Monday 29 May 2017

Symmetry, Learning and Sociomateriality

A number of ideas are bombarding me at the moment. Meeting Peter Rowlands has changed my perspective on things: this is what universities are really about: creating the possibility of encounter with radically new ideas. Peter is interested in reconfiguring the relation between classical and quantum mechanics. At the root of his approach are three simple concepts: the 'nilpotent' - an imaginary number when raised to a power produces zero; quarternions - 3-dimensional imaginary numbers invented by Hamilton which have peculiar properties; and, most importantly, symmetry.

In grappling with this (and I am still grappling with it... this blog is part of the process!) both symmetry and the nilpotent resonate with me in my thinking about cybernetics, learning, music and emotional life. The nilpotent puts the focus on nothing. The universe is about nothing. Now compare this to the importance of absence in  the work of Terry Deacon, or Bhaskar, or Lawson, or the apophatic in the ecological work of Ulanowicz. There is also the category theoretical work of Badiou who places particular emphasis on nothing in his graphs. Is absence nothing? In the sense that absenting is about something "not there"... zero is clearly not there. From Newton's third law (Rowlands has published a number of books about Newton), an obvious point to make is that the resultant force in the Universe is zero. More importantly, the somethings that we see in the universe are the product of constraints of things which we can't see (dark matter/energy). There is a nothingness about dark matter. But there is also nothing in the resultant totality of what we can see and what we can't. The real question is how something emerges from nothing.

In cybernetics, the concept of constraint takes the place of absence - although they are considered to be the same thing (Deacon, Ulanowicz, Lawson are all in agreement about this). The nilpotent idea seems to be mirrored in the tautology of Ashby's Law: a complex system can only be controlled by a system of equal or greater complexity. Something emerges from nothing, through the fact that at any particular level, systems are unstable: The complexity of system a and system b might be greatly different, thus necessitating systems at higher levels to participate in balancing the variety. This is a dynamic process. In terms of understanding it, this is a process that relies on broken symmetry.

Having a fundamental way of describing symmetry-breaking is something which mathematics struggles with. Perhaps the closest we get is in fractal geometry, or in the dynamics of Conway's game of life. But these are the result of heuristics and recursive functions rather than fundamental mathematical properties. The quaternions present a way of thinking about broken symmetry which is fundamental. i, j and k are all square roots of -1, so ii = jj = kk = -1. But ij is not equal to ji. This anti-commutative property gives quaternions the potential to articulate complex matrix structures which have a kind of 'handed-ness'. This abstract property becomes useful to describe the apparent handedness that we see in the universe, from subatomic particles to DNA to the Fibonacci structures in biology.

What's fascinating about this is that nilpotency and broken symmetry combined have remarkable generative properties. For Rowlands, one of the key things is the bridging of the gap between classical mechanics and quantum mechanics. In much social science writing (and in educational technology) it has become fashionable to cite quantum phenomena like "superposition" and "entanglement" as a way of articulating the complex 'sociomateriality' of social life. Many realists object to the woolly language. Scientists like Sokal object to the lack of understanding of physics - although some who promote sociomateriality do so from a scientific perspective - like Karen Barad. Part of the problem lies within physics. Classical mechanics and quantum mechanics are generally considered (not just by Barad) to be different kinds of thing. Rowlands argues that they are the same kind of thing - and in fact, quantum mechanics can be seen to be an entirely logical and consistent extension of classical mechanics. So Newton was more profoundly right about the universe than is widely accepted. Through Rowland's ideas of broken symmetry, issues like superposition and entanglement emerge as logical consequences of the conservation of mass and energy, and the non-conservation of time and space.

So here's a tantalising question: could learning be seen as a product of broken symmetry and nilpotency? My first instinct with these kinds of questions is to ask it of something like learning but more objectively observable: music. Can music be the result of broken symmetry and nilpotency? There have been many studies of the Fibonacci sequence in music - notably in Bartok and Debussy. I strongly suspect the answer to this question is yes. So learning? What is the symmetry of understanding or thinking? Is there a way of answering this question? At a deep level, these are questions about information - and through taking them as such, methods can be devised for exploring them. The way Rowlands is able to explain the emergence of something from nothing immediately suggests a new approach to one of the fundamental questions in the theory of information - the "Symbol grounding problem" (see

A nilpotent broken symmetry of learning would have to entail a nilpotent broken symmetry of education and other social structures. Might they be investigated in the same way? What about a nilpotent broken symmetry of politics? (Is that dialectic?) Are these too questions about information?


