The work of pedagogy – Wayne Hugo Keynote at the Legitimation Code Theory Conference – Cape Town – June 2015

And he dreamed, and behold a ladder set up on the earth, and the top of it reached to heaven: and behold the angels of God ascending and descending on it. And,

behold, the LORD stood above it

 In 1900, Freud published what proved to be one of the founding texts of the 20th Century - The Interpretation of Dreams. In it he laid out the operating principles of how dreams work. A dream is an expression of a wish that desperately wants to get out but is repressed, so it transforms or mutates itself into something that cannot easily be recognized. Two key operating principles that work this transformation are condensation and displacement.

Condensation works by condensing many different ideas into one representative, most of the ideas are acceptable, one is not, so the repressed wish gets through under cover of all the others.

Displacement worked by taking a small element and using it as a replacement for the larger unacceptable whole - the part gets through when the whole would not have.

Condensation works like a metaphor – many ideas from different domains are held as one; displacement works like metonymy - the part replaces the whole. The pedagogic process, like dreams, is hard to analyze. It isfluid, unpredictable, adapts to circumstances, can take many paths from one decision point and then many paths again. These pathings are directed towards a goal of learning something, and this something is part of an evergrowing knowledge base that needs to be made sense of by the human species to replicate itself, prevent its extinction, and hopefully make itself worthy of being theuniverse becoming aware of itself. More and more needs tobe learnt in less and less time and it is the pedagogic act that bridges this ever enlarging and narrowing gap. It makes the pedagogic process both heroic and tragic as it bravely climbs up and down increasingly difficult andproliferating ladders of knowledge.

Unlike a dream work that tries to smuggle a repressed item through censorship by twisting and hiding, pedagogicwork tries to throw a precise and clear light onto what needs to be learnt. Curiously, however, both the dream work and pedagogic work use condensation and displacement– but in very different ways and towards very different ends. Curiouser still, recent research in classrooms has thrown up two key operating principles of pedagogy in semantic gravity and semantic density that profoundly speak to how condensation and displacement pedagogically function. In this keynote I want to track the connectionsby acting out how condensation and displacement intersectwith semantic gravity and semantic density. Introduced like this, the keynote sounds overly esoteric, but I promise it is not. The intention is to open out in a clear way specific dimensions of how pedagogy works.

Semantic gravity and semantic density both have

‘semantic’ in front of them and semantics has to do with the study of how meaning works, and given that both pedagogic work and dream work engage continuously with meaning making, semantics is a key technical area for educational analysis to master. To get a grip on this area and the connection between dream work and pedagogic work we can start with a basic distinction developed by Jakobson – the axis of selection and the axis of combination. 

It simply points to the continuous process of selecting one word from a possible range and then combining it withanother word that also has many possible variations. We do this all the time when speaking or writing and it is the basic operating logic of pedagogy - to select from a number of possible options and then combine the selectionwith another selection - it is what forms a sequence.

The pedagogic purpose, however, is different to that of everyday communication. Pedagogy has built into it the drive to master the basic knowledge structures and practices necessary for human flourishing in the world, and this means it is a cumulative project of increasing complexity and differentiation, for the knowledge we needto reproduce our world is increasingly complex and differentiated, and has to be learnt anew by each generation thrown into this world. Everyday communicationbetween adults already assumes you know the background and context for the communication, enabling quick and light conversation. Garfinkel demonstrated this with his breaching experiments where he got experimenters to ask for clarification about taken for granted assumptions andmeanings in everyday situations. Here is an example:

SUBJECT: Hi. How is your girlfriend feeling?EXPERIMENTER: What do you mean “How is she feeling?” Do you mean physically or mentally?SUBJECT: I mean how is she feeling. What’s the matter with you?

The subject gets irritated by the request for technical clarification. Imagine a similar scene playing out in a

classroom:

TEACHER: What is the difference between emotions and feelingsSTUDENT: I am not sure. Maybe feelings are weaker than emotions?TEACHER: Good! Feelings are more low key, emotions more intense - so is joy an emotion or a feeling?STUDENT: An emotion because it is intense?TEACHER: Yes! and happiness?STUDENT: A feeling?TEACHER: Yes! Why?

As an aside, neither of these examples gets to the real complexity of feelings and emotions, especially of the passive aggressive type.

