this course is a scratching of a small part of the surface of the history of ideas.
in any generations, a few paradigms, or simply stories or examples capture the imagination of thinkers, and remain long enough to inform the manner in which they construct their picture of the world - whatever part of it they view. for good and bad reasons, when these ideas originate in a technical field, their outward diffusion as metaphors, into the culture as a whole, is difficult and slow.
in this country scientific journalism is undergoing a revival, but journalists are not good meters of the vitality of scientific ideas - except insofar as they themselves determine their progress. within recent years, the public has heard the words 'catastrophe,' 'fractal' and 'chaos,' and the latter two at least have passed into popular culture, chaos in the form of the butterfly effect, a tale that has seeped into the public consciousness of 'what the world is', its boundaries much greater than scientific meteorology.
in this course, we shall get an early taste of two new metaphors that sum to a paradigm, the sense that sufficiently complex systems inevitably evolve to a very precise balance between too much order, and too little, the pejorative connotation being that any system that strays too far from this border is in some sense poorly placed to survive. this region is called the 'edge of chaos.'
this proposal is semi-empirical: that is, it gets its justification as much from observation (in this case the observation of simulations on computers) as from analysis and thought. In a simulation the model is often a very complex digraph, or network. Very many situations can be portrayed as networks, and one is tempted to extrapolate features emerging from the study and simulation of networks in one clear context into regions much more noumenous. this was the death of catastrophe theory, and resistance is growing to to the wilder ambitions of the body of researchers in the hard sciences who are making use of these techniques.
will the metaphors make it out? are they too rigid, too loose? or are they critically poised to adapt as they move out into the intellectual landscape, and survive?