TRANSMISSION OF VARIETY 8/4 



very brief account mentions no less than sixteen major transforma- 

 tions through all of which something has been preserved, though 

 the superficial appearances have changed almost out of recognition. 



8/3. Complexity of coding. When considering such repeated 

 codings the observer may easily over-estimate the amount of com- 

 plexity that has been introduced. It not uncommonly happens that 

 the amount of complexity is nothing like as large as a first impression 

 might suggest. 



A simple example, showing how a complex coding may have 

 hidden simplicities, occurs when a simple one-one coding of the 

 alphabet is applied first to the message, then to the first coded form 

 to give a second (doubly-) coded form, then to the second coded 

 form, and so on for many codings. The final form might be thought 

 to be extremely mixed, and to need for its decoding as many opera- 

 tions backwards as were used forwards; in fact, as can easily be 

 verified, it differs from the original message only by as much as is 

 caused by a single application of some one-one coding. The final 

 message can thus be turned back to the original by a single operation. 



Ex. : Arrange the cards of a pack in order, and place it on the table face down- 

 wards. Cut. Cut again. Cut again and again until you are satisfied 

 that the original order is lost totally. Now pick the pack up and examine its 

 order ; how much order has been lost ? 



8/4. De-coding. The general study of codings is best introduced 

 by noticing some of the features of military codings. 



We must be careful from the beginning not to interpret "code" 

 too narrowly. At first we tend to think only of those methods 

 that turn each letter of the message to some other letter, but this 

 class is too restricted, for there are many other methods. Thus 

 the "Playfair" code operates on the letters in pairs, turning each 

 pair (a vector with two components ) to some other pair. Other 

 codes put the letters into some new arrangement, while others are 

 wholly arbitrary, turning, for instance, "two divisions will arrive" 

 to "Arthur". These considerations make it clear that if the coding 

 is a transformation, the operand is the whole message rather than a 

 letter (though the latter possibility is not excluded). The trans- 

 formation is therefore essentially of the form 



^ , Ml M2 M3 ... 



^i Q Q • • • 



where Mi, M2, ■ . . are the various messages and Q, C2, . . . are their 

 coded forms. A coding, then, is specified by a transformation. 



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