The pedagogic act partly exists in the everyday world, but it also specifically works with meanings that are notfully understood and need to be learnt. It makes distinctions, draws attention to features, responds positively to questions of clarification, pushes for formal conclusions, and evaluates responses. Pedagogy selects and combines for an increasing build up of complexity in a liminal state that exists between the known and the unknown, or in terms of Jacob’s ladder - from the profane to the sacred. It means that the trajectory of selection and combination is not a horizontal movement forward, but a diagonal movement upwards - it is a spiraling ladder not a track. The trajectory can circle back on itself to consolidate and check, but then it uses the consolidation as a step to spiral upwards.

How does this pedagogic act of selecting and combining result in increased complexity? 

Take the axis of selection - there is a need to be clear about what terms are selected, and to do this there has to be a stripping away of the multitudinous options and afocusing on a few select and ordered possibilities. Thereis a need to strip the possible selections down and keep their possible relations clear.  Note that this is

opposite of the way the dream work operates where proliferation and disguise happens so that the one repressed wish can find its way through. Why does pedagogy strip? Because local experiences are rich, varied, erratic, and contextually bound, resulting in it being difficult to work systematically with selection options.  A gorgeous smorgasbord of features presents itself, dripping with all the sauces of local life. It ishard to select one feature and clearly see its differences and relations to others, making it difficult to build up a knowledge structure that holds beyond localand contextual conditions. At this point I need to very clear about the move I am pushing towards in terms of pedagogy developing complexity - and that is to work withselection as abstraction. I define abstraction as a systematic process of selection that throws away masses of detail in order to focus on a specific property or relation of an object or process. It strips something down to the bare bones of what is needed - it abstracts, or takes away, not until nothing is left, but until something specific is isolated that can be worked with inits own terms. This is precisely the opposite way that a dream works, where extra masses of details and connections are added in to obscure and hide the key message so that it can smuggle through censorship unseen.

We can use how the Singapore Math programme teaches part whole relationships to demonstrate how details are stripped away to leave the essence - until only what is needed is foregrounded - nothing else.

Firstly we start in the thick of everyday living with a concrete object most children have - a ball - but insteadof playing with the ball in the messy complex world of the playground, much of the context is stripped away and left are only five balls in front of children on a desk. One child (Anne) is given three balls and another child (Bob) two balls and then the two groups of balls are put together and the total number of balls worked out. This can be repeated with different children but the total added will always be five. Once the children are comfortable with adding concrete objects, then the

concrete balls are drawn within boxes, asking a question of what the total number of balls are if Anne has three balls and Bob two balls, also represented as 3 + 2 = 5.

This is a double act of shifting from a concrete objects to abstract representation and of stripping away details,where what counts now is the number not who actually has the balls. The next move is getting the children to draw the boxes without the objects.

Again, there is a stripping away of detail so that the essential focus point of number without the token ball emerges, and also an increase of abstraction where simpleempty boxes represent the number of balls.  

The stripping away of detail is not enough yet to get at the part / whole concept. The box of three balls becomesone part and the box of two balls another part.

Eliminated are the individual balls as well as each individual number, left are just two parts and one whole - and the learners find the whole by adding the two parts.

The relationship between three quantities (the whole and 2 parts) is now all that is there is and the learner can be asked how to find the whole (add the two parts) and how to find the part when we are given the whole and the other part - subtract the known part from the known wholeto get the unknown part.

Part + Part = WholeWhole - Part = Part

Notice that this taking away of details eventually

results in only the specific actions and relations tied to the selection ‘part whole concept’ counting. It is these relations and connections that are worked with. Thepedagogic situation started out with a far richer and more embodied experience, because this was familiar and tangible, whereas the formalization of how part whole relations work is unfamiliar and highly specific. But notice, when the purity of the abstraction was reached, rules developed about how the part whole concept worked. The abstraction, operating at its purest, at its leanest,produced rules of operation that elaborated the abstraction, not in terms of extraneous details but in terms of how the parts and wholes work with each other - the simplification produced elaboration. We can put thisprocess into a mantra - in the difference find the same; within the same find difference.

This abstraction of the part whole concept is combined with other abstractions - for example the part whole concept is combined with the change concept and comparison concept to provide the basic foundations of mathematical thinking.

But each of these two other abstractions also have to move from concrete and embodied examples to a more abstract and specific formulation. These three abstractions, each of which have radically simplified thefocus now begin to produce relations and rules between themselves that develop an increasingly complex knowledgesystem that is not dependent on moving from the concrete and embodied to the abstract, but stays in the abstract world and generates rules from within its simplified space. 