Monday 22 May 2017

Sunday 21 May 2017

New technologies and Pathological Self-Organisation Dynamics

Because new communications technologies liberate individuals from the prevailing constraints of communication, it is often assumed that the new forces of self-organisation are benificent. Historical evidence for massive liberation of means of communication can tell a different story. Mechanisms of suppression, unforeseeable consequences of liberation - including incitement to revolt - revolution, war and institutional disestablishment follow the invention of printing; propaganda, anti-intellectualism, untramelled commercialism and totalitarianism followed telephone, cinema and TV; and the effects of unforseeable self-organising dynamics caused by the internet are only beginning to be apparent to us. It isn't just trolling, Trump and porn, its vulnerabilities that over-rationalised technical systems with no redundancy expose to malevolent forces that would seek their collapse (which we saw in the NHS last week).

What are these dynamics?

It's an obvious point that the invention of a new means of communication - be it printing or Twitter - presents new options for making utterances. Social systems are established on the basis of shared expectations about not only the nature of utterances (their content and meaning) but on the means by which they are made. The academic journal system, for example, relies on shared expectations for what an "academic" paper looks like, the process of review, citations, the community of scholars, etc. It has maintained these expectations supported by the institutional fabric of universities which continues to fetishise the journal, even when other media for intellectual debate and organisation become available. Journalism too relies on expectations of truth commensurate with the agency responsible for the journalism (some agencies are more trusted than others), and it again has resisted new self-organising dynamics presented by individuals who make different selections of their communication media: Trump.

But what happens then?

The introduction of new means of communication is the introduction of new uncertainties into the system. It increases entropy across institutional structures. What then appears to happen is a frantic dash to "bring things back under control". That is, reduce the entropy by quickly establishing new norms of practice.

Mark Carrigan spoke in some detail about this last week in a visit to my University. He criticised the increasing trend for universities to demand engagement with social media by academics as a criterion for "intellectual impact". What are the effects of this? The rich possibilities of the new media are attenuated to those few which amplify messages and "sell" intellectual positions. Carrigan rightly points out that this is to miss some of the really productive things that social media can do - not least in encouraging academics in the practice of keeping an open "commonplace book" (see

I'm wondering if there's a more general rule to be established relating to the increase in options for communicating, and its ensuing increase in uncertainty in communication. In the typical Shannon communication diagram (and indeed in Ashby's Law of Requisite Variety), there is no assumption that increasing the bandwidth of the channel affects either the sender or the receiver. The channel is there to illustrate the impact of noise on the communication, the things that the sender must do to counter noise, and the significance of having sufficient bandwidth to convey the complexity of the messages. Surplus bandwidth beyond what is necessary does not affect the sender.

But of course, it does. The communications sent from A to B are not just communications like Twitter messages "I am eating breakfast". They are also communications that "I am using Twitter". Indeed, the selection of the medium is also a selection of receiver (audience). This introduces a more complex dynamic which needs more than a blog post to unfold. But it means that as the means of communicating increases, so does the entropy of messages, and so does the levels of uncertainty in communicating systems.

This is what's blown up education, and it's what blew up the Catholic church in 1517. It's also what's enabled Trump's tweeting to move around conventional journalism and the political system as if it was the Maginot line. As the levels of uncertainty increase, the self-organisation dynamics lead to a solidification (almost a balkanisation - particularly in the case of Trump) of message-medium entities which become impervious to existing techniques for establishing rational dialogue. Government, because it cannot understand what is happening, is powerless to act to intervene in these self-organising processes (it should). Instead, it participates in the pathology.

We need a better theory and we need better analysis of what's happening.

Saturday 13 May 2017

The Evaluation of Adaptive Comparative Judgement as an Information Theoretical Problem

Adaptive Comparative Judgement is an assessment technique which has fascinated me for a long time (see Only recently, however, have I had the opportunity for trying it properly... and its application is not in education, but in medicine (higher education, for some reason, has been remarkably conservative in experimenting with the traditional methods of assessment!).

