Sunday, 1 January 2017

Descriptions, Metagames and Teaching

Over the last year, I have found myself creating videos for various purposes. Video is a powerful medium for communication, partly because it presents many simultaneous descriptions of the same thing: I will make the graphics, the text, the voice, animations. There are inflections in my voice too, and ways in which the content is structured when I present it. Each of these descriptions is redundant in the sense that any particular description could be removed, and the sense of what I am communicating is preserved: it just wouldn't be as effective. There is perhaps a general rule: the most powerful approach to teaching, the richest the array of descriptions which can be brought to bear in communicating.

Another way of looking at this is to say that if I want to communicate a concept A, and A is constrained by a set of factors (or other concepts), B,C,D and E, then the richest number of descriptions will apply not to A, but to E (the deepest constraint), because E will be a deep constraint not just of A, but of W, X, Y and Z...or anything else. If A is a very specific thing, constrained by a particular perspective, then A has to be imparted negatively through the multiple presentation of descriptions of the things which constrain it.  It is the way in which a child might be convinced of A, where there are multiple (and nested) Why? questions: ((((A)Why?)Why?)Why?)Why?)Why?

A few years ago, I wrote a paper with Loet Leydesdorff on Systems theory approaches to communication and organisation, drawing particular reference on the similarities between Stafford Beer's Viable System Model and Luhmann's social systems theory: see In it, I drew on Nigel Howard's metagame theory, arguing that both systems theories were effectively 'games' played with either members of an organisation (Beer) or the community of sociologists (Luhmann). It's been pretty ignored since, but my recent thinking about constraint has led me back to it.

So I'm asking whether there is a connection between the 'string rewriting' ideas that I touched on in my last post, and Howard's metagames as we presented it in the paper. The basic idea was that metagame trees (that is, decision trees about speculated strategies of opponent moves in games) quickly get enormously complex. They are so enormously complex that we, not being computers, easily forget sets of permutations and options which are logically possible. Certain speculations about the future are constrained by factors in the environment about which we have little knowledge. The effect of these constraints is to privilege one action over another. In the paper I argued that the action chosen was the one that emerged most dominant in all levels of recursion given the constraints - a kind of 'universal concept' which emerged through constraint. To find this mathematically, it was simply a matter of counting the outcome which was most dominant:

So in the above diagram, given the 'gaps' in reasoning (holes in the table), outcome Pa ,Pb emerges as dominant. But what does "emerging dominant" mean? In counting the number of times this particular outcome emerges at all levels of recursion, we are effectively counting the number of descriptions of this outcome. So Pa ,Pb can be described as (b)a and ((b)b)a) and ((b)a)b and so on. What we have then are ways of rewriting the string for outcome Pa ,P

Of course, these are the constraints seen from one player A's perspective imaging the constraints of player B. There is a point at which Player A and Player B have similar constraints: they will be able to exchange different and equivalent descriptions of a concept, and at this point they will have knowledge of the game each other is playing. At this point, the metagame of this game becomes the interesting thing: someone will break the rules. And then we learn something new.

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