Thursday, 15 November 2018

Stafford Beer's Critical Holism in Education

I gave a presentation about how Stafford Beer's work relates to education to a small group of people from the education faculty at Cambridge last week. I wanted to avoid presenting Beer's work as a kind of fait-accompli, where the Viable System Model (VSM), or Syntegration is the answer (I think this kind of evangelism is very off-putting). But his work is mind-blowing, and if he didn't "have the answer", he certainly had an important way of asking practical questions which is sorely missing from anything in the educational discourse today.

The problems - the reasons why the VSM or Syntegration isn't the answer - or indeed, any other cybernetic theory cannot provide a full answer - are that fundamental problems of time, meaning, emergence, non-ergodicity and coherence haven't been resolved in any of the systems sciences. This is why, for example, the question of agency in cybernetic descriptions is such a problematic question: "where's the person? They're in the recursions", which leads to a slight air of dissatisfaction. We can work to improve this situation - but this will only happen with a critical engagement with cybernetics.

This is not to take anything away from Beer. He nailed what he was doing and what cybernetics is really about: "Cybernetics is about holism". Yes. There are of course many many definitions of cybernetics, which describe it as "ways of thinking", or "ways of thinking about ways of thinking", "the art and science of defensible metaphors" (!), or "the science of effective organisation" - it all gets rather philosophical, giving a newcomer the feeling that they've arrived in some kind of cult. But, in the end, what unites them all is that they all deal with wholes. They all run counter to reductionism.

Holism has a bad name. It is rather closely associated with cults, with theories of everything. But this isn't what Beer meant. He was after (and indeed possessed) a science of holism (notwithstanding the problems raised above). If it is wholes we have to grapple with, and not parts, then we need to know how wholes work - and they are not simple things, but once opened out, they reveal a structure. It is this structure which can be studied and experimented with.

The structure unfolds because whatever whole is considered contains things which cannot be decided. I have recently preferred simply to talk about uncertainty. The point is that this uncertainty has to be dealt with, and by definition, it cannot be dealt with within the "whole". So any whole requires a metasystem - something which sits outside the whole and mops up the uncertainty. It does it, often, by imposing categories for dealing with the uncertainty. It's the metasystem where the reductionism goes on!

Beer knew that there were good and bad ways in which the relationship between a whole and a metasystem could work. If education is seen to be a "whole", then the metasystem has to mop up things like uncertainties over teacher and student "performance": it invents categories and metrics to measure teaching and learning. It even ties some of these metrics to the pay or job security of teachers. More recently it deploys technologies to reinforce these metrics. What happens? "explosive complexification".

Why do these uncertainties arise in the first place? What is it about the whole which invites pathological metasystemic regulation? There's a simple answer to this. It is the hierarchical structures of organisation which education adopts. These structures themselves are very poor at mopping up their own uncertainty: hierarchies attenuate complexity from their bottom to their top, and from the environment to each individual. The only mechanism they have for managing uncertainty is authoritarianism, and this eventually leads to collapse.

What is required are forms of organisation which manage their uncertainty effectively. In education, the most effective way any individual - whether teacher or learner - can manage their uncertainty is to talk to others: "What do you think?" The best form of educational organisation is one which creates the conditions for conversation. Here, Beer's holism suggests that the way to do this is to disrupt the metasystems of each individual. This is really what he attempted with his Syntegration technique. It's what Von Foerster articulated when he spoke about education's role in learning to ask "legitimate questions", or questions to which nobody knows the answer:

  1. “Education is neither a right nor a privilege: it is a necessity.” 
  1. “Education is learning to ask legitimate questions.” 

A society who has made these two discoveries will ultimately be able to discover the third and most utopian one:
  1. “A is better off when B is better off.” (Von Foerster, Understanding Understanding, p209)
Understanding how Von Foerster gets from 2 to 3 is core to appreciating the power of Beer's Critical Holism. 

Sunday, 28 October 2018

Transforming Education with Science and Creativity

I've had an amazing three weeks in Russia at the Far Eastern Federal University at Vladivostok. I visited in March to deliver training to 20 teachers for a new course which myself and a small team devised called "Global Scientific Dialogue". The plan was to get those 20 teachers to deliver a similar programme to 200 students in October. It was a daunting task: working with teachers in concert with delivering an innovative course to students. The teacher development was very successful, and I was quite euphoric when I came back in March - but well aware that dealing with 200 students was a different kettle of fish. Now, I can say that the whole thing looks like it has been a big success, with some important implications for how we should approach educational development in institutions.

I'm pleased that most of the students (not quite all - but nearly!) really enjoyed the course, and many have expressed a sense of personal transformation through the experience (similar to the teachers in March). But more importantly, the teachers who I met in March have all been extremely positive about their experiences of teaching it - this has been transformative for them too. This is despite numerous technical issues, which bedevil any initiative of this kind, but which somehow has not dented the underlying philosophy or creative approach.

It makes me think that we need to look at the teacher-learner relationship as a "whole system" and make interventions with the whole system. Global Scientific Dialogue was really a cybernetic intervention: conversation drove the whole thing, supported by technology, but importantly, this was not the kind of technologically-supported conversation that dominates thinking about educational technology today (threaded discussions, etc). More importantly, the cybernetics that drove it was also part of the content (although I didn't labour the point!)

A whole system intervention is obviously not an intervention in the "parts" of teaching and learning which we usually attempt with silly things like "curriculum review", "teacher development" or what goes by the name of "technology-enhanced learning". I think there is no point in trying to develop teaching practice (or indeed curriculum) in isolation from the participation of students. Nor is there any point in trying to "bully" teachers into getting the best approval ratings from their students, or using the "latest technology". All of this simply depresses people. What we've done in Vladivostok is different: it was an intervention with everyone - teachers, learners and managers. It was an attempt to transform relationships and create the conditions for conversation. It worked.

How did we bring together teachers from management, economics, biology and tourism together to work on a single module which students could also participate in? Simply by focusing the educational content of the course on current scientific developments and questions "to which nobody currently knows the answer". So students and teachers passed through sessions focusing on "wicked problems", on current developments in quantum mechanics (and quantum biology), in AI, in social software, in intersubjectivity and interdisciplinarity. With there being no answer to any of this stuff, students and staff were encouraged to engage in creative activities. We used all sorts of things, from Mary Flannagan's brilliant "grow a game", to drama, music, art, data analysis and product innovation. We also had a special day where expert practitioners from biology, soil science, drama, music, genetics and many other disciplines, could be freely consulted by the students. This day was particularly successful because it opened the eyes of students too often imprisoned by subjects like management or economics which lose sight of the technological and scientific developments which fundamentally affect the context within which any management is conducted. This is a nice post written in English by one of the students the experts' session:

As in March, teaching activities were coordinated with a kind of video lesson plan - which worked very well in coordinating large numbers of students doing the same kinds of activities coordinated by different teachers. We also supplied the students with some comparative judgement software and a range of texts which were assembled around the different themes of the course. The software asked the students to simply say which of two texts (chosen at random) were most interesting to them: it was really an activity designed to encourage the student to read and think.

Assessment was a combination of this comparison activity and the presentation of a "patchwork text" which produced highly individualised work in presentation sessions which were some of the most uplifting things I have seen in education. Not all students liked it ("it was too much like kindergarten," was a common comment from those who didn't), but it seems the vast majority found the experience of being focused on collaborative activity with people they didn't know before was truly liberating and built a foundation for future collaboration.

I've been incredibly lucky in Russia: not simply that immediate colleagues have run with crazy ideas, but that we had powerful backing from the senior management in the school, who have not just been supportive, but have taken an active interest in the development of the course. Russia has yet to feel the full force of the ravages of marketisation (although there's plenty of it, of course). But it doesn't seem to have been paralysed by reductionist metrics in the way that many UK institutions seem to have become.

That's a worry for the UK HE sector. Personally, as someone who simply wants to make education better, I don't think it matters where positive interventions occur. Young people of all countries are the future of the world, and I am both deeply impressed and grateful for the wonderful work of colleagues and students at the Far Eastern Federal University. 

Thursday, 20 September 2018

Are Technological Solutions Possible for the Human Problem of Education? Reflections on Stiglitz's thoughts on AI

In the final dialogue between physicist David Bohm and spiritual guru, Jiddhu Krishnamurti, Krishnamurti focuses on how "human problems" can be solved, why it is that they persist, and whether humanity could ever live without any problems at all. He says:
“I am asking in this dialogue whether it is possible to have no human problems at all - only technological problems, which can be solved. But human problems seem insoluble. Is it because of our education, our deep-rooted traditions, that we accept things as they are?”
After some considerable soul-searching Bohm responds
“I wonder if we should even call these things problems, you see. A problem would be something that is reasonably solvable. If you put the problem of how to achieve a certain result, then that presupposes that you can reasonably find a way to do it technologically. But psychologically, the problem cannot be looked at in that way; to propose a result you have to achieve, and then
find a way to do it.”
Bohm’s insight highlights the fundamental dichotomy of educational technology. Technology in education is approached - by institutions, teachers, and learners - as a solution to a human problem. Yet the human problem of education is not one for which the result one wants to achieve can be specified in a simple way such that technology can be proposed as a solution. Most commonly, attempts to solve human problems in this way simply creates a deeper problem, and it is this to which Krishnamurti is drawing attention. Krishnamurti’s suspicion that education might be a cause of human problems - that education attempts to solve human problems through technological intervention - would suggest that some blame for the state of the world must sit at education’s feet.

Education is a human problem to which institutions attempt to find solutions. There are many dimensions to the human problem of education: the problem of making distinctions, the problem of conversation, the problem of institutional organisation, the problem of science and knowledge, the problem of openness, the problem of collective decision and judgement, the problem of economics, and the problem of research into education itself. The human problem of education is part of all these problems. The extent to which education seems to be an exacerbating factor in the production of these problems may partly be due to the fact that we do not possess a metalanguage for human problems: a way of talking about the connectedness of human problems.

And yet I wonder if we saw human problems from a different perspective, we might be able to look upon our situation in an organisational way which might help us to find a better way of living with the technologies which, so often, contribute to our problems. What if we had a meta-language of human problems?

This week Joseph Stiglitz argued that Artificial Intelligence was the world's greatest threat (see, and a force which would lead the world to fascism. In response, what is needed, he argues, is a massive-scale amplification of education, to empower human critical faculties in being able to address the challenge of automated judgements and corporate surveillance.