ACJ is a technique of pair-wise assessment where individuals are asked to compare two examples of work, or (in my case) two medical scans. They are asked a simple question: Which is better? Which is more pathological? etc. The combination of many judges and many judgements produces a ranking from which a grading can be produced. ACJ inverts the traditional educational model of grading work to produce a ranking; it ranks work to produce a grading.

In medicine, ACJ has fascinated the doctors I am working with, but it also creates some confusion because it is so different from traditional pharmacological assessment. In the traditional assessment of the efficacy of drugs (for example), data is examined to see if the administration of the drug is an independent variable in the production of the patient getting better (the dependent variable). The efficacy of the drug is assessed against its administration to a wide variety of patients (whose individual differences are usually averaged-out in the statistical evaluation). In other words, in traditional clinical evaluation, there is a linear correlation between
P(patient) + X(drug) = O(outcome)
where outcome and drug are shown to be correlated across a variety of patients (or cases).

ACJ is not linear, but circular. The outcome from ACJ is what is hoped to be a reliable ranking: that is, a ranking which accords with the  judgements of the best experts. But it is not ACJ which does this - it is not an independent variable. It is a technique for coordinating the judgements of many individuals. Technically, there is no need for more than one expert judge to produce a perfect ranking. But the burden of producing consistent expert rankings for any single judge (however good they are) will be too great, and consistency will suffer. ACJ works by enlisting many experts in making many judgements to reduce the burden on a single expert, and to coordinate differences between experts in a kind of automatic arbitration.

Simply because it cannot be seen to be an independent variable does not mean that its efficacy cannot be evaluated. There are no independent variables in education - but we have a pretty good idea of what does and doesn't work.

What is happening in the ACJ process is that a ranking is communicated through the presentation of pairs of images to the collective judgements of those using the system. The process of communication occurs within a number of constraints:

  1. The ability of individual judges to make effective judgements
  2. The ease with which an individual judgement might be made (i.e. the degree of difference between the pairs)
  3. The quality of presentation of each case (if they are images, for example, the quality is important)

An individual's inability to make the right judgement amounts to the introduction of "noise" into the ranking process. With too much "noise" the ranking will be inaccurate.

The ease of making a judgement depends of the degree of difference, which in turn can be a measure of the relative entropy between two examples. If they are identical, then the relative entropy will be the same. Equally, if images are the same, the mutual information between them will be high, calculated as:
H(a) + H(b) - H(ab)
If the features of each item to be compared can be identified, and each of those features belongs to a set i, then the entropy of each case can be measured simply as a value for H, across all the values of x in the set i:

The ability to make distinctions between the different features will depend partly on the quality of images. This may introduce uncertainty in the identification of values of x in i.

What ACJ does is it deals with issues 1 and 2. Issue 3 is more complex because it introduces uncertainty as to how features might be distinguished. ACJ deals with 1 and 2 in the same way as any information theoretical problem deals with problems of transmission: it introduces redundancy.

That means that the number of comparisons needed to be made by each judge is dependent on the quality and consistency of the of the ranking which is produced. This can be measured by determining the distance between the ranking produced by the system and the ranking determined by experts.  Ranking comparisons can be made for the system as a whole, or for each judge. Through this process, individual judges may be removed or others added. Equally, new images may be introduced whose ranking is known relative to the existing ranking.

The evaluation of ACJ is a control problem, not a problem of identifying it as an independent variable. Fundamentally, if ACJ doesn't work, it will not be capable of producing a stable and consistent ranking - and this will be seen empirically. That means that the complexity of the judges performing ranking will not be as great as the complexity of the ranking which is input. The complexity of the input will depend on the number of features in each image, and the distance between each pair of images.

In training, we can reduce this complexity by having clear delineations of complexity between different images. This is the pedagogical approach. As the reliability of the trainee's judgements increase, so the complexity of the images can be increased.

In the clinical evaluation of ACJ, it is possible to produce a stabilised ranking by:

  1. removing noise by removing unreliable judges
  2. increasing redundancy by increasing the number of comparisons
  3. introducing new (more reliable) judges
  4. focusing judgements on particular areas of the ranking (so particular examples) where inconsistencies remain
As a control problem, what matters are the levers of control within the system. 

