13/9 AN INTRODUCTION TO CYBERNETICS 



two varieties can be distinguished : there is (i) the variety within the 

 basic class (2 for the coin, the number of distinct possible ages in B), 

 and (ii) the variety built up by using the basic class n times over (if 

 the vector has n components). In the example of the coin, the two 

 varieties are 2 and 64. In general, if the variety within the basic 

 class is k, and the vector has n components, each a member of the 

 class, then the two varieties are, at most, k, and k". In particular 

 it should be noticed that if the variety in the basic class has some 

 limit, then a suitably large value of n will enable the second variety 

 to be made larger than the limit. 



13/9. These considerations are applicable in many cases of regula- 

 tion. Suppose, for definiteness, that the water bath may be affected 

 in each minute by one of the three individual disturbances : 



(a) a draught of air cooHng it, 



(b) sunshine warming it, 



(c) a cold object being immersed in it. 



The variety is three, but this number is hardly representative of the 

 variety that will actually occur over a long time. Over a year, say, 

 the Grand Disturbance is a long vector, with perhaps some hundreds 

 of components. Thus one Grand Disturbance might be the vector 

 (i.e. the sequence) with 400 components: 



(a, b, a, b, b, a, c, b, b, c, c, b, b, . . . c, b, a, b). 



And if the individually correct responses are, respectively a, ^, and 

 y, then the Grand Response appropriate to this particular Disturb- 

 ance would be the vector (i.e. sequence) 



(a, ^, a, ^, p, a, y, ^, ^, y, y, ^, ^, . . . y, ^, a, ^). 



If there is no constraint in the Disturbance from component to 

 component as one goes from left to right, the whole set of possible 

 Disturbances has variety of S^oo; and the Grand Response must 

 have at least as much if full regulation is to be obtained. 



We now come to the point: the double sequence, as it occurred 

 in time, shows the characteristic constraint of a machine, i.e. it 

 defines a machine up to an isomorphism. Thus, in the example 

 just given, the events occurred in the order, from left to right: 



ababbacbbcc ..., etc. 



aj3aj^^ayl3^yy..., etc. 



(though not necessarily at equal time-intervals). It is now easily 



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