There's some essence of truth in Stiglitz's message: the threat to society lies in the imbalance between machines and humans - but the temptation is to blame the machines themselves (Stiglitz seems to do this). In the end, it is not machines that replace jobs with automation; it is human institutions - businesses, corporations, institutions and their leaders - which do this. They do it, I believe, because they react to increased environmental uncertainty, which itself is created by technology.  The answer to address the imbalance between humans and machines is not to empower the institutions! The machines - and particularly AI - is powerful because it is organised in a different way to humans. It is a heterarchy (a word coined by the founder of machine learning, Warren McCulloch), whereas human institutions are hierarchies. The root of the human problem is institutions misunderstanding the nature of the threat from their environment and mis-adapting so that they exacerbate the problem. This  appears to be Stiglitz's solution unfortunately.

The core issue is that there are ways of organising human institutions which are not hierarchical. This would be to organise so as to manage the uncertainties created by technology, rather than seek to defend existing institutional structures against them (and in the process make it worse).

What is needed is a meta-language of human problems.  There are ways in which humans can look at their problems and address new ways of organising themselves, sometimes using technologies. In all crises in human history we see precisely this kind of movement - eventually... after humans have been sufficiently stupid in attempting simple "technological solutions" to problems that things get so bad that no other options appear to be available. If I am worried about the state of the world now, it is that I don't think really reached "Max Stupidity" yet.

Tuesday, 4 September 2018

What is it about mind which imputes the agency of a creator? What is it about nature which gives rise to a mind that does this?

According to constructivism, mind wouldn't work without some kind of stochastic process - there has to be some randomness (Bateson says this). That means that consciousness and life itself emerges from accident and what we understand as self-organising processes. One of the problems with this view is that it gives a very poor account of time. Obviously, accidents happen in time, and self-organisation happens in time, but time is taken as a given: it is not accounted for in the system.

Physics sees time, space, mass and energy as a kind of unity. Laws of conservation operate as if viewed from one angle, what we see is mass, viewed from another, its energy; from one angle its space, from another its time. But physics also understands that not all things are conserved. Mass is conserved, time isn't. Charge is conserved but space isn't. We understand these things in terms of those things which remain the same and those things which don't; between identity and non-identity.

Bohm regarded time as being "enfolded" in the laws of nature - what he saw as the "implicate order". What nature then presents to us is not a "process" operating over time, but a multi-dimensional structure which reveals time. What is meant by "structure" is an ordering of symmetry and asymmetry, and this order manifests itself throughout both nature and mind. It is, as Bohm susggested, holographic: within any part of consciousness or experience, there are symmetries that relate to the whole.

I'm currently writing about music. Music's diachronic symmetries and its synchronic symmetries are related. All that separates them is that the time dimension is magnified in the former, and not in the latter. When we talk about learning "processes" it may be the same - particularly so for learning conversations: what occurs over time is related to the structure at any single point. These dimensions: time, space, matter, energy, rotate into one another.

This is important whenever we feel compelled to construct stories about "origins". The structure of the story which unfolds in time is related to a kind of ordinal structure of categories which are used in the story. Religious stories and scientific stories about origins are the same in this regard. Science, however, looks for deeper reinforcement of the structure of its stories from empirical observation. In terms of evolutionary narratives this is difficult because nobody really sees evolution in action: all that is seen are the homologies between natural phenomena and the measurement of their historical emergence. But the scientific search for resonant patterns needn't stop with evolution and the fossil record. It can look everywhere - into art, education, cells, the universe and subatomic particles.

Science advances by closing-in on the coherence of pattern between mind and nature. Eventually I think we will understand that our very desire to pursue science and get deeper coherence is in itself part of the pattern.

Mind is driven to impute the agency of a creator because it is driven towards coherence with the way nature works. Nature works holographically, enfolding all the elements of human experience in a structure which is incorporated into physiology of consciousness, and the operation of mind itself.

Constructivism's overlooking of time leads to error and the assumption of accident. I doubt there are accidents...

Sunday, 2 September 2018

Beyond Left and Right: What would a safe and fair society look like with its Macbeths and Shylocks?

These are not normal times. It's hard to compose anything coherent to say. Every day I find myself feeling astonished by Trump - the cutting of funding to the Palestinians is just the latest horror. But it's on top of so many other horrors, we have become numb.

Brexit and the EU is really too confusing. How is a rational position even possible? No Brexit? Well, so you like being run by international bankers and corporations, do you? Isn't it all their fault in the first place? Brexit? Well, you'd like Boris Johnson for Prime Minister would you, and the country to turn into a tax haven? To hell with the lot of them.

Have the Whitehall mandarins made the best of things in coming up with a proposal? Would anyone else be able to handle the situation much better? I doubt it... just a bit hair-splitting. The thing is impossible. And nobody talks about what anyone wants at the end of whatever it is they are campaigning for. UKIP argued "Get out of the EU!"... ok, but what then? The government argued "Stay in the EU!"... ok, but what for? ("because leaving would be too disruptive" isn't a good answer)

I'd like a fairer society. I'd like people to feel safe for their whole lives, and have the confidence that their children weren't going to sink into the gutter because of the machinations of global finance. I'd like to feel confident that weather extremes weren't going to cause floods in the UK and war in the other parts of the world. I'd like everyone to feel open and welcoming to everyone else, and not to perceive others as a threat. I'd like people to be able to talk to each other about important things, and not contain anxieties in their own heads, where they are driven to mental illness and sometimes suicide.

So many of our problems stem from the fact that nobody feels safe any more. The guarantees of safety which were set up after the second world war have now been completely dismantled. Lose your job? You're pretty much on your own. The rich buy more houses than they need because they want their children to feel safe. Bosses increase their salaries and pensions to the hilt because they fear loss of security in old age. Yet, in the end, as Keynes said, "we're all dead".

The question "Is a world of global safety possible?" has been troubling me. I've been thinking about a more nuanced version: "Is a world where Shakespeare isn't true possible?" That question I am really struggling with.

Shakespeare didn't talk in terms of left and right. He understood the machinery of the human soul to such an extent that the play of human passion could be presented in a way which seems eternal. How does he do it? I suspect because he understood something about the universe: that patterns are written all the way through nature. That nature, as David Bohm would put it, is holographic.

Our political positions are abstract codifications of the human passions. What motivates us, what we are driven towards - love, truth, money, sex, glory, beauty, etc - becomes "political" at some level. But in becoming political, a lot gets left out. This is, I think, one of the reasons why there are so many financial and sex scandals in politics: the codification isn't real. The Left talk of "solidarity" - all the time knowing that "solidarity" is an abstraction, and that what is left out is what internal party politics is about (this is what is happening with Corbyn at the moment). The right talk of "profit" or "freedom of choice" - all the time knowing that nobody is really free to choose anything: again these are abstractions, rather like the "Brexit" which has provided the backdrop for the most extraordinarily febrile in-fighting in the Tories.

So what would a future safe society look like with the Macbeths and Shylocks who will inevitably inhabit it? That's the question. 

Tuesday, 28 August 2018

University Closures and the coming Tsunami of Today's Students' Children

A number of commentators are predicting university closures on the back of significant realignments in enrolment to universities across the sector ( This year's A level students seem to have been able to select better (which means "higher ranking"... which may not mean very much!) institutions than their grades would have allowed in years past. Consequently, the middle and lower-ranking institutions who would have recruited those students have lost out, and this year, the loss has been big.

Universities are now competing businesses, and some of the competition has been rather unedifying (particularly the Essex University tweet against Leeds Beckett: These are competing businesses all making promises to students that they cannot possibly keep: statistics about average salaries, graduate premium, etc are made with all the confidence of a drunk Brexit commentator. Nobody knows what the future looks like, and a fast-changing labour situation promises little of the institutionally-guaranteed security of the past, whatever one's educational background is.

So, a considerable proportion of this year's intake into universities which trade on high reputations but with less experience of teaching mixed-ability classes, will end up disappointed with the performance of their educational investment.

Will they be more disappointed in Birmingham, Bolton or Buckingham? Who knows - it really depends on what happens in the world, whether they acquire any security in their lives, whether they see any difference between what they gain and what others who didn't go gain. But in an important way, it doesn't matter where they go. The effects will be the same, and they will hit all universities in the future.

The problem is not with this generation of students. It is with their children. In 25 years, will this generation of students be sufficiently satisfied with the actual return on investment of their degrees that they will recommend their children go to university? And, will they recommend a life of debt to their 18 year olds, when they could well be still repaying the debt they accrued all those years ago?

I think the likely answer is no. The implications are alarming, and although my generation will be retired (but our pensions may be in a far more precarious state than that which sparked the recent strike), we will witness this as grandparents, and see a society which has lost a vital part of the fabric which maintains civil society: a place where society goes to think.

When we look back from 25 years in the future, what will we conclude about the cause of the collapse of HE? I think we will see that setting institutions to compete against one another on the basis of market demands and false promises was a kind of cancer. It wasn't the poor performance of any one institution that caused the problem. All institutions produced the problem together by failing to work together, by failing to tell the truth to students, but instead feed them marketing nonsense,  and failing to change education into something that fitted the age we were living in. Consequently we ended up with a technological working and living environment that operated with the fleet-footedness of the conscious mind, whilst education simply tried to devise ever new "curricula" which maintained a stodgy Hogwarts feel whose Disneyfied impracticality, lack of fit to daily life, and sheer expense eventually alienated the population.

I'm not sure that a major collapse of HE isn't inevitable in 25 to 30 years. The urgent question for this generation is how to create a replacement: somewhere where society's thinking can still go on. Maybe it isn't helpful to call it a "university".

