-threatening, Morgan argues, they can actually become resources for change. Random systems develop an (albeit temporary) equilibrium as tension between two or more ‘attractor’ elements. These tensions will, every so often, lead to ‘bifurcation points’ due to changes in one or more of the attractor elements making the system unstable. Such ‘forks in the road’ lead to different futures and ways of operating for organizations.

Small changes can lead to huge consequences. The most famous example of this is the ‘butterfly effect’ where a small and insignificant event such as a butterfly flapping its wings in China can influence weather patterns on the other side of the world. The butterfly doesn’t cause in any meaningful sense the hurricane, but the tiny change it causes in its environment leads to another change and another change, and so on…

How can managers and leaders cope in the face of such chaos and complexity? Morgan suggests five key ideas:

  • Rethinking what we mean by ‘organization’ – especially in terms of hierarchy and control
  • Learning the art of managing and changing contexts
  • Learning how to use small changes to create large effects
  • Living with continuous transformation and emergent order as a natural state of affairs
  • Being open to new metaphors that can facilitiate processes of self-organization (Morgan, 1998:226)

What do we mean by ‘organization’?

Although somewhat frightening, chaos and complexity theory stresses that there is no ‘grand design’ or central organizing principle at work in such systems. Instead, ‘patterns have to emerge’ without being imposed. Hierarchy and control are temporary conditions or outcomes of the system, mere ‘snapshot points’ on a self-organizing journey (as Morgan puts it).

The fundamental role of managers is to shape and create “contexts” in which appropriate forms of self-organization can occur. (Morgan, 1998:227)

This is an extremely insightful point, and one that resonates with me. Take setting up a new online community, which I’ve done (and attempted to do) a few times. An authoritarian, top-down approach is guaranteed not to work in this arena. Instead, as I’ve attempted to do with EdTechRoundUp, procedures, norms and contexts are negotiated that allow the organization to evolve successfully.

Changing contexts

Sometimes, if a particular system is inappropriate within an organization – for example a school or hospital is ‘failing’ and not reaching external targets, then the role of managers and leaders is to cause instability that causes the system to change. The aim of such instability would be to cause those within the organization to re-assess their role and day-to-day practice to change the system for the better. ‘The important point,’ says Morgan, ‘is that the manager helps to create the conditions under which the new context can emerge.’ (1998:230) Without creating these conditions, organizations ‘end up trying to do the new in old ways.’ (ibid.)

Small changes -> large effects

If systems are conceived as involving several ‘attractors’ that are in tension, it follows that changes in context are achieved by either introducing new attractors or changing the influence each attractor possesses. Doing this will generate ‘bifurcation points’ that affect future development – often by creating ‘tensions between the status quo and alternative future states.’ (Morgan, 1998:231)

Creating a paradox leads to system instability, and therefore a need for a ‘reframing’ of the situation which would resolve this paradox. Managers and leaders need to help change the system incrementally so fundamental change occurs. Such incremental changes can create a ‘critical mass’ effect which leads to an overwhelming force for change.

Emergence as ‘natural’

Leaders and managers cannot force complex systems into lasting comprehensive changes. They can merely nudge and push a system in the desired direction. They should be aware of feedback loops and provide room for experimentation with ‘new realities’. Introducing new images and metaphors of the roles of individuals within the organization can help

3. Mutual causality

Feedback loopsChange, according to the theories outlined above, does not unfold in a linear fashion but via circular patterns (loops not lines). A does not cause B under such a system. Instead both A and B ‘are co-defined as a consequence of belonging to the same system of circular relations.’ (Morgan, 1998:234) Magorah Maruyama has shown how positive feedback loops can lead to complex systems:

[A] large homogenous plan attracts a farmer, who settles on a given spot. Other farmers follow, and one of them opens a tool shop. The shop becomes a meeting place, and a food stand is established next to the shop. Gradually, a village grows as merchants, suppliers, farmhands, and others are attracted to it… [T]he homogenous plan has been transformed by a series of positive feedback loops that amplify the effects of the initial differentiation. (Morgan, 1998:235)

Often, human nature makes us want to explain and analyze situations in terms of finding a specific ’cause’. However, phenomena actually reside within overall patterns of positive and negative feedback.

