7/25 AN INTRODUCTION TO CYBERNETICS 



the machines change step by step. The conditions are now as in 

 the previous section, and if we measure the variety in state over the 

 set of repHcates, and observe how the variety changes with time, we 

 shall see it fall to some minimum. When the variety has reached 

 its minimum under this input-value (Pi), let P be changed to some 

 new value (P2), the change being made uniformly and simultaneously 

 over the whole set of replicates. The change in value will change 

 the machine's graph from one form to another, as for example (if 



Under Pj, all those members that started at A, B ov D would go to 

 D, and those that started at C, E, or F would go to E. The variety, 

 after some time at Pj, would fall to 2 states. When P is changed 

 to P2, all those systems at D would go, in the first step, to E (for the 

 transformation is single-valued), and all those at E would go to B. 

 It is easy to see, therefore, that, provided the same change is made 

 to all, change of parameter-value to the whole set cannot increase the 

 set's variety. This is true, of course, whether D and E are states of 

 equilibrium or not. Now let the system continue under P2. The 

 two groups, once resting apart at D and E, will now both come to 

 B; here all will have the same state, and the variety will fall to zero. 

 Thus, change of parameter-value makes possible a fall to a new, and 

 lower, minimum. 



The condition that the change P^ —> Pi may lead to a further fall 

 in variety is clearly that two or more of Pj's states of equilibrium 

 lie in the same P2 basin. Since this will often happen we can make 

 the looser, but more vivid, statement that a uniform change at the 

 inputs of a set of transducers tends to drive the set's variety down. 



As the variety falls, so does the set change so that all its members 

 tend, at each moment, to be at the same state. In other words, 

 changes at the input of a transducer tend to make the system's 

 state (at a given moment) less dependent on the transducer's 

 individual initial state and more dependent on the particular sequence 

 of parameter-values used as input. 



The same fact can be looked at from another point of view. In 

 the argument just given, "the set" was taken, for clarity, to be a set 

 of replicates of one transducer, all behaving simultaneously. The 

 theorem is equally applicable to one transducer on a series of occa- 

 sions, provided the various initial times are brought into proper 



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