12/3 TEMPORARY INDEPENDENCE 



would state, in this case, both that energy, measurable in ergs, 

 is transmitted from A to B, and also that the behaviour of B 

 is determined by, or predictable from, that of A. If, however, 

 power is freely available to B, the transmission of energy from 

 A to B becomes irrelevant to the question of the control exerted. 

 It is easy, in fact, to devise a mechanism in which the flow of 

 both energy and matter is from B to A and yet the control is 

 exerted by A over B. Thus, suppose B contains a compressor 

 which pumps air at a constant rate into a cylinder, creating a 

 pressure that is shown on a dial. From the cylinder a pipe goes 

 to A, where there is a tap which allows air to escape and can 

 thus control the pressure in the cylinder. Now suppose a stranger 

 comes along; he knows nothing of the internal mechanism, 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 B, 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. 



Independence 



12/3. The test for independence can, in fact, be built up from 

 the results of primary operations (S. 2/10), without any reference 

 to other concepts or to knowledge of the system borrowed from 

 any other source. 



The basic definition simply makes formal what was used 

 intuitively in S. 4/12. To test whether a variable X has an effect 

 on a variable Y, the observer sets the system at a state, allows 

 one transition to occur, and notices the value of Y that follows. 

 (The new value of X does not matter.) He then sets the system 

 at a state that differs from the first only in the value of X (in 

 particular, Y must be returned to its original initial state). Again 

 he allows a transition to occur, and he notices again the value 

 of Y that results. (He thus obtains two transitions of Y from 

 two states that differ only in the value of X.) If these two values 

 of Y are the same, then Y is defined to be independent of X so 

 far as the particular initial states and other conditions are 

 concerned. 



By dependent we shall mean simply ' not independent '. 



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