Peter Senge, leadership guru and author of The Fifth Discipline believes that many systems are unstable because of delayed feedback between elements. This leads to people within organizations either underplaying or exaggerating their behaviours.

Morgan comes across as a great believer in loop analysis and presents some of his reasons for thinking so. Here are three of them:

  • It cultivates ‘systemic wisdom’ – the approaching of organizational problems from a mindset that respects patterns of mutual causality.
  • It provides insights on how small changes can have large effects.
  • It invites us to understand the patterns that lock the system into vicious circles because of positive feedback loops.

4. Dialectical change

ying-yangIt is a truism that we cannot fully understand something without knowing its opposite. You cannot truly know the meaning of ‘hot’ unless you understand what ‘cold’ means. You cannot conceive of ‘day’ without knowing ‘night’. And so on. Such dialectical philosophy has a long history and tradition, chiefly through Taoist philosophy which originated in ancient China. This philosophy understands the universe to be subject to the dynamic interplay of yin and yang, creative and destructive powers.

Dialectical principles

Taoist philosophy influenced the work of both Hegel and Marx who developed some of its principles into theories of social change. Morgan uses a neo-Marxian perspective in this section to settle upon three main principles:

Principle 1 – Whenever one person attempts to control another a process of resistance undermines that attempt. ‘The act of control itself sets up consequences that work against its effectiveness.’ (Morgan, 1998:245)

Principle 2 – Negations of negations retain something from that form, leading to an evolution in patterns of control.

Principle 3 – Changes in quantity lead to changes in quality. Water absorbs increases in temperature up to the boiling point. Camels can be loaded until the straw that breaks its back. ‘A process of control and countercontrol may continue until control is no longer possible, leading to a new phase of collaborative or destructive activity.’ (Morgan, 1998:245)

Putting these three principles together we can see that organizational arrangements set up contradictions and opposition by their very nature. This leads to a Hegelian process of negation and counter-negation. This process continues until a limit is reached and the qualitative state of the organization must change or be destroyed.

Dialectical management

Dialectic analysis has two main implications for management, believes Morgan:

  • Restructuring is not a solution to a problem as it is itself a manifestation of a deeper problem. Instead, they should be dealt with through ‘social and political initiatives.’ (Morgan, 1998:248) Contradictions can only be tacked through an appreciation of what is creating the context in which they are able to flourish.
  • Managers and leaders cannot wait for ‘macro-problems’ to present themselves. They must deal with ‘microflux’ in order to keep an organization running smoothly and understand ‘creative destruction.’

Managing paradox

If not managed properly, new initiatives or directions instituted to cause positive organizational change can become ‘mired in paradoxical tensions that undermine the desired change.’ (Morgan, 1998:249):

Although there may we ways of resolving the paradoxes, the fact that the tensions are experienced as contradictory may in itself be sufficient to negate transformational change. For example, if people feel that the new demands for “more innovation,” “improved morale,” “more collaboration,” “increased decentralization,” and so on, are inconsistent with what seems reasonable or possible, inertia is the most likely outcome. (Morgan, 1998:250)

To my mind, this seems almost as though leaders and managers, although being explicit about the organizational vision, should keep the purpose of other changes and maneuvers ‘hidden’ as this could prejudice their outcome?

‘Paradox,’ says Morgan (pace Kurt Lewin, whom he cites), ‘cannot be resolved by eliminating one side.’ (Morgan, 1998:251) The task of the manager or leader is to find a way to integrate competing elements. They must create new contexts that reframe the key contradictions in a positive way. For example, Japanese manufacturers have transformed a traditional paradox by showing how improving quality (by elimating waste, simplying processes, etc.) can lead to lower costs.

