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W, [control] procedures for generating a new control policy from some set of given policies; [function optimization] procedures for generating a new point in the domain of  from some set of given points. |
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 , plans for applying procedures from W to generate new policies [control] or points [function optimization] on the basis of observations. |
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e, an indexing set corresponding to the initial uncertainty about the ''law of motion" or the function to be optimized. |
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 ,the extension of the ranking J on control sequences to the plans inducing the sequences, assigning tÎ the average (or minimum, etc.) ranking over the uncertainty indexed by e. |
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6. Central Nervous Systems |
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Behavior is primarily adaptation to the environment under sensory guidance. It takes the organism away from harmful events and toward favorable ones, or introduces changes in the immediate environment that make survival more likely.
Hebb in A Textbook of Psychology (pp. 44-45) |
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I introduce this last example of an adaptive system with some hesitation. Not because the central nervous system (CNS hereafter) lacks qualifications as an adaptive systemon the contrary, this complex system exhibits a combination of breadth, flexibility, and rapidity of response unmatched by any other system known to manbut because there is so little prior mathematical theory aimed at explaining adaptive aspects of the CNS. Even an intuitive understanding of the relation between physiological micro-data and behavioral macro-data is only sporadically available. Perforce, mathematical theories enabling us to see some overall action of the CNS as a consequence of the actions and interactions of its parts are, when available at all, in their earliest formative stages. |
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Here, more than with the other examples, the initial advantage of the formal framework will be restatement of the familiar in a broader context. The best that can be hoped for at this stage is an occasional suggestion of new consequences of familiar facts: Without the advantages of a deductive theory, statements made within the framework can do little more than provide an experimenter with guideposts and cautions, suggesting possibilities and impossibilities, phenomena to anticipate, and conclusions to be accepted warily. This is a preliminary, heuristic stage marking the transition from unmathematical plausibility to the formal deductions of mathematical theory. In common with most heuristic and loose-textured |
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