FULLY CONNECTED SYSTEMS 11/6 



ments which affected the animal alternately. Such alternations 

 do occur. A cat, for instance, must learn to catch mice, which 

 tend to run towards corners, and birds, which tend to fly upwards ; 

 and the diving birds alternate between aerial and submarine 

 environments. Were the bird's nervous system like the homeo- 

 stat, step-function changes would occur until there arose a set of 

 values giving behaviour suitable to both environments, and this 

 set would then be terminal. That such a set is not impossible is 

 shown by the snake's mode of progression, which is suitable in 

 both undergrowth and water. 



11/6. But it is easily seen that the process cannot answer the 

 problems of this chapter. First, the process shows, contrary 

 to requirement, no gradation : when there occurs a set of step- 

 function values terminal for both environments, the animal be- 

 comes adapted ; prior to that it was unadapted. The second 

 reason is that any extensive adaptation in this way is very 

 improbable. 



This brings us to the most serious of the difficulties. A suc- 

 cessful trial, or a terminal field, is useful for adaptation only if it 

 occurs within some reasonable time : success at the millionth trial 

 is equivalent to failure. Consequently, the principle of ultra - 

 stability, while it guarantees that a field of a certain type will 

 be retained, guarantees much less than it seems to. If the delay 

 in reaching success were slight, a general increase in the system's 

 velocity of action might give sufficient compensation ; but in 

 fact the delay is likely to exceed the utmost possible compensa- 

 tion. For definiteness, take a numerical example. Suppose that 

 in some ultrastable system each field has a one in ten chance 

 of being stable with any given environment, and that the chances 

 are independent. Then the chance of a field being stable to two 

 environments will be one in a hundred, and to N environments 

 will be one in 10 N . The time that a system takes on the average 

 to find a stable field is proportional to the reciprocal of the prob- 

 ability (S. 23/2). Suppose that when N = 1 the average time 

 t taken to find a terminal field is 1 second, then 



t = ^.10 Y seconds. 



Try the effect of different values of N. Three environments will 

 require about a minute and a half. This might be tolerable. 



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