26 



Henry Quastler 



In infonnation theory, we use the word 'communication' in a wider sense 

 than usual — just as the word 'information' is used in a wider sense than usual. 

 We understand by 'communication' any relation between variables, accomplished 

 by any means whatsoever, conscious or otherwise, provided that it results in a 

 mutual reduction of uncertainty. For instance: if one watches one of two 

 tennis players, without looking at the other, he derives a considerable amount 

 of information about the unseen player's action. Thus, the seen player transmits 

 information about the unseen player — although in this case, the transmission 

 of information is incidental and not normally utilized, as one ordinarily looks 

 at both players. 



An Example of Two Related Variables 



The following example is purposely selected to represent an instance of 

 unintentional communication. The table below is based on Pearson and Lee's 

 measurements of heights on 1376 father-daughter pairs. To simplify the analysis, 

 we have grouped the data in coarse intervals of 3 in. each, and converted all 

 frequencies into percentages. 



Table II. Heights of Fathers and Daughters; Probabilities and 



Information Measures 



Joint probabilities of heights, pii,)) 

 (Pearson and Lee's data, 1376 father-daughter pairs) 



* height of fathers, in 3 in. intervals 

 t height of daughters, in 3 in. intervals 

 + center of intervals 



2.00 



Information Functions: 



H{x) = -S/'(/)log2/j(/) = 1.92 bits 



i 

 my) = -i:p(j)\og,p(j) = 2.00 bits 



H(x) + H(y) = 3.92 bits 



H{x,y) = -i:piij) log, p(i,j) = 3.70 bits 



ij 



Tix.y) = H(x) + H(y) - H{x,y) = 0.22 



bits 