I want to highlight the strangeness of what is happening - it is the stripping away of extraneous detail that results in increasing density of operations and rules as formal implications increasingly build upwards from the simple selection. Abstraction and densification do not happen simultaneously in this example, but the process ofabstraction and densification need each other. First you strip, then you elaborate. Instead of using the cornucopia of existence as the base for selection, now a precise and internally organized selection combination process arises.

Lets now take a look at a similar process, but use a Biology exemplar where a well understood situation or event is used as a template to grasp a situation that is

yet to be understood. I want to use the example used by both Maton and Martin to discuss how semantic density andsemantic gravity work - the humble cilia - tiny hairs in your respiratory system that move mucus away from your lungs to your throat. 

A teacher, needing to introduce this complex topic ‘cilia’ can start with a far more familiar experience - snot - and how it lands up coming out our noses or goingdown our throats where we swallow it into our stomachs.

Instead of selecting the term ‘cilia’ she could use a related everyday term ‘snot’ as a starter. When selectinghow to start she uses a metonymic term that is closely tied up with cilia but far better understood in everyday terms. Cilia move snot around - but rather than use the term ‘cilia’ she uses the term snot.

She uses the experienced and familiar part of the process as a representative for the whole process. The dream work also uses metonymy, only it takes the desired wish and hides it by selecting a small, obscure, associated part of the wish that will not raise the eyes of the censor. Pedagogic work bridges the gap between theknown and the unknown by starting with a known term and experience (snot) to reach towards the unknown term (cilia) and the unknown process of mucociliary clearance.Dream work starts with the desired wish and then obscuresit by using a less noticeable element of it.

The teacher could discuss everyday experiences of snot for a while, dried snot, runny snot, why do we have snot,and introduce a more technically appropriate term for snot - mucus.

There is a real puzzle around why we have mucus, and she could explain why through a metaphor. 

‘Mucus is basically the body’s flypaper’

Just like flypaper has a sticky substance that catch flies, so too is mucus sticky and it catches all the debris that comes into your nose or throat. 

Firstly she used an everyday term that is locationally very close to ‘cilia’ in snot (snot is moved by cilia)

and then uses a more technically accurate term - mucus, then she used a process from another domain (flypaper) tounderstand how mucus works. The dream work also uses locationally close terms to hide the wish, it uses associated terms to smuggle the meaning, and uses metaphors from another domain as a replacement for the actual wish.

Lets unpack how pedagogy uses metaphor to help bridge thegap between the known and unknown. The introductory metaphor helps understanding - mucus protects the body bytrapping debris on its sticky surface just like flypaper traps flies. A known process (flypaper trapping flies) helps understand an unknown process (mucus trapping debris) but it is also very dangerous, because there are elements to how flypaper works that do not relate to how mucus works, just as there were elements to soccer balls that did not relate to the part whole concept. Mucus flows through the respiratory system, carried by little hairs that move in a wave like way - shifting debris fromthe precious lungs up into the throat and down into the stomach where it can be destroyed by enzymes. There is nosuch similarity with flypaper - once stuck you stay. But the very absence of cilia on flypaper is useful for a teacher, it isolates a feature of mucus that sticky glue does not have - mucus moves, glue does not, and the reason it moves is because of millions of little hairs carrying the mucus inside of us. Suddenly Cilia come intoextreme focus - minute hairs waving around 15 times per second move the debris stuck in the mucus away from our precious lungs to the throat.

This isolation move where one element within the vast range of experience is foregrounded and the rest falls into the background is a vital pedagogic act. The teacherthrows away what is not needed, she strips the issue downto its vital processes, she lightens the load by only focusing on what counts. In the difference she isolates the same. Notice that this is opposite to the way a dreamworks with metaphor. A dream proliferates all sorts of associations into one metaphor so that the repressed element can get through censorship unseen. It uses associated meanings from other domains as a replacement or stand in for the repressed desire, so that the replacement can get through into the actual dream. Pedagogic work does the opposite. It uses metaphor to getthe element out in the open on its own, not hide it. Whena teacher focuses on cilia she abstracts away other details and other experiences, left in the spot light arethe millions of tiny hairs waving away in all of us. Whether we are old or young, black or white, male or female, Wayne or Karl, we have cilia beating away inside of us. It does not matter how many human beings we are talking about, all have cilia. By abstracting away unnecessary detail a universal process in human beings can be explored. Even the individual differences in how cilia function are left out of the account for now, left in focus is a general account of how cilia function. By lightening the load through abstraction, a process comes

