DESIGN FOR A BRAIN 13/9 



at equilibrium at any moment). Then the line of behaviour 

 will perform a sort of random walk around this value, the whole 

 reaching a state of equilibrium if and only if i should chance on 

 the extreme value of n. Thus we get essentially the same picture 

 as we got in S. 11/3: a system whose lines of behaviour are long 

 and complex, and whose chance of reaching an equilibrium in a 

 fairly short time is, if n is large, extremely small. In this case 

 the time taken by the whole to arrive at a state of equilibrium 

 will be extremely long, like 2\ of S. 11/5. 



13/9. Particularly worth noting is what happens if i should 

 happen to be large but not quite equal to n. Suppose, for in- 

 stance, i were 999 in a 1,000-variable system of the type now being 

 considered. The whole is now near to equilibrium, but what will 

 happen ? One variable is not at equilibrium and will change. 

 As the system is richly connected, most of the 999 other variables 

 will, at the next instant (or step), find themselves in changed 

 conditions; whether the state each is at is now equilibrial will 

 depend on factors such that (by hypothesis) 999p will still be 

 equilibrial, and thus i is likely to drop back simply to its average 

 value. Thus the richly-joined form of the polystable system, 

 even if it should get very near to equilibrium (in the sense that 

 most of its parts are so) will be unable to retain this nearness but 

 will almost certainly fall back to an average state. Such a system 

 is thus typically unable to retain partial or local successes. 



13/10. With the number n still large, and the probabilities p 

 still independent, contrast the behaviour of the previous section 

 (in which the system was assumed to be richly or completely 

 joined) with that of the polystable system in which the primary 

 joins between variables are scanty. (A similar system also occurs 

 if p is made very near to 1 ; for, by S. 12/17, as most of the variables 

 will be at states of equilibrium, and thus constant for most of the 

 time, the functional connexions will also be scanty.) How will i 

 behave in this case, especially as the scantiness approaches its 

 limit ? 



Consider the case in which the scantiness has actually reached 

 its limit. The system is now identical with one of n variables 

 that has no connexions between any of them; it is a ' system ' 

 only in the nominal sense. In it, any part that comes to a state 



170 



