Sunday, 19 February 2017

Revisiting Inquiry Based Learning: Uncertainty-based teaching

Through Liverpool University, I've become re-engaged in the issue of Inquiry-Based Learning (IBL) - this time under the guise of research-based teaching and learning. IBL was one of the major things that I worked on at the University of Bolton's Institute for Educational Cybernetics, where we created a curriculum framework for IBL courses, called IDIBL. At Bolton, it didn't work as well as we'd hoped, although a similar initiative had worked quite well at Anglia Ruskin University, and I've always felt that it was the right thing to do. It's good to see many of the ideas return - but this is an opportunity to rethink things.

The problem with IBL is that it can so often seem (as I overheard two Manchester University students complain about their IBL course) that it involves "the teachers not telling us anything, and us having to work stuff out for ourselves". This happens because IBL aims to loosen the vertical curriculum structure which "delivers" knowledge and skill from teacher to student (via textbook, VLE, exams), and reinforce horizontal self-organisation among students. On IDIBL this horizontal self-organisation was meant to happen in online communities - a similar idea to Siemens and Downes original MOOC. However, it turned out that establishing self-organising online learning communities was much more difficult than anticipated.

However, many teachers are naturally skilled at reducing the amount of vertical coordination in teaching. One wonderful engineering lecturer in Liverpool said "I used to go to lectures with loads of Powerpoint slides; now I go with a blank piece of paper, and use a visualiser to project my notes as we start a discussion". However, he also said "I think the dialogue in the class works with a relatively small number of students. I don't think it would work with a large number."

I think in order to  confirm or confound that hypothesis we need a better model of the problem. Dialogue is the key word: dialogue is what self-organisation really looks like in education. Online, I don't think what we get is dialogue as such. But we get something else. The differences between the different situations relate to what the phenomenologists call "inter-subjectivity" - the understanding we reach of each others' 'inner-worlds'. This, I think, is what is powerful in the engineering lecturer's technique - he reveals something of the inner world. If you watched Mozart improvising, or Picasso doodling, you would get a similar impression.

Part of what happens is a shared experience of time. Alfred Schutz points out that in pure intersubjective experience of face-to-face engagement (what he calls the "pure we-relation"), we "get old together". But we can watch Picasso doodling, we can "get old together" with him - even though he's dead. Doesn't it have a similar quality of revealing his inner life?

What if each of us did this kind of thing as part of "maintaining a dialogue"? What would it require? What are its properties?

I think the requirements are "courage", and the essential property of doing something like this is that it is an "expression of uncertainty".

Uncertainty is crucial to understanding IBL. It is not that self-organisation should be imposed on learners by teachers (which is what the Manchester students were complaining about). Self-organisation is a natural consequence of shifting the focus from certainty to uncertainty.

We are at a strange moment in the history of science. Today's science is data-driven, and largely contingent and probabilistic. Yet within this uncertain scientific world, we insist on maintaining the communication practices of the 18th century - journals speak of Newtonian certainties, evidence and so on. We are not generally good at appearing uncertain - either in front of our peers, or our students.

IBL as it was conceived in IDIBL, was a pedagogic 'certainty' for those of us who devised it, and there was an asymmetry between our certainty and the uncertainty we aimed to impose on the students. The engineering lecturer engages in uncertainty-based teaching: he is not sure where the lesson will go, and there will be areas in the discussion which will throw up things which he isn't sure about. Yet there are other things - and skills - which he is sure about. It's all there; it's all modelled for the students. In the mix of things about which one is certain, and the things about which one is uncertain, there is a clue as to what is happening:

It is not knowledge, but the contraints of knowing which are communicated. 

Picasso communicates the constraints of his drawing - the pen, the page, time, the movements of his body, his emerging intentions. He gives a glimpse as to how he negotiates them. The engineering lecturer does the same.

In conventional teaching, we rarely talk about our constraints. Most of the time, constraints are taken for granted - time, the lecture space, the online space, the assessment, prior knowledge, skill (or lack of it), and so on. In IBL, we forced self-organisation as a new kind of constraint - but again, failed to really discuss it as a constraint, or why it might be there. But to communicate uncertainty, the only thing that can be done is to be open and honest about the constraints in which we all try to fathom what is happening around us.

