Depth Psychology and Agent-based Modelling

It would seem to be common sense to say that no social or economic model which didn't take into account the psyche of individuals could possibly have any realistic hope of authenticity. Yet economics glosses over this omission: it would seem that it simply is too difficult. Keynes, to be fair, does spend a lot of time discussing the psychology of consumer: the idea of the 'propensity to consume', 'propensity to save' and 'liquidity preference' underpin his theory, although there is little detail as to how these might manifest in individuals beyond idealised reasoning about personal economic well-being.

However, Kahneman and others have started to unpick this rational model: people do strange things, particularly in the face of risk and anxiety. Kahneman's assertion is that people tend to overreact to small probability events, but underreact to medium and large probabilities. I think Axelrod's experiments with the Prisoners Dilemma echo these findings too. But losing rationality from the equation is just where our problems really start...

The real issue I think is that people are not the same, and certainly do not behave similarly in similar situations. However, the crowd dynamics (in situations where crowds are a factor) can create unusual social movements in response to small initial conditions (a la complexity theory). But even that doesn't allow us to think of people being the same. The real issue for me is that clearly we are different. How are we different? 


On the one hand, we behave rationally: we communicate, observe the behaviour of others, judge what might be in our best interests. But on the other hand, each of us hides vulnerabilities, dreams and desires that, even if they are not unique on a social level, appear to us to be utterly unique and fundamental to our identity. This sensual side and the rational side seem to co-exist. Personally, I believe that what keeps them working together is 'property'; or put another way a relationship to property is a way of balancing the needs of rational discourse with the sensual aspects of the personality.

In my agent-based model of communication and wellbeing, I am starting to consider these two mechanisms working together. But there are other problems which I am thinking about. For the sensual and vulnerable self has dimensions and depths which lie well beyond the making of rational discourse. The Freudian level of id, or Jung's shadow lurk behind the scenes often sticking a spanner in the works with regard to conscious behaviour.

This has led me to think about possible ways in which the subconscious might be modelled. One possibility is to model it as a sort of 'internal conversation': i.e. a conversation with an imaginary 'other', with the results of the internal conversation eventually moving into conscious communication after a process of selection (as in Luhmann). Another possibility is to elaborate Jung's archetypes as regulating levels in a subsystem of the 'conscious' (i.e. communicating) system (much as I discussed here: http://dailyimprovisation.blogspot.com/2011/05/luhmann-beer-harre-and-jungian.html)

Each of these are effectively internal reflexive 'mirrors' which turn a conversation in on itself for a period of time before that conversation emerges into the social system. It's a bit like a laser exciting photons before they have enough energy to be emitted in the beam. There are experiments to try: each configuration of 'mirrors' will produce different effects. I might hope that some of those effects have some bearing on what we actually see happening!

Staying cheerful despite...

The prognosis for the education system is very bleak. The changes that are occurring now will have devastating and irreparable consequences not just on education itself but on knowledge and consequently, I believe, civil society. But, on the bright side, we are still here and no-one appears to have died directly from a lack of education (although there are indications that lack of education indirectly leads to an early grave: http://news.bbc.co.uk/1/hi/education/8189498.stm) Even so, everyone's got to die sometime... just preferably not all at once!

In our period of bleakness, I think it would be more useful to spend time thinking about what has become of us rather than railing against the injustice of it all. There's some humour in that, and the humour can help us both manage the devastation and understand it. But beyond the jokes, what I think has become of us is that we have lost sight of our individuality and the sacredness of individual human life. Instead, we have become subsumed into the amorphous and mindless global communications networks which we have substituted for God.

The scary bit is the wiring.

Like the result of a medical experiment by Dr Moreau, every sinew, nerve and organ has been teased out of us, its signals analysed, and carefully connections made between them and the global network. The remarkableness of the engineering feat is only matched by the incompleteness of the knowledge that it took to undertake it. But our ability to discern the gaps in the knowledge have been compromised by the operation. Like Dr. Who's Cybermen, we are now wired-up; effectively prisoners to a global machine that is out of control, with the most powerful controls we once possessed - the ability to know something - taken away from us. It's no comfort to say that Heidegger predicted this.. we have cannibalised ourselves, becoming our own 'standing reserve', feeding on ourselves to drive our world. This is what the 'enframing' of technology does.