‘Creative destruction’

cc-nc-nd by =keepwalking07Dialectical processes directly affect innovation. New innovations lead to the destruction of established practice and displace old innovations. In turn, the solutions the innovations provide create a new set of problems, which require new innovations. And so the cycle continues. As Morgan notes, this leads to important implications – not least that innovations create the basis for their own downfall. :-p

Many companies embrace the above and succeed in chaotic and turbulent environments because they ‘systematically destroy the breakthroughs created by their own products and initiatives by coming up with better ones.’ (Morgan, 1998:253)

Although so-called ‘creative destruction’ can be a powerful tool, it leaders must take care that it is not over-emphasized. Destruction should be a by-product of evolution, not a conscious aim.

Conclusion

Morgan outlines what he believes to be the three main strengths and the one major limitation of the ‘flux and transformation’ metaphor.

Strengths

  • Offers new understandings of the nature and source of change.
  • Offers new horizons of thought that can be used to enrich our understanding of management and leadership.
  • Offers to leaders and managers a powerful new perspective on their role in facilitating emergent change.

Limitation

  • Is ‘powerless power’ a message that managers and leaders really want to hear?

I’m a bit more cautious about embracing a ‘chaos and complexity’ model of organizational change. I’m much more comfortable with the ‘brain’ metaphor that I blogged about recently. However, I can see that if an organization is striving to become the ‘best of the best’ a decentralized anti-structure as proposed here would perhaps be the best method to achieve this.

What are YOUR thoughts? 😀

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Are organizations like brains?

Images of OrganizationAs part of my Ed.D. course through the University of Durham I had to take some taught modules. One of them that I took back in 2006 was entitled Management, Leadership & Change. It was an excellent course from which I gained a lot. Unfortunately, unlike many of my classmates, I wasn’t then at a time where I could use this knowledge being then only just finished my second year of teaching. Now that I’m in a position that carries more responsibility, management responsbilities and leadership opportunities, it’s time to revisit that course and related reading.

One of the books I read for the Management, Leadership & Change module was Gareth Morgan’s Images of Organization. I found it a revelation, especially being so fond as I am of metaphor. Morgan uses eight metaphors as a lens through which to view organizations:

  1. Organizations as Machines
  2. Organizations as Organisms
  3. Organizations as Brains
  4. Organizations as Cultures
  5. Organizations as Political Systems
  6. Organizations as Psychic Prisons
  7. Organizations as Flux and Transformation
  8. Organizations as Instruments of Domination

Each of these perspectives teaches the reader something about organizations; it’s a very clever and interesting way of presenting insights.

Having just come across this neat overview of Daniel Goleman‘s idea of the various leadership styles, I wonder how much overlap/synergy there is between the two?

Goleman - Leadership Styles

I’m especially interested in the idea of organizations as ‘organisms’, ‘brains’ or ‘cultures’ as I believe these lenses to be the most powerful for effecting positive change. The remainder of this post will look at organizations as ‘brains’.

Organizations as brains

Morgan starts off the chapter comparing brains to holographs where ‘everything is enfolded in everything else’, there is not centre or point of control and, most importantly,

Pattern and order emerge from the process – it is not imposed. (Morgan, 1998:73)

The philosopher Daniel Dennett, someone who I read fairly widely at university during my undergraduate degree in Philosophy, suggests that our highly-ordered stream of consciousness is actually the result of ‘a more chaotic process where multiple possibilities are generated as a result of activity distributed throughout the brain.’ (ibid.) Competing parallel activities can make complementary and competing contributions into a coherent pattern.

‘Just In Time’ and perceived chaos

Morgan gives the example of ‘Just In Time’ (JIT) manufacturing as being a process that is highly organized yet without ‘boundaries and patterns of membership’:

To an outsider, it may be impossible to distinguish who is working for whom. The fundamental organization really rests int eh complex informaiton system that coordinates the activites of all the people and firms involves rather then the discrete organizations contributing different elements  to the process. (Morgan, 1998:75)

Clay Shirky - Here Comes EverybodyThe above leads Morgan to wonder whether it is better to refer to a ‘system of intelligence’ rather than an ‘organization’ when describing such states of affairs. These systems break what Herbert Simon, Nobel laureate, called the ‘bounded rationality’ of human beings. To my mind it’s Morgan picking up on the start of what Clay Shirky has shown to be completely revolutionary in his excellent Here Comes Everybody (which I’m currently reading).