Thursday, 16 February 2017

The problem of Information and Ergodicity

Information is not ergodic: the average surprisingness of an entire message is not the same as the surprisingess of a section of the message. So how does this affect the way we use Shannon equations? What makes information non-ergodic is the continual transformations of the games that we play when we communicate. A surprise for one game is different from a surprise in another.

The transformation from one game to another is a key part of Nigel Howard's metagame theory where a shift from a game with one set of rules, to a metagame of that game is prompted by a "paradox of rationality" - basically, a crisis. It is a bit like shifting up a level of bifurcation. Maybe even there's a shift up from one energy level to another (which makes the connection to Schroedinger and Kauffman). What's interesting is the cause of the shift.

In Howard, the crisis - his "paradox" of rationality - means that only the jump to the metagame can resolve the contradiction of the current game. The shift is a redescription of existing descriptions in new terms.

My examples for this are all emotional in some way - the experience of "crisis" is very real, but I think Luhmann is right that these things are social-systemic, not psychological. So, for example, in music the climax of the Liebestod at the end of Wagner's Tristan is a moment when constraints of pitch, harmony, rhythm, etc all coincide. It has a curious homology to orgasm. In intellectual life, Koestler's idea of "Bisociation" is also a synergy of multiple descriptions in a similar form. Luhmann's 'interpenetration' is another example, as is Schutz's 'intersubjectivity'. Bateson's levels of learning and Double-bind are further examples. Politically, there are some obvious examples of "regime change" at the moment - changing the game most obviously!

The result of this kind of process is that a distinction is made between the old game and the new one: a boundary produced. On one side of the boundary, there is a degree of entropy in the number of descriptions. On the other, there is a degree of synergy between those descriptions. It is these processes of continual game-change which are non-ergodic.

Whilst I doubt whether we should make Shannon entropy calculations across different games, Shannon is useful for counting within a single game - that would indicate how close a "regime change" might be. Shannon mutual information is itself a kind of game between sender and receiver. I think it would also be worth counting "game changes" - that seems do-able to me - the boundary-markers are the moments of synergy. [my physics colleague Peter Rowlands mentioned to me that he thought that the things that Boltzmann actually counted in statistical thermodynamics were 'bifurcations'. I don't fully understand what he means, but an intuitive reaction says that is a similar thing]

In Stuart Kauffman's "Investigations" he goes into quite a lot of detail about these transformation processes. It has woolly edges.. but "Investigations" is a powerful book - there's some value in it (I didn't like it at first). Kauffman's introduction to Ulanowicz's book "A Third Window" is quite revealing in terms of mapping the space between his ideas and those which centre more around Shannon. Both lines of thought have powerful contributions to make.

Tuesday, 7 February 2017

Finding the "Aesthetic Line"

The dynamics of human experience are such that there is continual blurring and shifting of focus. There are rare moments when focus brings revelation, insight and emancipation. At such moments, the contrapuntal lines of experience map each human being on each other. These are moments of solidarity. The opposite of this experience is where everyone is in the fog: every individual cannot see their own steps, let alone the steps of others. The feeling is of isolation, loss: anxiety pervades everything. At such times, it is not surprising that people clutch at straws: it's in these moments that the strong man appears, whipping up a collective fervour with tales about how things are, spewing falsehoods and directing hatred in perverse directions.

What it is that comes into focus at moments of revelation is a line: a set of connections between different levels of experience. It connects basic and immediate drives, with deep spiritual needs, the need to be loved, the need to belong. But I think lines may be drawn in two ways: either by excluding things, or by including things. The latter is much more difficult than the former. The former is the beloved technique of dictators.

We can consider two lines: the "Trump" line and the "Aesthetic" line. The Trump line is straight and unvarying. It 'straightens' all that it encounters (or perhaps, flattens it). It asserts the positive identity of itself and it threatens the existence of all which isn’t like it. By contrast, the "Aesthetic line" is sinuous, it bends and curls, whilst always maintaining its direction and purpose. The aesthetic line is like a tree branch or a river. It divides into other branches, or tributaries, always embracing the difference of its tributaries, but always aware of its one-ness. Each bend and curve in the aesthetic line is an inflection: a moment of additional description, which complements the descriptions of the line so far. The aesthetic line is formed of multiple descriptions (the L-System, which produced the picture below, is a set of string 'descriptions'); the "Trump" line is a single description.

