Thursday, 21 July 2016

Deep perspectives on Education: Time, Entropy and Intersubjectivity

For physicists, entropy and time are concepts which are tied-up together. Eddington's "arrow of time" is most generally seen as an increase in entropy (see

Boltzmann's Entropy however, is a measure of uncertainty about the state matter at a particular location. It is statistically expressed in his famous probabilistic equation. Basically, beneath all the interpretations laid upon it, it is counting.

With Shannon's appropriation of Boltzmann's equation, the entropy measure could be used for counting the surprisal in communication: in the way that we might look for disorder among atoms, we can look for (and count) disorder among symbols. One of the key features of Shannon's approach is the idea of the 'selection' of symbols, where the greater the number of symbols selected is an index of the communicating system's complexity, and the capacity requirements of the communicating channel (this was Shannon's practical purpose in developing his theory).

When we come to talk about human communication, selection at the level of symbols invites a more sophisticated idea of selection at the level of meaning. In Sociology, Niklas Luhmann developed this idea into an elaborate and complex theory of society. From here, entropy might be seen to provide the root of a theory of meaning. More profoundly, might we count to reveal meaning?

We need to take a step back. What was assumed in the physicist's conception of time in the first place? Phenomenologists would question the initial assumption about entropy because it failed to account for the perceiving subject's experience of entropy and time. It would also question the emphasis (so strong within physics) of the individual perceiving subject, when physical observations and scientific discoveries are not just individual, but social and intersubjective. These phenomenological issues were explored by Husserl, Bergson, Schutz, Merleau-Ponty and Heidegger (to name a few). It's worth noting that Bergson had an intriguing but rather unfruitful meeting with Einstein in the 1922 (see this - which sees their dispute as partly political - which led to extended debate.

I find Schutz's account of time interesting because it sees time emergent not from the experience of emerging physical disorder, but from the intersubjective experience between human beings: time always flows in a world of others. What may be important here is that meaning and mattering become prior to information. Also important is that those activities we do together - learning, working, playing. Schutz gives an account of what these things might be which I find far richer that the formalism of information theorists because it suggests that educational practice is the most important thing that human beings need to understand properly. Schutz is also critical to the entropy debate because his work was of seminal importance to Talcott Parsons, whose work on "double contingency" was fundamental to the development of Luhmann's theory.

Is there a middle ground between the Einstein, Bergson, Schutz, Luhmann viewpoint? Well, entropy is counting. Counting produces descriptions. Descriptions are communicated between people. Communication entails a continual intersubjective apprehension of time. Is it this intersubjective apprehension of time that we call 'education'?

Wednesday, 20 July 2016

Multiple Description Analysis in Health and Education

I'm doing some work on Patient Safety at the moment (in preparation for an online course). Among the most interesting features of this are the multi-level narrative descriptions which characterise most Patient Safety investigations. There is the account of the doctor/nurse/consultant/surgeon whose action most immediately leads to whatever adverse event is caused (death, removal of the wrong organ, instruments left inside the patient, administration of the wrong drugs, etc, etc). But then there is a chain of other causal factors: the labelling of the syringe, the power dynamics of the hospital, the stress of the environment, failures to communicate, etc. Each carries its own story with different stakeholders.... "the labelling did not feature an explicit warning for fear that it might confuse", or "the senior consultant who instructed the drug administration could not be overruled."

What's clear is that each stakeholder operates within constraints. Some of those constraints are analysable from examining different stories. Emphasis on particular words or themes in an account is a pattern of regularity which must be produced within some kind of constrained context. Accidents happen when constraints line up: the classic description of this in Patient Safety is Reason's "Swiss Cheese model" (see

Constraints are systemically generated: they are often the result of the social dynamics within which individuals participate. The constraints of an individual's practice are, in part, generated by the individual themselves. The way to avoid adverse incidents is for each individual to become more aware of the constraints bearing upon others in the organisation, and each individual's role in reproducing those constraints.

