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W. Ross Ashby

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Authored papers (3)

  • Every Good Regulator of a System Must Be a Model of That System1991ⓒ 725

    Any regulator that optimally controls a system must, as a mathematical necessity, contain a model of that system — this is the central theorem proved by Conant and Ashby, originally published in 1970 and reprinted in the 1991 volume *Facets of Systems Science* (IFSR Series, volume 7, pp. 511–519). Using set-theoretic machinery drawn from Bourbaki's 1958 *Théorie des Ensembles* and Riguet's 1948 work on binary relations (*Bull. Soc. Math. Fr.*, vol. 76, p. 114), the proof formalizes regulation as a mapping problem: a regulator R acts on a system S to produce outcomes in a goal set G, and the theorem establishes that the optimal such mapping is homomorphic to S — that is, the regulator's internal structure must mirror the causal structure of the regulated system. The method introduced is a formal set-theoretic proof of isomorphism between regulator and system, grounded in partition lattice theory as developed by Hartmanis and Stearns (1966) and prior information-theoretic work by Conant in *IEEE Trans. Systems Sci.*, vol. 5 (1969). Applied domains motivating the work include air traffic flows around New York, endocrine balances of the pregnant sheep, and money flows among banking centres. The paper argues this implies that effective control of any complex dynamic system cannot be achieved without the regulator embodying, explicitly or implicitly, a working model of that system — making model-building not merely useful but logically obligatory for good regulation.

  • Automaton Theory and Learning Systems (1967)
    referenced-only
  • Every Good Regulator of a System Must Be a Model of That System (1991)
    referenced-only

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