Tension and Thinking: A game-theoretical speculation
Jumat, 21 September 2012
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There's a lot of tension around at the moment! Maybe that's a good excuse to start thinking about what 'tension' might be, and what happens when it is released. I've previously remarked that I see this process as musical. I'm currently in the process of trying to characterise the process as a mathematical one.
Nigel Howard's work presents a picture of rational thought which progresses up levels of meta-games in pursuit of effective decisions. Howard describes how the outcomes from decisions, at the basic level, and at the meta-level, can be ordinal (so one outcome is quantifiably better or worse than another) or non-ordinal, or even semi-ordinal. This reflects the different kinds of decisions we have to make in different situations: playing Monopoly is different from playing politics.
The other difference in these situations is the role of coalitions. Coalitions do not occur in Monopoly; but they are a key part of strategy in politics (as Nick Clegg will tell you!). The games I'm really interested in are games of discourse - and they are essentially political: I utter an opinion; I seek your agreement; I aim to build a movement around my ideas; I challenge ideas I do not agree with; and so on. That would suggest that outcomes for games of discourse are related to the probability that coalitions will be established. In Niklas Luhmann's language, that means the outcome relates to the probability that my communication will be successful.
The only way I can judge if my communication will successful is to try to anticipate the likely response of others around me. That will inform the communication I make (I will judge it to fit the audience) and will lead me to think carefully and strategically about the coalition I might aim for. Anticipating means going up the meta-game tree. It means thinking "if I say this, x may say this, then I will respond; or if I say this, x may say this, and ..." All of those possibilities must be considered. But of course, there are too many of them!
When we think like this, some possibilities get explored, others do not. Why do we forget the ones we don't explore? Maybe it's because of things that have happened to us in the past which blinker us in some way. Attachments in childhood are always a good indicator of what isn't thought about. But here comes the rub: I think it is what we miss out that determines the course of action we eventually choose. This is because preferences in the metagame and the metametagame propagate downwards and produce a pattern of equilibrium points from which decisions are construed. It is the missing stuff, the stuff we don't consider, which is the determining factor in the establishment of these equilibrium points.
So it looks like this:
It is tension which produces the absence which is causal on the choice of action.
Tomorrow I shall talk about release, and the role of concepts and rationality in simplifying this game-tree and helping to manage the process of thinking.
Nigel Howard's work presents a picture of rational thought which progresses up levels of meta-games in pursuit of effective decisions. Howard describes how the outcomes from decisions, at the basic level, and at the meta-level, can be ordinal (so one outcome is quantifiably better or worse than another) or non-ordinal, or even semi-ordinal. This reflects the different kinds of decisions we have to make in different situations: playing Monopoly is different from playing politics.
The other difference in these situations is the role of coalitions. Coalitions do not occur in Monopoly; but they are a key part of strategy in politics (as Nick Clegg will tell you!). The games I'm really interested in are games of discourse - and they are essentially political: I utter an opinion; I seek your agreement; I aim to build a movement around my ideas; I challenge ideas I do not agree with; and so on. That would suggest that outcomes for games of discourse are related to the probability that coalitions will be established. In Niklas Luhmann's language, that means the outcome relates to the probability that my communication will be successful.
The only way I can judge if my communication will successful is to try to anticipate the likely response of others around me. That will inform the communication I make (I will judge it to fit the audience) and will lead me to think carefully and strategically about the coalition I might aim for. Anticipating means going up the meta-game tree. It means thinking "if I say this, x may say this, then I will respond; or if I say this, x may say this, and ..." All of those possibilities must be considered. But of course, there are too many of them!
When we think like this, some possibilities get explored, others do not. Why do we forget the ones we don't explore? Maybe it's because of things that have happened to us in the past which blinker us in some way. Attachments in childhood are always a good indicator of what isn't thought about. But here comes the rub: I think it is what we miss out that determines the course of action we eventually choose. This is because preferences in the metagame and the metametagame propagate downwards and produce a pattern of equilibrium points from which decisions are construed. It is the missing stuff, the stuff we don't consider, which is the determining factor in the establishment of these equilibrium points.
So it looks like this:
As the different levels of recursion increase (from M1 to M4), so things start to drop off. As things start to drop off, so a pattern of emphasis reveals certain equilibrium points at M1, and so determines the choice of action.
To me, this helps explain tension. Tension lies in the descending into meta-games and pursuing options at a meta-level. The deeper the tension, the more difficult it becomes to keep track of all the metagames. This is where things get forgotten.
It is tension which produces the absence which is causal on the choice of action.
Tomorrow I shall talk about release, and the role of concepts and rationality in simplifying this game-tree and helping to manage the process of thinking.
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