9/19 AN INTRODUCTION TO CYBERNETICS 



probabilities of X, 20/35; Z?, 9/35; c, 6/35 and entropies of Ex, 

 1-173; ///,, 0-971; //^, 0. So the entropy of the new series is 0-92 

 bits per letter — exactly the same as before ! 



This fact says uncompromisingly that no information was lost 

 when the (7's and a's were merged to A"s. It says, therefore, that 

 there must be some way of restoring the original four-letter message 

 from the three, of telling which of the Z's were a's and which were 

 ^'s. Closer examination shows that this can be done, strikingly 

 verifying the rather surprising prediction. 



Ex. : How is 



bbbcXbcXbbcXXXcXXbcXcXXXXXXXbb 

 to be de-coded to its original form? 



NOISE 



9/19. It may happen that the whole input to a transducer can be 

 divided into two or more components, and we wish to consider the 

 components individually. This happened in Ex. 8/17/3, where the 

 two messages were sent simultaneously through the same transducer 

 and recovered separately at the output. Sometimes, however, the 

 two inputs are not both completely deducible from the output. If 

 we are interested solely in one of the input components, as a source 

 of variety, regarding the other as merely an unavoidable nuisance, 

 then the situation is commonly described as that of a "message 

 corrupted by noise". 



It must be noticed that noise is in no intrinsic way distinguishable 

 from any other form of variety. Only when some recipient is given, 

 who will state which of the two is important to him, is a distinction 

 between message and noise possible. Thus suppose that over a wire 

 is coming both some conversation and some effects from a cathode 

 that is emitting irregularly. To someone who wants to hear the 

 conversation, the variations at the cathode are "noise"; but to the 

 engineer who is trying to make accurate measurements of what is 

 going on at the cathode, the conversation is "noise". "Noise" 

 is thus purely relative to some given recipient, who must say which 

 information he wants to ignore. 



The point is worth emphasis because, as one of the commonest 

 sources of uninteresting variety in electronic systems is the thermal 

 dance (Brownian movement) of the molecules and electrons, elec- 

 tronic engineers tend to use the word "noise" without qualification 

 to mean this particular source. Within their speciality they will 

 probably continue to use the word in this sense, but workers in 



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