In the fog of experience, lines are presented to us in a haze. We can only work out what they are by examining multiple hazy descriptions. The addition of hazy descriptions can gradually bring different levels of the line into focus. It is by accumulating descriptions that we work out what is what. It's a bit like the addition of waveforms which make up a complex wave in Fourier analysis. Each contributing waveform is a kind of "redundant description". But together they bring the concrete reality of a rich sound into focus.

Music and the arts reveal this kind of process. Any piece of music immediately presents multiple descriptions: a rhythm, melody, pitches, timbres, and so on. Each is an inflection on everything else; each inflection depends on everything else. On first presentation of multiple descriptions, we are in the fog. We cannot connect where things are going, where the lines are. Multiple descriptions at the same level clarify the situation. They negatively specify the pulse, direction, trajectory of where things are going. As the trajectory becomes clearer, new layers of description – descriptions about description, description about the ways in which descriptions are revealed, are all added. The deeper inflections become part of the whole. At some point, the "root" description – the description which generates all others - comes into view. There is a moment when the presentation of the root description – usually a harmony – brings a piece of music to a close.

The production of multiple descriptions and the emergence of lines does more to us that affect our own experience. They give us an insight into the experience of others. Finding the line is to find the connections between one another – to see the inner world of others is to discover new ways of organising ourselves and transcending adversity.

I think of the aesthetic line in the context of Nigel Howard's meta-game trees. Howard makes the point that the ascent to a meta-level is the reaction to a process of confusion at the existing level. Howard provides another way of thinking about transcending double-binds: we change the game. So when descriptions are presented they are joined up in ways which might at first appear that they contradict one another: this is the fog. The metagame tree needs to be reorganised in some way. New descriptions bring deeper reflection and articulation of more complete aesthetic lines. In this way, decisions are felt emotionally. 

At an analytical level, what concerns us is the redundancy of description on the one hand, and the inflections between different descriptions on the other. This is easy to see in music: various elements, like rhythm, tonality, harmony, pitch can display redundancy. Each represents a different inflection of the line. The need for novelty is inherent in the production of redundancy, and the need to generate new inflections at a deeper level - particularly when redundancy in a number of areas (like a continually repeated melody) is very high (as when things are repeated too much). 

The use of technology also brings very high degrees of redundancy, creating the need for novelty and new forms of inflection. In technocratic environments, new forms of inflection can be prohibited quite easily. This produces a general frustration and depression, with the end result that a more radical "change of the game" is generated. Trump is the result of an inability to vary the inflections of experience which has been produced by a toxic mixture of neoliberalism and technology. Unfortunately, his success means that there is a positive-feedback mechanism which will make the finding of the aesthetic line even harder.

Saturday, 4 February 2017

Ashby's Experimental Method in "Design for a Brain"

Ashby's Design for a Brain is a remarkable book containing a lot of detail about how Ashby saw cyberentics as a science. Some of the most interesting passages concern his defence of his own methodology as he sought to create a "mechanical brain", building on his earlier work with homeostats. In contrast to much second-order cybernetics, Ashby remains a down-to-earth and practical scientist. But he is looking at the world in a different way: he is exploring constraints and relations rather than causation. The principal relation which concerns him is the relation between the experimenter and the experimental situation. In this, of course, he is very close to second-order cybernetics - but with a penetration of analytical thought which has been unfortunately overlooked by many of his cybernetic colleagues.
"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. Thus if we were studying the swing of a pendulum in relation to its length we would be interested in its angular deviation at various times, but we would often ignore the chemical composition of the bob, the reflecting power of its surface, the electric conductivity of the suspending string, the specific gravity of the bob, its shape, the age of the alloy, its degree of bacterial contamination, and so on. The list of what might be ignored could be extended indefinitely. Faced with this infinite number of variables, the experimenter must, and of course does, select a definite number for examination - in other words, he defines the system." (Design for a Brain, pp15-16).