Multiple levels of description pertain to most areas of social life, including education. We do not worry about 'safety' in education because, unlike health (it seems to us) nobody dies. Actually, this isn't necessarily true: people do die from mistakes in education - it's just that it takes a very long time. It's as if the health system were to administer a very slow-acting poison whose action is highly complex. In order to understand the action of this slow poison, we have to be able to draw together the different narratives which relate to an individual's life and their education and the conditions under which the poison was administered.

It doesn't take much to imagine the broad themes of different narratives. We might start with the teacher's narrative: "Johnny was trouble... never interested in learning.", and Johnny's narrative "School was shit - it was obvious they didn't like me... so I found ways of subverting it", or the parents "economic circumstances meant we had no time to care", or social services "we had no resource to deal with this", or government ministers "Johnny should get on his bike and get a job", and so on.

What are the constraints within which each of the narratives emerges? The teacher's constraint which led them to say "Johnny was trouble" was partly the constraint of the formal education system which left no space to deal with Johnny's needs: "Trouble" meant not fitting in with the system. Johnny's constraint was finding ways of dealing with the imprisoned situation he found himself in which gave him no way of exploring his own inner desires, energy or curiosity. Analytically, if we were to measure constraints from the perspective of entropy in statements (the degree of surprisingness in particular statements), we would produce another description. Might this help?

The production of analytical descriptions from narrative descriptions has always been a key ingredient in the psychotherapeutic process. I think if we were to do this, we would find the greatest analytical constraints will bear upon the teachers: they are caught in a rigid system which cannot adapt. The least constraint, by contrast, will bear upon the 'rebel' student. There is no common ground between the constraints of the rebel and the constraints of the system. Such learners can die (eventually) of unmanageable complexity.

The same is true of patients who die in the care of an overly complex health system. Where the complexity of surgeons cannot be managed by junior doctors, or attempts to attenuate behaviour through drug labelling or checklists fail, or professionals in different departments do not communicate, the culprit is always unmanaged complexity: "I couldn't get the surgeon to listen to my concerns", "I worried that the labelling wasn't clear but couldn't talk about it", etc.

Adding analytical descriptions of constraints to the mix can help insofar as each description is an invitation to enter into conversation. When we talk about "organisational learning" what is meant is a communicative dynamic which leads to the identification and codification of new constraints. When common constraints are identified, everyone is changed. Most deeply, this is what education should do - it is what knowledge is really about. But it has real organisational consequences too - learning is always "organisational learning". 

Monday, 18 July 2016

The Object of Music - The Object of Learning

Following on from my last post on Ashby's distinction between 'System' and 'Object', I want to consider the two objects which hold the deepest fascination for me (and I know that this connection between music and learning is shared by many of my colleagues in educational technology). Ashby says that we cannot talk about an object; we can only identify variables which relate to an object, where this list of variables configures itself into what he calls a 'System'. However, one might then say, does this mean that any definition of a "system" is reductive?

In addressing this question, we have to consider what 'reductive' means. An approach is reductive if in its categorisation of variables in the environment, it deliberately overlooks some variables. In essence, the reductive approach overlooks the difficult problem in an attempt to find a solution to the easy problem. Reductionism is a process of omission.

It is not that leaving things out is a bad thing. Indeed, omission is a fundamental activity of all scientific discovery. The pathology of reduction occurs when what is left out is forgotten, and its critical inspection becomes increasingly difficult in a discourse delimited by the reduction itself. But this is not the fault of reduction itself. It is the fault of the way our discourse works, our universities teach, our journals publish, and so on: it is a fault of our epistemology that we lose sight of the negative context within which ideas are expressed. More precisely, it is the fault of a science which confuses description with explanation.

Music is a powerful corrective. Whatever analytical statements are made about it quickly reveal the explanatory gaps, and the bracketed-off variables. Statements of analysis are descriptions, and each analysis sparks a critical discussion. In learning, the same thing applies - except that the pathology of reduction becomes more embedded, and what is left out is forgotten. The result is a miserable educational experience. However, there is a homology between music and learning - what might be loosely called a 'similarity of phenomenological function' -  a kind of aesthetic sense.