to light that does not only work in one place at one time, but in all places and all times that humans have been around. In fact cilia are in all animals and most plants - suddenly we are exploring something that is happening all around the world all the time. In the difference find the same. This is similar to what happened with the part/whole concept - a process came to light that existed beyond its everyday instantiation, a process beyond soccer balls, a process that applies generally to all objects. By getting to understand how cilia work you are breaking the boundaries of your own local experiences and entering an abstract world. In tracking how a dream works, the very opposite process is happening – if we use Freud as our guide. The shift into the dream world of the analysand is a continued push intothe highly idiosyncratic and personal meaning world, not the isolation of something that generalizes across the world.

But abstraction brings with it strangeness. Cilia are strange, their name is strange, what they look like is strange, the way they work is strange. A teacher trying to convey to a student how the cilia functions has to work from the known to the unknown by using elements of the known. She has now closed in on her object of focus, found the sameness, but the details are still scant. Thisis a vital point – just because she has abstracted to theright focus point does not mean that there is any densityto the focus. It is still very light in terms of what it is, how it works, what systems in operates within, what its parts are etc etc. Hitting the correct level of abstraction in no ways guarantees that the concept is dense for the students – this needs to be actively workedon. She could focus on the function of cilia as a defencesystem and explain that the little hairs protect us from invasion. The tangible, observable way attackers are repelled by defenders using their hands can be used to help a student understand the hidden within the body way cilia form a defence barrier by moving pathogens in a wave like manner. The everyday understanding of defence barrier is used as a conceptual metaphor to understand the functioning of cilia. Defence barrier is closer to

how cilia functions than fly paper - it takes the studentacross the bridge from the known to the unknown and establishes a foothold on the other side. What the student would not know at this stage is that cilia are only one type of defence, and that the body actually has other defence mechanisms in skin, tears, large intestine,bladder and stomach.

Suddenly, what was an informal entry point becomes a formalized system that is beyond everyday common sense intuitions. The same term ‘defence barrier’ can either beused by a teacher to concretize a difficult to understand process; or as a part of an increasingly abstract and dense classification system. In the welter of difference she can metaphorically use ‘defence barrier’ to establish the focus; or she can specify and elaborate on the technical details held within defence barrier.

It is vital to get a handle on the difference. A teacher detailing how cilia are one of many defence barriers is not simplifying and concretizing, she is elaborating on an abstract level what the function of cilia are. ‘Unpacking’ defence barrier can either result in the complexity of the term increasing as the different mechanisms are elaborated on or decreasing as it is used in a common sense way. Unpacking a classification scheme into its elements is very different to using the term as a metaphorical bridge. Why? A classification scheme is a formal system where the specific and general terms are both abstract and the specification of the scheme only makes it more complex because more distinctions are made that all need to be held together. A conceptual metaphor simplifies by using an already understood template to understand something. It highlights elementary similarities and differences that reduce complexity through simple links that focus on what is needed and leave out what is unnecessary. 

Let me use another example as a test to see whether you get the point. A teacher unpacks what a cilia is by usingpart/whole relations. She shows how cilia are located within the body as a whole, then provides a picture of what cilia look like

before breaking it down into its parts.

As she unpacks the cilia from its location in a bigger whole to its functioning elementary parts - is she decreasing complexity or increasing complexity? As she gets to smaller and smaller elements is she not decreasing complexity? Are the smallest parts of the cilia not the least complex with complexity increasing with each move upwards from part to whole? By getting down to the smallest elements is she not simplifying ‘cilia’? No, each additional specification adds to the complexity. It’s not like because it is the smallest partit is the least complex, rather, the more you specify themore complex it gets. Unpacking something into its smallest parts increases complexity because you are increasing the amount of specification. To decrease complexity you have to take away some of the complexity by narrowing the amount of specification or using less

technical words. You might only stay with the cilia as ‘moving mucus around’ and not go into all of its parts, you might only go into how the cilia is a defence barrierwithout going into how it is only one of the lines of defence, you might even not refer to cilia at all and just stay with moving mucus. One part of the process stands in for the whole, making the discussion easier to understand. This is how metonymy works pedagogically, it allows the simpler part to stand in for the more complex whole. The complexity of the whole system is reduced to how one of the parts work. 

