CHAPTER 12 



Temporary Independence 



12/1. 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 state-determined, must be 

 ' properly isolated ' ; and some parameters in S. 6/2 were described 

 as ' ineffective '. So far the simple method of S. 4/12 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 ' independence ' of two dynamic systems 

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

 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- 

 nexion 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 controversy. 

 The criterion of physical connexion or separation is thus useless. 



12/2. Can we make the test for independence depend on whether 

 one variable (or system) gives energy or matter to the other ? 

 The suggestion is plausible, but experience with simple mechanisms 

 is misleading. When my finger strikes the key of a typewriter, 

 the movement of my finger determines the movement of the 

 type; and the finger also supplies the energy necessary for the 

 type's movement. The diagram 



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