Iteration, Iteration, Iteration

The agent of development
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Presented at The Developing Group, 3 Feb 2007

[An] important property of nonlinear systems is a consequence of the frequent occurrence of self-reinforcing feedback processes. In nonlinear systems, small changes may have dramatic effects because they may be amplified repeatedly by self-reinforcing feedback. Such nonlinear feedback processes are the basis of the instabilities and the sudden emergence of new forms of order that are so characteristic of self-organization. Mathematically, a feedback loop corresponds to a special kind of nonlinear process known as iteration.

Fritjof Capra, The Web of Life, p. 123

If you search for ‘iteration’ on the web you will find precious little outside the domain of mathematics and computing. And yet iteration is commonly seen in nature as a way for organisms to grow and develop and as a change process in an increasing number of psychotherapeutic procedures.

So what is iteration? We define it as:

A process that repeatedly applies a rule, computation or procedure to the result of the previous application of the rule, computation or procedure.

Iteration is thus a very simple feedback process and a “rule, computation or procedure” is often called an algorithm. Diagrammatically iteration looks like this:

A very common kind of iteration is calculating compound interest: In the first year you get interest on your capital. Then you get interest on your capital plus the first year’s interest, then you get interest on your capital plus the first and second year’s interest, and so on.

Iteration is usually used in one of three ways:

  • to solve nonlinear problem by getting closer and closer approximations to a solution (e.g. ‘the three body problem’)
  • to run an algorithm lots of times to see what happens (e.g. as in economic and climate forecasting).
  • to generate something new (e.g. as in fractal diagrams and certain psychotherapeutic practises).

Stephen Wolfram, in A New Kind of Science (full text available at: wolframscience.com) maintains that repeated iteration will always result in one of four conditions or “classes of behaviour”:

  1. Fixed Point Almost all initial conditions lead to exactly the same uniform final state.
  2. Periodic There are many different possible final states, but all of them consist of a set of simple structures that remain the same or repeat.
  3. Chaotic Seems random, although small scale structures are always seen at some level.
  4. Edge of Chaos A mixture of order and randomness with localised structures which on their own are fairly simple but these interact with one another in complicated ways.

In human terms, examples might be:

 1. Fixed Point “No comment”; “No comment”; “No comment”; …
 2. Periodic A loop, a habit or a (Transactional Analysis) Game
 3. Chaotic “A broad bean” (The first ‘random’ thing that came to mind!)
 4. Edge of Chaos All living things; an ‘A-ha’; “Funny”


In psychotherapy, iteration is usually achieved by repeatedly asking a single question of the client’s last answer to that question:

Symbolic Modelling

Examples of psychotherapeutic processes that make use of iteration are:

Originator: David Grove

Name of Process AlgorithmDirection
MaturingAnd then what happens?Forward in time to a new metaphor landscape.
Inter-generational HealingAnd where does that come from?Back in time to an original source or “redemptive metaphor”.
Clean WorldsAnd what’s outside/beyond that?Larger contexts to a new (prior) worldview or “cosmology”.
Meta Drivers

 – And what else do you know?

– And what else does that know?

– And is there anything else about that?

– And then what can happen?

– And is there anything else?

– And what do you know now?

Originators: Penny Tompkins & James Lawley

A Framework for ChangeAnd what needs to happen for that to happen?From desired outcome via causal links to the first step.

Originator: Steve Saunders

Truth WorkWhat needs to be true for that to be true?Core beliefs to seeing the “cosmic joke”.

Originator: Connirae Andreas

Core TransformationWhat does that do for you?Access states of Higher purpose / Core values.

Originator: Brandon Bays

The JourneyWhat’s beneath that? [Not sure about this. Can anyone confirm?]To drop through emotions into “the source”.

Originator: Michael Hall

The Mind BackTracking PatternAnd, behind that thought lies another thought … what thought do you find back there?To drop into a “Void of Nothingness”.

While modelling David Grove we recognised the relevance of iteration and so incorporated it into our models described in Metaphors in Mind:

Symbolic Modelling involves working with emergent properties, fuzzy categories, apparently illogical causal relations, multiple levels of simultaneous and systemic processes, iterative cycles and unexpected twists and turns. … 

Traditional linear, formulaic and analytical approaches to therapy are incongruent with the nature of Metaphor Landscapes. Instead we provided an alternative, iterative and systemic Five-Stage Process for Symbolic Modelling…. 

