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equipment. It is extremely easy to mistake the role played by a 

 language. In literature, it is well understood that a book can be trans- 

 lated into many different languages and still express approximately the 

 same ideas. Absolutely everything in physics which is discussed in 

 mathematical terms — every proof and every theorem — could be pre- 

 sented without any mathematical symbols or terms whatsoever. How- 

 ever, the length of time and the number of words involved would be so 

 great that most of the concepts of physics could not be developed within 

 a lifetime. 



The mathematical language tells us nothing new about the physical 

 universe. A knowledge of advanced calculus is in no way synonymous 

 with an understanding of intermediate physics. Nonetheless, it is 

 almost inconceivable that anyone would discuss the details of quantum 

 mechanics without considerable training in advanced mathematics. 

 In contrast, in Newton's day, all physical theorems could be expressed 

 and discussed in words rather than in mathematical symbols. 



Information theory consists of mathematical methods for assigning 

 quantitative values to information. It is a language and as such cannot 

 reveal anything new or unsuspected about the universe. It can help 

 to express ideas and theorems and to realize similarities and analogies 

 between widely diverse fields. Information theory is a successful 

 language in that it can achieve an economy in thought processes and 

 words. However, it is a far less successful language than calculus; its 

 applications are not as forceful and its economies are not nearly as 

 great. It is important in studying information theory neither to be 

 misled into assigning it too important a role nor to be blinded into 

 ignoring it altogether. 



2. information Theory — General Discussion 



Information theory consists of mathematical methods for quantifying 

 information. In order to do this, one must understand what is meant 

 by information. In the technical, restricted sense, information may be 

 regarded as removing uncertainty or doubt. From this point of view, 

 the ordering of randomly arranged objects is removing doubt concerning 

 their location, and hence, increasing their informational content. 



A few examples may help clarify this idea of information as the 

 removal of doubt. Suppose a teacher asks one of his students if he has 

 answered correctly at least three-quarters of the questions on a class 

 test. If the teacher has little previous knowledge of the student or his 

 work, either a "yes" or a "no" answer is equally probable. After 

 receiving the student's answer, -the teacher's uncertainty will be less, but 



