DESIGN FOR A BRAIN 4/6 



of behaviour must resemble that sketched in Figure 4/5/3. The 



other lines of the field could be added by considering what would 



^ happen after other disturbances 



(lines starting from points other 

 than A). Although having 

 different initial states, all the 

 lines would converge towards 0. 



4/6. In some of our examples, 

 for instance that of the cube, the 

 lines of behaviour terminate in a 

 point at which all movement 

 ceases. In other examples the 

 movement does not wholly cease ; 

 many a thermostat settles down, 

 when close to its resting state, 



Figure 4/5/3 : One line of behav- to a regular small oscillation, 



iour in the field of the Watt's We shall seldom be interested in 



governor. For clarity, the resting .. , . ., „ , . , 



state of the system has been used the details ot what happens at 



as origin. The system has been the exact centre, 

 displaced to A and then released. 



4/7. More important is the underlying theme that in all cases 

 the stable system is characterised by the fact that after a displace- 

 ment we can assign some bound to the subsequent movement of the 

 representative point, whereas in the unstable system such limita- 

 tion is either impossible or depends on facts outside the subject of 

 discussion. Thus, if a thermostat is set at 37° C. and displaced 

 to 40°, we can predict that in the future it will not go outside 

 specified limits, which might be, in one apparatus, 36° and 40°. 

 On the other hand, if the thermostat has been assembled with a 

 component reversed so that it is unstable (S. 4/14) and if it is 

 displaced to 40°, then we can give no limits to its subsequent 

 temperatures; unless we introduce such new topics as the melting- 

 point of its solder. 



4/8. These considerations bring us to the definitions. Given 

 the field of a state-determined system and a region in the field, 

 the region is stable if the lines of behaviour from all points in the 

 region stay within the region. 



Thus, in Figure 4/3/1 make a mark on either side of A to define 

 a region. All representative points within are led to A, and none 



48 



