Friday, 13 January 2023

Triad Chords as a "nice noise" (From Plankton to Puccini)

20 years ago, when the Lindsay string quartet retired from Manchester University, Ian Kemp - who had been an inspirational musical figure for me and so many others - returned from retirement to conduct a last "Lindsay session", playing Beethoven and Tippett (which was the favourite diet). Although Ian complained that he was "bad at hearing", his musical intellect remained sharp as tack. 

There was a passage in the music (I think it must have been Tippett) which was very unusual. So he asked, in his typical way, "what's going on here?". By this time, University academics of Kemp's temperament were very rare, and they had been replaced with younger people who were eager to please and were full of "musical analysis terminology". So Ian's question prompted much impressive-sounding jargon. "Perhaps," he said on hearing this, "but maybe it's just a nice noise". 

So what is a nice noise? We hear, with Western ears at least, the major triad as the epitome of musical consonance - a nice noise. It is a resting place, and the tonal geometric relations that form around the triad provide us not only with the "nice noise" of the chord itself, but an unfolding diachronic (and diatonic) space with which we can engineer a sense of arrival and homecoming in tonal music. 


When we learn about triads, we are introduced to the notation, and young pianists are taught how to shape their hands. But something gets added in both these cases. The triad is never "just" the notes. It is never "just the hand-shape". If it was "just the notes", then playing a triad with sine waves would be as satisfying as playing it on the piano. But it isn't - and this is my point: the triad's beauty lies in what occurs outside the notes. It lies in the noise that surrounds it. 

So much of music analysis manages to miss the music. I strongly suspect that Kemp's "nice noise" comment hit the music on the nose. Part of the key to understanding this (pardon the pun) lies in inspecting the relationship between a triad and a note.

Marina Frolova-Walker's fascinating lecture on the triad (see (38) Triads, Major and Minor - YouTubeP includes a nice demonstration of the overtone series and how this relates to the triad. But if we play a note and analyse its harmonics, we see the different harmonics at a couple of octaves above the fundamental note. If we add another note a third above the original note, what actually happens is the overall frequencies become "noisier" - there is a tussle between two fundamental notes which are nevertheless connected. 

Marina does say something about the experience of early musicians in hearing the consonance between two notes. This must have been fascinating and puzzling, because perception struggles to piece together the coherence of sounds which on the one hand interfere with each other, and on the other, agree with each other. The recursive operations of consciousness in the face of this oscillation is possibly comparable to the way that early art features recursive geometric tiling patterns (across many different cultures across the world)

Just as with the oscillations of perception with a tiling pattern, the oscillations of perception with a triad creates a dynamic dance between noise and consonance. As Marina illustrates at the beginning of her talk, Wagner completely understands and demonstrates this dance at the beginning of The Ring. 

The consonance of the triad is not static - it moves. But it moves in a way in which perception becomes fascinated. Understanding this also helps to explain why not everybody in the world has the same music. The issue is not about consonance and dissonance - it is about the relationship between stability, order and noise. Western harmony is one way of managing a dance between these factors, but it depends on particular kinds of social relation which reflect the society that favours that way of doing things. There are many others, just as there are many other kinds of society. 

The role of noise in creating order is much overlooked. Kemp's "nice noise", and the triad itself, is a dynamic relation between noise and order. An energy imbalance is inherent in the first note connecting the physiology of perception and action with the physics of sound. The noise around music is essential in driving forwards the process of unfolding immanent structures in the sound as more energy is produced, and the physiology of expectation adapts. 

I thought a while ago that there was a clear distinction between the synchronic aspects of music and the diachronic aspects. (I wrote about this here: Redundancies in the communication of music: An operationalization of Schutz's ‘Making Music Together’ - Johnson - 2021 - Systems Research and Behavioral Science - Wiley Online Library and here: Communicative Musicality, Learning and Energy: A Holographic Analysis of Sound Online and in the Classroom | SpringerLink). Now I think the synchronic aspects are much more dynamic than I realised. The ancient and medieval theorists who spoke of the divisions of the string and the harmonics ignored the role that perception plays in appreciating the beauty of "real" music, as opposed to mere mathematical relations. But now I see (and hear) that what happens to perception in the experience of the structure of sound is just as dynamic as what happens over time as sound develops. 

