What is the difference between the form of something and its structure? Much of my recent thinking has been about the form of knowledge, and I think this is distinct from the 'structure' of knowledge. Structure we might represent is 'maps', semantic graphs, etc... structure is a way of representing the content of something: it is merely a description. I think to describe a form, however, is to grapple with its causal significance. A form might be described as a model: maybe like a sculpture or a train-set. When I talk about the form of knowledge, I am thinking of knowledge not as a structure, but as a model. That is why my thoughts have particularly focused on topology.
In fact, it's topology and game theory which seem to be important. The concept of the 'topological game' may be the most natural way of synthesising the two. Alongside Niklas Luhmann, Gadamer, Ed Hutchins, and a few others, I think that communication is a 'game' we play. The object of the game is to remain viable, and the only way we can remain viable is to communicate. The basic dynamics of the game are that making a communication involves making some connection between our inner-world and the outer-world. A communication ultimately is an intervention (a move) in the outer-world. But a communication will only be successful if it can be processed and reproduced by other people. That means their inner-worlds can process our communications and make new outer-world communications. If our communication isn't successful, if it isn't reproduced in a way in which we can continue the communication, our viability is challenged. If we have too many unsuccessful communications which aren't reproduced, we will find it increasingly difficult make any sort of communication at all, and we lose the game.
This game is what the game theorists call a 'cooperative repeated game'. I think that within each player, what is built up is a horizon of expectations, or a landscape, upon which the likelihood of success of a particular communication can be judged. This landscape is constructed through the making of communications and their success of failure as the game progresses. That is where the topology fits. This is where we can talk about a person's knowledge as a 'form'. It is causally efficacious on the 'moves' that can be made and the horizon that can be seen at any point on the surface of the topology.