Wednesday, 22 August 2018

Marion Milner's Personal Learning Environment

Marion Milner's "A Life of One's Own" is a beautiful book documenting her self-analysis on the circumstances within which she is happy, over a period of 7 years. At the end of the book, she reflects on the relationship between introspection and science:

"During my explorations I had also discovered something about science. I had set out by using the scientific method of observations, to find out what made me happy and then found that it had led me beyond the range of science. For in observing what made me happy I had found something which could not be communicated, something which was an essentially private affair; whilst science, so they say, deals only with ‘whatever can be passed on from one social being to another’. 
I realised then that at one stage I had become disgusted with science for not giving me what was not in its power to give. One warm summer evening, steaming out of London on a weekend train, I caught a glimpse through the window of a fat old woman in apron and rolled sleeves surveying her grimy back garden from the door-step. At once I was seized with an impulse to know more about her, and then began wondering what the scientists who deal with different phases of social life could tell me. I had even got as far as resolving to read some books on sociology, when it suddenly dawned on me that that was not at all what I wanted: I wanted to know that woman as a person, a unique individual, not as a specimen. It was only later, when I read that science is concerned not with individuals but only with specimens, that I began to realise why I could not find what I wanted in science. For it seemed to be just the unique qualities of particular experiences which I wanted. When I considered anything that happened to me in terms of science, I had to split it up into parts and think only of those qualities which it had in common with others, as it lost that unique quality which it had as a whole, the 'thing-in- itselfness' which had so delighted me in wide perceiving. I wondered whether this was why sometimes, when I came out from reading in a scientific library, the first whiff of hot pavement, the glimpse of a mangy terrier grimed with soot, would make me feel as though I had risen from the dead. For this `dogness’ of the dog and `stoneness’ of the pavement which I loved so, were simply non-existent in abstract `dog’ and abstract `pavement’. It seemed to me that science could only talk about things and that discussion broke up and killed some essential quality of experience. Science was perhaps a system of charts for finding the way, but no amount of chart-studying would give to inlandsmen the smell of a wind from the sea."
 This identification of the map-territory problem which Korzybski famously identified, leads her on to a deeper reflection about learning and reading:
"I had come to the firm conclusion that reading must come after one had learnt the tricks for observing one’s mind, not before; since if it come before it is only too easy to accept technical concepts intellectually and use them as jargon, not as instrument for the real understanding of experience."
I am always telling students this! But then there's an extraordinary intuition about consciousness which resonates very strong with what science (particularly quantum mechanics) is telling us today... that consciousness has cellular origins:
"I had learnt that if I kept my thoughts still enough and looked beneath them, then I might sometimes know what was the real need, feel it like a child leaping in the womb, though so remotely that I might easily miss when over-busy with purposes. Really, then, I had found that there was an intuitive sense of how to live. For I had been forced to the conclusion that there was more in the mind than just reason and blind thinking, if only you knew how to look for it; the unconscious part of my mind seemed to be definitely something more than a storehouse for the confusions and shames I dared not face. For was there not also the wisdom which had shaped my body up through the years from a single cell? Certainly this was unconscious, my deliberate will had had no hand it. And yet I could see no way of escaping the idea that it was mind in some sense; nothing I had ever heard about chemistry made it possible for me to believe that such a job could happen as a result of the chance combining of molecules. Yet if it was my mind in some sense, why should I make a line between mind and body and limit its powers only to ordering the growth of cells? Certainly, my exploring had gradually made me aware of the existence of something – I can only call it a wisdom – something that seemed to be 'shaping my ends’, trying to express its purposes in pictorial symbols."

Monday, 20 August 2018

Is Educational Technology Over? (No - but we need to talk about consciousness and the universe)

I'm finding myself a bit dismayed by the state of the education system. It seems I'm not alone. Even my 18 year old daughter who survived education with good A-levels is committed to not going to university: "why do I want to pay for more school?". Even 10 years ago there was a lot of hope about what might be possible with technology, and personal technologies in particular presented opportunities for gaining knowledge which were unprecedented and which appeared like a significant threat to rigid institutional provision.

What has actually happened is that institutions have largely maintained their practices unchallenged. Rigid curricula are everywhere (although "curriculum review" seems to be a constancy these days),  and learning outcomes have made the assessment process an explicit exercise in measuring compliance with expectation rather than a consideration of understanding (things were better in the early 90s when I graduated). As David Sherlock reminded me the other day, the real threat to institutions now is not the current generation of students. It is their children.

One would hope that in the educational technology community (and education in general) there would be some soul-searching as to how we got it wrong and what to do next. Unfortunately, because educational technologists are mostly employed by institutions, their focus has shifted to how to keep their jobs and pay their mortgages rather than think of how the institution won over technology, and how we might fix what has become rather authoritarian and technocratic. The injustice of what has happened in education finds voice in various critical approaches to educational technology, which - from the institution's perspective - are now easily sidelined as a kind "two minutes hate": you can say what you like, but keep the VLE/portfolio/content-production going and keep the students happy!

All of this is market-driven nonsense. The environment of education is not a market; it is society as a whole in its scientific, historical, cultural, spiritual and emotional dimensions. Anthony Seldon is right that we barely touch any of these dimensions, and so our education is deficient. The suppression of understanding in favour of metrics of compliance is the most serious problem. Suppressing understanding is a route to alienation and mental illness. But we don't know how to measure understanding. We don't understand understanding.

David Bohm made the remark that "In the end thought produces results. But thought says it didn't do it". That is the problem we face: all our theories, critiques, technologies, experiments are the product of thought, or consciousness. Our thoughts about the physical world give us physics and biology. But the thinkability of those thoughts is emergent from the very biology that we thought of. It's a circular process.

Bohm thought that the way the universe really worked was as an expression of an "implicate order", where its expression articulated symmetries which recur throughout nature. Pattern was the key to apprehending the implicate order: the "pattern which connects" as Bateson put it, and the search for pattern and coherence in the symmetry between thought and nature was the driving force for intellectual inquiry, emancipation and understanding. A few years ago I asked Ernst von Glasersfeld "Where does the desire to learn come from?" He didn't have an answer. Bohm may have it, though.

One of the crucial elements to pattern is redundancy: the saying of the same thing in many different ways. It's what we do as teachers. It's what music and art do. It's what we do on Facebook when we share photos, and it's what I do on this blog. Technology has massively increased the degree of redundancy that we are immersed in. However, in our approach to technology, we have not focused on redundancy; we have focused on its opposite, "information". I think this is at the root of where we have gone wrong with our institutions.

Institutions were indeed threatened by the explosion of possibilities unleashed by technology. But they responded not by adapting their structures and practices but by wishing to maintain their structure. And they did this through attenuating patterns, producing more video resources, assembling more curricula, fetishising the VLE and the MOOC, and using the rationale of the market (which is an attenuation mechanism in its own right) to justify the whole thing. They became "information" organisations. Many years ago, Karl Pribram identified the problem "Redundancy in a world of Information". He highlights "values, redundancy, memory, - the enduring aspects of the word we live in - have been given short shrift of late in our scientific thinking." Pribram's model of consciousness drew heavily on Bohm.

Bohm's concept of consciousness and the universe is that it is a hologram: patterns are present at all levels, from thoughts to atomic structures. It is because of this holographic structure that he argued that dialogue was the most important thing in science and society.

We can use technology very differently. We can use it to harness the redundancy it produces. We can use the redundancy of technology to support rich dialogue in education. We can examine the self-organising processes of understanding for how they connect patterns. We can explore redundancies implicit in the expertise of academics and find new ways of communicating the patterns of their thought. We can create new contexts for conversation free from curriculum but with opportunities for students to pursue deep interests in dialogue. We can have a holographic education to fit our holographic consciousness. 

Saturday, 18 August 2018

Dialectical Materialism Without Matter

Here is a basic statement:

Matter, as far as anyone knows in physics, is composed of basic things like mass, charge, space and time. 

Of course, the key word in that first sentence is "knows". Mass, charge, space and time are ideas, the products of consciousness. Bhaskar tries to simplify this: there are "intransitive" mechanisms. But it doesn't get rid of the "knows" problem. And it gets more complicated because consciousness, which gives us all these ideas, itself appears to be emergent from the matter of physiology and brains.

Once we have got past the problem of "knows", we then have to think about "is composed of". "Is composed of" is a way of thinking about origins: where a story begins. What is it in our consciousness which leads us towards defining a beginning of a story? What is it in the structure of a story which determines an origin?

Marx's story of dialectical materialism grew from 19th century science, when evolutionary stories were much in vogue: first there was x, then there was y, then there was us... But there's no evidence for "first there was..." In fact, there is no evidence for evolution: evolutionary processes cannot be observed - Darwinism is abduction in the same way as creationism.

In Marxism, the relation between material conditions and consciousness is a tension between natural rights, equity and abundance against exploitation and power. Marxism draws its power from a fundamental emphasis on material origins.

But if we say that consciousness begins with physics, we are committing an epistemological error (thanks to Lou Kauffman for reinforcing this to me the other day!). Yet the lure of materialist origins is itself a phenomenon which cannot be discounted. There is something like "truth" in it.

Modern quantum mechanics is telling us something different about the nature of the physical world and historical emergence. In place of a mechanistic, sequential set of knock-on effects, its grappling with non-locality, superposition, uncertainty etc is suggesting that broken symmetries at different orders of reality create patterns in nature. David Bohm's idea of a "hologram" is, I think, the most powerful idea here: that the patterns of symmetry breaking at the smallest unit of nature are reproduced at higher orders. John Torday is suggesting that the symmetry breaking of consciousness itself is tied to symmetry breaking at the material level - particularly to that contained in our cells. Karl Pribram also held to a holographic view of consciousness, also influenced by Bohm.

There is a musical analogue here. Music appears to be composed of redundancies which articulate broken symmetries related to music's originating material. The different aspects of music's holographic structure become aligned and unaligned at various moments. This raises a question: when we think of material origins, are we really setting our consciousness on a path to find alignment between the broken symmetries of thought and the broken symmetries of biology and physics in its historical emergence?

SO... Materialism is holographic alignment between thought and physiology?

That's an interesting idea. So where does that leave exploitation or dialectics? They are accidental misalignments of the hologram: surface broken symmetries which are detached from deep resonances. Capitalism is noise.

What do we do with noise? Redundancy is what is required. The pattern is already written - it just needs amplifying.

Saturday, 11 August 2018

Does cybernetics understand complexity?

I'm writing a paper about music at the moment and questioning my understanding of the word "complex". That's a bit embarrassing for someone who considers themselves a cybernetician - a subject which is fundamentally concerned with complexity. This is a moment where I have to ask myself if I really understand what "complex" means.

This is the definition of complexity that I have believed up until this point, in a beautifully argued explanation by Ross Ashby:
"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) 
On the face of it, this is perfectly sensible. But there are things in life which are not like bicycles or brains, butchers or detectives.

