DESIGN FOR A BRAIN 13/5 



among its parameters must have been, when it started changing, 

 at least one that was itself changing. Picturesquely one might 

 say that change can come only from change. The reason is not 

 difficult to see. If variable or subsystem C is affected immediately 

 only by parameters A and B, and if A and B are constant over 

 some interval, and if, within this interval, C has gone from a state 

 c to the same state (i.e. if c is a state of equilibrium), then for 

 C to be consistent in its behaviour it must continue to repeat the 

 transition ' c to c ' so long as A and B retain their values, i.e. so 

 long as A and B remain constant. If C is state-determined, a 

 transition from c to some other state can occur only after A or B, 

 for whatever reason, has changed its value. 



Thus a state-determined subsystem that is at a state of equili- 

 brium and is surrounded by constant parameters (variables of 

 other subsystems perhaps) is, as it were, trapped in equilibrium. 

 Once at the state of equilibrium it cannot escape from it until an 

 external source of change allows it to change too. The sparks 

 that wander in charred paper give a vivid example of this property, 

 for each portion, even though combustible, is stable when cold; 

 one spark can become two, and various events can happen, but a 

 cold portion cannot develop a spark unless at least one adjacent 

 point has a spark. So long as one spark is left we cannot put 

 bounds to what may happen ; but if the whole should reach a state 

 of l no sparks ', then from that time on it is unchanging. 



Progression to equilibrium 



13/5. Let us now consider how a polystable system will move 

 towards its final state of equilibrium. From one point of view 

 there is nothing to discuss, for if the parts are state-determined 

 and the joining defined, the whole is a state-determined system 

 that, if released from an initial state, will go to a terminal cycle or 

 equilibrium by a line of behaviour exactly as in any other case. 

 The fact, however, that the polystable system has parts with 

 many equilibria, which will often stay constant for a time, adds 

 special features that deserve attention; for, as will be seen later, 

 they have interesting implications in the behaviours of living 

 organisms. 



13/6. A useful device for following the behaviour of these some- 

 what complex wholes is to find the value of the following index. 



174 