There is also something to say here about evolution, and the evolution of music. Michael Spitzer, with whom I've had the privilege of some detailed conversations recently alongside the biologist John Torday, has suggested that music is fundamentally connected to the ocean. He asked me a few weeks ago, after I'd given a talk on "music and epigenetics" about how the primeval ocean connects to Beethoven. It's a great question. Now, I think I would say that the ocean is a noisy environment (Michael says it is the most sonically rich environment on earth). The developmental process of life concerns the continual generation of order (negentropy). What do we need for this order-producing process? Information - in the form of selection is one thing. Constraint is the flip-side of information, and this is also required (technically, this is known as redundancy). But noise is critical. It's only with noise that the latent structures of organisms - from cells upwards - can be "shaken" into finding new ordered configurations. It's the same process - from plankton to Puccini! 

Monday, 26 December 2022

AI and Heterophony

Heterophony is a musical technique where the flow of a single melodic line is followed by many voices, where each voice has a slightly different variation. It is, like repetition and harmony, one of the fundamental forms of redundancy in music. It is also perhaps the most interesting because it reflects the ways in which a single structure unfolding over time can be represented in multiple ways. These multiple ways come together because the heterophony arises from the fact that we are all fundamentally the same, with a bit of variation. 

There is a certain sense in which AI is heterophonic. It obviously relies on redundancy in order to make its judgements, and with things like chatGPT, the redundancy is increasingly obvious not just in the AI itself, but in human-machine relations. All AI relies on the differences between heterophonic voices in order to learn. We seem to be similar in our own learning. 

From a musical point of view, heterophony is most closely associated with non-Western music. Among the western composers who developed it in their music, the most striking example is Britten. While some of Britten's heterophony is a kind of cultural appropriation, I've been wondering recently whether he discovered something in heterophony which was always in his music. The predominance of 7ths and contrary motion in his very early "Holiday Diary" suggests to me a kind of heterophony which, by the time of his last (3rd) quartet (https://youtu.be/AElJ08gIOOM - particularly the first and last movements) becomes distilled into a very simple and ethereal world of crystalline textures. The fact that he went via his discovery of Balinese music was not an indication of appropriation, but self discovery. Unlike Tippett, he didn't say much about his thought and processes, but like all great artists, he might have been picking something up from the future - or rather, something that connects the future with the past. 


There is something of this heterophonic aspect to early music (lots of it in the Fitzwilliam Virginal Book, for example). While parts move not so much in unison but in 3rds and 6ths, the rhythmic interplay of one part moving slowly and other parts moving much more quickly is very similar to the rhythms that unfold naturally through the interactions of heterophony. I'd always taken this rhythmic polyphony as a sign of unity in diversity, but the connection to heterophony gives it more depth for me - particularly now. 

So what about heterophony today? We have got used to a particular kind of redundancy in music produced through harmony and tonality. It is partly the product of the enlightenment, and it places the order of humanity above the order of nature. AI is generating a human-like order of utterances by decomposing a kind of natural order, and its decomposition process is both fundamentally heterophonic and fractal. AI works like a singer in a heterophonic choir, listening to where the tune is going, calculating which way it will go next, and checking to see if it was right or not. In this process, there is difference, form, fluctuation of constraint, expectation, and relation. 

We have an urgent need to understand this process, and heterophonic music provides us with one way of doing it. Also, perhaps curiously, it takes us away from the enlightenment mindset which on the one hand has given us so much, but which has also done so much damage to our environment. It is not Victorian orientalism to connect with fundamental processes that steer our collective will and judgement-making. But there may have been more to the pull of orientalism than mere fashion. I suspect Britten saw this. 

Maybe Britten wasn't tuning-in to the way AI works (how could he?), but rather he was tuning in to something that is intrinsic to our biology. Is our physiology heterophonic? Is quantum mechanics? The fact that our AI is is perhaps also a reflection that there is something in us which has always been this way. This, to me, is another reason for us to listen more carefully. Not that we should listen to the same thing, but look out for the stream and try to follow it. 

While there are tremendous technical advances being made at breakneck speed at the moment, understanding where we are culturally and spiritually is vital. We have existed for many decades in a fog where our ability to reconcile our physiology with our technology has led to a tragic disequilibrium. We have almost ceased to believe that a new equilibrium is possible. But it might be. 

