CONSTANCY AND INDEPENDENCE 



14/3 



can cause the pressure in the cylinder to fall. Now suppose a 

 stranger comes along ; he knows nothing of the internal mech- 

 anism, but tests the relations between the two variables : A, 

 the position of the tap, and B, the reading on the dial. By 

 direct testing he soon finds that A controls Z?, but that B has 

 no effect on A. The direction of control has thus no necessary 

 relation to the direction of flow of either energy or matter when 

 the system is such that all parts are supplied freely with energy. 



14/3. The factual content of the concept of one variable c con- 

 trolling ' another is now clear. A ' controls ' B if B's behaviour 

 depends on A, while A's does not depend on B. But first we 

 need a definition of ' independence '. Given a system that includes 

 two variables A and B, and two lines of behaviour ivhose initial 

 states differ only in the values of B, A is independent of B if A's 

 behaviours on the tzvo lines are identical. The definition can be 

 illustrated on the data in Table 14/3/1. On the two lines of 



Table 14/3/1 : Two lines of behaviour of a three- variable absolute system. 



behaviour the initial states are equal except for the values of B. 

 The subsequent behaviours of A on the two lines are identical. 

 So A is independent of B. (Independence within the range 

 covered by the table in no way restricts what may happen 

 outside it.) By the definition, C is not independent of B. 



By ' dependent ' will be meant simply 4 not independent '. 



The definition is given primarily by reference to two lines of 

 behaviour, for only in this form is the result of the criterion 



155 



