12/11 AN INTRODUCTION TO CYBERNETICS 



of S.2/17, a system at C will arrive at D in exactly two steps. If the 

 system is Markovian, however, it does not take a unique number of 

 steps; and the duration of the trajectory can be predicted only on 

 the average. Thus suppose the Markovian machine is 



with a a state of equilibrium. Start a great number of such systems 

 all at b. After the first step, half of them will have gone to a and 

 half will be still at b. At the second step, a half of those still at /) 

 will move over to a and a half (i.e. a quarter of the whole) will 

 remain at b. By continuing in this way we find that, of those that 

 were started at b, 



\ reach a after 1 step 



J- 2 



4 »» ?5 5? 



8 J» >' " 



^ 3 



and so on. The average time taken to get from Z? to a is thus 



Xl+ix2+ix3+ 



2 '- ^ ^ ^ - - ^^ - - ' ■ ■ ■ .^ 2 steps. 



2 T^ 4 



Some of the trajectories will be much longer than 2 steps. 



As is now well known, a system around a state of equilibrium 

 behaves as if "goal-seeking", the state being the goal. A corres- 

 ponding phenomenon appears in the Markovian case. Here, 

 instead of the system going determinately to the goal, it seems to 

 wander, indeterminately, among the states, consistently moving to 

 another when not at the state of equilibrium and equally consistently 

 stopping there when it chances upon that state. The state still 

 appears to have the relation of "goal" to the system, but the system 

 seems to get there by trying a random sequence of states and then 

 moving or sticking according to the state it has arrived at. Thus, 

 the objective properties of getting success by trial and error are shown 

 when a Markovian machine moves to a state of equilibrium. 



At this point it may be worth saying that the common name of 

 "trial and error" is about as misleading as it can be. "Trial" is in 

 the singular, whereas the essence of the method is that the attempts 

 go on and on. "Error" is also ill-chosen, for the important element 

 is the success at the end. "Hunt and stick" seems to describe the 

 process both more vividly and more accurately. I shall use it in 

 preference to the other. 



230 