Ashby points out that there are many many possible descriptions of a system and that they cannot all be considered. Where a system for Ashby is the interaction of variables, might it also be the overlap of possible descriptions? As such, one does not have to delimit the number of descriptions to a rigid array of variables. One may be free to continually add new descriptions into the mix. Each description is constrained in one way or another - each misses something out. In essence, with both music and learning, we can use descriptions to come to identify new things which we have left out.

If human understanding amounts to the extent to which we know each other's constraints, then the identification of what we all miss is a way to increasing knowledge.

Saturday, 16 July 2016

Ashby on Object, System and Complexity

These quotes are from a paper by George Klir called "W. Ross Ashby: a pioneer of systems science", International Journal of General Systems, vol. 38, no. 2, 2009.

System and Object:
At this point we must be clear about how a 'system' is to be defined. Our first impulse is to point at the pendulum and to say, the system is that thing there. This method, however, has a fundamental disadvantage: every material object contains no less than an infinity of variables and therefore of possible systems. The real pendulum, for instance, has not only length and position; it has also mass, temperature, electric conductivity, crystalline structure, chemical impurities, some radioactivity, velocity, reflecting power, tensile strength, a surface film of moisture, bacterial contamination, an optical absorption, elasticity, shape, specific gravity and so on and on. Any suggestion that we should study ‘all’ the facts is unrealistic, and actually the attempt is never made. What is necessary is that we should pick out and study the facts that are relevant to some main interest that is already given ... The system now means, not a thing, but a list of variables.  (Ashby, An Introduction to Cybernetics - 1956)
George Klir comments on this definition that:
It is rather surprising and, in my opinion, unfortunate that the fundamental difference between these two concepts, those of an object and a system, is still not properly appreciated. Yet, it is a difference which is at the very heart of systems science. Confusion arises when this difference is not recognised and, as some critics suggested, systems science becomes then the study of everything (every object) and is thus logically empty. 
Yes. If Systems Theory is seen as a theory of objects and not systems, it inevitably states empty metaphysical propositions. I think the logic and coherence lies in the distinctions which are made.

The word ‘complex’, as it may be applied to systems, has many possible meanings, and I must first make my use of it clear. There is no obvious or preeminent meaning, for although all would agree that the brain is complex and a bicycle simple, one has also to remember that to a butcher the brain of a sheep is simple while a bicycle, if studied exhaustively (as the only clue to a crime) may present a very great quantity of significant detail. Without further justification, I shall follow, in this paper, an interpretation of ‘complexity’ that I have used and found suitable for about ten years. I shall measure the degree of ‘complexity’ by the quantity of information required to describe the vital system. To the neurophysiologist the brain, as a feltwork of fibers and a soup of enzymes, is certainly complex; and equally the transmission of a detailed description of it would require much time. To a butcher the brain is simple, for he has to distinguish it from only about thirty other ‘meats’, so not more than log2 30, i.e., about five bits, are involved. This method admittedly makes a system’s complexity purely relative to a given observer; it rejects the attempt to measure an absolute, or intrinsic, complexity; but this acceptance of complexity as something in the eye of the beholder is, in my opinion, the only workable way of measuring complexity. (Ashby, 1973 - "Some peculiarities of Complex Systems", Cybernetic Medicine, Vol 9, no. 1)

Thursday, 14 July 2016

Hacking Conversation

Over the last two days, I've just been involved in a Hackathon for finding solutions to the problems of care homes. It's been an interesting experience, and one which I'm reflecting on as I am also involved in a project to run another Hackathon for Patient Safety in November. Although there was an emphasis on producing "solutions" to "problems", the most valuable thing about it has been (unsurprisingly) the conversations. In terms of solutions and problems, in my case, I have come away distinctly sceptical: are there definable 'problems'? Is there a solution?