Sunday, 6 November 2022

Viability and the AI business - Some thoughts on Musk, OpenAI and Twitter

Just for the sake of an intellectual exercise, imagine that through some unusual stroke of luck (or misfortune) someone finds themselves at the head of a venture which spins out of an AI-related academic project. As if one of those (usually hopeless) EU education projects actually produced something that somebody else not only wanted but was willing to pay a lot of money for. A number of things follow on from this. 

Firstly, the university who (probably) made life very difficult for the people who came up with and developed the idea, probably sneered at any claim that "this is important work", or at appeals to protect key people, late in the day turns round and says "this will make us millions! it's our intellectual property". While market conditions change quickly, the university drags its feet in negotiating a handover of IP and the writing of patents. Over a year goes by, everyone tears their hair out, but eventually things are signed. Universities have become very weird organisations that ape commercial practices without really understanding why they do it, or thinking about whether it is sensible. 

Secondly, a spin-out company with freedom to operate is one thing, but this needs funding. The mode of thinking for academic spin-outs is similar to the mode of thinking of academic projects - how to get funding? It should be said that VC funding cannot be gained unless you have experienced people who know how to deal with VC firms. But say, for the sake of argument (through another stroke of luck) that this is in place. The danger of this mode of thinking is that getting funding becomes the prime objective. There may be a point, however, where it is so obvious that a spin-out product is so desirable to potential customers, that the getting of funding is not a question. That raises the third question:

What kind of a business are we?

So you might have funding which might keep your operation going for a year or so before you need to be raising revenue through sales. What are the conditions for your viability?  This is where an AI business is weird and interesting, and this sheds light on Elon Musk, Twitter and OpenAI.

Successful and viable businesses typically have a set of operations which produce things - products, services, etc - for a customer base which pays for those products and services. Among the different regulating mechanisms within any such business will be some kind of operational management which ensures effective coordination of the production operations, marketing and so on. Since all businesses operate within changing market conditions, all viable businesses will develop an R&D arm which is scanning the horizon for new opportunities and advising on strategy. Some business will hire software developers to develop new solutions to internal operational challenges. R&D looks to the future and potential scenarios, operations are focused on the present - there is often tension between them, and good businesses balance one against the other. Interesting to note that Elon Musk's current restructuring of Twitter is basically trying to rebalance the relationship between R&D and operations within that company (which is losing money). 

An AI is a specific kind of technology. In the above scenario, it fits within a company's R&D structure. In itself, it is not about operations. Musk's OpenAI is a good example. It makes itself available as an API which can be plugged-in to the R&D operations of other businesses who will use it to automate writing tasks that would once have been a function within the operations of a company. Through adopting OpenAI services, those operations are restructured, people moved (or removed), and the operations restructured. 

Now look at OpenAI itself as a business. As a business, it appears to have few customer-facing  operations apart from sales and marketing. It develops and provides access to machine learning models which sit on the internet (although from a technological perspective, these models are just files which could sit anywhere - even on individual devices). Its customer-base is a community of users who integrate its services into high-end heavy usage corporate operations for which they pay subscriptions. OpenAI must maintain the scarcity of what it does (in the face of continual innovation in AI), and ensure that customers keep buying its services. That means that OpenAI's own R&D must outpace the R&D of its customers - or rather, OpenAI's customers see that a good chunk of their own R&D is best outsourced to OpenAI. 

I think this is a problematic business model because effective R&D relies on having a good model of the organisation of which it is part. R&D without a concrete set of business operations attached is potentially root-less - it's not part of a viable operation, and could therefore lack coherent direction. This may be the most important reason why Musk was so keen to buy Twitter: it gives him an operational infrastructure, to which he (no doubt) believes his R&D company (OpenAI) can restructure and make profitable. 

With a set of operations to manage, an AI business can grow its services and see the effect of its developments on the viability of the whole organisation. Some things will work, other things won't. Sometimes operational requirements will override whatever new innovation is suggested by R&D. Other times, the R&D is critical to maintain organisational effectiveness. Moreover, an AI business in this situation could extend its reach beyond a "host" organisation, offering services to other organisations. The only problem is that in doing so, other organisations might become competitors to the original host organisation. This requires new thinking about corporate cooperation and market competition. 

