8/15 



AN INTRODUCTION TO CYBERNETICS 



transmission goes on, S is affected (and its variety increased) by the 

 whole sequence, by the whole vector, and thus a variety of much 

 more than two can pass through R. A shrinkage in the capacity 

 of a channel can thus be compensated for (to keep the total variety 

 transmitted constant) by an increase in the length of the sequence — 

 a fact already noticed in the previous section, and one that will be 

 used frequently later. 



Ex. 1 : An absolute system rdominates a chain of transducers Ai, A2, A3, A4, . . .: 



A4 



A set of replicates commences with variety in T but with none in Ai, nor 

 in A2, etc. Show that after k steps the varieties in Ai, A2, . . ., Aj^ may be 

 non-zero but that those in ^k+i, Ak+2, ■ • • must still be zero (i.e. that T's 

 variety "cannot have spread farther than A^'\). 



Ex. 2: Of 27 coins, identical in appearance, one is known to be counterfeit 

 and to be light in weight. A balance is available and the counterfeit coin 

 is to be identified by a series of balancings, as few as possible. Without 

 finding the method — by regarding the balance as a transducer carrying 

 information from the coins to the observer — give a number below which 

 the number of balancings cannot fall. (Hint: What is the variety at a 

 single balancing if the results can be only: equality, left pan heavier, right 

 pan heavier?) 



8/15. Delay. The arrangement of the system of S.8/13: 



Q 



R 



can also be viewed as 



in which Q and R have been regarded as forming a single system 

 T which is, of course, absolute. If now an observer studies the 

 transfer of variety from T to S, with exactly the same events as those 

 of S.8/13 actually occurring, he will find that the variety is moving 

 across in small quantities, step by step, unUke the transfer of S.8/11, 

 which was complete in one step. 



The reason for the distinction is simply that in S.8/11 the whole 

 of the dominating system (T) had an immediate effect on the dom- 

 inated {U), while in S.8/13 T contained a part Q which had no 

 immediate effect on the receiver S. Q's effect had to be exerted 

 through R, and was thereby delayed. 



This more time-consuming transfer is common in real systems 

 simply because many of them are built of parts not all of which have 

 an immediate effect on the receiving system. Thus if the cerebral 

 cortex, as receiver, is affected by the environment (which has no 



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