THE ULTRASTABLE SYSTEM 



23/4 



It follows that if the changes of step-functions evoke fields whose 

 values of k 1 are distributed so that the probability of a field having 

 a A^-value between k x and k t + dk x is ^(k-^dk^ then in the terminal 

 fields the probablity is 



k 1 y)(k 1 )dk 1 



a) 



k 1 y)(k 1 )dk 1 



Figure 23/3/1 shows a possible distribution of values of k 1 in 



Figure 23/3/1 : Solid line : a distribution y^i) 5 broken line : 

 the corresponding distribution k^kj. 



the original fields (solid line), and how k ± would then be dis- 

 tributed in the terminal fields (broken line). The shift towards 

 the higher values of k x is clear. 



Fields with a low value of k v unsatisfactory for adaptation, 

 tend therefore not to be terminal. 



23/4. It was noticed in S. 13/4 that fields like A and B of Figure 

 13/4/1, though terminal, are defective in their persistence after 

 small random disturbances. This idea may be given more 

 precision. 



Assume that the small random disturbances cause displace- 

 ments which have some definite probability distribution, Gaussian 

 say, so that if applied to the representative point when it is at 

 some definite position in the field, there is a definite probability 

 k 2 that a random displacement will not carry the point beyond 

 the critical surface. Assume the representative point is always 

 at the resting state or resting cycle. Then any terminal field has 

 a unique value for k 2 . If the field contains a single resting state, 

 k 2 for that field is the probability, when the representative point 



239 



