Tuesday, 17 November 2015

Conservation of Constraint? - Some vague speculations about learning, music and violence

This is a very speculative post (well - that's partly what blogs should be about!). I've been ruminating about constraints for a number of years now. The technical measurable component of constraint presents itself in Shannon's redundancy measure. This is the inverse of the entropy calculation, which measures the average uncertainty of a message: the constraint is the thing which must be present in order to produce that uncertainty - for example, with regard to the uncertainty between words of a language, the grammar of that language performs this function. One of the functions that constraint performs is to ensure effective communication: grammars restrict choices, and structure things such that certain key aspects of meaning are emphasised or repeated.

Redundancy in information theory can refer to a number of things. On the one hand, it might refer to 'repeated information'. If we are to send a message in a noisy environment, it might be necessary to repeat it a few times. This kind of redundancy plays out over time. I would like to call it 'diachronic redundancy' or 'diachronic constraint'. Alternatively, there is redundancy where a message is conveyed simultaneously in different ways: I might say "I don't understand" whilst at the same time shrug my shoulders, or shake my head. Between the three different signals, the message is conveyed through a kind of connotative process. This type of redundancy is "synchronic redundancy", or perhaps "synchronic constraint".

Human communication obviously takes place within both synchronic and diachronic dimensions. However, I find myself sometimes more focused on diachronic processes in time which express redundancy (something repetitive like typing, or walking, or any kind of repetitive sequential action). Other times, I am deeply immersed in a multi-sensory contemplation of many different signals: when I study a painting, or listen to music, or have a deep conversation with somebody face-to-face over a beer. This is more synchronic. Then I am mindful that the diachronic gives way to the synchronic in the way that action gives way to reflection; in the way that contemplation is balanced by action.

So here's my question: is constraint conserved in human relations? Is the sum of diachronic and synchronic constraint constant? (assuming we have a way of easily measuring each). Music may provide some grounds for investigating this perhaps: the difference between moments of harmonic richness and moments of rhythmic drive.

There is an added complication however (of course!). Redundancy is measured by the formula:
1 - H/Hmax
and von Foerster convincingly argues that self-organisation and development works by increasing the bounds of  Hmax, or the 'maximum entropy' so that self-organising systems become more complex. (I wrote about this here: http://dailyimprovisation.blogspot.co.uk/2015/09/learning-gain-and-measurement-of-order.html) So it may be that constraint isn't conserved exactly, but rather the balance between diachronic and synchronic constraint gives rise to a mechanism for increasing the maximum entropy: increasing complexification. This, I think, is important in understanding the learning process.

Intuitively, we move between synchronic and diachronic constraints, as between contemplation and action, and along the way expand the domain within which constraints apply themselves. There's a link to Vygotsky here: the Zone of Proximal Development is a way of expressing the synchronic constraints (closeness of a teacher) in balance with the diachronic constraints (the particular activities a learner engages in on their own). Does the ZPD "draw out" synchronic constraints (teacher-pupil relationship) as diachronic constraint (scaffolded activity)?

Maybe there's also a link to terrorism (which is obviously on everyone's mind at the moment). What is it that leads people to carry out sequential, violent and repetitive activities like shooting people? This looks like a kind of diachronic constraint. The synchronic component is fanatical religion. Is terrorist violence a 'drawing-out' of repetitive diachronic activity from intense synchronic experience? Is this how the sense of exclusion and injustice (which is part of that synchronic experience) feeds into the execution of violent plans? Of course, in this case, it isn't stable; but is there an analysable relationship between the synchronic aspects and the diachronic execution? (Of course, the same applies to the military response by the state!). Perhaps this is over-thinking something at a very difficult time. But difficult times are valuable in producing a lot of thinking.... they are full of synchronic, multi-layered constraints.

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