CHAPTER 8 



The Ultrastable System 



8/1. Our problem, stated briefly at the end of Chapter 5, can 

 now be stated finally. The type-problem was the kitten whose 

 behaviour towards a fire was at first chaotic and unadapted, 

 but whose behaviour later became effective and adapted. We 

 have recognised (S. 5/8) that the property of being ' adapted ' 

 is equivalent to that of having the variables, both of the animal 

 and of the environment, so co-ordinated in their actions on one 

 another that the whole system is stable. We now know, from 

 S. 6/3 and 7/8, that an observed system can change from one 

 form of behaviour to another only if parameters have changed 

 value. Since we assumed originally that no deus ex machina 

 may act on it, the changes in the system must be due to step- 

 functions acting within the whole absolute system. Our problem 

 therefore takes the final form : Step-functions by their changes in 

 value are to change the behaviour of the system ; what can ensure 

 that the step functions shall change appropriately ? The answer is 

 provided by a principle, relating step-functions and fields, which 

 will now be described. 



8/2. In S. 7/8 it was shown that when a step-function changes 

 value, the field of the main variables is changed. The process 

 was illustrated in Figures 7/8/1 and 7/8/2. This is the action 

 of step-function on field. 



8/3. There is also a reciprocal action. Fields differ in the rela- 

 tion of their lines of behaviour to the critical states. Thus, if 

 a representative point is started at random in the region to the 

 left of the critical states in Figure 8/3/1, the proportion which 

 will encounter critical states is, in I — 1, in II — 0, and in III — 

 about a half. So, given a distribution of critical states and a 

 distribution of initial states, a change of field will, in general, 



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