THE ULTRASTABLE SYSTEM 



8/5 



[II 



Figure 8/3/1 : Three fields. The critical states are dotted. 



change the proportion of representative points encountering 

 critical states. 



The ultrastable system 



8/4. The two factors of the two preceding sections will now be 

 found to generate a process, for each in turn evokes the other's 

 action. The process is most clearly shown in what I shall call 

 an ultrastable system : one that is absolute and contains step- 

 functions in a sufficiently large number for us to be able to ignore 

 the finiteness of the number. Consider the field of its main 

 variables after the representative point has been released from 

 some state. If the field leads the point to a critical state, a 

 step-function will change value and the field will be changed. 

 If the new field again leads the point to a critical state, again 

 a step-function will change and again the field will be changed ; 

 and so on. The two factors, then, generate a process. 



8/5. Clearly, for the process to come to an end it is necessary 

 and sufficient that the new field should be of a form that does 

 not lead the representative point to a critical state. (Such a 

 field will be called terminal.) But the process may also be de- 

 scribed in rather different words : if we watch the main variables 

 only, we shall see field after field being rejected until one is 

 retained : the process is selective towards fields. 



As this selectivity is of the highest importance for the solution 

 of our problem, the principle of ultrastability will be stated 

 formally : an ultrastable system acts selectively towards the fields 

 of the main variables, rejecting those that lead the representative 

 point to a critical state but retaining those that do not. 



This principle is the tool we have been seeking ; the previous 



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