So we have a situation where metaphor, metonymy and instantiation can be used pedagogically to simplify a complex process, either by using an already understood and more tangible process (like flypaper) as a template, or to use a familiar part to stand in for the whole process (like snot), or by providing an instantiation (like a picture of the actual thing). When a teacher breaks down a classification scheme like ‘defence mechanism’ into its specific elements then she is increasing complexity; when a teacher goes into the parts of a whole then she is increasing complexity, when a teacher elaborates on what a type is then she is increasing complexity.

When a teacher uses a simpler and already understood classification scheme as a template to understand a more complex or less tangible scheme then she is reducing complexity; when a teacher uses a part to stand in for the whole then she is reducing complexity, when a teacheruses a token to exemplify a type then she is reducing complexity.

But just as a child learning the part whole concept suddenly found, within the abstraction that new relationswere produced that elaborated on the abstraction, so too,once a student learns what cilia are, she finds herself in a world where cilia is a part of a whole (respiratory system) that is just one of many systems inside our bodies - there are at least 10 others. The problem is that part/whole relations continue all the way up and allthe way down, with each part also being a whole that contains other parts within it, with those parts also being a whole for more parts. In a similar way with classification schemes, each general type (cilia) seems to have more general type above it (defense mechanism); has other types next to it – like flagellum - and each specification seems to have even more specifications below it. In order to cope with this astonishing complexity there must be some mechanism that does not work pedagogically from the known to the unknown by usingmore simple proxies (soccer balls, snot, flypaper), but rather stays with the complexity in its own terms. There must be a way to increase understanding that does not come from using an already understood template or a simpler part for the whole, a way that remains with the network of part whole relations and general/specific terms. Is there a way to reduce complexity without losingcomplexity, a way to handle complexity even as the complexity increases? Is there a way to throw away the ladder but still stay high? Yes there is and it goes to the core of how we learn. To understand how, we need to go inside our minds and explore how working memory functions. 

I know it’s a strange move at this point to shift from anaccount of the semantics of pedagogic work to cognitive

psychology, but there are two good reasons for doing so. Firstly cognitive psychology has a very interesting description of semantic memory that speaks directly to the issues described by semantic gravity and semantic density. And the second, related reason, is that it is often by going to other fields that one gets a grasp on your own area of focus.

Working memory is the current space we have in our minds for dealing with issues. If we had unlimited amounts of working memory and could pay attention to everything at once then learning all the parts of and types of things in the world would be easy. The problem is we don't. The memory span of young adults when pushed to its maximum isaround seven items, as discovered by Miller (1956) in hisfamous paper ‘The magical number seven, plus or minus two’.

At maximum we can keep about seven elements in our mind at the same time for around 15 seconds. However, most of our learning tasks do not involve simple elements, but ofdeciding what to do with an element: is it right or wrong, up or down, inside or outside, here or there, partof something, type of something? Notice that this means we usually hold a lot less than seven items because our working memory has some of its space taken up with decision-making processes of putting the element in relation to other elements. The more complex and unfamiliar the topic and decision to be made, the more

working memory is taken up with the options presented by the decision. 

You do need to repeat and go over what you are learning to embed it in long-term memory, but the repetition does not have to be in exactly the same form each time. Exactly the opposite, actually: it’s in making meaning ofthe element – of coming back to it from different angles and placing it within larger networks that give it a frame – that a shift from temporary to long-term memory happens. As a temporary memory shifts into long-term memory it transforms; and the reason why it changes is that it has to be inserted into already existing networksin long-term memory. You don’t just plonk something in long-term memory: it gets there in a more sustained and memorable way when you first get its essential meaning and second link it to other things you already know and understand. Getting the essential meaning and placing it in a larger network are really part and parcel of the same activity – making sense of something – because it isin seeing how the particular elements relate to other elements that the attachment of meaning happens. This means that the temporary memory has to be transformed into something that makes sense through connecting it to a relevant network. The larger and more dense the alreadyexisting set of connections, the more able you are to place an element in a bigger picture and see how it holdsthere, enabling its shift into long-term memory. As the gospel of Matthew noted, ‘Whoever has will be given more,and he will have an abundance. Whoever does not have, even what he has will be taken from him’ (Matthew 13:12, New International Version of the Bible). 