This is the most fascinating question about all AI businesses. They are surrogate R&D operations without operational attachments. If an AI was a human system it would be like the pathology of when a university's management believes it is the university (see this many times!), and that the current operations (academics, administrators) could be replaced by another set of operations. Equally mad is the belief that management is generic and transplantable, as in the idea of "institutional isomorphism".  Management without operations isn't viable. 

But it's technological form is different - AI exists as a concrete coherent thing that provides services to R&D which can be genuinely useful. These services require R&D themselves - which is the regulatory domain of the AI company itself, but the whole thing demands some kind of operational "host". An AI company is a kind of "virus", and its best chances of preserving its viability is reproduction in other hosts. Reproduction of the AI is in the interests of the original host because it grows the AI business, but it must do so in such a way that other hosts do not become competitors to each other. 

The dynamics of this are different to the traditional ways we think about organisational viability and competition. Traditional businesses compete for resources (sales, income) by acquiring market share in the products they produce. They may seek to establish monopolies by acquisition of competitors to remove threats and increase profits through creating scarcity in the market (which then requires regulation by government). But AI is presenting a dynamic of what might be called "organisational environmental endogenisation". That is to say, something in the environment which threatens the viability of organisations - AI - is endogenised (assimilated) within an organisational structure in order to transform that organisational structure so it is better able to maintain its viability and profitability. As part of maintaining its viability, growing the endogenised element and then getting it to "infect" other entities becomes a critical part of the viable operation. This is not to neutralise competition, but rather to increase the strength of the ecology within which organisations sit and within which they can continue to grow and develop better R&D operations. 

There is something a bit odious about Musk. But equally, there is something important happening around technology at the moment which presents organisational questions which are unavoidable for anyone looking at the future of business, organisational viability and society. It's urgent that we think this through. I'm incredibly fortunate to be in a position where I'm grappling with this at first hand. 

Tuesday, 25 October 2022

Postdigital values, Marion Milner and John Seddon

I'm giving a talk on Thursday at the Carnet Users Conference (https://cuc.carnet.hr/2022/en/programme/) as part of the extensive strand on "postdigital education". My talk has gone under the rather pompous title of "Practical Postdigital Axiology" - which is the title of a book chapter I am writing for the Postdigital group - but really this title is about something very simple. It's about "values" (axiology is the study of value), and values are things which result from processes in which each of us is an active participant. Importantly, technology provides new ways of influencing the processes involved in making and maintaining values. 

It's become fashionable in recent years to worry about the ethics of technology, and to write voluminous papers about what technology ought to be or how we should not use it. In most cases in this kind of discourse, there is an emotional component which is uninspected. It is what MacIntyre calls "emotivism" in ethical inquiry (in After Virtue), and it is part of what he blames for the decline in the intellectual rigour of ethical thought in modern times. 

I wonder if the emotivism that MacIntyre complains of relates more to mechanisms of value which precede ethics. Certainly, emotivist ethical thought is confused with value-based processes. The emotion comes through in expressing something as "unethical" when in fact what has happened is that there is a misalignment of values usually between those who make decisions, and those who are subject to those decisions. More deeply, this occurs because those in power believe they have the right to impose new conditions or technologies on others. This would not happen if we understood the benefit to all of effective organisation as that form of organisation where values are aligned. This suggests to me that the serious study of value - axiology - is what we should be focusing on. 

I think this approach to value is a core principle behind the idea of the "postdigital". This label has resulted from a mix of critique of technology alongside a deeper awareness that we are all now swimming in this stuff. A scientific appreciation of what we are swimming in is needed, and for me, the postdigital science has a key objective in understanding the mechanisms which underpin our social relations in an environment of technology. It is about understanding the "betweenness" of relations, and I think our values are a key things that sit between us. 

This orientation towards the betweenness of value is not new - indeed it predates the digital. In my talk, I am going to begin with Marion Milner, who in the early 1930s studied the education system from a psychoanalytic perspective. In her "The Human Problem in Schools", she sought to uncover the deeper psychodynamics that bound teachers, students and parents together in education. It is brilliant (and very practical) work which in education research has gone largely ignored. In her book, Milner made a striking statement:

"much of the time now spent in exhortation is fruitless; and that the same amount of time given to the attempt to understand what is happening would, very often, make it possible for difficult [students] to become co-operative rather than passively or actively resistant. It seems also to be true that very often it is not necessary to do anything; the implicit change in relationship that results when the adult is sympathetically aware of the child's difficulties is in itself sufficient."