If I was to point to three problems with Ashby's view, they are:

  1. The problem of reference and meaning: Ashby sees information as being about something - the brain to the butcher is information about something, just as it is to the brain surgeon.
  2. The problem of ergodicity - Ashby's examples are inanimate and static in the information they present - but nothing in life is really like this, and neither are observers (or what a friend of mine calls "systems of reference"). Whatever information is conveyed and how we think about information is not ergodic. That means that the features of its "alphabet" are different from one moment to the next. 
  3. The problem of the non-arbitrariness of the diachronic emergence of understanding. This is the really tricky one, but basically the fact that human agree on distinctions, that we are capable of love, that somehow we resonate with each other in the face of phenomena is not the product of a kind of random search for coherence in the manner of Ashby's "homeostat". There seems to be some underlying principle which guides it. 

Music and education are where these problems become most apparent. Bach's music, for example, is often called "complex" because of its counterpoint. But if you examine it closely, all Bach's music is simply an elaboration of chords which are rather like a hymn. And what Bach does with the chords is not to add entropy (or disorder); instead, he adds and overlays new patterns, or redundancies! His complexity arises from the interaction of redundancy. If he added entropy, the music would never have any coherence. But there's something else. These emergent patterns are not random. Each of them appears to be a re-articulation of some fundamental symmetry which is expressed through the whole thing - even when they appear to be initially "surprising". The music is holographic in the way that Bohm describes. Its aesthetic closure appears to be arrived at when sufficient redundant descriptions are overlaid and coordinate rather like different colours of the spectrum combine to make white light.

Cybernetics has no understanding of how this might happen as far as I can see. We need something else. 

Tuesday, 7 August 2018

Learning Analytics and the Ergodic Fallacy

Ergodicity is a statistical property of system whereby a measure of its behaviour over a particular time period is seen to be the same as a measure of its behaviour over a long period. It's often used in information theory as a way of describing the Shannon entropy of a system over one period of time to another. For example, Shannon measured the entropy of the English language as a distribution of letters. This measurement is ergodic to the extent that the shorter sample contains a representative sample of the grammar and syntax of the language, and that over a larger sample the value of the entropy of the language is no different.

The principles of ergodicity rely on some assumptions:
  1. the "alphabet" of what is counted is made explicit at the beginning and does not change. 
  2. the constraints which determine the distribution of symbols do not change
Shannon's reticence to apply information theory to the study of meaning, or the more profound features of living systems rested, I believe, on the fact that he knew that with living systems, neither of these assumptions about ergodicity are true. 

Living systems do not present a complete countable "alphabet" of things to count at the outset. Countable things are emergent: before you have fingers, you have cells.  Partly this is because the second assumption is wrong - the constraints within which living things grow and adapt are continually changing. Indeed, the very process of life is a process of auto-generating constraint - what the biologists call "autocatalysis".

Learning is part of a living process. Learning conversations are rather like dances where nobody quite knows the rules, and indeed, the rules change as it goes along. But somehow the whole thing has coherence. This is a mystery which I believe the analysis of music can help illuminate. Both music and learning conversations develop by creating new constraints and emerging new significant (countable) things. The dynamics and effectiveness of a learning conversation, as a piece of music, rests on how those constraints interact. It turns out that each new expression is a redundant expression - it says something that has already been said before but in a different way. 

So if learning is non-ergodic, why the hell do we think we can count it using Shannon formulae and other statistical devices? This point was missed by Kathy O'Neill's otherwise excellent "Weapons of Maths Destruction", where she instead focused on the latent (white male) agendas behind the analytic boom. She's right about the agendas, but the question is how they get there. 

Repressive agendas arise when a narrative is asserted about the way the world is which is wrong. Analytics is an excellent vehicle for this because the study of ergodicity and information theory is not widespread. But the agenda lies in the assertion of an alphabet being "fixed" which isn't fixed or universal, or that the "rules" of learning are universal and not emergent, or that learning conversations are indicated by clicks on a screen whose coherence is unimportant. 

The search for statistical techniques to examine non-ergodic phenomena is well underway - particularly in ecology (see for example or

In education, there simply isn't enough knowledge about complex systems. And in fact, nobody - yet - has an adequate statistical arsenal to shed any light on it in any field. So why are we behaving as if we do? Who's setting the agenda?

Thursday, 2 August 2018

The Synchronic and Diachronic Structure of Expertise and What it Means for the Future of Learning

Educational technology seems to have hit a brick wall, with emphasis on the generation of educational content in support of rigid curricula, adaptive "personal" learning systems, analytics of student engagement with content, alongside a plethora of management systems which are used as tools to measure teacher "performance" in coordinating often unmanageable workloads. What's been lost is emphasis on relationships, conversation, thoughtfulness, inquiry, exploration, experiment. Technology has supported an increasing authoritarianism in education, which itself (just as authoritarianism is in government today) is a reaction to increasing uncertainty in the world.

There are structural reasons why education has become more authoritarian, and one of them concerns the way we think about expertise. Education sees expertise within the purview of the individual. The expert is an individual who makes reliable and consistent judgements in whatever field they operate, which are consistent with the judgements of other experts in the same field. Expertise is a performance of trusted distinction-making.  The organisational hierarchy of education stems from the privileging of experts as teachers and assessors in making judgements about students. The university sets up structures to regulate the performance of expertise: external examiners, exam boards, quality improvement panels, education committees and so on.

At each level, there is the performance of expertise. But the performance of expertise has a structure which is at once synchronic and diachronic. Synchronically, the expert has acquired knowledge about the 'order of things'. Diachronically, the expert reveals their synchronic structure through conversation, or justification for the judgements they make. If they make this justification in conversation with a student, we call this a "learning conversation", and the learner, through this conversation, acquires an understanding of the synchronic structure of expertise, and hopefully some of the skills of justification which reveal their own understanding.

One of the fascinating question in educational technology is whether it is possible to convey synchronic understanding alongside the means of diachronic expression without the direct conversational contact with an expert. Is it possible to "bottle" expertise, and to reorganise learning conversations (without which there is no learning) in such a way that peer-based conversation can be organised around engagement with such a "bottled" expertise?

This has been something of a "wet dream" for the proponents of AI for many years, but these efforts do not appear to work. They usually revolve around trying to coordinate a diachronic unfolding of expertise guided by an algorithm, which articulates some codified domain of knowledge. Neither the conversation nor the synchronic structuring of the knowledge is particularly convincing. This is because of certain category mistakes which are made in design: the conversation with the computer is presented as being "functionally equivalent" to a conversation with a teacher. Yet this is to misunderstand the nature of conversation. Also the activities the student is asked to engage with are seen to be analogous to the activities that a real teacher would ask a student to do. But the computer is not a real teacher, so there seems little justification for assuming that the activities have the same purpose.

If we really want to explore whether the synchronic and diachronic performance of expertise can be conveyed in new ways, we have to rethink the distinction between conversation and activity in learning, and what it is one hopes to achieve through the learning process.

A clue as to how this might be done is to consider that the synchronic aspect of expertise is an ordering of relations. If an expert has a particular ordering of relations (between categories for distinguishing mistakes in a program, or features in a diagnosis), then what are the activities which might lead a learner to acquire a similar ordering of relations? In asking this question, there are more profound questions to ask of experts, rather than learners: what do you see as the most important thing? What is least important? How does a compare to b?

The diachronic revealing of synchronic structure often takes the form of an emotion. If a learner says b is better than a when the teacher knows that a is hugely better than b, they will exclaim "No!" and wave their arms about! But a more subtle distinction or mistake might elicit a more nuanced reaction. Learners learn much from these reactions.

What is striking about this is that the learning conversation itself takes a form which relates to the synchronic structure of expertise. This is much like the way the form of a piece of music derives from the structure of its originating moments. Therefore, if we were to bottle experts, then we should work towards a form of learning conversation which acquires the form of the structure of knowledge. I'm working on a project which is trying to do this at the moment. I'm not sure whether it can be done. But I'm not convinced it can't be done. The educational technology route that we are on at the moment, however, is futile. 

Wednesday, 1 August 2018

The Physiology of Understanding and Teaching

Most people assume that "knowing", "learning", "remembering", etc happens in brains. By implication, they mean that consciousness is a property of the brain. There is considerable evidence to support this: damaged brains usually produce impairment in cognitive function. However, although  sometimes radical changes in behaviour are observed in those with damaged brains, the humanness of the individual remains. Anybody who has had a relative with Alzheimers, a child with learning difficulties, or cared for someone after a serious accident knows this. The more profound changes occur in individuals around a person with brain damage: their behaviours change too, as accommodation is made for cognitive impairment, extraordinary efforts are made to support an individual in the expression of their identity in new ways which fit their new condition. Being human, it seems, involves rather more than an individual brain. It is not even in the "whole" person. It is in the whole community.

Processes of empathy and emotional connection are not separate from individual high level cognitive function. That we have believed that it is is largely the fault of an education system which seeks to categorise individuals, rather than explore and express relationships. The neural basis of consciousness has been further reinforced by assumptions about the brain being a computer. Neurons, axons and synapses seem like wires and connections, and the logical firing of one neuron seems to trigger knock-on firings of connected neurons, much in the same way that an electric signal triggers knock-on effects in a circuit. And indeed electricity plays an important role in the brain. The problem with this view is that it is a long and hard journey to get from knock-on causal effects to empathy and emotion. More often than not, the emotional aspect of consciousness is ignored.

Some physicists and neuroscientists have, however, taken a different view. David Bohm was highly aware of the importance of emotion in communication. In fact, he believed that direct emotional engagements provided a deeper scientific insight into the nature of the world than rationalistic talk. His theory of Quantum Mechanics, which is increasingly in vogue (see Adam Becker's new "What is Real?", not only united relativity with quantum mechanics (which had eluded Bohr), but made a connection between the structure and process of matter, and consciousness. We ought to know more about this in education.

The connection between matter and consciousness must work through physiology. Some like Terry Deacon have made the connection by examining how information works from the material world (see, psychology and through evolution. By focusing on those aspects of biology about which our knowledge is rather vague - like epigenesis - Deacon has emerged a theory of mind based on the study of semiotic communication. If there is a weakness to this, as with all theories of mind, it lies in the theory's ability to account for the way in which it thinks about itself. But I think this is important work.

