Paul Hirst and the nature of a "subject"

Paul Hirst's forms of knowledge was controversial. It embodied what M.F.D. Young he called an  "absolutist conception of a set of distinct forms of knowledge" whose correspondence to the traditional academic curriculum was, for Young, highly suspect. It looked like a somewhat reactionary move  (see http://www.philosophy-of-education.org/conferences/pdfs/white.pdf for more on this and the link with Hirst and Young). Yet, as R.S. Peters had pointed out, there must be something in the existence of maths, history, science, art rather than bingo or billiards that justified their presence in the curriculum. 

But with all such distinctions, there are many ways of looking at them. For example, we might see maths, science, religion, etc as distinct but related entities just as we see distinct and related fingers on our hand. At the same time, however, we may also see a set of relationships between our fingers (as Bateson pointed out), and in the same way seek to analyse the relationship between the different subjects on the curriculum. In this way, both Paul Hirst's conception of real distinctions between mathematics and art may co-exist with Young's relativist socio-historical processes. This approach carries some merit I believe. For all we might talk about the existence of maths, a maths lesson is in reality a moment in time. It tends last little more than an hour a day at most. It is followed by something different, just as the movement of a symphony contrast with one another.

It is this difference between subjects that interests me, and the ways in which the differences affect different kinds of people. At certain moments, certain people become animated and engaged: and not the same people at the same moments. Why might this be? It might have something to do with their particular state at a particular kind of day. Or it might be something deeper in them: a predisposition to that particular kind of moment in the day (in the same way as some people are of a melancholic or happy disposition). 

Are subjects moments? Or rather, is 'subject' the name that we give to a particular type of moment? The moment of mathematics is different from the moment of music. This is interesting not least because those who dig deep into any subject soon see that in reality it is not that much different from any other subject: music is the same as maths which deals with the same problems as philosophy and science, and so on. Reductionism is absurd.

Yet the moments of educational experience cannot, I think, be reduced to anything. Our abstracting of the curriculum is a way of creating the structural conditions for the reproduction of those moments. This is a bit like the codification of musical form or dances: a rondo is different from a sonata form; or a sarabande is different from gigue. We curse specialisation in the curriculum (particularly if it comes too early), but specialisation can be successful if the particular subject reveals a richness of moments. Music is the classic example of this. Here, there is the gamut of experience in a coherent form of expression and body of technique. Maths can reveal the same; science too. 

So why might we become mathematicians and not musicians or artists and not scientists? Specialisation draws us to the gamut of experience through the lens of the subject. But it is not maths, or science, or music: it is mathematicians, scientists and musicians. What we learn we learn of each other. I think there's something about absence here: about the abences that shape our thinking and our experience. We see someone else whose experience is shaped by a similar kind of absence: like two individuals with the same medical condition, there is a perception of shared constraint.

There are deep shaping influences on our experience. These shaping influences are no doubt different for each individual. I don't think there is a 'maths-shaped' absence or a 'music-shaped' absence. But whatever causes an enthusiasm and talent for music is drawn out through engagement with the subject matter of music. And in the presence of the subject matter, the causal power of the absence is revealed for others to see. Some will recognise it. And in this way musicians, mathematicians and historians are born.

Mathematics and Theory

There can be tendency to see mathematics and theory as two sides of the same coin. General relativity, for example, is a theory with mathematics that supports it. This mathematics gives the theory utility in enabling calculations in accordance with the theory. Moreover, the presence of mathematics in a theory, particularly if the mathematics affords calculation, can enhance the fiduciary quality of the theory: we say "ah, there's maths, and it seems to work - the theory must be correct". Economics (econometrics) suffers from this conflation particularly badly. And in econometrics, what happens is that all-too-frequently, the maths is not very good, and certainly doesn't 'work' in any real sense (it has little predictive and no explanatory power). Yet, its presence is a barrier to having a sensible discussion as to why or why not it doesn't work, or to explaining economic phenomena in a sensible way.