It's worth thinking about what this would mean in the broader educational context. What if ACJ was a standard method of assessment? What if the judgement by peers was itself open to judgement? In what ways might a system like this assess the stability and reliability of the rankings that arise? In what ways might it seek to identify "semantic noise"? In what ways might such a system adjust itself so to manipulate its control levers to produce reliability and to gradually improve the performance of those whose judgements might not be so good? 

The really interesting thing is that everything in ACJ is a short transaction. But it is a transaction which is entirely flexible and not constrained by the absurd forces of timetables and cohorts of students.

Wednesday 10 May 2017

The Managerial Destruction of Universities... but what do we do about it?

As I arrived at the University of Highlands and Islands for a conference on the "porous university", there was a picket line outside the college. Lecturers were striking about a deal agreed with the Scottish Government to establish equal pay among teaching staff across Scotland which had been reneged on by management of colleges. The regional salary difference can be as much as £12,000, so this clearly matters to a lot of people. It was a good turnout for the picket line (always an indication of how much things matter) - similar to the one when the University of Bolton sacked their UCU rep and his wife which made the national press (

It is right to protest, and it is right to strike. But sadly, none of this seems to work very well. Bad management seems to be unassailable, and pay and conditions continually seem to get worse.

At UHI, the porous university event was an opportunity to take the temperature of the effects of over 5 years of managerial pathology in universities across the country. The collective existential cry of pain by the group was alarming. The optimism, hope, passion and faith which is the hallmark of any vocation, and was certainly the hallmark of most who worked in education, has evaporated. It's been replaced with fear and dejection. Of course, an outside observer might remark "well, you've still got jobs!" - but that's to miss the point. People might still be being paid (some of them) but something has been broken in the covenant between education and society which has destroyed the fabric of a core part of the personal identities of those who work in education. It's the same kind of breaking of covenant and breaking of spirit that might be associated with a once healthy marriage which is destroyed by a breakdown of trust: indeed, one of my former Bolton colleagues described the spirit of those working for the institution as being like "the victims of an abusive relationship".

Lots of people have written about this. Stefan Collini has just published his latest collection of essays on Universities, "Speaking of Universities", which I was reading on the way up to Scotland. It's beautifully written. But what good does it do?

In the perverse monetised world of universities, the writing and publishing (in a high ranking journal) of a critique of the education system is absorbed and rewarded by the monetised education system. In its own way, it's "impact" (something Collini is very critical of). Weirdly, those who peddle the critique inadvertently support the managerial game. The university neutralises and sanitises criticism of itself and parades it as evidence of its 'inclusivity' and the embrace of opposing views, all the time continuing to screw lecturers and students into the ground.

A good example of this is provided by the University of Bolton who have established what they call a "centre for opposition studies" ( There are no Molotov cocktails on the front page - but a picture of the house of commons. This is sanitised opposition - neutralised, harmless. The message is "Opposition is about controlled debate" rather than genuine anger and struggle. Fuck off! This isn't a progressive way forwards: it is the result of a cynical and endemic conservatism.

I wouldn't want to accuse Collini of conservativism in the same way - and yet the symptoms of conservativism are there in the way that they exist in the kind of radical "history man" characters that pepper critical discourse. The main features of this?
  • A failure to grasp the potential of technology for changing the dimensions of the debate
  • A failure to reconcile deep scholarship with new possibilities for human organisation
  • A failure to suggest any constructive way of redesigning the system
If I was to be cynical, I would say that this is because of what Collini himself admits as the "comfortable chair in Cambridge" being a safe place to chuck bricks at the system. It is not really wishing to disrupt itself to the point that the chair is less comfortable. 

The disruption and transformation of the system will not come from within it. It will come from outside. There's quite a cocktail brewing outside the institution. One of the highlights of the UHI conference was the presentation by Alex Dunedin of Alex's scholarly contribution was powerful, but he himself is an inspiration. He exemplifies insightful scholarship without having set a "formal" foot inside a university ever. His life has been a far richer tapestry of chaos and redemption than any professor I know. Meeting Alex, you realise that "knowledge is everywhere" really means something if you want to think. You might then be tempted to think "University is redundant". But that might be going too far. However, the corporate managerialist "nasty university" I think will not hold sway for ever. People like Alex burn far brighter. 