Deacon does not align himself to quantum mechanics, but instead prefers to talk in terms of Newtonian ideas like the "physical work" which has to be performed on any physical medium in the process of transmitting information (there have to be electrons moving down a wire, or vibrations in the air, etc)

John Torday goes much deeper than this in a theory which has hit me with some force as being obviously right (I have to be careful here!), and an important missing link in our understanding of information. Torday's idea draws on Bohm basic idea of what he called the "holographic universe" (see Consciousness, Torday argues, arises from the evolution of the cell as the basic unit of physiology, and that cellular evolutionary process has been driven by the cell's adaptation to ambiguity in its environment. Moreover, the cellular adaptive processes reflects fundamental structural adaptations in pre-history. There is a pattern written throughout our flesh which connects us to one another and to a single point of origin. Torday is not the first to suggest that consciousness is holographic - Karl Pribram made this connection many years ago with his "holonomic brain theory" (see but Pribram based his work on Fourier analysis of cerebral activity. Torday's emphasis on cellular evolution is quite a few steps beyond this - which makes it important.

I wonder if another word for Torday's "ambiguity" in the environment is "broken symmetry". Broken symmetry is the process whereby quantum mechanics believes the structure of matter - atoms, molecules, etc - emerges. Whatever originating broken symmetry there was is written in new molecular adaptations later on, which in turn are performed in environmental contexts which twist the path of evolution in one way or another. Torday's biology emphasises the importance of stress from the environment, which causes cellular mechanisms to stretch and acquire new functions (swim bladders change into lungs, for example). And consciousness could be part of the same process.

What this means is that the essence of consciousness lies not in neural pathways, but in cellular evolutionary history. Torday suggests that we see this in moments of deep human connection - empathy, love, art. I would add "great teaching" to this. Bohm suggested something similar - that in music, for example, we could glimpse the fundamental structure of nature.

Understanding something deeply means becoming aware of a fundamental pattern of broken symmetry which connects us to a common point of origin. At its root, "understanding" and what we consider to be "spirituality" are the same thing. Because of this, it is critically important that we build an education system for understanding, not for the delivery of qualifications. To concentrate on the delivery of qualifications above understanding (which is most of what happens in today's universities), is to drive a wedge between our common origins, to isolate individuals who in truth are connected, and to create the conditions for what we call "mental illness".

As R.D.Laing noted, mental illness is not the sickness of the individual. It is the sickness of their environment. Being "mentally ill" is the only truly authentic reaction to that environment, only exacerbated by the naive attempts of others to "cure" the individual.

Torday is pointing the way to a scientific underpinning of the way we understand understanding. One may hope that the light of science may one day lead us out of this rather dark place we have ended up in!

Thursday, 26 July 2018

Dialectic and multiple description in Haydn

The slow movement of Haydn's piano sonata in C major, no. 50 is full of gestures which articulate a simple tonality, but which are so varied in their rhythm, range of the keyboard, dynamics, texture and lyricism maintain interest in what would otherwise be rather uninteresting music. But what Haydn actually does is anything but uninteresting: it is full of surprise, and is highly expressive. Where does the expression come from? This is Lang Lang playing it:

The contrast with the Bach sinfonia no 9 (which I looked at a couple of posts ago) couldn't be greater. Yet, I think the principle is the same. Haydn, like Bach, creates overlapping redundancies. But where Bach takes a chromatic harmonic structure and weaves motifs all the way through it, Haydn takes a relatively simple harmonic structure (I-V-I-IV-I-V-I...) Played as straight chords, these are not nearly as interesting as the Bach chorale chords with their diminished chords and exotic chromaticism. Which means that the reduction of the Haydn is even more unsurprising than the Bach - a very low entropy.

Haydn seems to add disorder through contrasting ideas: this is, after all, the composer who wrote a "representation of chaos" at the beginning of "The Creation", which does a similar thing. But like Bach, this is not disorder, it is redundancy. Basically, rhythm, articulation, range, figuration and dynamics are used to articulate the same basic simple tonality of the piece: one way of describing it follows another in often contrasting juxtaposition.

Each way of describing the tonality is not arbitrary, but unlike Bach, the redundancy of the added patterns does not run through the whole thing: it is episodic, frequently punctuated by silence, from which Haydn then surprises us again.

Silence is important in this process. Silence is when all the parameters of overlapping redundancies all tend towards the same thing. I suggested in my analysis of Bach, that this shared movement of entropy between different parts was an indication of a new idea: a new countable thing. And indeed so it is in Haydn. It's just that the ideas are layered sequentially rather than layered on top of one another.

Each closure to silence creates uncertainty as to what is coming next. Something seems to have been defined that is stable - will it be continued, or will something different follow? Haydn plays with this uncertainty, and when we do get a lyrical melody (the falling melody over an undulating accompaniment) it feels like a relief.

In dialectical theory, the succession of musical ideas might be considered to be like a "thesis", "antithesis", "synthesis" triad. But really, those three elements are different descriptions of the same thing, their juxtaposition a way of accumulating redundancies on a journey to creating a relationship between different descriptions whose interactions reveal the inner structure of the music, and which can close to silence without feeling the need for more. The tension that is established between different descriptions isn't "resolved" as such. It creates the conditions for the emergence of another description which is more fundamental than those which precede it. This new description coexists with its predecessors.

Such moments are felt emotionally.  Emotion and meaning in music is like a light-house which guides the generation of a set of redundant but never arbitrary descriptions which eventually together reveal some kind of insight into what underpins the whole thing.  

Freire and the Arbitrariness Problem in Learning Conversations: insight from music, maths and physics

If the cyberneticians were completely right about learning conversations, then conversations would have the form of a kind of Brownian motion: utterances would respond to utterances, learners and teachers may adapt to the utterances they hear, but the whole thing would be a kind of wandering in search of a point of resolution. This is why I think Pask believed that "Teach-back" was critical to the learning conversation - because without it, how could the learning conversation have any closure? So closure comes from a logical judgement as to whether the student has "taught back" what the teacher taught to them.

I don't think this is quite right, and more critically, it isn't what we see in aesthetic phenomena like music. The critical point is that utterances are not arbitrary. Learning conversations take a form which is found in their originating material. In music the originating material is in the initial musical ideas, the instruments, etc. In learning, the originating material is in the whole constitution of learners and teachers, and the subject domain. There is no originating point of a learning conversation which isn't bathed in personal biography, and histories and social structures which extend far beyond any individual life.

What appears to happen in music is that completion arises from the overlaying of multiple descriptions which unfold some originating idea. Eventually there is some kind of coordination between descriptions which means that a return to some originating state (silence) becomes a natural progression. This would suggest that those physicists who believe that everything comes from nothing (like Peter Rowlands) are right. Quantum mechanics holds some important messages for constructivists.

Composers say what they say by finding ways of generating multiple descriptions (redundancy) and layering redundancies over one another. But redundancies are not chosen arbitrarily. They emerge through a kind of symmetry-breaking process, where the originating principle of this symmetry breaking is implicit in the first instance.

Learning conversations are much like this I think. But what is the originating material of a symmetry breaking process in a learning conversation? It is the root of oppression within the individuals talking. Freire was right.

Closure does not arrive through teach-back - although this may be seen to be an epiphenomenon of closure. Closure arrives through the articulation of multiple descriptions of oppression. This may be what it is for something to "make sense" (c.f. Weick on sensemaking: "the ongoing retrospective development of plausible images that rationalize what people are doing").

What this means, most simply, is that the model of perturbation and response needs a historical dimension. The reflexive selection of utterances depends on the dynamic interplay between three dimensions:

  1. prediction based on what has just happened
  2. prediction based on a model of what is happening
  3. speculation on possible models of what might be happening, and what might be possible. 

Daniel Dubois's mathematical work on anticipatory systems identifies these three dimensions as "recursive", "incursive" and "hyperincursive". They are coexisting processes. Between them they produce elaborate fractal patterns like this:

When I first saw patterns like this, I thought it looked rather deterministic, too neat. But now I think that is not what the picture is showing. It is showing in an idealised way that the interaction between history, the present and future produces moments of symmetry breaking, from which new descriptions of the same thing can emerge. There are moments when multiple descriptions come together and produce moments of closure because the combination of past, present and future produce distinct moments of "resolution" (perhaps this might be in the big diamonds of the picture). 

More importantly, the stratification of this diagram suggests that utterances are not arbitrary. They exist in, and articulate a structure. Emancipation is the revealing of the structure through very careful articulation of levels of description: the production of redundancy. This is very similar to what composers do. It is also worth comparing to the stratification articulated in the quantum mechanical twin-slit experiment:

Stratification is not arbitrary. Learning conversations are not Brownian motion. They are layered accretions of redundant patterns - like music. 

Saturday, 21 July 2018

Redundancy and the Communication of Meaning in Music: Bach's 3-part Invention (Sinfonia) no. 9 in F minor

Hindemith chose Bach's F minor 3 part invention for analysis to demonstrate his theory of composition in "The craft of musical composition". It is a fascinating piece - one of Bach's most chromatic and expressive pieces of keyboard writing, and rather like other extraordinary musical moments (like Wagner's musical orgasm in Tristan), it raises the question "What is going on?". I like Hindemith's theory very much (although not as much as I like his music!), but his analysis sent me on my own analytical journey through the lens of information theory.

What happens in music, I believe, is the unfolding of a structure where multiple constraints are interwoven and overlaid. Information theory can provide some insight into this (as is discussed in a very recent paper from Loet Leydesdorff, myself and Inga Ivanova in the Journal of the Association for Information Science and Technology:, and particularly the meaningfulness of the communication.

When considering music from the perspective of information theory, there are three fundamental problems to be overcome:

  1. Music has no object of reference. So how is meaning communicated without reference?
  2. Music emerges over time, producing novelty and unfolding a diachronic structure which appears to be linked to its synchronic structure. For this reason, music is not ergodic, unlike the use of letters in a language: its entropy over one period of time is not the same as its entropy over a different period of time. 
  3. Music's unfolding novelty is not arbitrary: novelty in music appears to be a symmetry-breaking process similar to that found in epigenesis where both synchronic and diachronic symmetries gradually define structure
The first page of Bach's music looks like this:
Here's a performance:

The piece is fugal, and obviously in three parts, there is a very bare texture, and this bareness seems to contribute to the expressiveness of the music. However, there is a harmonic structure which is articulated throughout the piece, and a reduction of the harmonic written as chords per beat, looks something like this:

This kind of harmonic reduction is very common in music analysis as a method for getting at the "deep structure" of music (particularly in Schenker). It is typical of Bach's music that the harmonic reduction is very much like a chorale (hymn). In trying to understand how Bach's music works, we can start by asking about the relation between the harmonic reduction and the finished piece. 