There is a need for a new quest for personhood and individuality. But this can be no 'revolutionary' call - that would simply feed the global machine. It requires instead individuals seeking inside of them the vestiges of what survived the operation. To do that we need to see what 'enframing' did to us, how we have become, and how what we know ourselves to be is different from how we have become.

More specifically, I wonder if the wiring was achieved with an analytical understanding of the structures of cognition: essentially a synchronic model. We labeled those parts of cognition, mapped the brain, worked out what had what effect and so on. Then we wired ourselves up. There was never any consideration of the emergent effects, of the diachronic model.

When I look at myself, I might speculate on the synchronic aspects of my engagements with the world (like this blog). There are patterns to be seen, which I have tried to understand more precisely with models. But each moment has a history and future. Within that history and future there are also patterns: the note that is played and dies away; the glance that stays in the mind long after it was made; the loss that transforms everything.

What I may be beginning to think is that Jung is right: that there are a finite number of states in an infinite amount of time. Understanding the diachronic process is to understand the patterning of those finite states. Bringing better knowledge of the diachronic process together with the synchronic process is perhaps when we will start to unpick the wiring.

Luhmann, Beer, Harré and Jungian Individuation

I did a presentation on agent-based modelling on Tuesday. I think Luhmann can provide an adequate description of the 'outer world' and there is a broad description of how it arises from the inner world, but my work has concentrated on trying to use the distinctions of Beer's Viable System Model to get a deeper understanding of the 'inner world'. But in the model as it stands, there is significant lack of richness, although there is at least a simple way of differentiating people and the communications they make.

The challenge of describing the inner world has led me to think about what Jung says of individuation processes. Briefly, Jung makes a series of distinctions concerning the elements of the unconscious and conscious world. At the bottom of the unconscious world lie the 'shadow' (all that we are but are not consciously aware), and the anima (in men) or animus (in women), or the 'soul image' which is associated with the image of the opposite sex. Having confronted the 'soul image', the soul-image of the collective is encountered: what Jung characterises as the 'wise old man/great mother'. From the recognition of the collective shadow a deeper realisation of self is achieved.

Relating this to the work of Harré, Luhmann and Beer is what's fascinating me. Positioning Theory would situate the individuation process as some sort of adaptation of the 'storyline' of an individual. Individuation is usually performed with an analyst, so there may be some requirement for illocutionary acts (talking). Individuation might be seen as a particular activity dynamic where the analyst positions the patient in a way which is focused on their examination of their storylines.

With Luhmann, the psychic system is simply there to make selections about meaning, utterance and interpretation. But these depend on the state of the individual. Luhmann does say very much about how the structuring of the individual can affect these selections. Although common sense would suggest that the structuring of the individual, the storylines are a key determiner of the utterances that are made.

Beer provides distinctions about the inner world of the individual which might help here. Within systems 1-5, can we find the shadow or the anima? I wonder if both of those are about entropy in some way. Maybe by combining the distinctions about the 'emotion machine' (http://dailyimprovisation.blogspot.com/2011/02/luhmann-beer-and-emotion-machine.html) we can see that perhaps the shadow might be a combination of system 5 (loss of identity) and system 2 (fear and anxiety). The anima might be a combination of system 4 (idealisation), System 5 (identity) and system 2 (intuition). The wise old man, the collective soul, might be a combination of system 4 and system 5 (reidentifying with the collective). The self is the totality: it is a system 5 which embraces the tension between systems 3 and 4 and is able to position the communications and viability of the whole system most effectively.

I'm not sure.. but it's interesting. Thinking through the individuation process might help in understanding how our experience is wave-like, with motion through us from one regulating system to another. How might I implement this as a model?

The end of laissez-faire pedagogy?

It is not uncommon for institutional teaching and learning strategies to be delegated to individual academic departments. This tends to be done pragmatically on the basis that teaching and learning in different disciplinary areas presents very different challenges and are therefore best dealt with individually.

However, delegation can open the door to a lack of consistency in teaching and learning across departments, and presents a challenge to institutions to address problems in delivery. These coordination challenges also become economic challenges because of the link between the way teaching is delivered and the institutional costs involved: not just in staffing, but also with the effects of losing students.

Any attempt to standardise and centralise pedagogy would be resisted by academic departments as a loss of academic autonomy and freedom. But what does this mean? The central organisational question is whether academic freedom means the freedom to create and coordinate activities individually, to assess individually, to take individual responsibility for a module or class and to have the freedom to interpret the subject that is taught.