This is a practical axiological strategy. If in our educational research with technology, we sought to manage the "implicit change in relationship that results when the "teacher" or "manager" is sympathetically aware of the "other's" difficulties" then we would achieve far more. Partly this is because we would be aware of the uncertainties and contingencies in our own judgements and the judgements of others, and we would act (or not act) accordingly. What are presented as "ethical" problems are almost always the result unacknowledged uncertainties. Even with things like machine learning and "bias", the problem lies in the overlooking or ignoring of uncertainty in classification, not in any substantive problem of the technology. 

In my new job in the occupational health department at Manchester university (which is turning into something really interesting), there is a similar issue of value-related intervention. One of the emerging challenges in occupational health is the rising levels of stress and burnout - particularly in service industries. A few years ago I invited John Seddon to talk at a conference I organised on "Healthy Organisations". It was a weird, playful but emotional conference (two people cried because it was the first time they had a chance to express how exhausted they were), but Seddon's message struck home. It was that stress is produced by what he calls "Failure demand" - i.e. the system being misaligned and making more work for itself. The actual demand that the system is meant to manage is, according to Seddon, often stable. 

It strikes me that Seddon's call to "study the demand" is much the same idea as contained in Milner's statement. It is not, strictly speaking, to do nothing. But it is to listen to what is actually demanded by the environment and to respond to it appropriately. That way, we can understand the potential value conflicts that exist, and deal with them constructively. 


Friday, 14 October 2022

The Structure of Entropy

One of the things I've been doing recently in my academic work is examining the ebb-and-flow of experience as shifts in entropy in different dimensions. It began with a paper with Loet Leydesdorff for Systems Research and Behavioural Science on music: https://onlinelibrary.wiley.com/doi/full/10.1002/sres.2738?af=R, and a paper on the entropy of student reflection and personal learning https://www.tandfonline.com/doi/abs/10.1080/10494820.2020.1799030 and has continued in a recent paper on the sonic environment for Postdigital Science and education. 

I have been fascinated by the visualisations and entropy graphs of different phenomena, partly because it provides a way of comparing the shifts of entropy of different heterogenous variables all in the same scale: so, one can consider sound as frequency together with the entropy of words, together with the entropy of things happening in video. The principal feature of this is that the flow of experience is a counterpoint of different variables, and the fundamental theoretical question I have asked concerns the underlying mechanism which coordinates the dance between entropies.

Another way of talking about this dance is to say that entropy has a "structure". Loet Leydesdorff commented on this in conversation at the weekend after I shared some recent analysis of music with him (see below). Interestingly, to talk of the structure of entropy is to invite a recursion: there must be an entropy of structured entropy. Indeed, Shannon's equation is surprisingly flexible in being able to shed light on a vast range of problems. 

To understand why this might be important, we have to think about what happens in the flow of experience. I think one of the most important things that happens (again, I have got this from Loet) is that we anticipate things: we build models of the world so that we have some idea of what is going to happen next. These anticipatory models work with multiple descriptions of the world - there is "mutual redundancy" between the different variables which represent our experience, and I think Loet is right that this mutual redundancy produces an interference pattern which is a kind of fractal. It makes sense to think that anything anticipatory is fractal because in order to anticipate, we must be able to identify a pattern from past experience and map it on to possible future experience. Also, there is further evidence for this because it is basically how machine learning techniques like convolutional neural networks work.

Fractals are self-segmenting: the distinction between patterns at different orders of scale emerges from the self-referential dynamics which produce them. At certain regular points, the interference between different variables produces "nothing" - some gap in pattern which demarcates it. In the paper on music, I suggested that this production of nothing was related to the production of silence, and how music seems to play with redundancies (which is another way of producing nothing) as a way of eventually constructing an anticipation that a piece is going to end. 

I made this video last week about a Haydn piano sonata as a way of explaining my thinking to Loet:


The entropy graph I displayed here uses a Fast Fourier Transform to analyse the frequency of the sound, identifying the dominant pitch, the richness of the texture and the volume of the sound, and calculates the entropy of those variables. This graph illustrates the "structure of entropy" - and of course, eventually everything stops.

