7/23 THE ULTRASTABLE SYSTEM 



changes value during the construction, the main variables will be 

 found to form a state-determined system, and to have a definite 

 field. But on different occasions different fields may be found. 



7/21. These considerations throw light on an old problem in the 

 theory of mechanisms. 



Can a ' machine ' be at once determinate and capable of spon- 

 taneous change ? The question would be contradictory if posed 

 by one person, but it exists in fact because, when talking of living 

 organisms, one school maintains that they are strictly determinate 

 while another school maintains that they are capable of spon- 

 taneous change. Can the schools be reconciled ? 



The presence of step-mechanisms in a state-determined system 

 enables both schools to be right, provided that those who maintain 

 the determination are speaking of the system which comprises all 

 the variables, while those who maintain the possibility of spon- 

 taneous change are speaking of the main variables only. For the 

 whole system, which includes the step-mechanisms, has one field 

 only, and is completely state-determined (like Figure 7/20/1). 

 But the system of main variables may show as many different 

 forms of behaviour (like Figure 7/20/2, I and II) as the step- 

 mechanisms possess combinations of values. And if the step- 

 mechanisms are not accessible to observation, the change of the 

 main variables from one form of behaviour to another will seem 

 to be spontaneous, for no change or state in the main variables 

 can be assigned as its cause. 



7/22. If the system had contained two step-mechanisms, each 

 of two values, there would have been four fields of the main 

 variables. In general, n step-mechanisms, each of two values, 

 will give 2 n fields. A moderate number of step-mechanisms may 

 thus give a very much larger number of fields. 



7/23. After this digression on step-functions we can return to the 

 system of S. 7/9, with its corrective feedback, and consider its 

 behaviour. 



To bring the concepts into correspondence, we assume that the 

 main variables (the continuous) are in the environment, in R, 

 and in the essential variables. The step-functions will be in S. 

 It follows that their critical states will be distributed over those 

 regions of the main variables' phase-space at which the essential 



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