4/12 AN INTRODUCTION TO CYBERNETICS 



but will not depend on what value x has. The variables u and z are 

 said to have an immediate effect on y. 



It should be noticed, if the rigour is to be maintained, that the 

 presence or absence of an immediate effect, of u on ;■ say, can be 

 stated primarily only for two given states, which must have the same 

 values in their x, y, and z-components and must differ in their 

 M-components. For an immediate effect at one pair of states does 

 not, in general, restrict the possibilities at another pair of states. 

 Thus, the transformation mentioned above gives the transitions: 



(0,0,0,0) -^( , ,0, ) 



(1,0,0,0)-^ ( , ,0, ) 



(0,0,l,0)->( , ,0, ) 



(l,0,l,0)->( , ,2, ) 



(where irrelevant values have been omitted). The first two show that 

 in one region of space u does not have an immediate effect on y, 

 and the second two show that in another region it does. Strictly, 

 therefore, the question "what is the immediate effect of u on y'V 

 can be answered only for a given pair of states. Often, in simple 

 systems, the same answer is given over the whole phase space; if this 

 should happen we can then describe the immediate effect of u on v 

 unconditionally. Thus in the example above, u has an immediate 

 effect on v at all points but a particular few. 



This test, for «'s immediate effect on y, simply does in symbols 

 what the experimenter does when he wishes to test whether one 

 variable has an immediate effect on another: he fixes all variables 

 except this pair, and compares how one behaves when the other has 

 a value Uy with how it behaves when the other has the value W2- 



The same method is, in fact, used generally in everyday life. Thus, 

 if we go into a strange room and wish to turn on the light, and find 

 there are three switches, our problem is to find which switches are 

 and which are not having an effect on the light's behaviour. We 

 change one of the switches and observe whether this is followed by 

 a change in the light's behaviour. In this way we discover on which 

 switch the light is dependent. 



The test thus accords with common sense and has the advantage 

 of being applicable and interpretable even when we know nothing 

 of the real physical or other factors at work. It should be noticed 

 that the test requires no knowledge of extraneous factors: the result 

 is deduced directly from the system's observed behaviour, and 

 depends only on what the system does, not on why it does it. 



It was noticed above that a transducer may show any degree of 



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