Ashby goes on to describe specific examples of empirical practice:

"In chemical dynamics the variables  are often the concentrations of substances. Selected concentrations are brought together, and from a definite moment are allowed to interact while the temperature is held constant. The experimenter records the changes which the concentrations undergo with time.
In experimental psychology, the variables might be "the number of mistakes made by a rat on a trial in a maze" and "the amount of cerebral cortex which has been removed surgically" [ugh!]. The second variable is permanently under the experimenter's control. The experimenter starts the experiment and observes how the first variable changes with time while the second variable is held constant, or caused to change in some prescribed manner.
While a single primary operation may seem to yield little information, the power of the method lies in the fact that the experimenter can repeat it with variations, and can relate the different responses to the different variations. Thus, after one primary operation the next may be varied in any of three ways the system may be changed by the inclusion of new variables or by the omission of old; the initial state may be changed or the prescribed courses may be changed. By applying these variations systematically, in different patterns and groupings, the different responses may be interrelated to yield relations
By further orderly variations, these relations may be further interrelated to yield secondary, or hyper-relations; and so on. In this way the "machine" may be made to yield more and more complex information about its inner organisation." (pp17-18)
What Ashby was arguing was that the internal relations of a system - its internal constraints - are revealed by applying constraints to their investigation.  ("Relation" and "constraint" Ashby saw as synonymous terms)

As to the detail of what it means to apply constraint, Ashby argues that it is about creating regularity. This is not to suggest that regularities are necessarily real, or external to the observer, but that they arise in the relations between the experimenter and their subject.

"If, on testing, a system is found not to be regular, the experimenter is faced with the common problem of what to do with a system that will not give reproducible results. Somehow he must get regularity. The practical details vary from case to case, but in principle the necessity is always the same: he must try a new system. This means that new variables must be added to the previous set, or, more rarely, some irrelevant variables omitted."
I find "he must try a new system" a very powerful statement. So often in educational theory, psychology - even cybernetics - regularity is assumed at various levels of the system. It is treated as a foundation upon which all other variables are tested. Maturana's autopoietic theory, for example, makes great statements about the need to adapt to regularities in perception: as if regularities are real, the mechnaism of perception is regular too, and what needs to happen is that the two come together in some way. Ashby doesn't say this. If a scientist discovers a regularity, it exists in the relationships of the experimental situation. If they fail to find regularities, they seek (create) another experimental situation. The conclusion one might draw from this is that there are no real regularities beyond a relationship.

Ashby wrestles with the idea of objectivity always conscious that this is one of the fundamental criteria for a commonsense view of the world. He wants to make the distinction between a "natural system" and an "absolute system" and reflects the challenges of making association between the mechanisms of physics and those of biology. He asks:

"both science and common sense insist that if a system is to be studied with profit its variables must have some naturalness of association. But what is natural?"
His definition of naturalness of association is related to his definition of an "absolute system" where the state of a system in entirely dependent on its historical (previous) states.  With a operating definition of an absolute system, he sets the criteria for defining a "natural association". These criteria insist on some alignment to common sense, and some sense of "objectivity". In effect this places the scientist's own reflexivity in the frame: "only experience can show whether it [an idea of a system] is faulty or sound". It is not to deny objectivity, but it is to resituate as a relation, or a constraint.

Thursday, 2 February 2017

Multiple (redundant) Descriptions of the World: A Lesson for Teachers

Gregory Bateson's final book, Angels Fear, contains some fascinating details in his thinking which still require some unpicking. I was drawn back to it (it has been sitting on my shelf for many years now) by a wonderful paper by Peter Harries Jones on Bateson's concept of "bio-entropy" (see What caught my eye is the extent to which Bateson expands on his idea of "multiple description" which he first dealt with in Mind and Nature, and clearly aligns this to aesthetic experience, metaphor and redundancy. I'm particularly interested in the redundancy aspect, having just collaborated on a paper on redundancy with Loet Leydesdorff.

