A ‘center’ is a marked place in space or time or in a collection of objects, and surrounding it is a structure or pattern that supports it. The questions that concern us here are: ‘Why are there centers at all?’ ‘Why is a center at a particular X?’ Historical and combinatorial processes of centralization are reviewed, and a phenomenology and mechanisms are provided. Models considered include: stochastic markets with increasing returns to scale, codes as in DNA, combinatoric processes as in statistical mechanics, and differentiation in biology. Polycenters.
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