CONSTANCY AND INDEPENDENCE 14/11 



independence show a remarkable variety. Thus, in C, 1 domi- 

 nates 3 ; but in D, 3 dominates 1. As the variables become 

 more numerous so does the variety increase rapidly. 



The multiplicity of inter-connections possible in a telephone 

 exchange is due primarily to the widespread use of temporary 

 constancies. The example serves to remind us that 8 switching ' 

 is merely one of the changes producible by a re-distribution of 



+*• 



**• 



B 



Figure 14/10/2. 



constancies. For suppose a system has the diagram of imme- 

 diate effects shown in Figure 14/10/2. If an effect coming from 

 C goes down the branch AD only, then, for the branch BE to 

 be independent, B must be constant. How the constancy is 

 obtained is here irrelevant. When the effect from C is to be 

 4 switched ' to the BE branch, B must be freed and A must 

 become constant. Any system with a ' switching ' process must 

 use, therefore, an alterable distribution of constancies. Con- 

 versely, a system whose variables can be sometimes fluctuating and 

 sometimes constant is adequately equipped for switching. 



14/11. At this point it is convenient to consider what degree 

 of independence is shown in a system if some part is not directly 

 affected by some other part. To take an extreme case, to what 

 extent are two parts joined functionally if they have only a 



W x \ 



A B 



Figure 14/11/1. 



single variable in common — the parts A and B in Figure 14/11/1, 

 for instance, which share only the variable x ? It is shown in 

 S. 24/17 that if x is a full-function capable of unrestricted varia- 

 tion, then the two parts A and B are as effectively joined as if 



161 



