542 BELL SYSTEM TECHNICAL JOURNAL 



of the present discussion we would say that for certain of the «2 

 secondary selections the value of 52, the number of secondary symbols, 

 is so reduced that a summation of the information content over all 

 the characters gives a value equal to that derived from the total 

 number of primary selections involved. This may be written 



E log 52 = n log 5, (11) 



1 



where n is the total number of primary symbols or dot lengths assigned 

 to ^2 characters. This suggests that the primary symbols furnish 

 the most convenient basis for evaluating information. 



The discussion so far has dealt largely with telegraphy. When 

 we attempt to extend this idea to other forms of communication 

 certain generalizations need to be made. In speech, for example, we 

 might assume the primary selections to represent the choice of succes- 

 sive words. On that basis 5 would represent the number of available 

 words. For the first word of a conversation this would correspond 

 to the number of words in the language. For subsequent selections 

 the number would ordinarily be reduced because subsequent words 

 would have to combine in intelligible fashion with those preceding. 

 Such limitations, however, are limitations of interpretation only and 

 the system would be just as capable of transmitting a communication 

 in which all possible permutations of the words of the language were 

 intelligible. Moreover, a telephone system may be just as capable of 

 transmitting speech in one language as in another. Each word may 

 be spoken in a variety of ways and sung in a still greater variety. 

 This very large amount of information associated with the selection 

 of a single spoken word suggests that the word may better be regarded 

 as a secondary symbol, or sequence of primary symbols. Let us see 

 where this point of view leads us. 



.15 sec 



.16 sec. 



Fig. 2 



The actual physical embodiment of the word consists of an acoustic 

 or electrical disturbance which may be expressed as a magnitude-time 

 function as in Fig. 2, which shows an oscillographic record of a speech 

 sound. Such functions are also typical of other modes of communi- 

 cation, as will be discussed in more detail later. We have then to 

 examine the ability of such a continuous function to convey informa- 