Another bright note: Just look at our tools! The thing is, we have to use them differently and creatively. I did my bit for this effort. I suggested to one group I was chairing that instead of holding up their flipchart paper with incomprehensible scribbles on it, and talking quickly in a way that few take in, they instead passed the phone over the paper and made a video drawing attention to the different things on their paper. So paper became a video. And it's great!

Monday 8 May 2017

Educational Technologists: Who are we? What is our discipline?

I am an educational technologist. What does that mean?

I think we are at a key moment in the history of technology in education and there is a radical choice facing us.

We can either:

  • Use technology to uphold and reinforce the traditional distinctions of the institution. This means VLEs, MOOCs, Turnitin, etc. This enslaves individual brains and isolates them; 
The consequences of this are well summarised by Ivan Illich:
"Observations of the sickening effect of programmed environments show that people in them become indolent, impotent, narcissistic and apolitical. The political process breaks down, because people cease to be able to govern themselves; they demand to be managed."
The alternative?
  • We use technology to organise multiple human brains in institutions and outside them so that many brains think as one brain.

To do the latter, we need to think about what our discipline really is. I am going to argue that our discipline is one that crosses boundaries: it is the discipline of study into how distinctions are made, and what they do.

For many academics, the educational technologist looks after the VLE or does cool videos on MOOCs. They also the person academics seek help from when the techno-administrative burden of modern universities becomes overwhelming: how do I submit my marks, get my students on this course, etc. For some academics, the educational technologist is a kind of secretary - the equivalent of the secretary who would have done the academic's typing in the 1970s when typing was not considered to be an academic activity. Some academics blame the educational technologist for the overwhelming techno-administrative nightmare that constitutes so much of academic life today.

Certainly there is a boundary between the academy and the educational technologist. Like all boundaries, it has two sides. On the one hand, the academy pushes back on the technologists: it generally treats them with suspicion (if not disdain) - partly because it (rightly) sees a threat to its current practices in the technology. The educational technologists have tried to push back on the academy to get it to change, embrace open practice, realise the potential of the technology, etc. Right now, the academy is winning and educational technologists are rather despondent, reduced to producing "learning content" in packages like "storyline" which often reproduce work which already exists on YouTube.

This situation has partly arisen because of a lack of identity among learning technologists. In trying to ape the academy, they established themselves in groups like ALT or AACE as a "discipline". What discipline? What do they read? In reality, there is not much reading going on. There is quite a lot of writing and citing... but (I'll upset a few people here) most of this stuff is unreadable and confused (I include my own papers in this). In the defence of the educational technologist, this is partly because what they are really trying to talk about is so very difficult.

I believe we should admit our confusion and start from there. Then we realise that what we are doing is making distinctions. We make distinctions about learning like this:

or we might make cybernetic distinctions like this:
What is this? There are lines and boxes (or circles). 

What are the lines and boxes doing?

What are the lines around the boxes doing? (these are the most interesting)

Scientific communication is about coordinating distinctions. In coordinating distinctions, we also coordinate expectations. The academy, in its various disciplines, upholds its distinctions. However, as physicist David Bohm realised, scientists don't really communicate.

For Bohm, dialogue is a way to exploring the different distinctions we make. The demand of Bohmian scientific dialogue is to continually recalibrate distinctions in the light of the distinctions of others. More importantly, it is to embrace uncertainty  as the operating scientific principle.

Scientific Dialogue is about communicating uncertainty.

If we are recalibrating, then we are continually drawing and redrawing our boundaries. But this process is controlled by more fundamental organising principles which underlie the processes of a viable organism. It's perhaps a bit like this:

Here we see the death of boundaries, and the reorganisation of the organism. Much of what goes on here remains a mystery to biologists. Some are exploring the frontiers, however. Deep down, it seems to be about information...
or ecology:

Information, semiotics, ecology all concern the making of distinctions. There are a variety of mathematical approaches which underpin this. In fact, Charles Peirce, founder of semiotics, was also the founder of a mathematical approach to studying distinctions.  This is Peirce's attempts to fathom out a logic of distinctions:

And this is the very closely-related work of Cybernetician George Spencer-Brown:

When we talk about education, or technology, or biology... or anything... we are making distinctions.

