5/9 AN INTRODUCTION TO CYBERNETICS 



subject soon becomes somewhat mathematical; here it is sufficient 

 to notice that these questions are always capable of being answered, 

 at least in principle, by the process of actually tracing the changes as 

 the system moves successively through the states D(a), TD{a), 

 T^D{a), etc. (Compare S.3/9.) The sole objection to this simple, 

 fundamental, and reliable method is that it is apt to become ex- 

 ceedingly laborious in the complicated cases. It is, however, capable 

 of giving an answer in cases to which the more specialised methods 

 are inapplicable. In biological material, the methods described in 

 this chapter are likely to prove more useful than the more specialised ; 

 for the latter often are applicable only when the system is continuous 

 and linear, whereas the methods of this chapter are applicable 

 always. 



A specially simple and well known case occurs when the system 

 consists of parts between which there is feedback, and when this 

 has the very simple form of a single loop. A simple test for stability 

 (from a state of equilibrium assumed) is to consider the sequence of 

 changes that follow a small displacement, as it travels round the 

 loop. If the displacement ultimately arrives back at its place of 

 origin with size and sign so that, when added algebraically to the 

 initial displacement, the initial displacement is diminished, i.e. 

 brought nearer the state of equilibrium, then the system, around that 

 state of equilibrium, is (commonly) stable. The feedback, in this 

 case, is said to be "negative" (for it causes an eventual subtraction 

 from the initial displacement). 



The test is simple and convenient, and can often be carried out 

 mentally; but in the presence of any complications it is unreliable if 

 carried out in the simple form described above. The next section 

 gives an example of one way in which the rule may break down if 

 applied crudely. 



Ex. I : Identify a, D and T in Ex. 3/6/17. Is this system stable to this displace- 

 ment? 



Ex. 2: (Continued.) Contrast Ex. 3/6/19. 



Ex. 3 : Identify a and Tin Ex. 2/14/1 1 . Is it stable if D is any displacement from 

 «? 



Ex. 4: Take a child's train (one that runs on the floor, not on rails) and put the 

 line of carriages slightly out of straight. Let M be the set of states in which 

 the deviations from straightness nowhere exceed 5 '. Let T be the operation 

 of drawing it along by the locomotive. Is M stable under T? 



Ex. 5: (Continued.) Let U be the operation of pushing it backwards by the 

 locomotive. Is M stable under C/? 



Ex. 6 : Why do trains have their locomotives in front ? 



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