At first glance, from an information theory perspective, the block chords of the reduction seem to remove a considerable amount of entropy which exists in the movement of parts in the original. It does this by compressing the variety into single "beats", which taken as an entirety have an entropy of 0. However, the variety compression makes more apparent the shifting harmonies. Written in chord symbols, this is an extended I (tonic) - V (dominant) - I (tonic) movement, interspersed with diminished chords (which are harmonically ambiguous) and a oscillation between major and minor chords. But if one was to calculate the entropy of the harmony, it wouldn't be that great. 

However, to say that the meaningfulness of Bach's music is arrived at by adding entropy is misleading. If entropy was to be added, we would expect increasing disorder. But if disorder is what is added, then it is unlikely that a coherent harmonic reduction would be possible, and furthermore it is unlikely that the piece would have any coherence. 

The striking thing about comparing the harmonic reduction with the original is that it is not disorder (entropy) which is added. It is redundancy.

This is most obvious is the melodic motif which Bach uses throughout the piece: 
This expresses a number of patterns which are represented throughout: the 3-quaver rhythm followed by a quaver pause; the interval jump of a third and then a fall of a second (except for moments of higher tension when he breaks this); and the phrasing with emphasis on the second note. 

In fugal writing, where each voice imitates others, the redundancy of patterns like this motif is enhanced. But it is interspersed with other ideas: the variety of the pattern is broken in the second bar, with a closing motif which also gets repeated throughout:

Shannon information theory, derived from Boltzmann's thermodynamics, measures uncertainty or disorder. It does this by identifying features which can be counted, and calculates the probabilities of their occurrences. 

On observing Bach's piece, the two motifs identified might be considered to be "features", and their occurrences over time calculated. Equally, the occurrences of individual notes might be calculated, or the harmonic sequence identified in the harmonic reduction. But somehow this seems to miss the point. When we do Shannon analysis in text, we can identify words, and usually those words have reference, and so the communication of meaning can be inferred from the patterns of the words and their references (this is how big data techniques like Topic Modelling work)

The second problem about music's lack of ergodicity is more serious still. Whatever is counted at the beginning is not what can be counted at the end. Novelty arises through the unfolding. Since Shannon's formulae requires an index of features, how might it accommodate features which cannot be foreseen from the outset?

However, there are fundamental features for which the entropies can be calculated: notes, rhythm, intervals, harmony, etc. An emergent structure can be arrived at through the interaction between different constraints: music creates its own constraints. Every measurement of entropy of a particular feature is constrained by the measurements of entropies of other features: the choice of notes depends on the choice of harmony or rhythm, for example.

Seeing any measurement of entropy in this way means that any measurement of entropy is also an index of the constraints (or redundancies) that produce that measure of entropy. In this way, we do not need to engage with Shannon's formula for redundancy - which is good because it invokes the notion of "maximum entropy" which is a concept that is beyond measurement. 

Constraints work over time. The effect of one constraint on another results in changes to the entropies of different features. If one constraint changes at the same time as another, then there is some connection between them.

In considering the motif that Bach uses to structure his fugue, the intervals, the rhythm, the expression and the pattern of notes are all the same. That means that the entropies of each fundamental element relative to the others is tightly coupled. 

Does this means that tight coupling between fundamental features is a sign of an emergent cell or motif? I think it might, and of course, if tight coupling is identified as a new idea, then the new idea becomes a new feature in the analysis, upon which its own entropy can be calculated relative to other features. 

At the end of a piece, there is tight coupling between everything. Everything dissolves into silence. The important thing is that everything dissolves into what it came from. This is directly related to problem 3 above: novelty is not arbitrary. All novelty articulates different descriptions of the whole. Nothing (silence) is arrived at when those descriptions come together in the same way that the colour spectrum comes together to produce white light. 

Music is profound in its communication of meaning because it expresses something fundamental in our own biological structure. In music's unfolding broken symmetry, we recognise our own unfolding broken symmetry. This principle is behind what I think Alfred Schutz saw in his paper "Making Music Together". When education really works, it has exactly this same property expressed in the loving relations between human beings.

Tuesday, 17 July 2018

How is music meaningful? An Information Theoretical approach to analyse the communication of meaning without reference

These are notes for a paper on music. It is not meant to be in any way coherent yet!

1 Introduction

Over the centuries that music has been considered as a scientific phenomenon, focus has tended to fall on music’s relation to number and proportion which has been the subject of scholarly debate since antiquity. In scientific texts on music from the Pythagoras to the enlightenment, focus has tended to fall on those aspects of sound which are synchronic, of which the most significant is harmony and the proportional relation between tones. Emerging scientific awareness of the physical properties of sound led scientists to consider deeper analysis of the universe. This scientific inquiry exhibited feedback with music itself: deeper scientific understanding inspired by music, harmony and proportion led to scientific advance in the manufacture of musical instruments and the consequent emergence of stylistic norms.

Less attention has been placed on music’s diachronic structure, despite the fact that synchronic factors such as timbre and harmony appear strongly related to diachronic unfolding, and that the diachronic dimension of music typifies what Rosen calls, “the reconciling of dynamic opposites is at the heart of the classical style”. In more recent years, the role of music in understanding psychosocial and biological domains has increased. Recent work around the area of “Communicative Musicality” has focused more on the diachronic unfolding alongside its synchronic structure, for it is here that it has been suggested the root of music’s communication of meaning lies, and that this communication is, in the suggestion of Langer, a “picture of emotional life”

Diachronic structures present challenges for analysis, partly because dialectical resolution between temporally separated moments necessarily entails novelty, while the analysis throws up fundamental issues of growth within complexes of constraint. These topics of emerging novelty within interacting constraints has absorbed scientific investigation in biology and ecology in recent years. Our contribution here is to point to the homologous analysis of innovation in discourse, and so we draw on insights into dynamics of meaning-making within systems which have reference as a way of considering the meaning-making within music which has no reference, with the aim of providing insights into both. The value of music for science is that it focuses attention on the ineffable aspects of knowledge: a reminder of how much remains unknown, how the reductionism of the enlightenment remains limited, and how other scientific perspectives, theories and experiments remain possible. And for those scientists for whom music is a source of great beauty, no contemplation of the mysteries of the universe could not consider the mysteries of music.

2 What do we mean by meaning?

Any analysis of meaning invites the question “what do we mean by meaning?” For an understanding of meaning to be meaningful, that understanding must participate in the very dynamics of meaning communication that it attempts to describe. It may be because of the fundamental problems of trying to identify meaning that focus has tended to shift towards understanding “reference” which is more readily identifiable. There is some consensus among scholars focused on the problem that meaning is not a “thing” but an ongoing process: whether one calls this process “semiosis” (Peirce), or Whitehead’s idea of meaning, or the result of the management of cybernetic “variety” (complexity). The problem of meaning lies in the very attempt to classify it: while reference can be understood as a “codification” or “classification”, meaning appears to drive the oscillating dynamic between classification and process in mental process. So there is a fundamental question: is meaning codifiable? For Niklas Luhmann, this question was fundamental to his theory of “social systems”. Luhmann believed that social systems operate autopoietically by generating and reproducing communicative structures of transpersonal relations. Through utterances, codes of communication are established which constraint the consciousness of individuals who reproduce and transform those codified structures. Luhmann saw the different social systems of society as self-organising discourses which interact with one another. Thus, the “economic system” is distinct from the “legal system” or the “art system”. Meaning is encoded in the ongoing dynamics of the social system. An individual’s utterance is meaningful because the individual’s participation in a social system leads to coordinated action by virtue of the fact that one has some certainty that others are playing the same game: one is in-tune with the utterances of others, and with the codified social system within which one is operating. Luhmann borrowed a term which Parson’s invented, inspired by Schutz’s work, “double contingency”. All utterances are made within an environment of expectation of the imagined responses of the other (what Parsons calls “Ego” and “Alter”) 

The problem with this perspective is that meaning results from a kind of social harmony: meaning ‘conforms’. Fromm, for example, criticizes this attitude as the “cybernetic fallacy”: “I am as others wish me to be”. Yet meaningful things are usually surprising. An accident in the street is meaningful to all who witness it but it outside the normal codified social discourse. Even in ordinary language, one emphasizes what is meaningful by changing the pitch of volume of ones’ voice for emphasis on a particular word, or gesturing to some object as yet unseen by others “look at that!”. Whatever we mean by meaning, the coordination of social intercourse and mutual understanding is one aspect, but novelty or surprise is the critical element for something to be called “meaningful”. It is important to note that one could not have surprise without the establishment of a some kind of ‘background’.
However, there is a further complication. It is not that surprise punctuates a steady background of codified discourse. Codified discourse creates the conditions for novelty. The effects of this have been noted in ecology (Ulanowicz) and biology (Deacon). The establishment of regularity and pattern appears to create the conditions for the generation of novelty in a process which is sometimes characterized as “autocatalytic” (Deacon, Ulanowicz, Kauffman). This, however, is a chicken and egg situation: it is that meaning is established through novelty and surprise against a stable background, or is it the stable background which gives rise to the production of novelty which in turn is deemed to be meaningful.

This dichotomy can be rephrased in terms of information theory. This is not to make a claim for a quantitative index of meaning, but a more modest claim that quantitative techniques can be used to bring greater focus to the fundamental problem of the communication of meaning. Our assertion is that this understanding can be aided through the establishment of codified constraints through techniques of quantitative analysis in order to establish a foundation for a discourse on the meta-analysis of meaningful communication. This claim has underpinned prior work in communication systems and economic innovation, where one of us has analysed the production of novelty as the result of interacting discourses between the scientific community, governments and industries. Novelty, it is argued, results from mutual information between discourses (in other words, similarly codified names or objects of reference), alongside a background of mutual redundancy or pattern. Information theory provides a way of measuring both of these factors. In conceiving of communication in this way, there is a dilemma as to whether it is the pattern of redundancy which is critical to communication or whether it is the codified object of reference. Music, we argue, suggests that it is the latter.

3 Asking profound questions

In considering music from the perspective of information theory, we are challenged to address some fundamental questions: 
1. What does one count in music?
2. From where does musical structure emerge?
3. What is the relation between music’s synchronic structure and its diachronic unfolding?
4. Why is musical experience universal?

