CHAPTER 19 



The Absolute System 



(Some of the definitions already given are re- 

 peated here for convenience) 



19/1. A system of n variables will usually be represented by 

 x v . . . , x n , or sometimes more briefly by x. n will be assumed 

 finite ; a system with an infinite number of variables (e.g. that 

 of S. 19/23), where xi is a continuous function of i, will be 

 replaced by a system in which i is discontinuous and n finite, 

 and which differs from the original system by some negligible 

 amount. 



19/2. Each variable x% is a function of the time t ; it will 

 sometimes be written as xi(t) for emphasis. It must be single- 

 valued, but need not be continuous. A constant may be 

 regarded as a variable which undergoes zero change. 



19/3. The state of a system at a time t is the set of numerical 

 values of x^t), . . . , x n (t). Two states are ' equal ' if n equalities 

 exist between the corresponding pairs. 



19/4. A line of behaviour is specified by a succession of states 

 and the time-intervals between them. Two lines of behaviour 

 which differ only in the absolute times of their initial states are 

 equal. 



19/5. A geometrical co-ordinate space with n axes x v . . . , x n , 

 and a dynamic system with variables x v . . . , x n provide 

 a one-one correspondence between each point of the space 

 (within some region) and each state of the system. The region 

 is the system's ' phase-space '. 



19/6. A primary operation discovers the system's behaviour by 



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