So here's Bateson being very clear that our science is really a science of description:
"When we study the biological world, what we are doing is studying multiple events of communication. In this communicating about commuinication, we are particularly interested in describing injunctions or commands - messages that might be said to have causal effect in the functioning in the biological world - and in the system of premises which underlies all messages and makes them coherent. [...] Having noted that the communicative fabric of the living world is ordered, pervasive, and determinant even to the point where one might say of it, this is what men have meant by God, we move ahead in the effort to describe its regularities with some trepidation, looking both for patterns and gaps in the weave.
Biologists looking at the natural world create their descriptions, for even their most objective recorded data are artifacts of human perception and selection. A description can never resemble the thing described - above all, the description can never be the thing described." (Angels Fear, p151)
He summarises his position later on:

  1. The data of the scientist studying biological phenomena are created by him. They are descriptions of descriptions, forms of forms.
  2. At the same time, message material, descriptions, injunctions, and forms (call them what you will) are already immanent in the biological phenomena. This it is to be internally organised, alive.
  3. All forms, descriptions, etc - including those immanent in the organisms - are like language. They are discontinuous and distortive.
  4. The forms are totally necessary if we are to understand both the freedoms and the rigidities of living systems. They are to the total process as the axle is to the wheel. By restricting the motion and preventing its movement in other planes, the axle gives the wheel a smoothness in moving in the chosen plane.
This last point is incredibly important for teachers to understand. The operative word in point 4 is "understand". Understanding is gained by apprehending forms, or patterns - or constraints. In education we ask "what are the constraints bearing upon this student? How can we overcome them?" How do we go about learning about the learner's constraint? We apply constraint. We say "do this activity" or "read this" or "let's play a game" or even "do this test". These are crude constraints but with their application, the constraints of the learner become clearer. We will then adjust the constraints we choose to apply next. 

Bateson makes the connection between constraint and redundancy, and moreover he makes the connection between the multiple descriptions of the world and the redundancy between descriptions. Our many descriptions overlap. It is in the overlap that we understand constraint. So the activities chosen by a teacher present new descriptions (often of what the learner already knows) which overlap in particular ways. To specify an activity, to recommend a text, to give a judgement - all these are additional descriptions to those which comprise the learner's understanding. The teacher's skill is knowing how to mix these new descriptions: it is in understanding the degree of redundancy between them and the learner, and observing the new constraints that are revealed. 

The golden rule of teaching is that constraint is the path by which constraint is understood. 

Tim Farron on University Compromise Agreements: some reflections on my experiences at the University of Bolton

The Times Higher Educational Supplement has become strangely less attractive since it stopped printing its institutional index on the back page. I rarely opened the plastic cover, but always checked to see the nice things said about my current institution (Liverpool), and any scandalous stories that emanated from my previous institution (Bolton).  Bolton was hardly in there unfortunately - something I found a little weird since it seemed that almost every week there was some new crazy 'WTF??' moment which caused consternation in corridors, and would have brought some colour and excitement onto the THES pages. This week I noticed a short entry about Tim Farron's appeal for the banning of "compromise agreements" in academia which reminded me of my experience in Bolton.

I left Bolton in 2015 when my department was closed. It was a bitter and hurtful experience. The department had been very good and successful for many years with an international reputation for educational technology research. I find that the injustice and hurt of the closure stays with me - even though I am very happy where I am now and appreciate that I might have been done a huge favour. I loved Bolton, and believed passionately in "widening participation" - although this became a corrupted ideal in the world of marketised education, and particularly so in the hands of Bolton's management. Injustice hurts, and the closure of my department was a period (a week!) of the most appalling abuse of power I have ever experienced (Trump looks very familiar to me, as he will to anyone who has had experience of Bolton's VC).

In the same week that my department was closed, the Vice Chancellor summarily sacked his Pro-VC, the UCU rep. and his wife (see He blamed the UCU rep for a Daily Mail story about the purchase of his new house in Bolton (for which the University lent him £960,000) and a staff awayday which cost £100,000 ( at the Lake District hotel where the VC kept his yacht (a moment of excellent journalistic manipulation as everyone exclaims: "he's got a fucking yacht!"). Also in the same week, we were all invited to congratulate the VC on becoming a "Deputy Lieutenant" for the Queen - which apparently allows him to dress up like this: - that's him on the left)

When I left, I signed a "compromise agreement" - making me fearful of repeating anything negative even if it was already in the public domain. Fear is powerful - even when everything is in the public domain!