This depends on what we think the essence of teaching is. Freedom of individuals to control particular curriculum areas with regard to how things are delivered is a view of teaching and learning which is centred on the person of the teacher. However, if teaching is more about teachers making communications with the intention of nurturing communications by learners (which I think it is), then we can examine each of the areas of responsibility that teachers have as ways of making communication.

Does the teacher need the freedom to design their own activities in order to convey their understanding of the subject? Does the teacher need to control assessment in order to help their student reach a critical appreciation of the subject? Does each teacher need direct and personal control over each class in order to convey their understanding of a subject?

I think the answer to these questions is 'not necessarily'. Teachers can reveal their understanding through individual feedback in activity contexts which do not necessarily have to be of their own making. The organisational imperative for this to happen will be the economics of University education.

The Case for Radical Reorganisation of Education

Harsh economic necessity and the need to live within our means is the fundamental cause of the crisis in Higher Education. But beneath the economics and ideology of public services, there is a deeper crisis which I think concerns the fundamental difficulty in coordinating education. Education is too expensive, and continues to be expensive because the methods we have for coordinating it seem ineffective.

I think the first problem we have to face is one of 'variety management': one teacher, many students; one course, many teachers; one nation, many institutions; and so on... Coordinating many teachers, all of whom have different approaches to dealing with their students can get terribly bureaucratic, and as a result, expensive: the costs associated which processes which have nothing to do with the experience the students receive start to explode. Where are the intervention points to optimise the system?

Teachers managing the variety of their learners in different ways is potentially the root of the problem. The variety management that teachers engage in is multi-level: production of resources, design of activities, classroom management, design of assignments, student feedback, etc. Not all of this variety management has an equal effect in terms of benefit to the student.

Choosing the types of activity that are engaged in and coordinating those activities at the highest level does not necessarily need to be performed by the teacher. Indeed, in organising teachers by subjects and modules, a small part of this coordination is currently taken away from them. But ultimately, they tend to individually end up reinventing everything from scratch in the name of “academic freedom”

This is a problem of reductionism. Knowledge has got compartmentalised into boxes, and those boxes are used to coordinate education, but the content of the boxes is open to interpretation – particularly in a post-modernist environment. Basically, nobody any longer understands the fundamental coordinating principle. So they make it up as they go along, guided not by knowledge, but academic procedure: the achievement of learning outcomes and assessment criteria. These are the real inheritors of the knowledge-coordination mechanism.

Universities are about knowledge. I agree with Newman when he says that the purpose of a university is to teach Universal Knowledge. It is important to appreciate that this is not an appeal to theology. Newman makes this quite clear: 

“If its object were scientific and philosophical discovery, I do not see why a University should have students; if religious training, I do not see how it can the seat of literature and science.” 

I think I might add to what Newman says and remark that teaching Universal knowledge is about maintaining it, which is identical to maintaining civil society. At a time when Universities are seen as ‘knowledge creators’ (whatever that means!) or ‘innovation factories’ (equally meaningless), Newman’s point is easy to lose.

The central point which relates to the teaching activities of a university is “what is the relationship between knowledge and learning activity?”. In the language of learning outcomes, this is addressed by saying that activity has an outcome which is knowledge. Really? Where exactly is this ‘outcome’??

If activity produces anything observable then it is communication not knowledge. As the medium of knowledge, communication is a good thing, but it is not to be confused (as it usually is) with knowledge. Knowledge, on the other hand, certainly is expressed through certain communications: some of them more powerful than others. When someone professes “This is what I KNOW” what occurs is a rich, authentic and powerful human performance. Such communications occur in a context of other communications, and those communications will have played a role in establishing the conditions for this moment of truth.

This is the nature of activity in establishing patterns of communication which can contribute to the conditions for apprehending knowledge. Activities were once face-to-face conversations in a social setting – often occurring around the coordinating device of the curriculum. Now they are more typically complex skilled performances with online tools. Those tools are reproducible and ubiquitous. That means the activities people engage in with them are also potentially ubiquitous. Because of this, there is no need for teachers to continually reinvent activities or resources or even to individually manage their coordination. What teachers have to do is to nurture the communications that occur in activity contexts: by revealing their knowledge and their desire to help others through feedback to their learners (if they have no desire to reveal their knowledge, or certainly no desire to help others, then clearly they should not be teaching!)

