14/10 



DESIGN FOR A BRAIN 



tinuity is not necessary : a segment may be poisoned, or anaes- 

 thetised, or frozen ; what is necessary is that the segment should 

 be unvarying. 



Physical separation, already noticed to give no certain inde- 

 pendence, is sometimes effective because it sometimes creates an 

 intervening region of constancy. 



14/10. The example of Figure 14/8/1 showed one way in which 

 the constancy of a set of variables could affect the independencies 

 within a system. The range of ways is, however, much greater. 

 To demonstrate the variety we need a rule by which we can 

 make the appropriate modifications in the diagram of ultimate 

 effects when one or more of the variables are held constant. The 

 rule is proved in S. 24/14 : — Take the diagram of immediate 

 effects. If a variable V is constant, remove all arrows whose 

 heads are at V ; then, treating this modified diagram as one of 

 immediate effects, complete the diagram of ultimate effects, using 



1-^2 



\/\ 



4-* 



R C D F 



1^=§=±=2 \-±-*z2 1r< 2 1 t 2 



[IXIIXH/I 



^3 4 ± — ^ 3 4-« 3 4-* 



Figure 14/10/1 : If a four-variable system has the diagram of immediate 

 effects A, and if 1 and 2 are part-functions, then its diagram of ultimate 

 effects will be B, C, D or E as none, 1, 2, or both 1 and 2 become 

 inactive, respectively. 



the rule of S. 14/6. The resulting diagram will be that of the 

 ultimate effects, and therefore of the independencies, when V is 

 constant. (It will be noticed that the effect of making V constant 

 cannot be deduced from the diagram of ultimate effects alone.) 

 Thus, if the system of Figure 14/10/1 has the diagram of imme- 

 diate effects A, then the diagram of ultimate effects will be B, C, 

 D or E according as none, 1, 2, or both 1 and 2 are constant, 

 respectively. 



It can be seen that with only four variables, and with only 

 two of the four possibly becoming constant, the patterns of 



160 