It is a commonplace to remark that maths is like music. But in a very deep way, this can be seen to be true. In fact, maths is like most arts: it's fundamental concern is with form, not calculation. What is revealed by mathematicians are the peculiar forms that our logical faculties - those essential quality of human beings - can take. There are, of course, many strange things that occur. Louis Kauffman showed me this mathematical 'joke' for example:

Euler's identity tells us that:

That means that:

this is where the funny thing happens.. because i appears to re-enter the equation in this way...

which produces this infinite regress:

This is the joke... But I have to confess I didn't really get it when I first saw it, thinking that the joke was in the infinite regress. I confidently taught this back to someone else (puzzling why I wasn't really laughing), only half understanding it (but in the hope that in explaining it I might understand it better...), but Louis pointed out what the real joke was: how can an imaginary number equal a real number?

What's relevant here though is the way that mathematicians think. This is a revealing of logical form. It has a kind of 'cadential' structure (to use a musical analogy): it is satisfying and beautiful. 

Theory on the other hand, is not like this. As I explained yesterday, I think theory is the result of an attempt to reveal this kind of beauty which effectively fails. Theory is a way of accounting for the failure. [this is my theory!]. 

Of course, mathematics has 'theory'. Louis uses category theory to work out his thinking about eigenform and time (which he also explained to me). Is such a theory (like category theory) a theory in the same sense as Luhmann's theory of communication, or Baudrillard's theory of symbolic exchange and hyper-reality? I think they are different, and an artistic metaphor can help expose how they are different.

I wonder if a mathematical theory is like some base material upon which the sculptor works to reveal a form. Category theory is like the 'material' basis whose logical structure can then be exposed through the work of a mathematician. Although most social theories aspire towards this same foundational goal, they tend to be ill-defined, and hence a slippery foundation for making any defensible statements (Baudrillard is particularly bad with this). It may be that the failure of such foundations feeds back into the need to prop-up bad theories with more bad theories. 

It is here that I wonder if listening carefully to the mathematicians and the artists might be a more sensible thing to do, rather than to get increasingly bogged-down with theories...

What is a theory?

I love theory. That's why I love cybernetics. But theory brings it's problems. I want to be right about my  theory. And my theory (which is right) confounds other theories which are wrong. "And it's mine." I'm paraphrasing from the Monty Python sketch about this: Anne Elk's Theory about the Brontosaurus...

Why are we driven to create theory? Do we need it? Whilst we might talk about a search for truth, we also know that truth is to be found by coming to know each other. And coming to know each other is not achieved by trying to convince everyone that my theory is right (because everyone else's theories are right to them!)

I'm thinking about a definition of theory. This is a theory about theory... I want to be right about this...(!) But before I get into the recursion of that, here is the theory of theory that I am thinking about (and it's mine!):

Theory is an epiphenomenon of an attempt to act well

In other words, I do not set out to create a theory; I set out to act well. Theory is a side-effect. But if I act really well, and the product is increased love of one another and increased knowledge, there is no need for anything more; no need for theory. That leads me to a correction of my definition:

Theory is an epiphenomenon of a failed attempt to act well

Now let's deal with the recursion. My theorising is a side-effect of an attempt to act well. My well-intentioned action also leads to my current theory about theory. This action is intended to focus on love and action rather than theory. Yet the action is only partially successful: new theory is the result.

Of course, theory is only really theory if it is articulated (in an academic conference for example). The articulation of a theory is a failed attempt to act well. But less unsuccessful actions can avoid explicit articulation of  a theory whilst using deep insights (which a theory might try to express) to cause change to happen in other ways. I think powerful questioning is one of the best ways of doing this.

Powerful questioning requires insight, humanity and love. It causes deep reflection and the overcoming of barriers. Its expression is open; its effect is social. The insight, humanity and love never needs to be expressed as theory because it is powerful action in its own right.