The variety management that teachers are required to perform relates to the personal and personalised feedback of knowledge. There is no direct need for them to deal with the other aspects of variety management. Most of that can be centralised: the provision of tools, the identification of scenarios, the coordination of activity, the coordination of assessment points. Teachers need to make sure those activities work by stimulating communication and feeding back with regard to assessments.

Emancipation is the art of prolonging a beautiful life

One of the longest-running debates within Critical Realism concerns the role of absence. In "Dialectic: the Pulse of Freedom" Bhaskar introduced a new 'turn' in Critical Realism, introducing 'Dialectical Critical Realism' which contextualised original critical realism within a dialectical process which, Bhaskar argues, was driven by determinate (i.e. concrete and identifiable) absence.

Dialectic is a very hard book, and much discussion has surrounded the topic, much of it sceptical. I count myself among the sceptics. The real problem is to be able to point to anything 'real' about absence without drawing on rather crass examples (the absence of rains leading to famine, for example; the absence of a treaty leading to genocide, etc). This is in contrast to original critical realism, which pointed to the real phenomena in the world and in asking how scientific knowledge about them might be possible, posited mechanisms as an explanation. Bhaskar's argument is that mechanisms are stratified and tensed in history, and that processes operate within those time structures driven by the absences at any particular time point: the injustice that persists, the things that can't be explained, and so on. That may be fair enough, but he then goes on to say that absences are real, in the same way that mechanisms are real, which for many is a step too far. Then it gets complicated: are absences the drivers of mechanisms, or mechanisms the drivers of absences? Are absences in the mind or 'out there'? Bhaskar (I think) is saying the latter.

I've been thinking about all this in the context of music. Withholding the root of a chord is a common musical technique for prolonging musical expression: Wagner's Prelude to Tristan and Isolde is the classic example, but 16th century polyphony is similar. Absenting the root suspends expectation, withholds a resolution or finality, creates more tension, gives direction, moves towards something, raises expectations. Because of the absence, the music keeps driving forwards. But if we think like this, the issue is neither absence nor mechanism, but prolongation: another word for viability.

We can go a bit further here. Because a distributed cognition approach to music would then start to identify absence within the mechanisms of regulation between individual viability and the world 'out there'. In this sense, absence may well be 'out there'. Moreover, it being 'out there' is a fundamental component to the viability of each of us. One might almost say that we rely on there being real absences in the world: without them, we wouldn't exist. 

However, this is then to privilege mechanisms over absence. The mechanism detects the absence. But what drives the mechanism? Answer: absence! This seems very paradoxical! Is there progress?

That of course is a leading question (quite literally!). Bhaskar's view on dialectic is that there is an emancipatory force in the world driven by absence ("the pulse of freedom"). It is the role of philosophy to identify and unpick determinate absences, and that this is an emancipatory project. I find the latent utopianism here hard to stomach. Absence may well be real, but it is wrapped up in processes of prolongation and viability. If there is emancipation to be had, I think it lies in the possibility of an individuals finding a way through the absences of the world which harmonise with their own viability.

Like the art of prolonging a beautiful piece of music, emancipation is the art of prolonging a beautiful life.

Ibn Khaldun and Educational Economy

Ibn Khaldun was a remarkable 15th century social theorist and early economist whose ideas foreshadow those of Durkheim, Marx, Bourdieu and Giddens. His work was based on a close examination of desert societies in the 15th century, highlighting the processes of development of rich and poor. Khaldun has been on my mind following my return from Ras Al Khaimah. His concept of Asabiyyah describes the emergent processes of social transformation following invasion by nomadic groups, and the gradual assimilation of the dominant 'culture'.

Whilst there are don't appear to be any immediate parallels between a medieval context of frequent invasion and decay of civilisations, the processes Khaldun describes have modern counterparts in terms of social capital and social networks. But what I am part of (and practically every other UK and US university at the moment) is some sort of incursion (although of course, welcomed!) into Arab culture with a European model of education. How might Khaldun see this?

Education is welcomed into the culture as a way of diversifying an economy: as a service industry, education is big business. Students for foreign universities are spread between the native populations and migrant workers (or offspring from them). There are more native students for more prestigious universities, whereas for less prestigious institutions, there are more migrants. There are often significant differences in political power between migrant workers and natives: but the power imbalances can often serve as a motivator which drives individuals towards increased capability and education. Foreign educational institutions similarly find themselves as migrant institutions with fewer rights to property and disadvantaged legal status.

