23/4 DESIGN FOR A BRAIN 



is at the resting state, that the application of a single random dis- 

 turbance will not take the representative point beyond the critical 

 surface. If the field has a resting cycle, k 2 is the average of the 

 values when the representative point is on the many portions of 

 the cycle, the value for each portion being weighted according 

 to the time spent by the representative point in that portion. For 

 more complex fields, k 2 could be defined, but a more detailed 

 study is not necessary here. 



Suppose that the ultrastable system, when the step-functions 

 undergo random changes, yields terminal fields whose values of k 2 

 are distributed so that the proportion falling between k 2 and 

 k 2 + dk 2 is cf>(k 2 )dk 2 . If to such fields, with k 2 lying between such 

 limits, we apply one random disturbance, a proportion k 2 will 

 not be changed ; but the proportion 1 — k 2 will be changed, and 

 will be replaced by new terminal fields ; their values of k 2 will be 

 distributed again as <j)(k 2 )dk 2 , and this distribution will be added 

 to that of the unchanged fields. In this way it is easy to show 

 that the final distribution X{k 2 ) equals 



where A is a constant. 



Examination of the form of the distribution k{k 2 ) shows that 

 it is cf>{k 2 ) heavily weighted in favour of the values of k 2 near 1. 

 Such fields can only be those with the resting state or cycle near 

 the centre of the region. So the result confirms the common- 

 sense argument of S. 13/4. It will be noticed that the deduction 

 is independent of the particular form of the distribution of 

 disturbances. 



References 



Asiiby, W. Ross. The physical origin of adaptation by trial and error. 



Journal of general Psychology, 32, 13 ; 1945. 

 Idem. The nervous system as physical machine : with special reference to 



the origin of adaptive behaviour. Mind, 56, 1 ; 1947. 



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