Whilst listening to the 'pitches'  at the event, I was often aware of the kind of behaviour that is described in Cohen and March's "Garbage can" model of organisational decision-making. Essentially, what tends to happen is that the really difficult problems that need to be talked about are deemed too difficult to talk about, and in their place discussants rummage around in the "garbage bin" of possible tools or interventions which might address a 'do-able' intervention. So the important things get left behind in pursuit of deciding to do something, and solutions are found to problems which are essentially defined by the technologies chosen to address them. So the webcam on the door solves the problem of identifying a person looking into a camera while they are stood at the door; the hearing test app solves the problem of delivering a hearing test when you're carrying a phone; etc. But what about the important stuff?

What really interested me was the dynamics of the conversations within the groups. There were all kinds of individuals there; some with experience of caring, some with experience of managing care, some with experience of developing tools, some with experience of business, and so on. Each person has a particular world-view which they bring to proceedings. If one were to draw these world views, it would look something like this:

It tends to be either the top or the bottom of the diagram which manifests itself - people are either open to be confused and generally open to possibilities, or they come with a set of categories which are quite firm as their way of viewing the world. There tends to be a disconnect between the holistic thinking and the categories. Some with specific categories will not admit to any vagueness in their position; some with open positions will object to over-specification of categories. The diagram represents different levels of constraint on thinking; fixed categories and certain opinions produce predictable regularities of behaviour and response which suggest rigid constraints. Vague philosophical positions manifest as unpredictable and often creative behaviour which indicate less constraint. Both groups may be open to moving to a middle position which admits some confusion with some defined categories.

Tension in a group emerges in a number of different ways,. Two people with fixed ideas can have very different ideas, and an ideological conflict ensues. A holistic thinker may be frustrated by the rigid thinker and questions them about their certainty, whilst the rigid thinker asserts their categories. Each person has a model of the others contextualised within their own model of the world. So the holistic thinker will know that the rigid thinker needs to become less certain of their categories, so they will question them. The rigid thinker will believe the holistic thinker to be wasting time or not focusing, and will demand concentration on a particular issue for which the rigid thinker already knows the categories. This forceful increasing of constraint can cause problems and tension, just as the holist's questioning can be unsettling for the rigid thinker. However, it is more complicated still. Because whilst the holist will reject some rigid categories, they will have other rigid categories which they will defend vigorously. Typically, a third dynamic is necessary to address this conflict situation.

A third person is able not only to observe the nature of another individual, but also the dynamic of the interaction between two other people. This knowledge of the dynamics as constraints shift up and down, tensions are exposed, and so on, provides the critical extra dimension for reaching some sort of cooperation. It helps if at least one person in a group of three has a richer model of complexity which maps more precisely the relationship between a set of rigid concepts and holistic vagueness. Typically this person will be a teacher, and whether they consider themselves such or not, they will the chief coordinator of the discussion. The map of the interconnection of ideas at different levels will at least provide them with the means of steering a discussion where gentle increases and decreases in constraint become possible. When I've found myself in this role, I've found my knowledge of cybernetics extremely valuable.

It is possible to map out these conversations as a kind of 'tetralogue' (I should do this!). In reading the constraints operating on other participants, one trick is to discover some other constraint bearing upon a 'rigid' person which might account for their way of thinking, but not in the way that the rigid thinker would want to admit (they believe their categories are perfectly rational and unarguable): then a powerful question might be asked which throws the rigid person into confusion causing them to reorient their thinking. For example, "What happened to your dad when he was in the care home?" With everyone in a state of disorientation, then concepts can be reformed.

There are probably some more specific categories which belong to this model of conversation!

Tuesday, 12 July 2016

Explanation and Description in Learning Analytics

The act of analysis is ambiguous. On the one hand, analysis is a process of seeking explanations for phenomena. For example, a musical analysis will seek to provide answers to questions about the experience of a piece of music. For those who uphold the techniques of analysis as providing access to some latent truth, the analysis will explain why such and such is the case, or (most commonly) defend value judgements. Schenker's musical analyses, for example, were used by Schenker to make value distinctions between different kinds of music. It may well be the case that Schenker's search for a cosmological explanation drove him to develop his analytical technique in the first place. The search for totalising explanation is largely responsible for music theories from antiquity onwards.