Understanding how organizations can become capable of learning in a brain-like way is similar to understanding how robots and other objects in the study of Cybernetics are able to ‘learn’. The latter discipline involves negative feedback. That is to say error-detection and correction happens automatically to maintain a course towards a desired goal. In order to be able to self-regulate, systems must be able to:

  1. Sense, monitor, and scan significant aspects of their environment.
  2. Relate this information to the operating norms that guide system behavior.
  3. Detect significant deviations form these norms, and
  4. Initiate corrective action when discrepancies are detected. (Morgan, 1998:77)

This negative feedback system is only as good as the procedures and standards that underlie it. So long as the action defined by these procedures and standards is appropriate dealing with the changes encountered, everything is fine. The ‘intelligence’ of the system breaks down, however, when these are not adequate leading to negative feedback attempting to maintain an inappropriate pattern of behaviour.

In order to prevent the above happening (so called ‘single-loop learning’) the model of ‘double-loop learning’ has been promoted by Donald Schön and Chris Argyris. This builds in a self-review ‘loop’ to the learning process:

Double-Loop Learning

Image cc-by-sa Ed Batista

There are three major barriers to double-loop learning: budgets, bureaucracy and accountability. One of the most famous examples of double-loop learning and organization being thwarted by these three barriers came with the US Challenger space shuttle explosion.

Learning organizations

So, how are ‘learning organizations’ created? Insights from cybernetics would suggest the following:

  • Scanning and anticipating change in the wider environment
  • Developing an ability to question, challenge and change operating norms and assumptions
  • Allow appropriate directions and patterns of organization to emerge (Morgan, 1998:82)

Morgan follows this with stressing the importance of ‘framing and reframing’ which reminds me of Lord Bilimoria’s discussion of the value of regular SWOT analyses (see this post). ‘Many organizations,’ says Morgan, ‘become myopic, accepting their current reality as the reality.’ (Morgan, 1998:84)

Organizations that embrace double-loop learning sound like the type of places I want to be part of:

For successful double-loop learning to occur, organizations much develop cultures that support change and risk taking; embrace the idea that in rapidly changing circumstances with high degrees of uncertainty, problems and errors are inevitable; promote an openness that encourages dialogue and the expression of conflicting points of view; recognize that legitimate error, which arises from the uncertainty and lack of control in a situation, can be used as a resource for new learning; recognize that since genuine learning is usually action based, organizations must find ways of helping to create experiments and probes so that they lear through doing in a productive way. (Morgan, 1998:85)

Emergent organization

Coming back to the metaphor of brains, the intelligence of the brain is not predetermined. It is not centrally driven. It is emergent. A top-down approach to management leads to single-loop learning and therefore is the opposite of such a model of emergence. To prevent chaos and incoherence targets should take the form of vision and value-sharing.

Morgan continues on to articulate a vision of ‘holographic organization’ based on five principles:

  1. Build the ‘whole’ into the ‘parts’ (i.e. ‘networked intelligence’)
  2. The importance of redundancy
  3. Requisite variety (i.e. ‘internal complexity must match that of the environment’)
  4. Minimum Specs (i.e. don’t define more that is absolutely necesssary)
  5. Learn to learn (i.e. ‘double-loop learning’)

Conclusion

After fleshing out these princples, Morgan concludes this chapter with listing the strengths and limitations of the brain metaphor.

Strengths:

  • Gives clear guidelines for creating learning organizations
  • Shows how IT can support the evolution of organizations
  • Gives a new theory of management based on the principles of self-organization
  • Addresses the importance of dealing with paradox

Limitations:

  • There could be conflict between the requirements of organizational learning and the realities of power and control
  • Learning for the sake of learning can become just another ideology

I can live with these limitations. I think the ‘organization as brain’ metaphor has a lot going for it. What do YOU think? 😀

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