9/20 AN INTRODUCTION TO CYBERNETICS 



Ex. 1 : What is the coding, of first input to output, if the second output is kept 

 constant (i) at F; (ii) at G? 



Ex.2: \ system of three states— P, Q, R—is to transmit changes at two inputs, 

 a and ^, each of which can take two states. The states of the inputs and of 

 the system change in step. Is noise-free transmission possible ? 



9/20. Distortion. It should be noticed that falsification of a 

 message is not necessarily identical with the effect of noise. "If a 

 particular transmitted signal always produces the same received 

 signal, i.e. the received signal is a definite function of the transmitted 

 signal, then the effect may be called distortion. If this function has 

 an inverse — no two transmitted signals producing the same received 

 signal — distortion may be corrected, at least in principle, by merely 

 performing the inverse functional operation on the received signal." 

 (Shannon.) 



Ex. 1 : Is the change by which the erect object falls on to the retina inverted a 

 distortion or a corruption ? 



Ex. 2: A tension applied to a muscle evokes a steady stream of impulses whose 

 frequency is not proportional to the tension. Is the deviation from pro- 

 portionality a distortion or a corruption? 



Ex. 3 : (Continued.) If the nerve carrying the impulses is subjected to alcohol 

 vapour of sufficient strength it will cease to conduct for all tensions. Is 

 this a distortion or a corruption ? 



9/21. Equivocation. A suitable measure for the degree of corrup- 

 tion has not, so far as I am aware, been developed for use in the 

 basic cases. In the case of the channel that transmits incessantly, 

 however, Shannon has developed the appropriate measure. 



It is assumed first that both the original signals and the received 

 signals form Markov chains of the type defined in S.9/4. The data 

 of the messages can then be presented in a form which shows the 

 frequencies (or probabilities) with which all the possible combinations 

 of the vector (symbol sent, symbol received) occur. Thus, to use 

 an example of Shannon's suppose O's and I's are being sent, and that 

 the probabilities (here relative frequencies) of the symbols being 

 received are: 



Symbol sent 11 



Symbol received 10 1 



Probability 0-495 0-005 0-005 0-495 



Of every thousand symbols sent, ten arrive in the wrong form, an 

 error of one per cent. 

 At first sight this "one per cent wrong" might seem the natural 



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