4/9 DESIGN FOR A BRAIN 



A is then found to be stable, and the line from B unstable. This 

 example makes it obvious that the concept of ' stability ' belongs 

 primarily to a line of behaviour, not to a whole field. In particular 

 it should be noted that in all cases the definition gives a unique 

 answer once the line, the region, and the initial state are given. 



The examples above have been selected to test the definition 

 severely. Sometimes the fields are simpler. In the field of the 

 cube, for instance, it is possible to draw many boundaries, each oval 

 in shape, such that all lines within the boundary are stable. The 

 field of the Watt's governor is also of this type. It will be noticed 

 that before we can discuss stability in a particular case we must 

 always define which region of the phase-space we are referring to. 



A field within a given region is ' stable ' if every line of behaviour 

 in the region is stable. A system is ' stable ' if its field is stable. 



4/9. A resting state is one from which an absolute system does 

 not move when released. Such states occur in Figure 4/3/1 at 

 A and B, and in Figure 4/5/1 at the origin. 



Although the variables do not change value when at a resting 

 state this invariance does not imply that the ' machine ' itself is 

 inactive. Thus, a steady Watt's governor implies that the engine 

 is working at a non-zero rate. And a living muscle, even if 

 unchanging in tension, is continually active in metabolism. 

 4 Resting ' applies to the variables, not necessarily to the ' machine ' 



that yields the variables. 



4/10. If a line of behaviour is 

 re-entrant to itself, the system 

 undergoes a recurrent cycle. If 

 the cycle is wholly contained in 

 a given region, and the lines of 

 behaviour lead into the cycle, the 

 cycle is stable. 



Such a cycle is commonly shown 

 by thermostats which, after correct- 

 ing any gross displacement, settle 

 down to a steady oscillation. In 

 such a case the field will show, 



not convergence to a point but convergence to a cycle, such as is 



shown exaggerated in Figure 4/10/1. 



48 



Figure 4/10/1. 