A distinction has an inside and an outside. We usually forget the outside because we want to communicate the inside. We only know the outside of the distinction by listening.

It is the same in physics - particularly Quantum physics. 

And this is becoming important for the future of computing. Quantum computers are programmed using a kind of "musical score" - like this from the IBM Quantum Experience computer:

So what does all this mean?

Well, it means that science has to embrace uncertainty as an operating principle. Yet science in the academy is still tied to traditional ways of communicating. The academic paper does not communicate uncertainty.

To communicate uncertainty, we need to listen to the outside of our distinctions.

Our scientific institutions need to reconfigure their practices so that the distinction between education and society is realigned to progress society's scientific knowledge.

It is not to say that distinction between education and society should be removed. But that a discipline of examining ecologies of distinctions is essential for a new science of uncertainty to prosper.

It also means that new media should be deployed to communicate uncertainty and understanding on a much wider basis than can be achieved with academic papers. Where we have struggled is in being able to listen to large numbers of people in a coherent way.

This is one way in which we might do this...

It involves doctors and learners using Adaptive Comparative Judgement tools as a means of making diagnoses of retinal scans in examining Diabetic Retinopathy. Adaptive Comparative Judgement is a technique of getting lots of people to make simple comparisons in order to arrive at a ranking of those scans, with the most pathological at one end, and the normal at the other. In addition to this, there is a simple way in which learners can be trained to do this themselves:

Other technological means of getting many brains to act as one brain include BitCoin and the BlockChain that sits behind it...

The MIT Digital Certificates project is exploring ways in which a blockchain might decentralise education...

What about the distinctions between education and society? How might they be better managed?

What about the distinctions between critique and functionalism and phenomenology in education?

Well, the critique only exists because it has something to push against. The thing it pushed against exists partly because of the existence of the critique (and indeed, it embraces the critique!)... We have a knot.

We should understand how it works....

Saturday 6 May 2017

@siobhandavies and Double Description at @WhitworthArt ... and reflections on Music and Education

Living around the corner from the Whitworth Art gallery means that I often make serendipitous discoveries. I popped into the gallery on my way into the city centre centre this morning and found Siobhan Davies and Helka Kaski doing this as part of their work "Material / Rearranged / to / be" - a dance work inspired by photographs from the Warburg Institute collection:

There's something very cybernetic about what they are doing - indeed, the whole installation's emphasis on action and reflection is very similar to the theme of the American Society for Cybernetics conference in 2013 (see This is rather better than we managed in Bolton!

If the cybernetician Gregory Bateson wasn't the first thinker to have considered the importance of 'multiple descriptions of the world' - particularly in the distinction between connotation and denotation, he certainly thought more analytically about it than anyone else. We live with multiple descriptions of the same thing. In cybernetic information-theoretic terms, we are immersed in redundancy. Why does Siobhan Davies have two dancers mimicking each other? Because the dual presentation is more powerful - perhaps (and this is tricky) more real  - than the single description.

In a world of austerity, what gets stripped away is redundancy. We streamline, introduce efficiencies, 'de-layer' (a horrible phrase that was used to sack a load of people in my former university), get rid of the dead wood (blind to the fact that the really dead wood is usually making the decisions!). The arts are fundamentally about generating multiple descriptions - redundancies. It's hardly surprising that governments see them as surplus to requirements under austerity.  But it spells a slow death of civilisation.

Warren McCulloch - one of the founders of Cybernetics and the inventor of Neural Networks - took particular interest in naval history as well as brains. He was fascinated by how Nelson organised his navy. Of course, there were the flag signals from ship to ship. But what if it was foggy? Nelson ensured that each captain of each ship was trained to act on their own initiative understanding the heuristics of how to effectively self-organise even if they couldn't communicate with other ships. McCulloch called this Redundancy of Potential Command, pointing out that the ultra-plastic brain appeared to work on the same principles. This was not command and control - it was generating sufficient redundancy so as to facilitate the emergence of effective self-organisation. In effect, Nelson organised the many brains of his naval captains to act as one brain.

