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THE BOLE OF MODELS IN THEORETICAL BIOLOGY 205

inputs. Two systems which are represented by the identical Ashby black box, or morę precisely by the state transition table of this unit, may be said to be similar in regard to organization. In a report called “Models in Cybernetics” George (1960) suggests that two systems are cybernetic models if they can execute the same “effective procedurę” (or algorithm). The specific verification procedurę for a self-organizing system model is to place it in a certain type of “emdronment” and see if it can achieve the same degree of organization, defined by “states,” as the prototype.

Very central to the study of self-organizing models is the concept of an automation, which may be defined as a “black box with states.” Space precludes discussion of the enormous body of automata theory literaturę; a good introduction to the subject is provided in a recent volume of Arbib (1964). Suffice it to say that there exists a substantial body of theory dealing with “isomorphisms of automata,” which implies similarity comparisons. Two automata may be held to be similar either if they produce the same result when presented with the same inputs or when they have the same state transition tables. The Turing machinę is a very generał type of symbol-processing automaton based on a state transition table; similarity of Turing machines is defined in the same sense as that of automata.

Many publications on the subject of self-organization are available. Symposia volumes or collections on this subject include those of Yovits et al. (1962), von Foerster and Zopf (1962), and Bernard and Karę (1962). These include a wide variety of articles dealing with models of vision and perception, nerve nets, hearing and olfaction, brain algorithms of various types, and abstract self-organization.

The concept of a self-organizing system model has also been used in connection with social organization. The use of mathematical models of social organization was fully discussed as early as 1950 by Deutsch (1951). An early report on Computer simulation of self-organization was provided by Farley and Clark (1954) and dealt with the problem of purposeful leaming in a nerve net. Pertinent reports include those of Meier (1961) on generał social organization, Gullahom and Gullahom (1964) on human interaction and hierarchy development in smali groups, and Beer (1964) or Cyert and associates (1959) on cybernetic organization of commercial firms. In the Soviet Union Maslov (1964) has discussed the construction of Computer models of sociological control, and this type of simulation is also suggested by a number of other Soviet cybemeticists. Kolmogorov (1961) asserts that Computer algorithms