14/6 



DESIGN FOR A BRAIN 



The system's responses to tests for independence will show that 

 y is independent of x, and that z is independent of both. The 

 same set of independencies would be found if we tested the three 

 machines when their linkages were 



The distinction appears when we test the immediate effect be- 

 tween z and x. For if in both cases we fix y, we shall find in 

 the first that x is independent of 2, but in the second that x is 

 not independent of z. 



Given a system's diagram of immediate effects, its diagram 

 of ultimate effects is formed by adding to every pair of arrows 

 joined tail to head a third arrow going from tail to head, like 

 2 — > x above, and by repeating this process until no further 

 additions are possible. Thus, the diagram of immediate effects 

 I in Figure 14/6/1 would yield the diagram of ultimate effects II. 



>■ 2 



K2 



n 



Figure 14/6/1. 



The diagram of ultimate effects shows directly and completely 

 the independencies in the system. Thus, from II of the figure 

 we see that variable 1 is independent of 2, 3, and 4, and that 

 the latter three are dependent on all the others. 



14/7. If, in a system, some of the variables are independent 

 of the remainder, while the remainder are not independent of 

 the first set, then the first set dominates the remainder. Thus, 

 in Figure 14/6/1, variable 1 dominates 2, 3, and 4. And in 

 the diagram of S. 6/6 the animal dominates the recorders. 



The effects of constancy 



14/8. So far the independencies have been assumed permanent : 

 we now study the conditions under which they can alter. 

 Suppose an absolute system of eight variables has the diagram 



158 



