THE ABSOLUTE SYSTEM 19/20 



not from an examination of the material substance of the system 

 (S. 14/1), which may be misleading and in any case presupposes 

 that we know beforehand what makes for isolation and what 

 does not, but from a direct test on the behaviour itself. 



Closely related to this in a fundamental way is the fact that 

 Shannon's concept of a ' noiseless transducer ' is identical in defini- 

 tion with my definition of an absolute system. Thus he defines 

 such a transducer as one that, having states a and an input 

 x y will, if in state a n and given input x n> change to a new state 

 a„+i that is a function only of x n and a n : 



a «+l = g(Vn, a n ) 

 Though expressed in a superficially different form, this equation 

 is identical with my ' canonical ' equation, for it says simply 

 that if the parameters x and the state of the system are given, 

 then the system's next step is determined. Thus the com- 

 munication engineer, if he were to observe the physicist and the 

 psychologist for the first time, would say that they seem to 

 prefer to work with noiseless systems. His remark would not 

 be as trite as it seems, for from it flow far-reaching consequences 

 and the possibilities of rigorous deduction. 



19/18. A second feature which makes absoluteness important 

 is that its presence establishes, by appeal only to the behaviour, 

 that the system of variables is complete, i.e. that it includes all 

 the variables necessary for the specification of the system. 



19/19. When we assemble a machine, we usually know the 

 canonical equations directly. If, for instance, certain masses, 

 springs, magnets, be put together in a certain way the mathe- 

 matical physicist knows how to write down the differential 

 equations specifying the subsequent behaviour. 



His equations are not always in our canonical form, but they 

 can always be converted to this form provided that the system 

 is isolated, i.e. not subjected to arbitrary interference, and is 

 determinate. 



19/20. In general there are two methods for studying a dynamic 

 system. One method is to know the properties of the parts 

 and the pattern of assembly. With this knowledge the canonical 



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