The period of unemployment that followed was very frightening. I would be overcome with waves of anger and physical pain. It felt like I'd been physically assaulted. There were moments when I wanted to die. This was obviously very distressing for my wife and daughter too, in a year when my daughter had also had a very serious accident.

Now Tim Farron, leader of the Liberal Democrats, has been getting fired-up about "compromise agreements" and the prevention of people speaking-out against the abuse of power by management (see All I can say is "About bloody time!". Farron said:
“Universities are supposed to be bastions of free speech and forthright opinions, yet our research has shown that confidentiality clauses may have been used not only to avoid dirty laundry being aired in public but now are just common practice in higher education,[...] This is simply outrageous. These gagging orders have a deterrent effect, employers seem to think that employees will just sign away the right to whistleblow. [...] The cold wind of gagging staff and stifled debate, much in the public interest, is going through the halls of our bastions of enlightenment and tolerance. This must end, these practices must be stopped.”
Despite massive protests and the involvement of local MPs, Bolton remains under the same regime. The VC covers himself with the blessings of establishment figures: baronesses, earls, judges, Prince Edward (FFS), the former Bishop of Manchester. It's a sickening charade. The University is in the process of negotiating a merger with two neighbouring FE institutions which together will become responsible for the educational futures of many thousands of young people in the region and beyond. It all begins to look "too big to fail". What government minister will challenge him? To cap it all, he awarded himself a 10% pay rise this year.

"Too big to fail" seems to have been the plan for Bolton's VC in his previous job at Doncaster College. It was a very similar plan to the one unfolding now. It ended like this:

This passage is interesting:
"Earlier this year principal Rowland Foote and finance director Tony Myers were suspended amid a probe into the college's financial management, and the college abandoned a restructuring plan that would have seen 140 lecturing jobs axed. Mr Foote later resigned and was replaced by interim principal John Taylor, while Bill Webster - one of two deputy principals at the college - left the institution."
Fast-forward 10 years, and we find the same Bill Webster formerly of the University and now as principal of Bolton College!

We have to talk about this. We have to talk about these people. We are all custodians of educational institutions, but some senior managers (not just in Bolton) behave like pirates, grabbing things for themselves. In the week when Parliament has decided to discuss how we deal with the pirate who's just taken over the US, we must turn our attention to the pirates who (unlike Trump as president) have had the luxury of being protected by the neo-liberal establishment. In the end, it's about heading-off a disaster before things really get out of control. 

Sunday, 29 January 2017

Options and Selection in Evolution

When we think about selection - for example, natural selection, or the selection of symbols to create or decode a message (Shannon), or the selection of meanings of that message (Luhmann) - there is an implicit notion that selection is a bit like selecting cereal in the supermarket. There is a variety of cereal, and the capacity to select must equal the degree of variety (this is basically a rephrasing of Ashby's Law of requisite variety). Rather like Herbert Spencer's presentation of natural selection as "survival of the fittest", this concept of selection has a close relation to capitalism - both as it manifested in the 19th century economy, and in the 19th century schoolroom (which must, as Richard Lewontin pointed out, have influenced Darwin).

The problem with this idea is that it is assumed that the options available for choosing are somehow independent from the agents that make the choice, and independent from the processes of choosing. But the idea of independent varieties from which a selection is made is a misapprehension. It leads to confusion when we think about how humans learnt that certain things were poison. It is easily imagined that blackberries and poison ivy might have been on the same "menu" at some point in history as "things that potentially could be consumed", and through the unfortunate choices of some individuals, there was social "learning" and the poison ivy was dropped. But the "menu" evolved with the species - the physical manifestation of "food" was inseparable from practices of feeding which had developed alongside the development of society. The eating of poison ivy was always an eccentricity - a transgression which which would have been felt by anybody committing it before they even touched the ivy. The taste for novelty is always transgressive in this way - the story of Adam and Eve and the apple carries some truth in conveying this transgressive behaviour.

