8/11 AN INTRODUCTION TO CYBERNETICS 



a transducer, or variety passing from one transducer to another, 

 yet the phrase is dangerously misleading. Though an envelope can 

 contain a message, the single message, being unique, cannot show 

 variety; so an envelope, though it can contain a message, cannot 

 contain variety: only a set of envelopes can do that. Similarly, 

 variety cannot exist in a transducer (at any given moment), for a 

 particular transducer at a particular moment is in one, and only one, 

 state. A transducer therefore cannot "contain" variety. What 

 can happen is that a number of transducers (possibly of identical 

 construction), at some given moment, can show variety in the states 

 occupied ; and similarly one transducer, on a number of occasions, 

 can show variety in the states it occupied on the various occasions. 



(What is said here repeats something of what was said in S.7/5, 

 but the matter can hardly be over-emphasised.) 



It must be remembered always that the concepts of "variety", 

 as used in this book, and that of "information", as used in com- 

 munication theory, imply reference to some set, not to an individual. 

 Any attempt to treat variety or information as a thing that can exist 

 in another thing is likely to lead to difficult "problems" that should 

 never have arisen. 



8/11. Transmission at one step. Having considered how variety 

 changes in a single transducer, we can now consider how it passes 

 from one system to another, from TXo U say, where T is an absolute 

 system and [/ is a transducer. 



As has just been said, we assume that many replicates exist, identical 

 in construction (i.e. in transformation) but able to be in various 

 states independently of each other. If, at a given moment, the 

 r's have a certain variety, we want to find how soon that variety 

 spreads to the C/'s. Suppose that, at the given moment, the Ts 

 are occupying nj- distinct states and the f/'s are occupying n^. (The 

 following argument will be followed more easily if the reader will 

 compose a simple and manageable example for T and U on which 

 the argument can be traced.) 



Tis acting as parameter to U, and to each state of Twill correspond 

 a graph of U. The set of t/'s will therefore have as many graphs 

 as the r's have values, i.e. n^ graphs. This means that from each 

 t/-state there may occur up to nj different transitions (provided by 

 the nj different graphs), i.e. from the t/-state a representative point 

 may pass to any one of not more than n-p t/-states. A set of C/'s 



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