So what would I do if I were not to produce a theory of theory? Psychotherapist Graham Barnes, who gave a wonderful talk at the American Society for Cybernetics today, has given me a response. Or rather, a question. It is:

"Is my world loving?"

Theory, conversation and teaching

I'm thinking back to my experiences as a music student in Manchester University, and particularly to the privilege of being present in some wonderful seminars with the Lindsay string quartet which were led by Professor Ian Kemp. Kemp was a remarkable teacher whose knowledge of music combined deep theoretical insight with practical common sense and an awareness of music's power. He always valued the experiences of those without theoretical baggage - they had the 'fresh ears' which he and his academic colleagues lost long ago. He was adept at asking penetrating questions of those who were listening for the first time, privileging the value of their experiences and explicitly demonstrating that value to those whose academic music careers had led them to be less open in their hearing.

As I was conducting a workshop on education and technology yesterday at the American Cybernetic Society conference, I was thinking about this approach. The Lindsay seminars were interesting because they combined performance with conversation. They had the form of a masterclass which went beyond simply playing the music, but sought to ask more profound questions about what it all meant. Yesterday in my workshop, I organised people into doing a role-play against a scenario (I did this before with Keith Smyth in our Strategy Cascade events: see http://strategycascade.wordpress.com/). The groups were sent off to play the roles they had been given. They talked, argued, and eventually came to some conclusions which they reported. Thinking about it now, I wonder if this is equivalent to the 'performance' aspect of the music by the Lindsays. 


When they reported back, I tried to coordinated a deeper discussion about learning activity in general, the relation of technology to it, and what happens during a learning activity in terms of how we come to know each other better. Is this (I now ask myself) related in some way to what Kemp did when he would lead a discussion about what the music meant, or how else it could be played? I'm not sure... but I would like to think they might be related. Not just because I would like to be like Ian Kemp as a teacher, but also because it gives me a greater sense of connection between doing something which is clearly profound (talking about music) with doing something rather more prosaic (talking about technology and universities).


I believe the value in any kind of  learning activity is that it focuses the object of knowledge on coming to know each other. Theorists tend not to think like this. Their object of knowledge is an abstraction which tends to only exist in a few brains (or maybe one - the teacher's). That can lead to pathologies of power, imposed authority and potential alienation of students. The ASC conference this year is celebrating the centenary of  Gregory Bateson, and it's been interesting to observe that Bateson had tremendous theoretical insights, but tended to convey these 'from the front'. Kemp was not like this. He was not anti-theory (he knew and was fascinated by lots of theory), but instead of seeing it as an 'answer', he saw it as a tool for guiding his own questioning which in turn would lead out from his students insights which were powerful and valuable. 


I'm nowhere near doing that with my work on educational technology and cybernetics, but I do think it's a good thing to aim for. I think this is the best way to see theory. In a sense it is to make it disappear. If a theory is a good one it can help us to ask powerful questions that elicit powerful responses from those who know nothing of the theory. In the social sciences, I believe we are the theory; theories are not external to us. The power of our theory is in the depth of the insight we gain into each other; it is in our capacity to make each other think and to love each other more.

Meditation, Recursion and Science

I'm at the American Society for Cybernetics conference in Asilomar at the moment, presenting on what I'm increasingly seeing as 'recursive visualisation': the harnessing of real-time technologies for ways of organising groups of people to examine available information and identify what's meaningful to them. With so much information, making group decisions about what's meaningful is difficult. Typically, power relations assert themselves as a way out of the confusion: the boss decides and everyone follows. Technology, I believe, may  provide an alternative to this.

Real-time technologies allow us to 1. look at information; 2. look at our looking at information; 3. look at our looking at our looking at information; etc. A recursive real-time dynamic can be revealing of underlying patterns of meaning-making in each other. What do we find? I think we find out something about  the absences that are shared amongst the group, and in identifying shared absences, we can identify a meaningful course of action. The recursive process is a process of making shared absences determinable. It works in the same way that a fractal (like a mandelbrot set) gradually acquires definition with each iteration of the recursive algorithm. So we go from this:

to this...