That's what Davies does here: two brains act as one brain.

This also happens in music... but it hardly ever happens in education. In education, each brain is examined as if it is separate from every other brain. The stupidity of this is becoming more and more apparent and the desperate attempts of the education system to scale-up to meet the needs of society stretch its traditional ways of operating to breaking point. Yet it doesn't have to be like this.

In a project with the China Medical Association we are exploring how technologies might facilitate the making of collective judgements about medical conditions. Using an assessment technology called "Adaptive Comparative Judgement" each brain is asked to make simple comparisons like "which of these scans displays a condition in more urgent need of treatment?". With enough people making the judgements and each person making enough judgements, many brains act as one brain in producing a ranking of the various scans which can then be used to prioritise treatment. In practice, it feels like a kind of orchestration. It is the most intelligent use of technology in education I have ever been involved with.

Orchestration is of course a musical term. Musicians are traditionally orchestrated using a score, but there is much more going on. The fine degrees of self-coordination between players is heuristic at a deep level (much like Davies's dance). The performance and the document which describes the manner of the performance are all descriptions of the same thing too. It's redundancy all the way down.

I was mindful of this as I put together this video of my score for a piece I wrote 10 years ago called "The Governor's Veil" with a recording of its performance. In video, with the score following the sound, the double description and the redundancies become much more noticeable.


Thursday 4 May 2017

Teaching, Music and the life of Emotions: a response to distinctions between thinking and knowing

Music makes tangible aspects of emotional life which underpin conscious processes of being – within which one might include learning, thinking, reflecting, teaching, acting, and so on. In education, we place so much emphasis on knowledge because knowledge can be turned into an object. People make absurd and indefensible distinctions between “thinking” and “knowing”, “reflecting” and “acting”, “creating” and “copying” partly because there is no framework for thinking beyond objects; equally nobody challenges them because they are only left with feelings of doubt or alienation that they can barely articulate. The emotional life cannot be objectified: it presents itself “through a glass, darkly”. Only the arts, and particularly music succeeds in “painting the glass”.

In Suzanne Langer’s view, composers and performers are epistemologists of the emotions: in their abstract sonic constructions they articulate what they know about what it is to feel. What they construct is a passage of time over which, they hope, the feelings of listeners and performers will somehow be coordinated to the point that one person might look at another and know that they are feeling the same thing. It is a coordination of the inner world of the many; a moment where the many brains think as one brain. This is the most fundamental essence of social existence.

We each have something of the composer in us in the sense that we (sometimes) express our feelings. But composers do more than this. They articulate what they know about what it is to feel, and their expression is a set of instructions for the reproduction of a temporal form. In mathematics, this kind of expression through a set of instructions is called “E-Prime” ( It’s a bit like the kind of games that people sometimes play: “think of a number between 1 and 10; double it; divide by …”. But similar in kind though such games are, they have nothing of the sophistication of music.

Great teachers do something similar to composers. To begin with, they work with in an immensely complex domain. Broadly, the teacher’s job is to express their understanding of a subject. But when we inquire as to what it is to "express understanding", we are left with the same thing as in music: it is to express what it feels like to know their subject. In great hands, the subject they express and the feelings they reveal are coordinated to the point that what is conveyed is their knowledge of what it is to feel knowing what they do.

Talking about emotions is difficult. It is much easier to talk of knowledge, or to talk about creativity, or thinking in loose rhetorical terms, avoiding any specifics. It is easy to point to pictures of brain scans and make assertions about correlations between neural structures and experiences - which somehow takes the soul of it and gives license to bullies to tell everyone else how to teach based on the brutal "evidence" of neuroscience. Any child will know they are lying. 

We can talk about emotion more intelligently. Wise heads in the past - some from cybernetics - made important progress in this. Bateson's concept of Bio-entropy is, I think the closest description we have of what happens (I had a great chat to Ambj√∂rn Naeve about this yesterday). We should start with music: it is the essence of connotation. It presents the richness of the interaction of multiple descriptions of the world which was at the heart of Bateson's message. It is ecological, and it's ecology is so explicitly ruled by redundancies. And perhaps the most hopeful sign is that the very idea of counterpoint is beginning to take centre stage not just in the way that we analyse ecologies, but in the way that the quantum physicists are programming their remarkable computers. 

