2/16 DESIGN FOR A BRAIN 



is both necessary and sufficient ; so all state-determined systems 

 are absolute. We shall use this fact repeatedly. 



The field of an absolute system is characteristic : from every 

 point there goes only one line of behaviour whether the point is 

 initial on the line or not. The field of the two-variable system 

 just mentioned is sketched in Figure 2/15/1 ; through every point 

 passes only one line. 



These relations may be made clearer if this field is contrasted 

 with one that is regular but not absolute. Figure 2/15/2 shows 



such a field (the system is described 

 in S. 19/15). The system's regularity 

 would be established if we found that 

 the system, started at A, always went 

 to A\ and, started at B, always went 

 to B\ But such a system is not 

 absolute ; for to say that the repre- 

 sentative point is leaving C is insuf- 

 ficient to define its future line of 

 behaviour, which may go to A' or B' . 

 Figure 2/15/2 : The field Even if the lines from A and B always 

 Figure ijfivi. 8110 ™ in ran to A' and B', the regularity in 



no way restricts what would happen 

 if the system were started at C : it might go to D. If 

 the system were absolute, the lines CA', CB\ and CD would 

 coincide. 



A system's absoluteness is determined by its field ; the property 

 is therefore wholly objective. 



An absolute system's field does not change with time. 



2/16. We can now return to the question of what we mean when 

 we say that a system's variables have a c natural ' association. 

 What we need is not a verbal explanation but a definition, which 

 must have these properties : 



(1) it must be in the form of a test, separating all systems 



into two classes ; 



(2) its application must be wholly objective ; 



(3) its result must agree with common sense in typical and 



undisputed cases. 

 The third property makes clear that we cannot expect a proposed 

 definition to be established by a few lines of verbal argument : 



