Tendency to Categorisation
I would rather resist the tendency for categorisation which is endemic to academic practices, and thus inevitable in a PhD. I see this as mostly a spurious attempt to assert control over a dynamically complex environment, to effect a false simplicity, what Ackoff described as academics defining problems (which are solvable) as compared to the mess which people must deal with. There are various ways to slice the pie, which belie the perceptual framework and purpose of the pie-cutter; we shall be exploring theoretical frameworks later, but again, which theoretical framework to adopt. I am not satisfied with any of it. That is not to say that we can not make progress, but that near-all the ways laid out for us as academics adopt unsatisfactory theoretical position which inform practical methods and result in output of thesis and reports which are not applicable for practice in schools. If this is the necessary modus operandi of academia, then I am not fit to conduct a PhD. However, if it is not necessary, then it behooves me to point out the theoretical error, consequential methodological fault, and to propose an alternative.
Ideally, I would like to provide a mathematical model of the problem space, but to do so would be to adopt the customary misuse of mathematics (graphic ‘models’ using lines and words to map relationships between concepts, or misuse of statistical modelling and its stochastic philosophical basis). I have also been restricted from adopting prevelant tools to within the frame of reference (academics reading this paper), and I am forced to adopt an ‘object-based’ positionality, regarding students and teachers through a theoretical lens, even to the point of using ‘telescopic’ methodology, indicating the distance we as academic readers adopt in our study of ‘them’, the ‘other’. This positionality of the ‘altern‘ is well known in social anthropology, and is implicit, inherent, and apparently unavoidable in ‘harder’ social sciences such as Information System Department.
It might be suggested that I adopt qualitative methods in the PhD research, but these suffer from the same epistemological assumptions, highlighted strongly in critical realism. It might be further suggested I explore the problem within a ‘softer’ discipline like social anthropology, a discipline which allows a more post-modern, interpretivist lattitude. But this misses the point: the disorder is in the adoption of ‘hard’ science methodology in social sciences. It is suggested that social science is itself a mess. It is the unfortunate combination, and re-combination, of wholesale adoption of the authority of mathematical techniques which have evolved in the study of objects (geometry, statistics), with the false precision of ‘categorisation’ and ‘logic’. I am not saying anything new. Bhaskar has pointed out the latter as the ‘epistemological fallacy’, while the scientific endeavour of ‘after-the-fact’ experimentation and analysis has been criticised by many phenomenologists, well summarised and exemplified by Shotter.
Simple Solutions are Excluded
I would like to put forward a simple potential solution for low-level disruption in secondary school, a solution I derived as a teacher. But the theoretical tools are not sufficiently understood and adopted by academics who are in the whole suffering from the same problem that teachers are, and indeed all adults within paid hierarchical structures. The solution can never be created from within. It appears, from my experience of Information School academics and reviewers, and a reasonable review of academic literature, and observance of the critical and chronic disorder of practice-theory divide and replication crisis that the problem is systematic beyond school structures. If social science had comparable gains to the hard sciences in the last 100 years, it would be equipped with the economic and political tools to support the scientific evidence of our environmental degradation. Sadly, science is as much a political football as education is, something I heard my fellow teachers complain of throughout my teaching career. There appears to be no way out of this problem, something certain the postmodernists attempted to conceal in their explication: their powerlessness, the futility of the western philosophical tradition. Nevertheless, philosophy departments continue and indeed thrive in a consumer led world. Business as usual. Much like a recent trend in chess, despite its death-knell when Kasparov was defeated by an AI twenty years ago. Which is to say, that AI will no doubt eradicate the need for much academic practices, but the legacy and the ‘entertainment’ of such mental practices will continue, like the games of chess. Indeed, philosophy and much of social sciences as Wittgenstein’s language games.
Of course stochastic processes are useful for big-data analysis. What is being described, or admitted, is the mess that is mathematical methods to the psycho-social condition we find ourselves in, as academics in university, as teachers in school, or indeed politicians in goverment and business leaders in companies. Removed from the frontline of environmental sufferance, we can continue operating in our cities. There appears to be no way out of this problem.