What's now interesting me is that this process of 'recursive visualisation' is not a million miles away from medieval practices of copying of manuscripts. What it amounts to is a collaborative meditation on artefacts, and a shared activity in re-realising those artefacts. 

Are we simply learning to become scribes again?

Here's another way of looking at recursive visualisation:

It's the same thing, isn't it? A book which has been copied containing an image of someone copying. I'm finding this quite fascinating.

What is more interesting is the relationship between the Scriptorium and the monastery and then the University. These were places of meditation and learning. What went on was profoundly hermeneutic: a reinspection and re-evaluation of ideas: looking again, and again, and again. What emerged? Was it too a shared conception of absence? In the case of the monastery, of God.

Early scientific knowledge also emerged in these circumstances, and I find that interesting as we think of new ways to do science, to avoid the pathologies of reductionism which our modern universities are so beholden to. I believe we need a participative, reflexive, and common-sense science. That means (I think) harnessing the power of recursive inspection to reveal shared absences: for science, although since the enlightenment, science has focused on the positive, working at the heart of the greatest  scientific discoveries has been an acknowledgment of absence (particularly with people like Newton and Einstein).

So the question is "can technology deliver a different form of scientific enterprise?" I believe it can, and I believe we need to invest resources into trying to make it happen.

The Institution of Education

Institutions everywhere are in crisis: banks, newspapers, political institutions, legal institutions, religious institutions, health institutions... and educational institutions. Beneath all the complexities of each crisis, there seems to be a common thread: the erosion of public trust. We expect our institutions to perform a safe-guarding function for fundamental aspects of our social life: institutions are 'safe'. Banks safeguard our money; the press safeguards our freedom of speech; political institutions safeguard our human rights; legal institutions safeguard justice; religious institutions safeguard morality; health institutions safeguard our right to life; educational institutions safeguard our right to think and to develop our minds, whilst also being a vehicle for accessing employment. The most corrosive thing that can happen to an institution is for the thing that it is meant to safeguard to be seen explicitly to be threatened by the form and function of that institution.

This is what is being seen in the banks at the moment. But what I am interested in is the institution of education, and how the institution of education's role in safeguarding our right to think and develop our minds is increasingly being seen to be under threat by the conduct of the institution itself. What is the nature of the threat? It lies in the various pathologies of education, which in turn are connected to pathologies in science, and in pathologies of all the other institutions: the pathology of education is inseparable from the pathology of politics, or health, or the banks, or newspapers, or the courts or the church.

Freedom of thought is not as easy as it might seem. Received 'wisdom' quickly establishes its own hegemony supported by publishers, scientific communities, the media, and government funding councils. Step outside received wisdom at your peril as an academic: the case of Professor Andrew Wakefield, who raised the question of the link between MMR and autism, is a salutory lesson for any scientist. Skeptics are no longer called skeptics, but deniers. Wiser scientific minds value skeptics (James Lovelock has recently praised the climate change skeptics for keeping climate scientists on their toes and causing a continual self critique and reevaluation). This is very important, but in the highly charged academic environment, it is very difficult.

Often the problems are political. Health cases, like Wakefield's, are a classic case. Into this category also go the HIV/AIDS causal link skeptics (which got Thabo Mbeki into such trouble!). Yet there are important questions to answer there too (what if the conspiracy theorists were right - what sort of collapse in the institution of health would follow a revelation that it was antiretroviral drugs that caused people to die??). But irrespective of politics, little medical research goes without funding from major drugs companies. Walk around any major teaching hospital today, and you will see units funded by Glaxo, AstraZeneca, Pfizer, etc. Surely the consequences of this are obvious? And then we should ask how the drug companies relate to the food companies - to agriculture reseach, GM and so on. So we have to start thinking about things like statins and their relationship to increased fructose in diets (see http://people.csail.mit.edu/seneff/why_statins_dont_really_work.html). Scary stuff.

