8/17 



AN INTRODUCTION TO CYBERNETICS 



Ex. 1 : (See Ex. 2/14/1 1.) If A'" is at the point (0,0) and B" at (0,1), reconstruct 

 the position oi A. 



Ex. 2: A transducer has two parameters: a (which can take the values a or A) 

 and j8 (which can take the values b or B). Its states — W,X, Y,Z — are trans- 

 formed according to : 



Two messages, one a series of a-values and the other a series of )3-values, 

 are transmitted simultaneously, commencing together. If the recipient is 

 interested only in the a-message, can he always re-construct it, regardless 

 of what is sent by /3? (Hint: S.8/6.) 

 Ex. 3: Join rods by hinge-pins, as shown in Fig. S/n/l: 



Co 5) 



Fig. 8/17/1 



(The pinned and hinged joints have been separated to show the construction.) 

 f is a pivot, fixed to a base, on which the rod R can rotate ; similarly for Q 

 and S. The rod M passes over P without connexion ; similarly for A'^ and 

 Q. A tubular constraint C ensures that all movements, for smaU arcs, shall 

 be to right or left (as represented in the Figure) only. 



Movements at A and B will cause movements at L and A'^ and so to Y 

 and Z, and the whole can be regarded as a device for sending the messages 

 "position of A" and "position of 5", via L and N, to the outputs Y and Z. 

 It will be found that, with B held fixed, movements at A cause movements 

 of both L and A'^; similarly, with A held fixed, movements at B also affect 

 both L and A^. Simultaneous messages from A and B thus pass through 

 both L and A'^ simultaneously, and evidently meet there. Do the messages 

 interact destructively ? (Hint : How does Y move if A alone moves ?) 

 Ex. 4: (Continued.) Find the algebraic relation between the positions at 

 A, B, y and Z. What does "decoding" mean in this algebraic form? 



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