Which is precisely what ABC state does: it provides the space for non-institutional activity. And it is precisely because it was formed with non-institutional partners, that is children, that gives it validity. And it is thus expected that such a solution will be invisible to teaching practice, and neglected in academia, and even resisted by those who read this. Nevertheless, the ABC State intervention is simple. Simple enough for young people to adopt. The problem is, the system of adults. This is not to say that the ABC State ‘works’. It is merely an information-system tool. Students will not magically develop the skills to collaborate. They are not ‘innocent’ or ‘blank slates’, but already exhibit various states of institutionalisation resulting from formal education (learning to ‘behave’), while experiencing a wide variety of cultural practices while living at home, which anthropologists may term ‘enculturation’, or therapists ‘personality’, or sociologists ‘dispositions’. We are operating within institutional contexts, secondary schools and in our case university departments, with paid roles and job-titles and remits. This is much ‘harder’ in social ontological terms than the ‘softer’ psychological proclivities or dispositions or psychic forms which inform our thought, feeling, action. Children are inherently ‘softer’ in their state, than adults. Pullman’s imaginative rendition of a changeable ‘demon’ for children which fixes in adulthood, comes to mind; a more accurate model might be that the adults fulfilling specific roles have fixed ‘demons’, and it is this ‘fixedness’ which constitute the cogwheels of our institutional social ontology.
Are We Trapped in Institutional Forms?
To escape from this, we require the adoption of certain conceptual forms which do not map well to ‘categories’ and ‘logic’. The mathematics of fractals, for example, or the oddity of Mobius strip, have only had minor impact on the social sciences. Fractals have evolved from iterative geometry, and have significant application in biology. It is not surprising that nature is predominantly non-linear in biological nature, as compared to the relative simplicity of physical nature. It is the physics of natural objects which has developed most of the mathematical methods we have evolved, and the stochastic development in particle physics. The adoption of fractal mathematics to social sciences has been minimal, and certainly there is no formal application in language or psycho-social space that I know of — other than as metaphor, in the same way conceptual models are represented using triangles of associated terms, eg Bandura agent-relationship-environment.
I am not in a position to offer a fundamental for mathematising social dynamics. The equivalent to ‘distance’, the primary measurement in physics. Nor an alternative to the geometry, which is inherently spatial in nature, and thus bears structural contiguity with physical objects, despite their 2d reduction. The shape of a triangle can be formed in the constellation of stars, a circle abstracted from a flower-head. The fundamental of psycho-social engagement is not physical. It may be emergent from physical basis, brains and responses to physical behaviours. With the most basic adoption of a HIERARCHY of emergence, there are generative mechanisms which have no determination from a lower level. Indeed, we may even entertain influence from a higher ontological striation: the eyeball which tracks the words on this page move according to some higher level intention, not the intentionality of the eye-ball (though a minor aspect of this construct may exist in the neuronal structure of the eye, or the brain structure which evolved from tracking objects like birds; the intentionality of composing meaning is still well within our hypothetical understanding of academia, even though computers appear to be simulating it rather well).
A Mathematics of our Psycho-Social State
The fundamental for the ‘mapping’ of psycho-social dynamics remains outwith the efforts of this PhD: however, the core practice which is suggested, is contained in this PhD. It is described as ABC state meta-method (and the Reflexive Reading meta-method which was rejected in the first Confirmation Report). The self-enclosed nature of ABC State, that the data derived is useful for the practitioners, tacitly imbedded within individual behaviours, nominally evaluated and expressed by participants, operating at the collective level while interfacing with the institutional role of the teacher, bears the principle upon which fundamental of psycho-social dynamic may be discovered. ABC state is ‘data’, in that an ABC may be attributed to a class. It is ‘information’ in that the ABC data may be interpreted as a possible description of the social dynamics within a class. The ABC State is ‘knowledge’ in that teachers may act upon this data, behave in prescribed ways, and indeed be receptive to non-institutionalised or spontaneous thoughts, feelings or actions. It is ‘wisdom’, in that the ABC state is contingent on not only the students, but the teacher, and indeed anyone who interacts with said class. It is, almost entirely, vacuous to non-interacting participants. This goes for other teachers, or indeed academics. However, if any adult, teacher or academic, was to interact with a class, this evaluation, and its longitudinal evaluation may prove helpful. It would be wise to consider it, and to compare it with the actual experience the adult may have with that class. It may correlate to the interacting adult’s own notion of what ABC state means, and it may differ. This is inherent in the ABC state tool. It is a meta-method. It is necessarily meta-cognitive, or meta-evaluative, or meta-theory.
