TRANSMISSION OF VARIETY 8/17 



interact. Nevertheless the interaction is not destructive to the 

 information about where the treasure and the weapons are, for, 

 given the positions of A'" and B'", those of A and B can always be 

 reconstructed, i.e. the messages are still capable of being exactly 

 decoded. 



The conditions necessary that two messages should not interfere 

 destructively can be found by considering the basic fact of coding — 

 that a set of messages are converted to a set of transforms (S.8/4) 

 — and by using the fact that any two messages of different type can be 

 laid side by side and considered as components of one "vector" 

 message, just as any two variables can always be regarded as com- 

 ponents of one vector. Thus if, in the example of the printed letter, 

 X represents the variable "which message of the 26" and y represents 

 the variable "which of the two", then the printed symbol is a coding 

 of the single message {x,y). 



Suppose it is given that the two messages x and y do not interfere 

 destructively. This implies that both x's and j^'s values are recon- 

 structible from the received form. It follows that if two primary 

 messages are distinct, then their coded forms must be distinct 

 (for otherwise unique decoding would not be possible). From this 

 it follows that, if the interaction is to be non-destructive, the variety 

 in the received forms must be not less than that in the original. 

 This condition holds in the example of the printed letter, for both 

 the original messages and the printed form have variety of 26 x 2. 



The fact that chaos does not necessarily occur when two messages 

 meet in the same channel is of great importance in neuro-physiology, 

 especially in that of the cerebral cortex. Here the richness of 

 connexion is so great that much mixing of messages must inevitably 

 occur, if only from the lack of any method for keeping them apart. 

 Thus a stream of impulses coming from the auditory cortex and 

 carrying information relevant to one reaction may meet a stream of 

 impulses coming from the visual cortex carrying information relevant 

 to some other reaction. It has been an outstanding problem in 

 neurophysiology to know how destructive interaction and chaos is 

 avoided. 



The discussion of this section has shown, however, that the prob- 

 lem is badly stated. Chaos does not necessarily occur when two 

 messages meet, even though each affects the same physical set of 

 variables. Through all the changes, provided that no variety is 

 lost and that the mechanism is determinate in its details, the two 

 messages can continue to exist, passing merely from one coding to 

 another. All that is necessary for their recovery is a suitable inverter; 

 and, as S.8/7 showed, its construction is always possible. 



159 



