DYNAMIC SYSTEMS 2/17 



it must be treated as a working hypothesis and used ; only experi- 

 ence can show whether it is faulty or sound. 



From here on I shall treat a ' natural ' system as equivalent to 

 an i absolute ' system. Various reasons might be given to make 

 the equivalence plausible, but they would prove nothing and I 

 shall omit them. Much stronger is the evidence in the Appendix. 

 There it will be found that the equivalence brings clarity where 

 there might be confusion ; and it enables proof to be given to 

 propositions which, though clear to physical intuition, cannot 

 be proved without it. The equivalence, in short, is indispens- 

 able. 



Why the concept is so important can be indicated briefly. 

 When working with determinate systems the experimenter always 

 assumes that, if he is interested in certain variables, he can find 

 a set of variables that (1) includes those variables, and (2) has 

 the property that if all is known about the set at one instant the 

 behaviour of all the variables will be predictable. The assump- 

 tion is implicit in almost all science, but, being fundamental, it 

 is seldom mentioned explicitly. Temple, though, refers to ' . . . 

 the fundamental assumption of macrophysics that a complete 

 knowledge of the present state of a system furnishes sufficient 

 data to determine definitely its state at any future time or its 

 response to any external influence '. Laplace made the same 

 assumption about the whole universe when he stated that, given 

 its state at one instant, its future progress should be calculable. 

 The definition given above makes this assumption precise and 

 gives it in a form ready for use in the later chapters. 



2/17. To conclude, here is an example to illustrate this chapter's 

 method. 



Suppose someone constructed two simple pendulums, hung them 

 so that they swung independently, and from this l machine ' 

 brought to an observation panel the following six variables : 



(v) the angular deviation of the first pendulum 



(w) „ „ „ „ „ second 



(x) the angular momentum of the first pendulum 



{y) 9, » » ,, a second „ 



(z) the brightness of their illumination 



(t) the time. 

 The experimenter, knowing nothing of the real 4 machine ', or of 



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