7/22 AN INTRODUCTION TO CYBERNETICS 



The subject might then be given a sequence such as A2, B5, C3, B5, 

 C3, A2, A2, C3, and so on. 



Now this sequence, as a sequence of vectors with two components, 

 shows constraint; and if learning is to occur the constraint is neces- 

 sary; for without constraint A would be followed equally by 2, 3 

 or 5 ; and the subject would be unable to form any specific associa- 

 tions. Thus learning is possible only to the extent that the sequence 

 shows constraint. 



The same is true of learning a maze. For this to occur the maze 

 must retain the same pattern from day to day during the period of 

 learning. Were the maze to show no constraint, the animal would 

 be unable to develop the particular (and appropriate) way of be- 

 having. Thus, learning is worth while only when the environment 

 shows constraint. (The subject is taken up again in S.13/7.) 



VARIETY IN MACHINES 



7/22. We can now turn to considering how variety is affected by a 

 machine's activities, making our way towards an understanding of 

 what happens to information when it is handled by a machine. 

 First, let us notice a fundamental peculiarity of the single-valued 

 transformation in its relation to variety. 



Consider for instance the single-valued transformation 



^ B C C 



and apply it to some set of the operands, e.g. 



BBACCCAABA 

 The result is CCBCCCBBCB 



What is important is that the variety in the set has fallen from 3 to 

 2. A further transformation by Z leads to all C's, with a variety 

 of 1. 



The reader can easily satisfy himself that such a set, operated on 

 by a single-valued transformation, can never increase in variety, 

 and usually falls. The reason for the fall can readily be identified. 



In the graph, a confluence of arrows ^ can occur, but a 



divergence <^ is impossible. Whenever the transformation 



makes two states change to one, variety is lost; and there is no 

 contrary process to replace the loss. 



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