Although the five stages are presented sequentially, the process is not a linear procedure; rather it is an emergent, systemic and iterative way of conducting psychotherapy. … 

The whole process can take place in less than an hour or it may require many iterative cycles

You will also see the iterative possibilities in the first five of The Six Approaches detailed in Chapter 8 of Metaphors in Mind:

By repeatedly directing the client’s attention to a single aspect of their metaphor landscape you encourage them to concentrate on one form, one space, one time. This invites them to notice additional parts, additional attributes, additional functions and additional relationships — each with the potential for initiating change.

By repeatedly directing the client’s attention to their metaphor landscape’s multiple forms, places and times you encourage them to accumulate more and more perceptions into one simultaneous mindbody space. This invites them to identify patterns of relationships, patterns of patterns and patterns of organisation. As a result they recognise higher and higher levels of communion, of cooperation, of interdependency, of connection to something larger — the next inclusive whole.

By repeatedly directing the client’s attention to the edge, to outside and beyond the boundaries of their metaphor landscape you encourage them to notice what is external, to discover new forms and relationships over a larger area, to widen contexts and to extend ranges — all in the service of a broader perspective.

By repeatedly directing the client’s attention to either the origin or consequences of the symbolic event currently in their awareness, you encourage them to sequentially shift the locus of the perceptual present to before ‘the beginning’ or after ‘the end’. This invites them to make historical connections, identify patterns which repeat over time, encounter new resources or (re)discover a sense of their purpose — any of which can lead to a reorganisation of existing perceptions.

By repeatedly inviting the client to discover what needs to happen for a change to take place in their metaphor landscape, you encourage them to find the logical associations between the first thing that needs to happen and all the subsequent things that need to happen for a desired change to occur. In this way a symbol’s function can be enacted or its intention satisfied, and this inevitably influences other parts of the Landscape.

More than repetition

There is a difference between iteration and straightforward repetition. Iteration involves the extra element of feeding back the output of running the previous procedure so that it becomes the input of the next running of the procedure.

In an Enlightenment Intensive process participants are requested to “Tell me who you are” over and over (for anywhere between three days and three weeks!). It’s very repetitive but it’s not iteration because the previous response is not necessarily involved in the next round of “Tell me who you are.” However, participants eventually realise that if they keep giving the same class of answer nothing new happens, and so they do take into account their last set of answers as they search for new responses. In this respect, the participant makes it an iterative process but iteration is not inherent in the procedure.

Inherent progression

Once you get the idea you can see that some questions have an inherent progressive or directional quality and hence can be used as an iteration algorithm without the need to use any of the client’s words:

And is there anything else?
And is there anything else about that?
And then what happens?
And what happens (just) before that?
And where does that come from?
And what needs to happen for that to happen?
And what do you know now?
And what’s beyond (beneath/above; outside/inside) that?

The italicised words give these questions their progressive quality.

Other questions require the facilitator to encourage a progression by continually using the client’s last answer:

And what kind of [last answer] is that?
Where/whereabouts [last answer]?

Deeper patterns

When a series of results generated by an iterative process are examined they sometimes have an underlying pattern indicating a deeper level of organisation at work (e.g. The Fibonacci Sequence and Power-Law distributions) These patterns often seem ‘spooky’ because, without a creator, it is not obvious why such consistent patterns should exist.

The cost of iteration

Iteration is becoming recognised as a factor in business — and that the medium of iteration makes a big difference:

Iterating on paper? Cheap.

Iterating in software? Still pretty cheap.

Iterating the Airbus A380? Not so cheap:

Run safety checks; which identify potentially unsafe features; which require modifications; which require the safety checks to be run again; which identify other potential unsafe features; which require modifications; which require the safety checks to be run again; …

The result? Iteration led to painful penalties and increased time-to-market costs as Airbus had to reduce production from a planned 25 planes in a year to 9. In Artful Making, Robert Austin and Lee Devin contrast the cost of iteration with the cost of exploration. They look at iteration in industrial and knowledge work, and how the iteration cost curve changes over a project.

Other references

David Grove with Carol Wilson Six degrees of Freedom: Intuitive Problem Solving with Emergent Knowledge (ReSource Magazine, Summer 2005).

L. Michael Hall & Bobby G. Bodenhamer, ‘Will the Thought in the Back of Your Mind Please Stand Up?’.

Steven Saunders, ‘About 4th Generation NLP – Emergent, Clean Facilitation’, Nov 2006.

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