13/15 AN INTRODUCTION TO CYBERNETICS 



as are used for measuring variety and information (S.7/7 and 9/11) 

 and they can be measured either directly or logarithmically. 



The measure, besides being convenient, has the natural property 

 that it specifies the capacity that the channel C must have 



Designer 



Machine 



C 



if the transmission of the necessary variety or information from 

 Designer to Machine is to be possible. 



It will be noticed that this method does nothing to answer the 

 question "how much design is there in this machine (without 

 reference to what it might have been)?" for the measure exists only 

 over the set of possibilities. It apphes, not to the thing that results, 

 but to the act of conummication (S. 13/11). 



The exercises will help to give reality to the somewhat abstract 

 arguments, and will show that they agree satisfactorily with what is 

 evident intuitively. 



Ex. 1 : At one stage in the design of a certain electrical machine, three distinct 

 ohmic resistances must have their values decided on. Each may have any 

 one of the values 10, 15, 22, 33, 47, 67 or 100 ohms independently. How 

 much variety must the designer supply (by the law of Requisite Variety) 

 if the possibilities are to be reduced to one? 



Ex. 2: (Continued. A similar three is to have its resistances selected to the 

 nearest ohm, i.e. from the set 10, 11, 12, . . ., 99, 100. How much variety 

 must the designer now supply ? 



Ex. 3 : Three resistances can each have the value of 10, 20 or 30 ohms. If 

 they are connected in parallel, how much variety must the designer supply 

 if the possible electrical properties are to be reduced to one ? 



Ex. 4 : How much design is needed if the decision lies between the two machines, 

 both with states a, b, c, d: 



abed abed 



j and I ? 



babe c b c a 



Ex. 5 : How much design goes to the production of a penny stamp, (i) as con- 

 sisting of 15,000 half-tone dots each of which may be at any one of 10 

 intensities? (ii) as the final form selected by Her Majesty from three sub- 

 mitted forms ? Explain the lack of agreement. 



Ex. 6 : How much variety must be supplied to reduce to one the possible machines 

 on a given n states? (Hint: Ex. Ijlji.) 



Ex. 1: (Continued.) Similarly when the machine's states number n and the 

 input's states (after design) number /. 



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