More modestly, analysis provides a description. Schenker's graphs describe music in a particular way. Many other kinds of description are possible, and each focuses attention on one particular aspect or another - Schenker, for example, privileges tonal structure above rhythm. In a world of analytical and critical pluralism, there are many different kinds of description available. Music analysts tend to choose one method or the other, thus buying into a particular ontological stance at the outset, or seek to combine methods and perform some kind of triangulation in their results.

How Learning Analytics relates to this ambiguity of analysis is an important question. Whether Learning Analytics does or does not seek to provide explanations, it is open to be interpreted in this way, making the sometimes spurious correlations which appear in analytic reports (for example, between different pedagogies and learner outcomes) potentially dangerous. When analysing the dynamics of learning analytics, we have to consider the social positioning of an analytic report within the organisational context of education.

Everyone has theories about why things do and don't happen in education. However, only those in positions of power have access to large datasets of everything that happens. Consequently, analytical statements are made by the powerful. These are statements about the behaviour and desired outcomes of those with less power - learners and (often) teachers. Judgements are based on that data which can be captured; data which cannot be captured is ignored. Not only are analytic statements produced by the powerful, they are presented to the even-more-powerful who can exercise their power by changing policies, institutional organisation, staff management, etc. Since educational institutions are immensely confusing, analytic reports have the attraction of summarising outcomes and presenting correlations between interventions and outcomes, which will suggest some kind of management intervention at a high level. Simplistic causal thinking is tempting: "The students have left the course because...". In the face of dismal events, and a powerful statement of correlation between interventions and those events, is it hard to say in the board meeting that "it is only a description".

To take the analytic report as an explanation to be acted on is like making a judgement about Hamlet's state of mind by reading a second hand account of the movie of the play within the play. The power of data analysis is that it presents itself not as a subjective account, but as rational, algorithmically-generated and objective. Yet just as a teacher would direct a learner to read Hamlet, view interpretations, read criticism and so on, so a manager should explore analytics as descriptions, compare different descriptions, ask questions about the institution, about the learners, etc. Fundamentally, any analytics should open up a richer conversation, not close it down. It is only by the path of exploring multi-layered descriptions that managers may become experts in their institutions, just as we would wish learners become experts in Hamlet. The problem is that the managerial space for inquiry about the institution is even more restricted than the learner's space for inquiry. But to situate analytics as description can open this up.

It can also open up the space for learner conversation. Recently, I've been experimenting with analytical reports with students in Liverpool. They are on work placement in medical institutions at the moment, equipped with an iPad e-portfolio system. The e-portfolio system was lacking a reporting engine, so there was an opportunity to do something different. Every Friday, the learners are sent by email a PDF summary of their activity. They all receive this at the same time, and consequently, they all talk to each other about what it contains. In the early weeks, it simply kept a count of the skills practiced which were identified in their portfolio submissions:

After a couple of weeks, it was possible to add a word cloud to this, and encourage the students to reflect on what they were seeing most frequently.

It was important to keep the students posting during their placements, and so a measure of their frequency of posting was the next addition to the report:
What's interesting about this is that after each report, there is a spike in the behaviour of the students as they react to the different descriptions of the data they are presented with. Since everyone knows that everyone else has also got their reports at the same time, it is inevitable that they will make comparisons between each other: the timing of the reporting and the fact that it is pushed to the students, rather than requiring them to log-in to a dashboard (which many will not do) seems to be significant. 

Most broadly, it appears that the report and its contents act as a constraint which directs the students into conversation and action in much the same way as presenting them with new learning content, or a learning activity might do. Analytics as description is pedagogical. The possibilities for extending this and producing new kinds of description of user action can open out into all sorts of things... But it is not just the contents of the analytical report which matters; the use of time as a constraint also matters - doing things at the same time - particularly with a distributed group - is powerful. 