The mathematical potential lies in the sensitivity we might bring to the ABC state. The nominal data of ABC state is hardly precise. However, it frames what we are interested in: the psycho-social dynamic. Within the ABC state, is a potential mapping of intention as exhibited by individuals and manifested collectively. And the ABC state is also fractal in nature, where the ABC state of the class, is similar to the ABC state of the individual, or the school as an instance of an institution, or education as an institution, and other institutions such as academia, or indeed the entire social structure of western living. There are self-similar forms between categorising and linear logic (thinking), with personality and dyadic relations (conversing), organisations and institutional logics (school and university). ABC state correlates the individual with the collective, or part with whole, with the part being an active agency and the whole being a sum of all active agencies; correctly speaking it is whole and other wholes in a non-linear arrangement. Less like linear thinking and more like imaginative, emotional, or ‘spiritual’ ‘thinking’, and engagements across a dinner table or at a party, or the meshwork of organisations; that is, non-linear engagement. ABC provides a framework for this non-linear engagement. The benefit of any bunch of human beings establishing an ‘A’ state amongst themselves, is a greater sensitivity to the psycho-social dynamics by which mathematisation becomes more feasible. That is, when people listen to one another in a harmonious way; where there are not ‘thirty people’ in a room, but rather a unity of attention, or motive, or purpose, or behaviour, while at the same time a diversity of attention, motive, purpose, behaviour.
This may appear contradictory, and indeed it is according to standard logic, law of excluded middle, etc. However, we are operating within non-linear logics. We ares imply attempting to provide ourselves with such meta-methods which help us coordinate ourselves according to these non-linear practices (achieving an A state) rather than collapsing back to linear practices (achieving a C state). Our global sibling status, in our differing cultures and social structures, are C-state. We will not be able to resolve the level of disorder we exhibit if we remain at C state. We must pursue potentials for achieving A state amongst us. Whether this is in classes with students as peers, or amongst us as academics as peers, or between organisations as adults, as peers. And I suggest, it might be useful for social science to lead in this way. To derive methods which are conducive for enabling A state, and thereby demonstrating the skills, attitude, mentality and behaviour which exemplifies A state.
What will this Maths Look Like?
At some point, we may then introduce a form of mathematics which is reflexive in practice. It is not a mathematics of objects, but a mathematics of subjects. That is, this new form of mathematics is not about projecting shapes or algebra on the physical world, but to reflect on the mathematics as representing our psycho-social state. This may appear outlandish or extreme, but it is actually rather mundane and is happening already. It is what children see when they learn numbers, or shapes, or algebra, or words. It is simply we are not often listening to what they think or see or feel when they are engaging these ‘virtual’ forms. We have been adopting techniques which treat them as objects, rather than subjects. Another, more prosaic example would be to observe the simulation of birds flocking on a computer screen: the computer program does not have a definition of flocking, it is an emergent phenomenon of multi-agent modelling. The observation that it is ‘flocking’ is made by the observer. There is an ontological phenomenon of ‘flocking’ best exemplified by starling murmuration perhaps. But again, the birds are not ‘flocking’. They are doing whatever each bird is doing, the result is the phenomenon we can observe externally (or another bird perhaps) as flocking. This mental image (at whatever level of mind which observes it) is enough to amaze humans, and to invite other starlings to join in — not to ‘flock’ but to operate whatever the rules are (ie stay close, head in the same direction). The individual is not ‘flocking’; the collective is ‘flocking’. Such is the state of ABC state: an A state is ‘flocking’. At some point, we may introduce a graph, or some algebra, that is not ‘about’ psycho-social dynamics, but reflect the individual’s understanding or experience of psycho-social dynamics. More precisely than a film, book, music and other complex symbolic presentations, as we resonate, appreciate, enjoy. That is, a more full-bodied ‘understanding’ of our psycho-social condition.