What is interesting about connecting things into networksis that the element now holds as a moment in a bigger picture. If you understand the big picture, then you havethe elements of the picture contained within it. This is a vital point regarding the intersection of pedagogy withthe four slots of working memory,

The reason is that the big picture with all its elements

holds as one thing, needing only one slot of working memory. It is really hard, almost impossible, to increasethe number of slots you have in working memory. It is fareasier to develop your understanding of the connections between elements and build them up into a bigger pattern that holds, and become acquainted with how the pattern works, until a point is reached where the whole pattern condenses into one functioning unit.

This is what experts do. They don’t have more slots in their working memory than novices: it’s partly that they work with bigger chunks and this makes it look as if they have really quick, sharp minds. There is a classic test that reveals this involving chess grandmasters, A-level (mid-range) players, and novices (De Groot, 1965). Each set of characters were given two to ten seconds to memorize a chessboard position with 25 pieces. Grandmasters were astounding, recreating positions from scratch with 93% accuracy. 

That’s basically getting only two of twenty-five pieces in the wrong place. A-level players were able to get approximately half the pieces in the right place and novices only a third. It would seem that grandmasters have photographic memories. I say ‘seem’ because if you take the same 25 chess pieces and put them randomly on the chessboard, then suddenly the grandmaster’s memory isonly as good as the novice next to him. He was not remembering 25 individual pieces and their places; he wasremembering patterns of pieces.

The thousands of hours spent playing and studying chess meant that the grandmaster was not playing with individual pieces, but with patterns of pieces, and patterns of patterns, each of which holds as one chunk. 

You can see this if you watch the grandmaster closely as he reconstructs the board from memory. First, he thinks alittle and then places around six pieces down quickly. Then he thinks again before placing around another six down, and so on with the third and fourth sets. The setting down of the pieces occurs in bursts of patterns, not of individual pieces. The novice works with individual pieces rather than with patterns and so is really limited in this task. 

How does this apply to the pedagogic problem of teaching the complexity of ‘cilia’? When starting to learn about cilia, it is hard to hold more than seven elements at thesame time. Lets take the defence barrier artifact.  Firstthe word cilia - it has five letters - and initially it is hard to learn how to say it and spell it. But once youconcentrate and practice it and use it, it chunks from five letters into one word. What does it do? It sweeps away trapped organisms. What does the trapping? - mucus. But now that the cilia as a defence mechanism is held as a chunk you have six other defence mechanisms until eventually defence mechanisms of the body hold as one bigchunk. What has happened here? We can use a second mantra- the many have become one and increased by one - the many letters became one word and were increased by one word; cilia and mucus hold together as the functioning parts of the defence mechanism within the respiratory tract and are increased by one - the respiratory tract asdefence mechanism; and the respiratory tract is one of many defence mechanisms which hold together as defence mechanisms of the body. With each inclusion into a biggerset ‘cilia’ became more dense, but as the chunking process happened it remained simple to work with.

Notice how, even though the description of ‘cilia’ is getting increasingly complex, each ‘pocket of complexity’is tied up into a whole that can be used as an element ofanother whole. The many can be used as a one in relation to other manys. The many parts become one whole, the manytokens become one type, the specific terms are held together by a more general term - the complex becomes simple, only to be used as a launching pad for more complexity. There is no limit on how large these chunks can be, or how many levels there are packed inside of them, they can still be used in a way that only takes up a single slot in working memory, leaving space for relating it to other chunks.  All the intricate innards are stored in long term memory within extended and deep networks. That is partly why experts can work intelligently with massive problems - they are not working with each individual micro element as one part ofthe problem, but chunking the problem up into big possible patterns and working through the options, with the intricacies of the patterns held in long term memory. 

So here we have a form of ‘simplification’ that does not make the actual issue more basic by using metaphorical and metonymical proxies, simplification comes from how the parts are coherently tied up into a whole, so that the whole can be used as a single thing rather than its guts hanging out all over the show. The complex becomes simple and is used to understand something even more complex, which itself then becomes simple to be used as an element of an even greater complexity. This develops aformal and principled network of meanings that are increasingly dense, but still clear. Cognitive psychologyuses the term semantic memory to describe this process ofbuilding up formal meanings into dense networks and juxtaposes it to episodic memory that refers to how everyday meanings and experiences consolidate into a lived substratum. It does not take a genius to recognize that there are strong similarities to the everyday specialized distinction used in the sociology of pedagogy.

