THE ERROR-CONTROLLED REGULATOR 12/12 



Movement to a goal by the process of hunt and stick is thus 

 homologous, by 8.12/8, to movement by a determinate trajectory, 

 for both are the movement of a machine to a state of equilibrium. 

 With caution, we can apply the same set of principles and arguments 

 to both. 



Ex. 1 : What states of equilibrium has the system of Ex. 12/10/1 ? 

 Ex. 2: A Markovian machine has matrix 



I 



a 

 b 

 c 



d 

 e 



f 



It is started at a on many occasions; how would its behaviour be described 

 in the language of rat-maze psychology ? 



MARKOVIAN REGULATION 



12/12. The progression of a single Markovian machine to a state 

 of equilibrium is much less orderly than that of a determinate 

 machine, so the Markovian type is little used in the regulators of 

 industry. In comparison with the smooth and direct regulation of 

 an ordinary servo-mechanism it must seem fumbling indeed. 

 Nevertheless, living organisms use this more general method freely, 

 for a machine that uses it is, on the whole, much more easily con- 

 structed and maintained; for the same reason it tends to be less 

 upset by minor injuries. It is in fact often used for many simple 

 regulations where speed and efficiency are not of importance. 



A first example occurs when the occupant of a room wishes to 

 regulate the number of flies in the room at, or near, zero. Putting a 

 flypaper at a suitable site causes no determinate change in the number 

 of flies. Nevertheless, the only state of equilibrium for each fly is 

 now "on the paper", and the state of equilibrium for "number of 

 flies not on the paper" is zero. The method is primitive but it has 

 the great virtues of demanding little and of working sufficiently well 

 in practice. 



A similar method of regulation is that often used by the golfer 

 who is looking for a lost ball in an area known to contain it. The 

 states are his positions in the area, and his rule is, for all the states 

 but one, "go on wandering"; for one however it is "stop the wander- 

 ing". Though not perhaps ideal, the method is none the less capable 

 of giving a simple regulation. 



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