Bearing in mind the contrast between these different social groups, the distinctions that Khaldun draws on to highlight the relationship between urban civilisation (kingdoms) and Bedouin civilisation (nomadic) may be a useful starting point. One of the principal questions is to examine the viability of this situation, and the viability of 'nomadic' educational businesses. Political imbalance and injustice acts to adjust the distribution of risks in society, and the anxiety that results focuses on education to manage it. The principle political inequalities are often not inequalities of wealth, but of risk. This suggests a more general point that increasing wealth in a super-rich country does not bring increasing political power or more even distribution of risk.

In a society of unequal risk distribution, education is attractive because only education and the capability that can arise from it can give increased flexibility in response to managing risk. Increases in capital in terms of property are less possible (housing, for example, is only available for rent): what counts is the increase in social capital - particularly the ability to influence the ruling power; this depends on property relations to ideas and skills.

However, there's a catch here. Good education depends on good teaching. If teachers do not have sufficient educational capital to maintain their own wellbeing and flexibility in an unequal society, they will not be happy: and it's rare for an unhappy teacher teach well. The status of migrant teachers is the same as for other migrant workers. In this way, what appears as education might not be able to deliver in terms of the increase in personal and social capital. I suspect this is the case for most educational incursions in unequal societies, however prestigious.

This is not insoluble. It requires a rethink as to how education might be organised. The fundamental issue is to treat the doctor at the same time as the patient. To do this, I think that learning activities, particularly those involving overseas contacts (from more equal societies) can work magic. Activity constrains communications; but it does so to enable them. Global coordination of activity is now possible.  It means organising education around tools and scenarios rather than curricula. With this, a viable future for nomadic educational  incursions
might be a possibility.

Critical Realism, the Sciences and the Arts

Critical Realism, the philosophy of Roy Bhaskar, Margaret Archer and a number of acolytes is a philosophical critique of the nature of causation. It is grounded in a re-examination of scientific knowledge and asks the question "given that we have scientific knowledge of the world, what must the world be like?" In responding to this, it argues that Hume's theory of causation (that scientists construct causes in the light of reproducible experiment) is wrong. Bhaskar is not the only person to say this: his supervisor, Rom Harre said much the same thing in his "Causal Powers". Bhaskar argues that the Humean mistake has had knock-on effects on the social sciences, where social science has tried to compensate for the lack of reproducible experiments (with statistics, probabilities, textual analysis, etc) so as to similarly facilitate a process of 'constructing causes' in an attempt to make defensible claims about the social world. A variety of social science methodologies do this - for example, the Grounded Theory of Glaser and Strauss.

I think Bhaskar's argument here is pretty solid, and it has led to some practical innovations like Pawson and Tilley's Realistic Evaluation, which I find far more sensible than most of the available social science methods. But my concern recently has been with the arts, not science. How does Bhaskar's argument transfer to the arts?

Where scientists concern themselves with cause, I think artists concern themselves with form. Form and Cause are related - at least for Aristotle, and I think both are related to knowledge. Artistic knowledge is different from scientific knowledge: but Shakespeare will still leave us astounded at insights into human nature and life that the most penetrating scientists barely touch.

Bhaskar's argument for scientists is that they do not construct causes, they discover them. Similarly, I think artists do not construct forms, they discover them. Picasso's famous comment "I do not seek, I find" would bear this out I think. But in much contemporary art (and particularly music) there is a tendency to focus on abstract phenomena and discover forms: mathematical series, formulae, concepts. I wonder if this is the analogue of the 'reproducible experiment' in the sciences. Are artists drawn to these things because the possibility of discovering universal form is questioned? It is as if the discovery of abstract form is used as a way of making artistically defensible claims about the world. This seems to me to be a methodological (or technical) error.

The question for the arts is "What is the form discovered by art delimited by?" Those artists who focus on abstract forms consider that the abstraction is the delimitation. I think the delimitation is always the world, and the challenge for artists is to find a way of discovering the form of our world today. This is a related enterprise to social science, for understanding the causes of our world is inextricably entwined with understanding its form.

My only reservation with this position is that artistic technique is always a delimitation of sorts: artists work by restricting themselves. But this restriction serves to control the form that they deal with and their own agency in manipulating it. That is technique: a necessary attenuation. But the challenge is to ensure that technique serves the discovery of form, rather than merely reveal itself.

Axelrod, Cultural Diffusion and Rationality

There's something fascinating about Axelrod's model of cultural diffusion - particularly if you select the 'bubble mode' in the applet below (which I stuck into the Wookie widget server). It has a particularly realistic biological quality which I've always missed in most cellular automata models. However, there are still a great many questions where I think Luhmann and Beer's thinking might provide some deeper insights.