Working memory copes with the massive expansion of meanings needed to be mastered, because it only needs to ensure that no matter how large or complex the process, it can be held as one element. Weirdly, even though the problem space being worked within gets harder and denser,working memory does not have to overload, it continues using its four slots, shifting the weight to long term memory networks that can be infinitely expanded within semantic memory. 

Linguistics point to a very similar process to chunking in the way language works with nominalization and grammatical metaphor. Cilia have been the example used throughout, so let’s stay with it. We now know that Ciliaare little hairs that move in a wavelike manner and carrymucous up and out the lungs, into the throat, from where it can be swallowed into the stomach or spat out. Would it not be useful to tie up this whole process with a single term, so it can be used in a sentence with other terms. Combine mucus and cilia into one term - mucociliary –

and combine it with its function of clearing pathogens and allergens from the lungs - clearance - and what do you get - mucociliary clearance. 

Lets put it in a sentence

‘Mucociliary clearance is the most important defence mechanism of the respiratory system’

The action of cilia clearing secretions becomes a noun, the action of defending becomes a noun ‘defence mechanism’ and the action of breathing becomes a noun ‘respiratory system’ and they can all be held together and related in one sentence. Processes are condensed intonouns that can be used as objects in relation to each other. Each of these terms contains a wealth of detail inside of it, but working memory only has around four slots, so it is key to take the complex process and name it as one thing so that it can be used in relation to other things - the many become one and are increased by one - the many actions of mucus and cilia shifting pathogens away from the lungs becomes one thing - mucociliary clearance - and is increased by one - you nowhave this term that has arisen from the process and is anindependent unit holding the process together as a term that can be used separately and combined with other condensed terms.

The earlier examples of metaphorical and metonymic substitution reduced complexity by radically simplifying

the focus point, here we have condensation that increasescomplexity by allowing the many dynamics of the process to be held as one thing so that it can be used in relation to other processes and things. Pedagogy, working between the known and the unknown has to use whatis already known as its base domain - but now what is already known is of two distinct types - the first is theeveryday contextual local world of rich experiences; the second is a more formal network of concepts, processes and links. Pedagogy has to work from the everyday world to the specialized and back again; only when it returns to the everyday things have changed, the everyday exists in a new light.

The home you return to is the same but seen differently.But pedagogy also has to work within the specialized in its own terms, and it would seem that we have been able to describe some of the successful ways pedagogy works between the everyday and specialized and within the specialized by using metaphor, metonymy, instantiation, abstraction and condensation. We can get our students from the everyday to the specialized, and then we can stay in the specialized and develop their abilities within it, even though we are working with very limited means. Within the difference we can find the same, and

within the same we can develop difference. These many differences can condense into one principle, and this principle can become a principle that operates with otherprinciples, resulting in the many becoming one again and again in a spiraling growth of complexity. 

So far so good. The issue is that knowledge is not standing still, it is rapidly growing, not only in amountbut in types. There are many different kinds of specialization and these are increasing whilst at the same time the amount of knowledge needed to be mastered in each specialization and between specialization  is also growing. We might have described how the ladders of pedagogy cope with mountains of knowledge; but the problem is these mountains are both growing and proliferating. Its not only pedagogy that has to work with issues of condensation - curriculum too has to struggle with how to compress all of this information into a manageable set the next generation can master to continue the growth. This is a version of condensation, where more and more has to be compressed into less and less. Initially, parental and communal forms of education were sufficient to transfer the knowledge and skill pool from one generation to another, but with the age of enlightenment and industrialization came the increased production of knowledge, resulting in a gap forming between what communal and folk forms of educationcould do and the increasing pool of specialized knowledgeneeded in a modernizing world. 

Formal schooling arose partly to meet this gap, but this has only resulted in more specialization and increased knowledge production. The basics never go away, but they have to be mastered more quickly and in condensed form toallow time and space for all the higher levels. What took all the time of teaching (a) is condensed into smaller and smaller intensities to allow space for b and then b and c and then b and c and d.

