6/7 DESIGN FOR A BRAIN 



parameter and thus avoid using unnecessarily large numbers 

 of parameters. 



A more extensive generalisation is provided if we replace 

 4 change of parameter ' by ' change of initial state '. It will be 

 shown (S. 7/7 and 21/4) that if a variable, or parameter, stays 

 constant over some period it may, within the period, be regarded 

 indifferently as inside or outside the system — as variable or para- 

 meter. If, therefore, a contact switch, once set, stays as the 

 experimenter leaves it, we may, if we please, regard it as part of 

 the system. Then what was a comparison between two lines of 

 behaviour from two fields (of a set of variables a, b, c, say) under 

 the change of a parameter p from p' to p", becomes a comparison 

 between two lines of behaviour of the four-variable system from 

 the initial states a, b, c, p' and a, b, c, p" . 4 Applying a stimulus ' 

 is now equivalent to ' releasing from a different initial state ' ; 

 and this will be used as its most general representation. 



Parameter and stability 



6/7. We now reach the main point of the chapter. Because 

 a change of parameter-value changes the field, and because a 

 system's stability depends on its field, a change of parameter- 

 value will in general change a system's stability in some way. 



A simple example is given by a mixture of hydrogen, nitrogen, 

 and ammonia, which combine or dissociate until the concentra- 

 tions reach the resting state. If the mixture was originally derived 

 from pure ammonia, the single variable 4 percentage dissociated ' 

 forms a one-variable absolute system. Among its parameters 

 are temperature and pressure. As is well known, changes in these 

 parameters affect the position of the resting state. 



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

 parameters with only a simple shift of resting state. 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, 

 resting states may be moved, single resting states may become 

 multiple, resting states may become cycles ; and so on. Figure 

 21/5/1 provides an illustration. 



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



78 



