READING RATES 513 



In these experiments the randomized hsts may be regarded as an in- 

 formation source consisting of a sequence of code elements or sjmibols 

 (words) in which there is no correlation between successive symbols. If 

 in making up the lists the sth word of the vocabulary is used with a 

 normalized probability ps , the entropy in H in bits per word, and hence 

 the amount of information per word, is 



H = -J2ps log2 Ps bits (1.1) 



s 



If all words appear with an equal probabilitj^ 1/?/? where m is the number 

 of words in the vocabulary, as in the case of experiments 1-3, ps is 1/m 

 for each of the ni words and in this special case 



H = log2 m (1.2) 



In the case of scrambled prose, for instance, the probabilities are 

 different for different words. This will be true also if in making up word 

 lists we choose words randomly from a box containing different numbers 

 of different words. 



Let ts be the time taken to read the sth w^ord of the ^'ocabulary. Let 

 us assume that ts is the same for the sth word no matter what context that 

 word appears in in the randomized list. If this is so, the average reading 

 time per word, t, will be 



t = Z Psts (1.3) 



s 



the word rate will be 1/t, and the information rate R will be 



IT Z P» l0g2 Ps 



i 2^ Psts 



s 



Suppose we have available a vocabulary of words and know the 

 reading time ts for each word. The problem is to choose ps in terms of ts 

 as to maximize R. This is easily done; however the result can also be 

 obtained as a special case of the problem treated in Appendix 4 of "The 

 Alathematical Theory of Communication."^ In Shannon's ^ii'\ the sub- 

 scripts i, j refer to passing from state i to state j. In our case there is 

 only one state, and ^{/'^ should be identified with ts for all i and j. 

 Similarly, we identify pi/"^ with ps . C is the maximum rate, so log2 

 W = C. Shannon's equation 



PiJ =^.^^ ' 



