DESIGN FOR A BRAIN 6/8 



reach the state of equilibrium. If the mixture was originally 

 derived from pure ammonia, the single variable ' percentage 

 dissociated ' forms a one-variable state-determined system. 

 Among its parameters are temperature and pressure. As is well 

 known, changes in these parameters affect the position of the 

 state of equilibrium. 



Such a system is simple and responds to the changes of the 

 parameters with only a simple shift of equilibrium. No such 

 limitation applies generally. Change of parameter-value may 

 result in any change which can be produced by the substitution of 

 one field for another: stable systems may become unstable, states 

 of equilibrium may be moved, single states of equilibrium may 

 become multiple, states of equilibrium may become cycles; and 

 so on. Figure 21/8/1 provides an illustration. 



Here we need only the relationship, which is reciprocal: in 

 a state-determined system, a change of stability can only be due to 

 change of value of a parameter, and change of value of a parameter 

 causes a change in stability. 



Equilibria of part and whole 



6/8. In general, as S. 4/18 showed, the relation between the 

 stabilities of the parts and that of the whole may be complex, 

 and may require specialised methods for its treatment. There is, 

 however, one quite simple relationship that will be of the greatest 

 use to us and which can be readily described. 



Suppose we join two parts, A with variables u and v, and B 

 with variables w, x and y. If A's variables have values 7 and 2, 

 and B's have values 3, 1 and 5, then the whole is, naturally, a 

 system with the five variables u, v, w, x and y; and in the cor- 

 responding state the variables of the whole have the values 7, 

 2, 3, 1 and 5 respectively. 



Suppose now that this state — (7, 2, 3, 1, 5) — of the whole is a 

 state of equilibrium of the whole. This implies that the transi- 

 tion is from that state to itself (S. 4/4). This implies that A, 

 with the values 3, 1, 5 on its parameters, goes from (7, 2) to (7, 2); 

 i.e. does not change. Thus, the whole's being at a state of equili- 

 brium at (7, 2, 3, 1, 5) implies that A, when at (7, 2), with values 

 (3, 1, 5) on its parameters, must be at a state of equilibrium. 

 Similarly B, when its parameters are at (7, 2), must have a state 



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