Then there is the pathology of publishers, who themselves are increasingly wanting to turn education to their own purposes. It's not just with the technologies of journal submission systems which increasingly box-in knowledge into categories that it doesn't fit, or the locking-away of research, or their crucial role in the establishment of academic reputations, but the increasing influence that they have on the very fabric of academic institutions. Government research funding is directly linked to the judgments and behaviour of publishers. Once again, it becomes difficult if not impossible to step outside the system. Increasingly a post in an academic institution - in effect, the right to teach and pass on ones' knowledge - is dependent upon this unholy alliance of judgments and mechanisms.

And related to the publishers, also wanting to get in on the education act, are the global technology companies. Apple has been most active in promoting its e-book standard (actually it's not a standard - it's Apple's deliberate 'breaking' of the EPUB standard (which is a standard), to hook institutions into buying their content through the Apple AppStore). Google's offering of an educational app-suite is a similarly sneaky way of trying to lock-in learners. Banks too, despite the public ire, know that student finances are big business and will be lobbying hard to take it on. With financial institutions and technology companies getting into the mix, it seems to me naive to suppose that there won't be some impact on what actually goes on during learning.

But the institution of education is full of people wanting to keep their jobs. That's always the root of institutional pathology. Self-interest narrows the vision, clouds the judgment and before long the purpose of the institution has been forgotten. In whose interests is this? To what purpose does it serve?

These are the questions which need to be addressed. If the purpose is to safeguard important things, and we see that our institutions are now incapable of safeguarding those things, what should we do? I think there are two questions that should be directed at the institution of education. They are:

1. "How should we safeguard our right to think and develop our minds?"
2. "How should we safeguard fair access to employment?"

These I believe are separable issues (although not separate). 1. concerns research; 2. concerns teaching and assessment. They are linked because research is employment, and therefore it requires some means of providing fair access to it. Both issues have become corrupted by institutional pathologies. 

To deal with 1, I think we need an environment for doing a 'commonsense science'. This is a science which is participatory, diverse and (fundamentally) mixed-ability. It puts as much emphasis on teaching as it does thinking. But the hope is that by being participatory, a critical pursuit of knowledge will be uncorrupted by vested interests of publishers, funders, technology companies, etc. I shall expand on this more in later posts.

To deal with 2, I think we need to consider the role of risk production in learning and assessment, and design teaching and assessment programmes such that learners do not bear undue risks. Assessment criteria should be transparent and available for inspection before a decision to study is taken. Institutions make money (and learners often feel duped) because of a lack of transparency of what is expected. Once more, I will elaborate on this later.

But in summary, we need to rethink what our institutions do and how they do it. We need to address the desire for institutional employees to keep their jobs. But the safeguarding function of institutions does not imply preservation and stasis. Like tradition, safeguarding must be alive, innovative and responsive. Perhaps more than anything, we need a science to understand the interlinked roles of our institutions in allowing spaces to think, resources to be managed, health to be maintained, quality of life to be improved, freedoms to be upheld. I suspect this science will need to focus on the relationship between our knowledge of the physical world and knowledge of the information environment within which we all swim.

Attachment, Security and Conservative Policy

The Conservative government in the UK is producing some eye-watering policy statements at the moment, the most striking one of which appeared today in the form of a proposal to prevent under 25 year-olds from accessing housing benefit. The press speculation is that this is a political move within the Conservative party designed to appeal to hard-core Tory voters (the ones who bemoan scrounging youths who have babies to get council housing).

I don't want to criticise the policy in this post. I want to think how something which appears so oblivious and cavalier regarding the stresses bearing on young people, can be considered by the Conservative party and their supporters as a good idea. I think that in explaining this, we might get a clearer picture on the  real effects of the policy, rather than simply mud-slinging at the government.

