7/10 AN INTRODUCTION TO CYBERNETICS 



however, the order were given that no man was to stand at the left 

 of a man who was taller than himself, the constraint would be 

 severe; for it would, in fact, allow only one order of standing 

 (unless two men were of exactly the same height). The intensity 

 of the constraint is thus shown by the reduction it causes in the 

 number of possible arrangements. 



7/lOi It seems that constraints cannot be classified in any simple 

 way, for they include all cases in which a set, for any reason, is 

 smaller than it might be. Here I can discuss only certain types of 

 outstanding commonness and importance, leaving the reader to add 

 further types if his special interests should lead him to them. 



7/11. Constraint in vectors. Sometimes the elements of a set are 

 vectors, and have components. Thus the traffic signal of S.7/8 

 was a vector of three components, each of which could take two 

 values. In such cases a common and important constraint occurs 

 if the actual number of vectors that occurs under defined conditions 

 is fewer than the total number of vectors possible without conditions 

 (i.e. when each component takes its full range of values indepen- 

 dently of the values taken by the other components). Thus, in the 

 case of the traffic Hghts, when Red and Yellow are both lit, only 

 Green unlit occurs, the vector with Green ht being absent. 



It should be noticed that a set of vectors provides several varieties, 

 which must be identified individually if confusion is not to occur. 

 Consider, for instance, the vector of S.3/5: 



(Age of car, Horse-power, Colour). 



The first component will have some definite variety, and so will 

 the second component, and the third. The three varieties need 

 not be equal. And the variety in the set of vectors will be diff"erent 

 again. 



The variety in the set of vectors has, however, one invariable 

 relation to the varieties of the components — it cannot exceed their 

 sum (if we think in logarithms, as is more convenient here). Thus, 

 if a car may have any one of 10 ages, of 8 horse-powers, and of 12 

 colours, then the variety in the types of car cannot exceed 3-3 + 3-0 

 + 3-6 bits, i.e. 9-9 bits. 



7/12. The components are independent when the variety in the 

 whole of some given set of vectors equals the sum of the (logarithmic) 

 varieties in the individual components. If it were found, for instance, 

 that all 960 types of car could be observed within some defined set 



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