TRANSMISSION OF INFORMATION ■ 539 



The number of possible sequences of secondary symbols that can 

 result from W2 secondary selections is 



52"2 = 5"'"^ (3) 



Now «iW2 is the number n of selections of primary symbols that would 

 have been necessary to produce the same sequence had there been 

 no mechanism for grouping the primary symbols into secondary 

 symbols. Thus we see that the total number of possible sequences 

 is 5" regardless of whether or not the primary symbols are grouped 

 for purposes of interpretation. 



This number 5" is then the number of possible sequences which we 

 set out to find in the hope that it could be used as a measure of the 

 information involved. Let us see how well it meets the requirements 

 of such a measure. 



For a particular system and mode of operation 5 may be assumed 

 to be fixed and the number of selections n increases as the communi- 

 cation proceeds. Hence with this measure the amount of information 

 transmitted would increase exponentially with the number of selections 

 and the contribution of a single selection to the total information 

 transmitted would progressively increase. Doubtless some such 

 increase does often occur in communication as viewed from the 

 psychological standpoint. For example, the single word "yes" or 

 "no," when coming at the end of a protracted discussion, may have 

 an extraordinarily great significance. However, such cases are the 

 exception rather than the rule. The constant changing of the subject 

 of discussion, and even of the individuals involved, has the effect in 

 practice of confining the cumulative action of this exponential relation 

 to comparatively short periods. 



Moreover we are setting up a measure which is to be independent of 

 psychological factors. When we consider a physical transmission 

 system we find no such exponential increase in the facilities necessary 

 for transmitting the results of successive selections. The various 

 primary symbols involved are just as distinguishable at the receiving 

 end for one primary selection as for another. A telegraph system 

 finds one ten-word message no more difficult to transmit than the one 

 which preceded it. A telephone system which transmits speech suc- 

 cessfully now will continue to do so as long as the system remains 

 unchanged. In order then for a measure of information to be of 

 practical engineering value it should be of such a nature that the in- 

 formation is proportional to the number of selections. The number of 

 possible sequences is therefore not suitable for use directly as a measure 

 of information. 