 Does there not come a time when schools just cannot copewith the amount of new knowledge required to be mastered,no matter how good the pedagogy? And can the same not be

said for our children? Will it eventually become impossible for them to learn all that is expected of them? Are we not already finding that we have to cram more and more stuff into our curricula just to keep pace with all the new additions? Many high schools now teach calculus, a mathematics topic that used to be the preserve of universities, and similar pressures are on science, biology, geography, and accounting. This resultsin compressing more and more stuff earlier and earlier until something has to give. If scientific knowledge is increasing all the time, then surely this flood must spill over into the school curriculum? The seriousness ofthis pressure becomes more intense when we realize that scientific knowledge is not just growing, it’s growing exponentially. Rather than simple linear growth that addsnew elements, the growth is doubling and then doubling again.

A good example of this can be seen in the number of mathematics publications that doubles every fifteen yearsor so. Eventually is there not going to come a point when, like Scotty on Star Trek, we exclaim ‘We cannae

make it go 'ny faster!’ 

Maybe we are reaching a saturation point where the exponential accumulation of knowledge has to slow down. Rather than an exponential curve upwards we are hitting aset of real world constraints that will flatten the curve.

The cost of learning the previous generation’s accumulated knowledge, as it continually increases in both amount and complexity, has to reach a human end point, or does it, given our ability to abstract, condense and then critically reflect on the process?

If we take a look at the mean age at which Nobel Prize winners made their breakthrough discoveries, we find it is going up in time.

The same trend is happening with significant inventors. In 1900 the breakthroughs tended to happen at around the age of 32; by 2000 it had gone up to 38. A longer period of training and mastery is needed. If we put a scientistas a baby in the middle of a circle that represents all s/he needs to master in order to get to the point where anew breakthrough is possible, represented by reaching thecircumference of a circle, then in 1900 the scientist hadless distance to travel than in 2000. 

Even though it’s taking longer for scientists to reach mastery levels that enable breakthrough, there is no corresponding increase in productivity over the age of 40. We still age in the same way. The reason why there ismore knowledge being continually added has to do with thegrowing population of scientists, not that individual scientists are producing more in old age (with exceptions, of course.) In 2000 scientists are taking longer to get to the point where breakthroughs are made, but still showing the same drop off in productivity afterhitting 40, probably due to assorted family commitments and mid-life crises. 

Scientists have responded in part to this dilemma by intensifying the focus of their specialization, thus reducing the amount of content and time needed before breakthrough becomes possible. But this results in such narrowing that it becomes difficult to see the bigger picture and get a sense of the possible applications of the research, and a drop in innovation potential. Anothertrick used by scientists is to take drugs that concentrate the mind, the only problem being that this enables intense focus on details whilst disenabling emergence of the big picture.

Is it possible that we are faced with a tidal wave of knowledge threatening our future ability to innovate? Canwe improve the way we educate to the point where we keep abreast of the increasing amount and complexity of knowledge?  Can we condense and compact what needs to be learnt while at the same time working out the most effective ways to teach what is most important in the first thirty years of an individual’s educational history? Or should we search for another way of living life on this planet and doing this thing called education? The worrying aspect about the above discussionis that improvements in education will probably only delay saturation point, not get rid of it. Maybe some kind of leveling off is what is needed. Maybe, even with

education, we cannot continue with a growth mindset, maybe a different model is needed. If Z  simply represents the amount of knowledge and t the amount of time used for education, and assuming we can go from our current efficiencies in education (B) to a more supercharged education (C), are we not simply delaying the inevitable at massive cost to our children who will start education at three and graduate at thirty, working all day and studying every night simply to get to a pointwhere something interesting can be said? Japanese children are already feeling the pressure. Their evenings, weekends and holidays are all sacrificed in thestruggle to master the ever-growing pile of knowledge. Isthere a limit, where no matter how efficient education is, and no matter how hard students learn, there comes a point where we just cannot learn anymore in a lifetime, where the upward curve of learning new knowledge has to flatten out, as indicated by the super charged education line? Or given our ability to chunk information into bigger and more cohesive systems, and our ability to condense more and more information into tighter and tighter networks that get denser and denser, can we not keep moving learning upwards and outwards until we becomegods, or fall down trying, or even more sadly, watch our children fall to a burning earth as the ladder becomes more like the eye of a needle?

In conclusion, the concepts of metaphor and metonymy, abstraction and density might give us some purchase on the pedagogic mechanisms that takes us from the profane to the sacred, elaborate on the sacred, and then move back to the profane again, but in no way gives us an ethical answer to whether this is a dream or nightmare orwhat kind of enlightenment is to be sought. We have only presented the work of pedagogy, not what it is working for or towards.

Thank you