CHAPTER 14 



Constancy and Independence 



14/1. Several times we have used, without definition, the con- 

 cept of one variable or system being ' independent ' of another. 

 It was stated that a system, to be absolute, must be 4 properly 

 isolated ' ; some parameters in S. 6/2 were described as 4 ineffec- 

 tive ' ; and iterated ultrastable systems were defined as ' wholly 

 independent ' of each other. So far a simple understanding has 

 been adequate. But as it is now intended to treat of systems 

 that are neither wholly joined nor wholly separated, a more 

 rigorous method is necessary. 



The concept of the l independence ' of two dynamic systems 

 might at first seem simple : is not a lack of material connection 

 sufficient ? Examples soon show that this criterion is unreliable. 

 Two electrical parts may be in firm mechanical union, yet if 

 the bond is an insulator the two parts may be functionally inde- 

 pendent. And two reflex mechanisms in the spinal cord may be 

 inextricably interwoven, and yet be functionally independent. 



On the other hand, one system may have no material con- 

 nection with another and yet be affected by it markedly : the 

 radio receiver, for instance, in its relation to the transmitter. 

 Even the widest separation we can conceive — the distance between 

 our planet and the most distant nebulae — is no guarantee of 

 functional separation ; for the light emitted by those nebulae 

 is yet capable of stirring the astronomers of this planet into con- 

 troversy. The criterion of connection or separation is thus useless. 



14/2. This attempted criterion obtained its data by a direct 

 examination of the real ' machine '. The examination not only 

 failed in its object but violated the rule of S. 2/8. What we 

 need is a test that uses only information obtained by primary 

 operations. 



It is convenient to approach the subject by first clarifying 

 what we mean by one system c controlling ' or ' affecting ' another. 



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