I'm thinking about the implications of this. If analytics is treated as description rather than explanation, then the emphasis on its use becomes pedagogical, not directorial: it is about stimulating conversation. In our teaching practice online, universities tend to remain committed to producing content to stimulate discussion, and it often doesn't work. Wouldn't it be better if they stimulated conversation with imaginative analytic descriptions of activity so far? Could that steer us away from the pathological content-production cycle most e-learning units are obsessed by? I'd like to explore this. 

More important are the implications for management. If management sees learning analytics as descriptive rather than explanatory, then it too is a prompt for management discussion. It should support the learning processes of managers as they seek to become experts in the life of the institution. It ought to drive them to inquire more deeply about life on the ground. I think if we could make this really happen, we would have much healthier institutions.

Friday, 8 July 2016

A counterpoint of constraints in learning

There is a space to open up between the study of learning, technology and living and the study of art - and particularly music. Fundamentally, this space concerns the study of constraint - how constraints emerge, how they shift, what their effects are, and so on. There is a counterpoint of constraint which is, I think, available for inspection.

The counterpoint of learning can be elaborated by an example: learners enrolled on a course are subject to different constraints which partly result from interactions which have occurred prior to their meeting each other (from family, previous experiences, etc). The moment at which they meet is a moment when each of them voluntarily subjects themselves to the same constraint (the course). This constraint will create a complex dynamic with the other constraints they are subject to: they will turn to each other and ask "why did you decide to do this?", "what are you interested in?", and so on. The pattern of constraints which each is enmeshed in will vary from some fixed concepts about the world (opinions and values) and some less defined vague experiences, where the connection between concrete experiences and vagueness is poorly defined: confusion will often hold rigid but inflexible concepts in place. Each is likely to have different concepts. As they learn more about each other, they will identify each other's constraints, and will agree or disagree. The more rigid the concepts the higher the chances of disagreement. Conflicts and cliques ensue.

Then another element to the counterpoint: the teacher exercises their own constraints on the students. They will organise the learners into groups or activities, making judgements about the most appropriate activities to engage the students in to loosen rigid concepts or tighten vague thinking. The teacher is guided by their own set of relations between rigid concepts and vague thinking - but often the teacher has some kind of map which guides them from confusion to clarity, and from clarity back to confusion. They navigate this map in conversation with the students. Moving from rigid concepts to questioning vagueness and then to redefined clarity involves skillful navigation. The parables of Jesus are an excellent and very gentle example of how this can be achieved.

There are moments when there are distinct constraints operating independently - concrete opinion, practical difficulties, course criteria, timetables, etc. There are other moments where somehow everything shifts together, things are realigned, views are transformed. Just as there are moments in a Bach fugue where there are clear moments of independence, and then something happens which affects everything else. Each voice exercises a variety of constraint on the others. There are many dimensions to the constraint - pitch, melody, harmony, rhythm, dynamics and so on.
In learning, the common constraints of timetable, assessment, lectures, etc shape all other constraints. But just as in music, this is a dialectical process - it triggers behaviour from the other learners which partly is in response to the common constraint, but mixed with the individual constraints each carries with them (I can't possibly do this assignment by then because of my family commitments). Time as a constraint in learning is probably as important as rhythm in music - it binds together (which is a problem in the asynchronous way that the web works). Also, when parts come together, their interactions create a shared context within which new possibilities emerge. When learners come together the shared "system"  which they create together has different self-organising potential from that occupied by an individual. 

In more formal terms, coming together increases the 'maximum entropy' of the coupled system creating greater scope for self-organisation. Conversely, where there there is a well-defined activity or skill for a learner to perform, the maximum entropy is kept stable, and the learner must develop their self-organisation capacity in order to succeed.  Knowledge (and eventually wisdom) arises in the acquired flexibility to move up and down the loosening-tightening axis in one's relation with others. Interestingly, this knowledge of the dynamics of constraint is what I think happens when we learn how a piece of music 'goes': we understand its entropic structure.