Tuesday 2 May 2017

Relative Entropy in the Analysis of Educational Video

Relative entropy is a calculation much used by quantum physicists to measure degrees of entanglement between subatomic particles. Its formal form is the Kullback-Leibler equation:
It isn't as scary as it looks (information theory rarely is!) - it's basically a metric of distance between a probability distribution P and a distribution Q. If two subatomic particles are entangled (in other words, their behaviour will be coordinated), then the distance between the probability distribution of their behaviour (their expected states) will be zero. 

That Quantum physics tells us something we already know about nature and social life is reflected in the various fluffy uses of "entanglement" (e.g. Latour, Barad, etc) in the social science literature. But this is rarely done with any real insight into what it actually means. It basically seems to say "it's complex, init!".

I'm grateful to Loet Leydesdorff for pointing me in the direction of Kullback-Leibler after I requested some degree of measurement for the synergy between different entropy values for different variables. My inspiration for asking this was in thinking about music. Music presents many descriptions to us: rhythm, melody, harmony, timbre, dynamics, etc. Something happens in music when the change in any of these dimensions is accompanied with a similar change in another dimension: so the rhythm changes with melody, for example. At these moment, we often detect some new idea or motif - it's at these moments that things grow. Basically, I'm drawing on a musical experiment I did a few years ago:

The same kind of technique can be applied to the analysis of video. Like music, video presents many different descriptions of things. 

I've been looking at Vi Hart's wonderful video on Fibonacci numbers and spirals. 

There are a rich range of descriptions contained in this video, and I was wondering how the probability distribution of each description relates to the distribution of other descriptions. So I've been doing some analysis, using Kinovea for video analysis, Puredata for analysis of the pitch and rhythm of speech, and using YouTube to produce a transcript of the video from which I can do some entropy calculations. 

After munching on the data and converting it into a form I can deal with, I've imported it all into a Jupyter notebook using Python's Panda dataframes, queried it using sql (using the pysqldf library), and done entropy calculations on the whole thing. 

My code is still a bit rubbish, but it's beginning to tell me things. For example, I can look at the changes in entropy of the transcribed text over window periods as the video progresses. So here is a list of the first 20 seconds in 5-second chunks:

0-5: -0.25206419825534054
5-10: -0.24292065819269668
10-15: -0.3868528072345415
15-20: -0.3333333333333334

Now I can do the same for the 'events' which occur in the video. Here I was a bit stuck to describe things, so that when she drew a spiral, I wrote "spiral". She draws a lot of spirals, so the entropy is uninteresting...

0-5: 0
5-10: 0
10-15: 0
15-20: 0

What? Well, maybe there's an error in my coding - I might go back and add some more detail to my analysis. She keeps on drawing spirals, and therefore the entropy is 0.

What about the pitch of her voice? That's the interesting one... I used PD to do this using fiddle~ (I first played with Fiddle~ in PD years ago in improvisation: - it just goes to show the importance of documenting everything that we do!)
Now the pitches are more interesting than the video events:

0-5: -0.4533324434922346
5-10: -0.366932572935196
15-20: -0.6913119495075026

Is there a correlation there? Well, the range of pitches in the voice increases with the variety of vocabulary used in the text. Perhaps that isn't surprising. But it's not surprising for a reason which has everything to do with relative entropy: the entropy of the use of words is likely to be coupled with the pitch, because with more words, there are more syllables and potentially more opportunities for variety in the pitch. Over a more extended period of time, and taking into account that events do occur in the video which increase its entropy, we can start to examine the relationship between the different aspects of what happens. 

The fact that there is a kind of stable ritual of drawing spirals which runs alongside an increase in the variety of words spoken and pitches used suggests that the actions in the video are a kind of 'accompaniment' to the words that are spoken. To begin with, the ritual of drawing spirals is a kind a 'drone' against which other things happen. As in music, the drone maintains the coherence of the piece. 

Image if she started differently: if she started by doing the maths straight away.. then it would have a very different dynamic. The entropies would also be very different.