This should change the way we think about 'selection' and 'variety'. It may be a mistake, for example, to think of the environment having high variety, and individual humans having to attenuate it (as in Beer's Viable System Model). At one level, this is a correct description, yet it overlooks the fact that the attenuation of the environment is something done by the species over history, not by individuals in the moment. Some variety is only "out there" because of historical transgressions. What produces this variety? - or rather, what produces the need to transgress? Colloquially, our thirst for "variety" comes from boredom. It comes from curiosity about what lies beyond the predictable, or a critique of what becomes the norm. From this perspective, redundancies born out of repetition become indicative of the quest for increased variety. This thirst for novelty born from redundancy is most clearly evident in music.

Music generates redundancies at many levels: melodies, pitches, rhythms, harmonies, tonal movements - they all serve to create a non-equilibrium dynamic. Tonal resolutions affirm redundancies of tonality, whilst sowing the seed for the novelty that then may follow. I remember the wonderful Ian Kemp, when discussing Beethoven string quartets at the Lindsay quartet sessions at Manchester University, would often rhetorically ask at the end of a movement, "Well what is he going to do now?... something different!". The "something different" is not a selection from the menu of what has gone before. It is a complete shift in perspective which breaks with the rules of what was established to this point. The genius is that the perspectival shift then makes the connection to what went before.

Bateson's process of bio-entropy is a description of this. The trick is to hover between structural rigidity and amorphous flexibility. Bateson put the tension as between "rigour" - which at extreme brings "paralytic death", and "imagination" which at extreme brings madness (Mind and Nature, "Time is Out of Joint"). In Robert Ulanowicz's statistical ecology, there is a similar Batesonian balance between rigidity and flexibility, as there is in Krippendorff's lattice of constraints (see

I suspect selection is a more complex game than Shannon supposes. Our choices are descriptions. Our transgressions are wild poetic metaphors which only at the deepest level connect us to normal life. In Nigel Howard's metagame theory, such wild metaphors are deeper level metagames that transform the game everyone else is playing into something new. I've struggled to understand where and how these metagames arise. The best I can suggest is that as mutual information rises in communicative exchanges, so the degree of "boredom" rises because messages become predictable. That means that the descriptions of A match the descriptions of B. What this boredom actually is is the increasing realisation of the uselessness of rational selection: this is a moment of Nigel Howard's "breakdown of rationality". Bateson would call it a double-bind. To escape it, at some point A or B will generate a new kind of description unknown in the communication so far. This shakes things up. At a deep level, there will be some connection to what has gone before, but at the surface level, it will be radically different - maybe even disturbing.

In music this unfolds in time. It is the distinction between a 1st and 2nd subject in sonata form, or perhaps at a micro-level, between a fugal subject and its countersubject. A theme or section in the music is coherent because it exists within a set of constraints. Descriptions are made within those constraints. The "transgressive" exploration of something different occurs when the constraints change. This can happen when redundancies in many elements coincide: so, for example, a rhythm is repeated alongside a repeated sequence of notes, or a harmony is reinforced (the classic example is in the climax of the Liebestod in Wagner's Tristan). These redundancies reduce the richness of descriptions which can be produced, highlighting more fundamental constraints, which can then be a seed for the production of a new branch of descriptions. It is, of course, also what happens in orgasm.

I've been trying to create an agent-based model which behaves a bit like this. It's a challenge which has left me with some fundamental questions about Shannon redundancy. The most important question is whether Shannon redundancy is the same as McCulloch's idea of "Redundancy of potential command" which he saw in neural structures (and in Nelson's navy!) Redundancy of potential command is the number of alternatives I have for performing function x. Shannon redundancy is the number of alternative descriptions I have for x. McCulloch can be easily visualised as alternative pathways through the brain. Shannon redundancy is typically thought about (and measured) as repetition. I think the two concepts are related, but the connection requires us to see that repetition is never really repetition; no two events are the same.

Each repetition which is counted by Shannon, reveals subtle differences in constraint behind the description that a is the same as b. Each repetition brings into focus the structure of constraint. Each overlapping of redundancy (like the rhythm and the melody) brings the most fundamental constraint more into focus. As it is brought more into focus, so new possibilities become more thinkable. It may be like fractal image compression, or discrete wavelet transforms...