4 Information and Redundancy in Music: Consideration of an ‘Alberti bass’

Music exhibits a high degree of redundancy. Musical structure relies on regularity, and in all cases of the establishment of pattern and regularity, music presents multiple levels of interacting pattern. For example, an ‘Alberti bass’ establishes regularity, or redundancy, in the continual rhythmic pulse of the notes that form a harmony. It also exhibits regularity in the notes that are used, and the pattern of intervals which are formed through the articulation of those notes. It also exhibits regularity in the harmony which is articulated through these patterns. Its sound spectrum identifies a coherent pattern. Indeed, there is no case of a musical pattern which is not subject to multiple versions of redundant patterning: even if a regular pattern is established on a drum, the pattern is produced in the sound, the silence, the emphasis of particular beats, the acoustic variation from one beat to another, and so on. Multiple levels of overlapping redundancy means that no single musical event is ever exactly the same. This immediately presents a problem for the combinatorics of information theory, which seeks to count occurrences of like-events. No event is ever exactly ‘like’ another because the interactions of the different constraints for each single event overlaps in different ways. The determination of a category of event that can be counted is a human choice. The best that might be claimed is that one event has a ‘family resemblance’ to another.

The Alberti bass, like any accompaniment, sets up an expectation that some variety will occur which sits within the constraints that are established. The critical thing is that the expectation is not for continuation, but for variety. How can this expectation for variety be explained?

In conventional information theoretical analysis, the entropy of something is basically a summation of the probabilities of the occurrences of the variety of different codified events which are deemed to be possible and can be counted. This approach suffers from an inability to account for those events which emerge as novel, and which could not have been foreseen at the outset. In other words, information theory needs to be able to account for an dynamically self-generating alphabet.
Considering the constraint, or the redundancy within which events occur presents a possibility for focusing on the context of existing or potentially new events. But since the calculation of redundancy requires the identification of information together with the estimation of the “maximum redundancy”, this estimation is also restricted in calculating novelty.

However, we have suggested that the root of the counting problem is that nothing is exactly the same as something else. But, some things are more alike than others. If an information theoretical approach can be used to identify the criteria for establishing likeness, or unlikeness, then this might be used as a generative principle for generating the likeness of things which emerge but cannot be seen at the outset. Since novelty emerges against the context of redundancy, and redundancy itself generates novelty, a test of this approach is whether it can predict the conditions for the production of novelty.
In other words, it has to be able to distinguish the dynamics between the Alberti bass which articulates a harmony for 2 seconds, and an Alberti bass which articulates the same harmony for more than 1 minute with no apparent variation (as is the case with some minimalist music).

  • How do our swift and ethereal thoughts move our heavy and intricately mobile bodies so our actions obey the spirit of our conscious, speaking Self?
  • How do we appreciate mindfulness in one another and share what is in each other’s personal and coherent consciousness when all we may perceive is the touch, the sight, the hearing the taste and smell of one another’s bodies and their moving?
These questions echo the concern of Schutz, who in his seminal paper, “Making Music Together” identifies that music is special because it appears to communicate without reference. Music occupies a privileged position in the information sciences as a phenomenon which makes itself available to multiple descriptions of its function, from notation to the spectral analysis of sound waves. Schutz’s essential insight was the musical meaning-making arose from the tuning-in of one person to another, through the shared experience of time.

This insight has turned out to be prescient. Recent research suggests that that there is a shared psychology or “synrhythmia” and amphoteronomy involved in musical engagement. How then might this phenomenon be considered to be meaningful, in the absence of reference, which in other symbolically codified contexts (e.g. Language), meaning appears to be generated in other ways which can be more explicitly explained through understanding the nature of “signs”.

5 Communicative Musicality and Shannon Entropy

Recent studies on communicative musicality have reinforced Schutz’s view that the meaningfulness of musical communication rests on a shared sense of time. The relation between music and time makes manifest many deep philosophical problems: music unfolds in time, but it also expresses time, where time in music does not move at the same speed: music is capable of making time stand still. If time is considered as a dimension of constraint, alongside all the other manifestations that music presents, then the use of time as a constraint on the analysis of music itself can help unpick the dynamics of those other constraints. While one might distinguish clock-time from psychological time, what might be considered psychological time is in reality the many interacting constraints, while clock-time is an imaginary single description allows us at least to carve up experience in ways that can be codified.

Over time, music displays many changes and produces much novelty. Old patterns give way to new patterns. At the root of all these patterns are some fundamental features which might be counted in the first instance:
1. Pitch
2. Rhythm
3. Interval
4. Harmony
5. Dynamics
6. Timbre

So what is the pattern of the Alberti bass?

If it’s note pattern is C-G-E-G-C-G-E-G, and its rhythm is q-q-q-q-q-q-q-q and its harmony is a C major triad, and intervallic relations are 5, -3, 3, -5, 5, -3, 3, -5, over a period of time, the entropy for each element will be;
1. Pitch: -0.232
2. Rhythm: 1
3. Interval: 0.2342
4. Harmony: 1
5. Dynamics:

The important thing here is that novelty becomes necessary if there is insufficient variation between interacting constraints. If mutual redundancy is high, then it also means that there is very high mutual information. The phrasing of an Alberti bass is an important feature of its performance. For musicians it is often considered that the Alberti pattern should be played as a melody.

Consider the opening of Mozart’s piano sonata

The playing of the C in the right hand creates an entropy of sound. Each sound decays, but the decay of C above the decay of the Alberti bass means that the context of the patterns of the other constraints changes. This means that the first bar can be considered as a combination of constraints.

The surprise comes at the beginning of the second bar. Here the pattern of the constraint of the melody changes because a different harmony is articulated, together with a sharp interval drop (a 6th), an accent, followed by a rhythmic innovation in the ornamental turn. Therefore the characteristic of the surprise is a change in entropy in multiple dimensions at once.

It is not enough to surprise somebody by simply saying “boo!”. One says “boo!” with an increased voice, a change of tone, a body gesture, and so on. The stillness which is previous to this is a manifestation of entropies which are aligned.

The intellectual challenge is to work out a generative principle for a surprise.

6 A generative principle of surprise and mental process

The differentiation between different dimensions of music is an indication of the perceptual capacity expressed through relations between listeners and performers. The articulation and play between different dimensions creates the conditions for communicating conscious process. If entropies are all common across a core set of variables, then there is effectively collapse of the differentiating principles. All becomes one. But the collapse of all into one is a precursor to the establishing of something new.
In music’s unfolding process a system of immediate perception works hand-in-hand with a meta-system of expectations (an anticipatory system). This can be expressed in terms of a system’s relation to its meta-system. Because the metasystem coordinates the system, circumstances can arise where the metasystem becomes fused to the system, so that differences identified by the system become equivalent to different identified by the metasystem. In such a case, the separation between system and metasystem breaks down. The cadence is the most telling example of this. In a cadence, many aspects of constraint work together all tending towards a silence: harmony, melody, dynamics, rhythm, and so forth.

Bach’s music provides a good example of the ways in which a simple harmonic rhythm becomes embellished with levels of counterpoint, which are in effect, ways of increasing entropy in different dimensions. The melody of a Bach chorale has a particular melodic entropy, while the harmony and the bass imply a different entropy. Played “straight”, the music as a sequence of chords isn’t very interesting: the regular pulse of chords creates an expectation of harmonic progress towards the tonal centre, where all the entropies come together at the cadence:

Bach is the master of adding “interest” to this music, whereby he increases entropy in each voice by making their independent rhythms more varied, with patterns established and shared from one voice to another:

By doing this, there is never a complete “break-down” of the system: there is some latent counterpoint between different entropies in the music, meaning that even at an intermediate cadence, the next phrase is necessary to continue to unfold the logic of the conflicting overlapping redundancies.

This is the difference between Baroque music and the music of the classical period. In the classical period, short gestures simply collapse into nothing, for the system to reconstruct itself in a different way. In the Baroque, total collapse is delayed until the final cadence. The breaking-down of the system creates the conditions for the reconstruction of stratified layers of distinction-making through a process of autocatalysis. Novelty emerges from this process of restratifying a destratified system. The destratified system exhibits a cyclic process whereby different elements create constraints which reinforce each other, much like the dynamics of a hypercycle described in chemistry, or what is described in ecology as autocatalysis.

Novelty arises as a symptom of the autocatalyzing relation between different constraints, where the amplification of pattern identifies new differences which can feed into the restratification of constructs in different levels of the system.

This can be represented cybernetically as a series of transductions at different levels. Shannon entropy of fundamental features can be used as a means of being able to generate higher level features as manifestations of convergence of lower-level features, and consequently the identification of new pattern.

It is not that music resonates with circadian rhythms. Music articulates an evolutionary dynamics which is itself encoded into the evolutionary biohistory of the cell.

7 Musical Novelty and the Problem of Ergodicity

In his introduction to the concept of entropy in information, Shannon discusses the role of transduction between senders and receivers in the communication of a message. A transducer, according to Shannon, encodes a message into signals which are transmitted in a way such that they can be successfully received across a communication medium which may degrade or disrupt the transmission. In order to overcome signal degradation, the sending transducer must add extra bits to the communication – or redundancy – such that the receiver has sufficient leeway in being able to correctly identify the message.
Music differs from this Shannon-type communication because the redundan- cies of its elements are central to the content of music’s communication: music consists primarily of pattern. Moreover, music’s redundancy is apparent both in its diachronic aspects (for example, the regularity of a rhythm or pulse), and in its synchronic aspects (for example, the overtones of a particular sound). Music’s unfolding is an unfolding between its synchronic and diachronic redun- dancy. Shannon entropy is a measure of the capacity of a system to generate variety. Shannon’s equations and his communication diagram re-represent the fundamental cybernetic principle of Ashby’s Law of Requisite Variety, which states that in order for one system to control another, it must have at least equal variety. In order for sender and receiver to communicate, the variety of the sender in transmitting the different symbols of the message must be at least equal to the variety of the receiver which reassembles those symbols into the information content. The two transducers, sender and receiver, communicate because they maintain stable distinctions between each other: information has been transferred from sender to receiver when the receiver is able to predict the message. Shannon describes this emergent predictive capacity in terms of the ‘memory’ within the transducers. It is rather like the ability to recognise a tune on hearing the first couple of notes.

In using Shannon to understand the diachronic aspects of music, we must address one of the weaknesses of Shannon’s equation in that it demands an index of elements which comprise a message (for example, letters in the alphabet). In cases where the index of elements is stable, then the calculation of entropy over a long stretch of communication will approximate to entropy over shorter stretches since the basic ordering of the elements will be the similar. This property is called ergodicity and applies to those cases where the elements of a communication can be clearly identified. Music, however, is not ergodic in its unfolding: its elements which might be indexed in Shannon’s equations are emergent. Music’s unfolding reveals new motifs, themes, moods and dynamics. None of these can be known at the outset of a piece of music.