Family attachments are complicated. Whether you are wealthy or whether you are poor, the meaningfulness of your life depends on the well-being and success of those closest to you.  Consider that you are a banker, Peter, with two children (Jonathan, 10 and Rebecca, 12) living in a large house in the suburbs (say Harpenden). You have about £1m in investments, some of it in property which you have purchased in London. Your children are at private school, because you passionately believe that anything less will damage their chances of doing well in life. Your wife looks after the children and doesn't work (her zero income is useful for balancing out the tax burden of property income!). You love your children, and your marriage ticks along in a orderly manner without too much undue stress (of course, the healthy financial situation helps with that). You work very hard, rarely getting home before 9 or 10pm.

You are obviously worried about the economic situation. The government being broke and the ensuing recession will threaten your business. Losing your job (which is highly paid) is a possibility. If that happened, then those you love will be affected. The children will have to leave their schools, the houses may have to be sold, the children will not inherit them and get that precious foot-on-the-ladder in the property market. And your marriage, whilst ticking along fine in times of abundance, will be much heavier-going if times are hard ("did she really only marry me for my money?" you think). In short, there is a dark fear lurking in the background. How to avert this?

With the same clarity that  you apply in your professional dealings, the answer is obvious. The government cannot continue to go overdrawn by an additional £2bn a month. The country must live within its means. Where does the money get spent? Housing benefit? For the young? Why can't they live with their parents (everyone should do their bit)?

But the motivation is a fear for security. In fact, the security which has been built up, and which now is protected probably has its roots deep in the childhoods of the bankers themselves. The fears of loss, the memories of their own parents' struggles, of the desire "not to repeat their mistakes" all play in the minds of those who would gladly rip into the public sector in a cleansing ritual of 'financial responsibility'. Jonathan and Rebecca themselves are only the latest in the production-line of this kind of biological programming.

But Brian,21, is the butt of this particular social experiment. He's not worked for 6 months (an apprenticeship in a local garage finished recently - badly). He grew up with a mother who was barely in control of her life. Numerous men passed through the family, some nice, others not. She herself struggled to give Brian her attention - there was too much to deal with; she was too tired. Brian has struggled to maintain relationships, either romantically or socially.

He still sleeps at home. Although he doesn't really sleep - it's unbearable. He longs to get out. But he can't. There is nothing he can do. If he is thrown out, he will be on the streets (he has spent a few nights on the streets in the past). Nobody seems able to help him.

With damaged attachments like this, it is hard to see what is meaningful in Brian's life. Yet there are things which cheer him up. He sees pretty girls - they cheer him up; he watches the football in the pub; and a packet of cigarettes or a spliff will do the trick. He dreams, as anyone else dreams, of love and security. Yet when he wakes, the dream only feeds the frustration of the disconnect between fantasy and reality. There used to be people to help him (that's where the apprenticeship came from). But those support programmes have been cut. Everyone around him, like his mother, has no time, is too tired.

The point about this is that the malaise the Brian suffers from is the same as the malaise that drives Peter to want to make Brian's life even less bearable. Peter's worries have led to the  cuts to the services that might have helped Brian. Yet the similarity between the situations is lost in the political rhetoric.

What it is to be human is precisely what it is to live together. We know this from our own families and those we love. The question about government expenditure and Conservative policy is a question about where we draw the line between those we care for immediately near us, and those whose fates have a causal bearing on our own. David Cameron, and Peter, would like to draw the line around their immediate family. Yet the security they crave cannot arise from exacerbating cruel circumstances of those who are not in the immediate circle. Seeing the connected attachment situation makes this clear.

The £2bn deficit is a sign of a regulatory problem. But in order to identify the causal relations that underly this  regulatory problem, the deeper mechanisms of human living and loving must be inspected. Greater realism about attachments at all levels of society may shed a new light on these problems.