14/15 



DESIGN FOR A BRAIN 



of the two active variables ; and so on. If all the variables 

 are inactive, the line becomes a point. Thus a three-variable 



system might give the line of behaviour 

 shown in Figure 14/15/1. 



An absolute system composed of 

 part-functions has also the property 

 that if a variable changes from inactive 

 to active, then amongst the variables 

 which affect that variable directly 

 there must, at that moment, have 

 been at least one which was active. 

 One might say, more vividly but 

 less accurately, that activity in one 

 variable can be obtained only from 

 activity in others. A proof is given 

 in S. 24/16, but the reason is not 

 difficult to see. Suppose for simplicity that a variable A is 

 directly affected only by B and C, so that the diagram of 

 immediate effects is 



B C 



Figure 14/15/1. In the dif- 

 ferent stages the active 

 variables are : A, y ; B, y 

 and z; C, z; D, x\ E, y; 

 F, x and 2. 



Suppose that over a finite interval of time all three have been 

 constant, and that the whole is absolute. If B and C remain 

 at these constant values, and if A is started at the same value 

 as before, then by the absoluteness A's behaviour must be the 

 same as before, i.e. A must stay constant. The property has 

 nothing to do with energy or its conservation ; nor does it attempt 

 to dogmatise about what real 4 machines ' can or cannot do ; it 

 simply says that if B and C remain constant and A changes from 

 inactive to active, then the system cannot be absolute — in other 

 words, it is not completely isolated. 



The sparks which wander in charred paper give a vivid picture 

 of this property : they can spread, one can become multiple, or 

 several can converge ; but no spark can arise in an unburning 

 region. 



14/16. Part-functions were introduced primarily in the hope 

 that they would provide a system more readily stabilised than 

 one of full-functions. It can now be shown that this is so. 



164 