In order to address this, some basic reconsideration of the relationship between order and disorder in music is required. In Shannon, order is determined by the distribution of symbols within constraints: Shannon information gives an indication of the constraint operating on the distribution. The letters in a language, for example, are constrained by the rules of grammar and spelling. If passages of text are ergodic in their order it is because the constraint operating on it is constant. Non-ergodic
communication like music result from emergent constraints. This means that music generates its own constraint.

In Shannon’s theory, the measure of constraint is redundancy. So to say that music is largely redundant means that music participates in the continual gen- eration of its own constraints. Our technical and empirical question is whether there is a way of characterising the emergent generation of constraint within Shannon’s equations.

To address the problem of emergent features, we need to address the problem of symbol-grounding. Stated most simply, the symbol grounding problem concerns the emergence of complex language from simple origins. Complex symbols and features can only emerge as a result of interactions between simple components. A further complication is that complex structures are neither arbitrary nor are they perfectly symmetrical. Indeed, if the complex structures of music, like the complex structures of nature are to be described in terms of their emergence from simple origins, they are characterized by a “broken symmetry”. In this sense, musical emergence is in line with recent thinking in physics considering the symmetry of the universe, whereby very small fluctuations cause the formation of discrete patterns.

Symmetry-breaking is a principle by which an analysis involving Shannon entropy of simple components may be used to generate more complex structures. In the next section we explain how this principle can be operationalized into a coherent information-theoretical approach to music using Shannon’s idea of Relative Entropy.

8 Relative Entropy and Symmetry-Breaking

As we have stated, music exhibits many dimensions of constraint which overlap. Each constraint dimension interferes with every other. So what happens if the entropy of two dimensions of music change in parallel? This situation can be compared to the joint pairing of meta-system and system which was discussed earlier.
If the constraint of redundancy of the many different descriptions of sound (synchronic and diachronically) constrain each other, then the effect of the re- dundancy of one kind of description in music on another would produce non- equilibrium dynamics that could be constitutive of new forms of pattern, new redundancy and emergent constraint. This effect of one aspect of redundancy on another can be measured with Shannon’s concept of relative entropy.

The effect of multiple constraints operating together in this way is similar to the dynamics of autocatalysis: where effectively one constraint amplifies the conditions for the other constraint. What is to stop this process leading to positive feedback? The new constraint, or new dynamic within the whole system is necessary to maintain the stability of the other constraints.

So what happens in the case of the Alberti bass? The relative entropy of the notes played, the rhythm, intervals, and so on would lead to collapse of distinctions between the components: a new component is necessary to attenuate the dynamic.

This helps explain the changes to the relative entropy in Mozart’s sonata. But does it help to explain minimalism? In the music of Glass, there is variation of timbre, and the gradual off-setting of the accompanimental patterns also helps to give the piece structure.

However, whilst the explanation for relative entropy helps to explain why novelty – new ideas, motifs, harmonies, etc. are necessary, it does not help to explain the forms that they take.
In order to understand this, we have to understand the symmetry-breaking principle is working hand-in-hand with the autocatalytic effects of the overlap of redundancy. Novelty is never arbitrary; it is always in “harmony” with what is always there. What this means is that novelty often takes the form of one change to one dimension, whilst other dimensions remain similar in constitution.
Harmony is another way of describing a redundant description. The melody of Mozart’s piano sonata is redundant in the sense that it reinforces the harmony of the accompaniment. The listener is presented with an alternative description of something that had gone before. The redundancy is both synchronic and diachronic.

From a mathematical perspective, what occurs is a shift in entropies over time between different parts.

The coincidence of entropy relations between parts over a period of time is an indication of the emergence of novelty. Symmetry breaking occurs because the essential way out of the hypercycle is the focus on some small difference from which some new structure might emerge. This might be because the combined entropies of multiple levels throw into relief other aspects of variation in the texture.

This would explain the symmetry-breaking of the addition of new voices, the subtle organic changes in harmony and so forth. However, it does not account for the dialectical features of much classical music. However, what must be noted is that the common pattern before any dialectical moment in music is that there is punctuation or silence or cadence. For example, in the Mozart example, the first four-bar phrase if followed by a more ornamental passage where whilst the harmony remains the same, a semiquaver rhythm takes over in the right hand, and in the process introducing more entropy into the diachronic structure.

Once again, within the dialectical features of music, it is not the case that musical moments are arbitrary. Moreover, it is the case that the choice of dialectical moments in which seem to continually surprise but relate to previous elements. Both in the process of composing music, and in the process of listening to it, what is striking is that the shared experience between composer, performer and listener is of a shared profundity. Where does this profundity come from?

The concept of relative entropy is fundamental to all Shannon’s equations. The basic measure of entropy is relative to a notional concept of maximum entropy. This is explicit in Shannon’s equation for redundancy, where in order to specify constraint producing a particular value of entropy, the scalar value of entropy has to be turned into a vector representing the ratio between entropy and maximum entropy. The measurement of mutual information, which is the index of how much information has been transferred, is a measurement the en- tropy of the sender relative to the entropy of the receiver. The problem is that nobody has a clear idea of what maximum entropy actually is, beyond a general statement (borrowed from Ashby) that it is the measurement of the maximum number of states in a system. In a non-ergodic emergent communication, there is no possibility of being able to establish maximum entropy. Relative entropy necessarily involves studying the change of entropy in one dimension relative to the change of entropy in another. One section of music over a particular time period might exhibit a set of descriptions or variables, each of which can be as- signed an entropy (for example, the rhythm or the distribution of notes played). At a different point in time, the relationship between the entropies of the same variables will be different. If we assume that the cause of this difference is the emergent effects of one constraint over another then it would be possible to plot the shifts in entropy from one point to the next and study their relative effects, producing a graph.

Such an approach is revealing because it highlights where entropies move together and where they move apart. What it doesn’t do is address the non- ergodicity problem of where new categories of description – with new entropies – are produced, how to identify them, and how to think about the effect that new categories of redundancy have on existing categories. Does the emergence of a new theme override its origins? Does the articulation of a deeper structure override the articulation of the parts which constitute it? However, the analysis can progress from relative entropy to address these questions if we begin by looking at the patterns of relative entropy from an initial set of variables (say, notes, dynamics, rhythm, harmony). If new dimensions are seen to be emergent from particular patterns of inter-relation between these initial dimensions, then a mechanism for the identification of new dimensions can be articulated. In effect, this is a second-order analysis of first-order changes in relative entropy.

A second point is to say that first-order, second-order and n-order dimen- sions of constraint will each interfere with each other over time. The experience of listening to music is a process of shifts between different orders of description. In Schenker’s music analytical graphs, this basic idea is represented as differ- ent layers of description from deep structure, middleground and foreground. A Shannon equivalent is relative entropy, relative entropy of relative entropy, relative entropy of relative entropy of relative entropy. . . and so on. In the analysis of music (for example, Herbert Brun) and in methods for the construction of musical composition (Xenakis), Shannon entropy has fascinated music scholars. Here we offer a new perspective drawing on the application of Shannon entropy to the analysis of scientific discourse. In this work, we have explored how mu- tual redundancy between different dimensions of communication in a discourse can be used as an index of meaning. In applying this approach to music, we consider the ways in which emergent mutual redundancy and relative entropy between different descriptions of music as it unfolds can identify similar patterns of meaning making in musical communication.

9 Common origins expressed through time

One of the problems of Shannon entropy and the transduction which is essentially expressed by is that, as an aspect of Ashby’s law, it is fundamentally conservative: the Shannon communicative model manages variety. In the same way that the different levels of regulation within Beer’s viable system model work together to articulate coherence of the whole. What Shannon entropy does not do is to articulate a dynamic whereby new things are created. Yet in order to account for music’s continual evolution, and also to account for the shared recognition of profundity, we need an account of the generation of profundity from some common, and simple, origin. 

Beer suggested a way of doing this in his later work which articulates his “Platform for change”. Here the process of emergence is fundamentally about the management of uncertainty.
Uncertainty is an important metaphor for understanding music. After all, for any composer, the question is always “what should I do next?” The choices that are faced by a composer are innumerable. In biology, there is evidence that cellular organization also is coordinated around uncertainty (Torday)

Uncertainty is an aspect of variety: it is basically the failure of a meta system to manage the variety of a system: or at least to fail to identify that which needs to be attenuated, or to attend to the appropriate thing. Yet the dialectical truth of music is that identity is always preserved amidst fluctuating degrees of uncertainty. This can be drawn as a diagram whereby whatever category is identified, which might be rhythm, notes, or whatever is counted within Shannon entropy contains within it its own uncertainty of effective identification.

The uncertainty of identification must be managed through the identification of a category, and this process – a metaprocess of categorical identification – interferes with other processes. In effect it codifies particular events in particular values. Yet the values which are codified will be challenged or changed at some point.

The coordination of uncertainty produces a generative dynamic which can under certain circumstances produce a symmetry. But the critical question is why the symmetry which is produced is common. An answer may lie in the origin of the cell.

I’ve got a diagram to show this. The fundamental feature of an improved mechanism to explain the emergent dynamics of musical innovation is that there is a dual transduction process: an inner transduction process which maintains balance within the identity of an entity, and an outer transduction process which maintains the relation between the identity and its environment. It should be noted that it is precisely this mechanism that exists in cellular communication through the production of protein receptors on the cell surface and the interaction between cells on the outside.

10 Communicative Musicality and relative entropy

Schutz’s understanding that musical communication as a shared experience of time now requires some reflection. If music is the shared experience of time, then what can an approach to understanding of entropy contribute to our understanding of time? The intersubjective experience of music where a shared object of sound provides a common context for the articulation of personal experience and consequently the creating of a ground of being for communication. In this can facilitate the sharing of words, of codified aspects of communication which Luhmann talks about. The remarkable thing with music is that the symmetry breaking of one individual is remarkably like the symmetry breaking of another individual. The choices for advanced emergent structures do not appear to be arbitrary. This may well be because of the synchronic structure of the materiality of sound. However it may go deeper than this. It may be that the essential physical constitution of the cell carries with it some pre-echoes of the physics of sound, which may at some point be united in fundamental physical mechanisms (probably quantum mechanical). There is an empirical need to search for the biological roots of music’s contact with biology. The work in communicative musicality provides a starting point for doing this.