13/12 THE SYSTEM WITH LOCAL STABILITIES 



of equilibrium must remain there, for no disturbance can come 

 to it. So if two states of the whole, earlier and later, are com- 

 pared, all parts contributing to i in the earlier will contribute in 

 the later; so the value of i cannot fall with time. It will, of course, 

 usually increase. Thus, this type of system goes to its final state 

 of equilibrium progressively. Its progression, in fact, is like that 

 of Case 3 of S. 11/5; for the final equilibrium has only to wait for 

 the part that takes longest. The time that the whole takes will 

 therefore be like T 3 , and thus not excessively long. 



13/11. The two types of polystable system are at opposite poles, 

 and systems in the real world will seldom be found to correspond 

 precisely with either. Nevertheless, the two types are important 

 by the strategy of S. 2/17, for they provide clear-cut types with 

 clear-cut properties; if a real system is similar to either, we may 

 legitimately argue that its properties will approximate to those 

 of the nearer. 



Polystable systems midway between the two will show a some- 

 what confused picture. Subsystems will be formed (e.g. as in 

 S. 12/17) with kaleidoscopic variety and will persist only for short 

 times ; some will hold stable for a brief interval, only to be changed 

 and to disintegrate as delimitable subsystems. The number of 

 variables stable, i, will keep tending to climb up, as a few sub- 

 systems hold stable, only to fall back by a larger or smaller 

 amount as they become unstable. Oscillations will be large, until 

 one swing happens to land i at the value n, where it will stick. 



More interesting to us will be the systems nearer the limit of 

 disconnexion, when i's tendency to increase cumulatively is better 

 marked, so that i, although oscillating somewhat and often slipping 

 back a little, shows a recognisable tendency to move to the value 

 n. This is the sort of system that, after the experimenter has 

 seen i repeatedly return to n after displacement, is apt to make 

 him feel that i is ' trying ' to get to n. ' 



13/12. So far we have discussed only the first case of S. 12/15; 

 what if the polystable system were composed of parts that all had 

 their states of equilibrium characterised by a threshold ? This 

 question will specially interest the neurophysiologist, though it 

 will be of less interest to those who are intending to work with 

 adapting systems of other types. 



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