Some of Axelrod's most significant work stems from his examination of the Prisoner's Dilemma. He famously challenged a number of computer scientists to come up with algorithms which could deal with the repeated prisoners' dilemma. He identified that ultimately, cooperative 'altruistic' strategies seemed to be more effective in the long term, and that an evolved approach might lead to these sorts of strategies. Whilst I find this fascinating, I'm tempted to remark that a strategy isn't 'forgiving' or 'altruistic'; people are. And what goes on in people is rather more than the calculation of next moves in the prisoners dilemma. Tooth ache or an annoying twitch is more likely to sway things one way or another.

The fundamental issue relates to the locus of rationality. If a strategy is rational then it's locus is in someone's head, and that head causes the strategy to be rational because the head processes the available data and produces a logical conclusion. However, rationality may not be quite like this. With a distributed cognition approach, rationality (or what we think rationality is) exists in communications. The extent to which communications can be successfully made, we can deem these to be rational. In this sense, it is not whether someone wins or loses the prisoner's dilemma, but whether the move that a person makes can be deemed 'within the game'. Attributing mental causes to that rationality is inevitably an act of conjecture.

If rationality is simply about making successful communications (communications which are understood), then the question is not about the causes of rational behaviour, but about the causes of communication. With regard to communication, and thinking about Luhmann, I think there is a secondary mechanism at work which relates to sensuality, and this works hand-in-hand with communication processes. When we consider the full complexity of this, rational strategies for the prisoners' dilemma (altruistic, greedy, etc) seem a bit shallow.

The cultural diffusion model has, I think, gone down a similar path to identifying mental causes for strategy. The boundaries in the model reflect degrees of cultural affinity. But cultural affinity depends on the extent to which people can have conversations, and that depends on their ability to make communications at a number of levels. Are cultural boundaries in the world or are they in people? I think this is where we need Positioning Theory!

Agent-based modelling and Waves of Personal Regulation

I presented an agent-based model of communication the other week at the CAL11 conference in Manchester. The construction of agents in this model is one where each agent has three levels of personal regulation which relate to three types of communicative act that they can make: Exhortation, Disruption and Coercion. The communications that an individual makes are probabilistically related to their individual state at any point in time (whether their regulation is focused on Disruption, Coercion or Exhortation). This is a simple choice determined by the relative values of their communication.

To run the model, select the number of starting people (the first slider which says 'starting-...'), and click setup, then click go. You can change the transparency of communication by altering the comms-r slider. When people are red, they are unhappy! You can add individual people by clicking 'add person'. Clicking 'disrupt-every...' is interesting. You can click and drag people from one part of the screen to another (this is like building teams). And obviously you can slow it down.


Internal regulation is affected by the communications they receive from others, and there is a need (in order to remain happy and viable) to make communications which will result in communications which will continue the maintenance of wellbeing. Thus agents 'position' themselves with one another.

In my model at present, each regulating mechanism is basically a type of 'random walk' where, on perceiving new communications, the regulation of each individual at each level is adjusted by various 'deltas' (values which are added or taken away from the current value). Each adjustment to each regulating level has a consequent effect on other regulating levels, and furthermore on future communication.

In my presentation, I demonstrated how this setup could demonstrate some 'critical incidents' in the university e-learning strategy, like the use of champions to stimulate new practice, or the increase in transparency of communication to stimulated richer activity and greater cohesion amongst staff, or the effects of large-scale disruptions like changing the platform. But I think the reaction of individual agents is at the moment too 'quick' to adjust to new circumstances.

This is why I am asking whether my agents could instead have regulating systems which were based on waves rather than random walks. This might introduce new elements of unpredictability into their behaviour, and would also introduce some degree of latency in their responses, but I think all of these things are real: we have to wait for colleagues to 'come round' to new ways of thinking. In such cases, something is going on inside them... is it that they have to wait for cyclic (harmonic) functions to reach particular points before they feel able to change?

Another way of thinking this through is to think that each communication we make has a 'resonance' - past echoes in the environment have some bearing on what happens in the present. Echoes may decay according to harmonic rules... Sugata Mitra wrote a paper where a similar idea of playing with time with cellular automata produced some fascinating results... (see http://www.complex-systems.com/pdf/16-3-1.pdf)