We often refer to education as being 'complex' without analysing exactly how it is complex. There is a tendency to jump onto the theme of 'complexity' almost as an excuse for not looking deeper - where sociological linguistic sophistication overrides analytical exploration. I think the recent trend for sociomaterial views on educational technology are particularly guilty of this: "it's all entangled, and any attempt to explore the entanglements in analytical detail risks reductionism". Well... yes - to a point, and yes, there is a high degree of interdependence of 'variables' in education, but there are dynamics, and it is possible to have a constructive discussion in exploring how those dynamics work.
The study of complex interactions between variables was something which was a key issue in Ashby's later work, and which was subsequently developed by Klir and Krippendorff. The lattice diagram on the right is a representation of the ways in which the complex ('entangled') interactions between four variables may be decomposed in stages into different relations between distinct domains of interaction. So at the top, there is a single domain of interaction and four variables (messy): this might be written as ABCD. This can be decomposed into four domains of interaction with three variables (coloured red): ABC:BCD:ABD:CDA. These can decompose further into three domains of interaction, two of which have three variables (red), and one (green) which has 2 variables. And so on. At the bottom we end up with four separate domains (blue), A:B:C:D each with a single variable. We have reductionism at this level.
Ashby called this 'constraint analysis', or 'cylindrance'. From top to bottom in the diagram, there are increasing levels of constraint that are applied. The single variable situation at the bottom, A:B:C:D is highly ordered, but a lot of the complexity in the system in stages before this has been lost. Entropy (uncertainty) here is low, and consequently, constraint is high. Another way of looking at it is to say that there is order but there is no flexibility.
The top situation ABCD has high entropy - it's a messy situation from which no clear distinctions can be drawn. However, the messy situation is adaptable in a way that the bottom of the diagram is not. I think the distinction between the top and the bottom of the diagram is very similar to Stafford Beer's VSM where System 3 dictates operations with little input from System 4 (A:B:C:D) or when System 4 flies off into fantasies about future scenarios and possibilities, but operational management is lost (ABCD). Ulanowicz has a similar situation in his ecological diagrams. The bottom would be described by Bateson as "Rigour without imagination" = 'paralytic death', whilst the top is "Imagination without rigour" = 'madness'!
The interesting thing in all this is that distinctions have to be agreed. A, B, C and D are constructed. This, to me, is where this diagram really helps. When faced with an unknown situation, we initially cannot make distinctions: ABCD. Discursively, there will be the exploration of possibilities: ABC: BCD:ABD:ACD. What happens between us as each of us explores these different constraints? Is there a process of locating where we might be in the diagram? I suspect it's something like this.
To locate oneself in this diagram is to become aware of the constraints that one is subject to, and to identify the constraints which bear upon others. For example, as someone who tends to be allergic to positivist psychology, I tend to see the psychologist's distinctions as being closer to A:B:C:D, (for example, the distinctions between senses) where I might think more in terms of ABC:CDA:BCD... I will identify the constraint operating on the psychologist as some kind of functionalist epistemology which I will feel is mistaken. Different constraints produce more than different epistemologies - it produces different politics (I find most Tories A:B:C:D, whereas the Left tend to be ABC:CDA...)
What about in teaching and learning? Teachers have to identify the constraints bearing upon a learner. Essentially they ask "where's the blockage?" The confused learner will not be able to make distinctions: ABCD. The learner who is able to perform successfully in exams will be (at some level) at A:B:C:D. But education is not simply to produce A:B:C:D because that gives the learner no flexibility. It is to integrate the production of A:B:C:D as part of a repertoire where they maintain flexibility and balance - even to the point of being able to dissaggregate, recombine and critique A:B:C:D back into AB:AC:DA... etc - the point where certainties become questions once more. That presents another way of looking at the diagram: to move top to bottom is to work towards certainty; to go from bottom to top is to ask questions.
Very often teaching is concerned with breaking down established certainties in the learner and getting them to unpick them. So we often find ourselves as teachers starting at A:B:C:D and moving towards ABCD. In order to do this successfully, a diagnostic process has to identify the constraints bearing upon the learner. But equally importantly, the teacher has to have a map of those constraints so that they can navigate a path of confusion, re-establishment of new distinctions, and so on.
I've got to think more about this. It is (in a way) the detail of Pask's conversation theory - except that Pask tended regard the teaching process as one where distinctions were agreed, rather than constraints being coordinated. There is a fundamental question as to whether education begins at the top and moves down (which would produce Von Foerster's 'trivial machine'), or whether it begins at the bottom and moves up, to settle oscillating in the middle somewhere. The latter is a much more emotional (and for me, a more realistic) process.