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Sunday, 25 September 2016
In the network each node has a map of the network and a map of its own internal states. When the link between two nodes becomes active they attempt to align their network maps. If this succeeds then the strength and bandwidth of the link is increased, if it fails then it is weakened, and if it fails badly the link is strengthened but reversed in phase. If there is a positive alignment between network maps then a further alignment of internal maps, with appropriate phase changes, is attempted - corresponding effects also arise when a link is strengthened without agreement. The success or failure of this second manoeuvre affects the nature of the link in the same manner as the first. Any change in a link has effects on all the other nodes joined to the two ends, which may support the change or resist it; either way their own further links are also altered as a result. These changes are not immediate but come with a delay which varies with the quality of each link. Thus the network is always in action, reconfiguring itself as changes propagate through it. Once its structure is complicated enough, meaning that there are a sufficient number of different kinds of nodes, then its continual, but not necessarily continuous, dynamic is largely supported endogenously. The number of emergent phenomena, of group formation and dissolution, of invasion, colonisation, atomisation and so on is unlimited. These phenomena are marked by a sharp drop in complexity: one no longer needs N dimensions of phase space to understand the action, where N is a multiple of some power of the number of nodes, but just two or three or four. At this level an understanding of the process can be included in the map belonging to a single node. Such an understanding is nevertheless rare enough that it forms an isolating factor in the nodes in which it arises, making agreement between maps difficult and so weakening their links with all their immediate neighbours. This description of something we all understand very well is complicated only because it attempts to begin from simple premises.
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