I think learning and curiosity is like this too. It too is full of redundancy, and the entropy of learning has a similar kind of dance to music. Indeed, sound is one of the key variables in learning (this is what my recent PDSE paper is about). But it's not just sound. Light also is critical - it's so interesting that our computer screens basically produce patterns of light, and yet there is so little research on light's impact on learning. And indeed, the entropy of light and the entropy of sound can be related in exactly the same way that I explore the entropy of the frequency in this video.

As to what structures the dance of entropy, I think we have to look to our physiology. It is as if there is a deeper dance going on between our physiology and our interactions with our environment. What drives that? It's probably deep in our cells - in our evolutionary history - but something drives us to shape entropies in the way we do. 

Sunday, 2 October 2022

Sleeping and Learning

If learning is about making new distinctions, there is a question about how we know a distinction. Since all distinctions have two sides (an inside and an outside) our knowledge of a new distinction must be able to apprehend both sides of it. So we must be able to cross the thresholds of our distinctions. At the same time, if we are not inside our distinctions - if we are not able to use them as a lens to view the world - they are useless in a practical way. Yet the distinctions which make up our lens are dependent on our being able to cross their threshold and see no distinctions. Is this sleep and dreaming?

We don't understand why we sleep. Except that we know that if we don't sleep, we die. That suggests that it is not just our conscious distinctions that require stepping outside of themselves, but the  physiological distinctions between cells, organs, etc. If they break down, we're dead. 

At the same time, we know - at least anecdotally - that we learn in our sleep. We wake up in the morning having not been able to do something the day before, and find ourselves improved in our performance. Possibly because we've got "more energy" - but what's that? Thinking about distinctions necessitating boundary crossing helps here.

The Freudian "primary process" is the dream world of no distinctions. The world of the new baby. The "secondary process" is the regulating filter which channels the energy from the primary process into useful distinctions which (for adults at least) are conditioned by the social conventions of the "superego". (Talcott Parsons correctly recognised that Freud's superego was sociological). More to the point, this psychodynamic process between ego, id and superego was continual: a kind of pulse between the "oceanic" primary process and the secondary process. 

In education, the superego rules, and technology has ensured that its grip on the imagination of staff and students has become every more brutal. But technology outside education stimulates and suppresses the id: from cat videos to shopping to porn, we can inhabit a simulated oceanic state. Only in sleep itself is there some contact with the reality of the id.  

What have we missed in the way that we think about learning? When we examine our metrics for competency, our "constructive alignments", assessment schemes, etc, we seem to have assumed that the distinctions of learning are fixed: once we learning something it stays there. In conscious experience this looks like a sensible proposition. But to assume this misses the possibility that our distinctions appear persistent precisely because they result from a dynamic process of distinction and undistinction. 

To be clearer about this, the deepest encounter with the oceanic experience comes through an intersubjective acknowledgement of uncertainty. That can be the best teaching - not the delivery of content, or the forcing of distinctions written in textbooks, but the revealing of understanding by a teacher to the point of revealing of uncertainty. "I'm not sure what this means - what do you think?"

I've written about this kind of thing here: Digitalization and Uncertainty in the University: Coherence and Collegiality Through a Metacurriculum (springer.com), and this last week I got a further reminder of the importance of this approach in an EU project which Danielle Hagood and I led around digitalization. In both cases, technology was the stimulus for uncertainty and dialogue. It is the technology which takes us to the oceanic state, from where (and this was quite obvious in my EU project) new distinctions and new thinking emerges. 

The dialogical is the closest thing we have to the primary process in education - it is rather like music because it connects us to more fundamental mechanisms. John Torday suggested in conversation last week that in sleep our cells realign themselves with their evolutionary origins, effectively connecting our waking thoughts (what Bohm calls the "explicate order") with fundamental nature ("implicate order"). That's a wild idea - but I quite like it!

Wednesday, 21 September 2022

About Learning and de-growth

Seymour Papert argued that we do not have a word for the art of learning in the same way that we have words for the art of teaching (pedagogy, didactics) (see his "A word for learning": http://ccl.northwestern.edu/constructionism/2012LS452/assignments/2/wordforlearning.9-24.pdf). Papert then suggests the word "mathetics", drawing attention to the fact that "mathematics" appropriated the word for learning to refer to its specialised practices, when the word "Mathematikos" simply meant "disposed to learn". There may be deeper things to explore in this etymological relationship. 

