24/14 



DESIGN FOR A BRAIN 



It will be recognised that [/] and [F], the differential and 

 integral matrices, are the matrix equivalents of the diagrams of 



A. 



■^2 

 A 



B 



—►3 



Figure 24/14/1. 



immediate and ultimate effects respectively. Thus the diagram 

 of immediate effects A in Figure 24/14/1 yields the diagram of 

 ultimate effects B. For the system, [/] is 



assuming (S. 24/10) that the terms in the main diagonal are all R. 

 Then 



in 



[f? = 



and the sum /+[/]+ l/T + L/T gives 



This, by S. 24/10, is the integral matrix. If it is compared directly 

 with B of the Figure, the agreement will be found complete. 

 Thus, it may be verified in both that x x dominates the system of 



it/05 ^3 anu & a. 



The rule of S. 14/10 for the formation of the diagram of ulti- 

 mate effects when a variable is an inactive part-function can now 

 be proved. For the effect on the differential matrix of a part- 

 function xi being inactive is to make all the elements in the i-th. 

 row zero, except the element in the main diagonal. Exactly 

 the same change is caused in the differential matrix if we remove 

 those arrows whose heads are at a&i. After these two changes 



248 



