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Thursday, January 13, 2005

New concepts in complexity theory  

Christopher Alexander
I have made a crude estimate comparing the number of possible configurations in a given building design problem.

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The number of configurations both in the good pile and in the all pile are immense -- immense beyond imagining. There is therefor no shortage of good solutions to any given problem. But it is the ratio of the two numbers which staggers the imagination. The ration between the two numbers is, in rough terms, about 10E12000. Furthermore, although there are huge numbers of possible good configurations, these good ones are sparsely scattered throughout configuration space

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In general we may characterize this task, as a task of walking through configuration space, until we reach good results. The assumption is that there are (indeed, there must be) some kinds of paths through configuration space which can get a system to the good places.

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In Book 2. I have shown how living structure arises when reached by a series of movements in configuration space which are "structure-preserving" paths.

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These are real explanations, which have practical effects in real practical buildings. And what it amounts to, in informal language, is that the transformations represent a coded and precise way that aesthetics - the impulse towards beauty - play a decisive role in the co-adaptation of complex systems.

Topics: Christopher Alexander | Meaning | Design


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