9/22 AN INTRODUCTION TO CYBERNETICS 



Ex.4: Find -plogz P when p is 000025. (Hint: Write p as 2-5 x 10"4 

 and use (i)). 



Ex. 5 : During a blood count, lymphocytes and monocytes are being examined 

 under the microscope and discriminated by the haematologist. If he 

 mistakes one in every hundred lymphocytes for a monocyte, and one in 

 every two hundred monocytes for a lymphocyte, and if these cells occur 

 in the blood in the ratio of 19 lymphocytes to 1 monocyte, what is his 

 equivocation ? (Hint : Use the results of the previous two exercises.) 



9/22. Error-free transmission. We now come to Shannon's 

 fundamental theorem on the transmission of information in the 

 presence of noise (i.e. when other, irrelevant, inputs are active). 

 It might be thought that when messages are sent through a channel 

 that subjects each message to a definite chance of being altered at 

 random, then the possibiUty of receiving a message that is correct 

 with certainty would be impossible. Shannon however has shown 

 conclusively that this view, however plausible, is mistaken. Reliable 

 messages can be transmitted over an unreliable channel. The 

 reader who finds this incredible must go to Shannon's book for the 

 proof; here I state only the result. 



Let the information to be transmitted be of quantity H, and sup- 

 pose the equivocation to be E, so that information of amount H — E 

 is received. (It is assumed, as in all Shannon's book, that the 

 transmission is incessant.) What the theorem says is that if the 

 channel capacity be increased by an amount not less than E — by 

 the provision perhaps of another channel in parallel — then it is 

 possible so to encode the messages that the fraction of errors still 

 persisting may be brought as near zero as one pleases. (The price 

 of a very small fraction of errors is delay in the transmission ; for 

 enough message-symbols must accumulate to make the average of 

 the accumulated material approach the value of the average over all 

 time.) 



Conversely, with less delay, one can still make the errors as 

 few as one pleases by increasing the channel capacity beyond the 

 minimal quantity E. 



The importance of this theorem can hardly be overestimated in 

 its contribution to our understanding of how an intricately connected 

 system such as the cerebral cortex can conduct messages without 

 each message gradually becoming so corrupted by error and inter- 

 ference as to be useless. What the theorem says is that if plenty of 

 channel capacity is available then the errors may be kept down to 

 any level desired. Now in the brain, and especially in the cortex, 

 there is little restriction in channel capacity, for more can usually be 



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