Saturday 22 September 2012

"Release", Concepts and Understanding: More Mathematical Speculations

To summarise from yesterday, I have argued that 'tension', the feeling of questioning, curiosity, anxiety in the face of problems, is a product of entrenchment in meta-games where we lose our way, or struggle to cope with the proliferation of options as we try to consider what we should do (see I have argued that it is what we lose, what we forget, what is absent, which has the primal causal bearing on what we choose to do. For so many in academia in the UK at the moment, the classic example of this thinking would be to ask yourself (in the face of uncertainty and insane managerialism), "should I get another job?"

Now I come to consider the fact that in the face of immense confusion, we do find ways of making decisions. We do, in fact, find a way of satisfactorily simplifying the endless complexity of meta-games and meta-meta-games in order to identify clear 'equilibrium points' from which we can make a decision. The moment at which we manage to collapse the complexity of meta-game trees and see the entirety more simply is the moment when we have 'understood' something. I will argue that this moment depends on us 'grasping a concept'. Indeed, it is this moment which appears to us as 'meaningful': it is the moment when our expectations (in the form of meta-strategies, and meta-meta-strategies) are restructured.

Given the immense complexity of the higher-level metagames (see M4 above), and M5 would be another power of 2, and M6 a further power bigger, how can this ever be navigated?

But the complexity is overwhelming if strategies a and b are fundamentally different. But what if they were conceptually connected? And what if the strategy a/a or a/b was essentially the same as strategy a or strategy b? And what if the strategy a/a/a/a or a/a/b/a was also essentially the same as strategy a?

This kind of a strategy would be a recursive strategy. A strategy that was applicable to many layers of recursion of the metagame. Cybernetics, in fact, is a discipline which specialises in recursive strategies. Beer's Viable System Model is a classic example of a  recursive strategy: it's concepts are applicable whether questions are asked about the organisation, the individuals, or even the cells that make up the individuals. It is clear that were such a recursive strategy to be discovered, then the tree of games and metagames becomes simplified greatly. That means that the equilibrium points are more easily discernable in the light of the recursive strategy that is used.

The moment at which a recursive strategy is discovered and applied, is the moment at which new understanding is realised. It is the moment at which tension is released (although briefly). It is where the complexity of the meta-game tree collapses through the application of a recursive strategy, to reveal clear equilibrium points.

Our next question is to consider how such recursive strategies are discovered. Tomorrow, I will argue that recursive strategies grow from the realisation of shared absence, and that as the metagame tree for each individual reveals itself, so too do the absences which contribute to the communicative decisions for each individual.

No comments: