42 Information Storage and Neural Control 



With regard to word production, Simon argues that an author 

 selects words not only by association with other words he has 

 already put down in this passage but by imitation of the language 

 as well. In other words, the next word which an author will choose 

 is determined by the frequency distribution of his present effort, 

 i.e., the subject under discussion, and by the statistical properties 

 of the language he is using. We thus need to postulate two "birth 

 processes." Further, we will consider a passage of fixed length, 

 as is reasonable if we consider that our sample under analysis is 

 but a segment selected from the author's total word production. 

 Thus, we must postulate a "death process" which specifies which 

 words are dropped from the sample at one end of the passage as 

 we add words at the other end. 



Let (3 be the proportion of words added by imitation, and let 

 f*{i) be the relative frequency of words which have occurred 

 exactly / times each. The following assumptions shall prove to 

 be sufficient. 



Birth Processes 



i. The probability of adding a word, already having occurred 



i times, by association is {\-^)i f*{i)- 

 ii. The probability of adding a word, already having occurred 

 i times, by imitation is ^{i-c) /*(i). 



Death Process 



iii. If a word of frequency i is dropped, all instances of that 

 particular word are dropped; this occurs with proba- 

 bility /*(z). 



Note that in both birth processes, the probability of adding a 

 word is proportional to the total number of occurrences of that 

 word and all other words used equally often. The assumption 

 that a word will be chosen with probability proportional to its 

 own frequency is a special case of our assumptions i. and ii.; 

 hence, the assumptions used are more general. The factors in- 

 volving jS are self explanatory. The constant, c, appearing in 

 assumption ii. may be made plausible by the following considera- 

 tions. In any given passage, not all of the words in the language 

 will have been used yet. We wish to allow the possibility that 



