11/5 AN INTRODUCTION TO CYBERNETICS 



It will be seen that diflferent arrangements within the table, and 

 different numbers of states available to D and R, can give rise to a 

 variety of situations from the point of view of R. 



Table 11/4/1 



Ex. 1 : With Table 11/4/1, can R always win if the target is d1 



Ex. 2: (Continued.) What transformation should R use? 



Ex. 3 : (Continued.) If a is the target and D, for some reason, never plays 5, 

 how can R simpHfy his method of play? 



Ex. 4: A guest is coming to dinner, but the butler does not know who. He 

 knows only that it may be Mr. A, who drinks only sherry or wine, Mrs. B, 

 who drinks only gin or brandy, or Mr. C, who drinks only red wine, brandy, 

 or sherry. In the cellar he finds he has only whisky, gin, and sherry. Can 

 he find something acceptable to the guest, whoever comes ? 



11/5. Can any general statement be made about i?'s modes of 

 play and prospects of success? 



If full generality is allowed in the Table, the possibilities are so 

 many, arbitrary and complicated that little can be said. There is 

 one type, however, that allows a precise statement and is at the 

 same time sufficiently general to be of interest. (It is also funda- 

 mental in the theory of regulation.) 



From all possible tables let us ehminate those that make i?'s game 

 too easy to be of interest. Ex. 11/4/3 showed that if a column 

 contains repetitions, i?'s play need not be discriminating; that is, 

 R need not change his move with each change of Z)'s move. Let us 

 consider, then, only those tables in which no column contains a 

 repeated outcome. When this is so R must select his move on full 

 knowledge of D's move; i.e. any change of D's move must require 

 a change on i?'s part. (Nothing is assumed here about how the 

 outcomes in one column are related to those in another, so these 

 relations are unrestricted.) Such a Table is 11/5/1. Now, some 

 target being given, let R specify what his move will be for each move 

 by D. What is essential is that, win or lose, he must specify 



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