We tend to think of learning as a kind of growth. As we learn, we know "more stuff", we gain "more knowledge", and we might even imagine that we get bigger heads! Babies start small and get bigger (up to a point), and as they get bigger they learn. Learning produces material artefacts which certainly do increase in size - before the internet, knowing more stuff meant more books, and (perhaps) a bigger library (to display as our zoom background!). The bigger the library the cleverer the people.

I was listening to Neil Selwyn talking about "de-growth" as a possible response to climate change and thinking about how education might support this (here: https://media.ed.ac.uk/playlist/dedicated/79280571/1_6u9a41zh/1_l7anxlgx). Crudely, we imagine that our ecological crisis is caused because things have grown too big, and that to address it, we need to "degrow". But what do we mean by "big" or even "growth"? My favourite source for thinking about this is Illich's "Tools for Conviviality". He talks about the outsized growth of technology and institutions beginning as beneficent, and becoming malevolent. The causes for the transition from beneficence to malevolence are mysterious - they may lie in our physiology and evolutionary biology (that's another post). But the actual manifestation of pathology is not size - it is a reduction in variety. Illich's clearest example is 100 shovels and 100 people digging a hole, which is eventually replaced by one person and a JCB. Which has the greater variety? The loss of variety as the technology becomes more powerful results in an increase in the creation of scarcity - and the "regimes of scarcity" are the ultimate propellent for positive feedback loops and accelerating crisis. 

The ecological crisis is a crisis resulting from the loss of variety caused by modern living, and within modern living, we must include education. No human institution excels in the art of producing scarcity more than education. The rocket fuel for the rest of the ecological crisis lies at the classroom door. But we can't seem to help ourselves. We see education as the solution to our troubles, not the cause! Education will teach us to "de-grow"... quick! roll-up for "degrowth 101"! Why do we do this? It is because we mistake education for learning. 

We tend not to see learning but instead see "education" in the same way that we tend not to see health but instead see "health systems". "Education" (and "health systems") get bigger and more powerful - rather like the library which forms part of educational institutions. As they get bigger and more powerful they lose variety (look at the NHS today). But "learning" (and "health") do not grow or get bigger. Both of these terms refer to processes which relate an organism (a person, a community, an institution) with its environment. These terms relate to the capacity of any organism to maintain their viability within their environment - indeed "health" and "learning" are deeply connected concepts. Learning is not about growth, but about homeostasis. 

Having said this, it's obvious that as we get older, we learn more stuff, we can do more things, we talk to more people, and so on. But we are really in a continual process of communion with a changing environment. Babies may seem to learn to scream to get attention, but their physiological context is changing alongside an epigenetic environment within which what it is to remain viable is a continual moving target. The education system appears to be a way of forcing certain kinds of environmental change, and as a result insisting on certain physiological responses (which appear to reproduce regimes of scarcity, and social inequality). Indeed, what we call "growth" is an outward manifestation of an unfolding of physiological potential in a changing environment. If growth was as fundamental as the "de-growth" people say, why does anything stop growing?

So if learning is not about growth, but about the viability of an organism in an environment, how can we visualise it differently? One way is to think about it mathematically - and so to draw back to the origin of the word for mathematics, mathematikos and "mathetic". If learning is a process of variety management, and a developing environment has differing levels of variety (and indeed, increasing entropy), then learning is really a process of finding a kind of resonance with that environment. These orders of variety and variety management might be rather like orders of prime numbers, or different levels of scale in a fractal, or different orders of infinity. Mathematically, we might be able to see learning in geometrical forms produced through cymatic patterns:

or knot topologies, 

Or Fourier analysis, or even in Stafford Beer's syntegrity Icosahedron (see Beer's book "Beyond Dispute" https://edisciplinas.usp.br/pluginfile.php/3355083/mod_resource/content/1/Stafford%20Beer_Beyond%20Dispute.pdf):

These forms are expressions of relations, not quantifications of size. If we see size (and growth) as the problem we don't only miss the point, but we feed the pathology. 

We urgently need a more scientific approach to learning. We are going to need our technologies to achieve this. This is not ed-tech, but technology that is necessary to help us understand the nature of relationship. I fear that for those consumed with ed-tech, blaming it for the demise of "education", a different kind of approach to technology and a more scientific approach to learning is not a thinkable thought. 

I feel the need to make this thinkable is now very important.