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Information, SMI, and Entropy


An Example of Specific Information

Let us consider the example of finding a book in the library. If someone goes into a large library to borrow a copy of "War and Peace", it will take only a few minutes to find the book when the library is in a good state of order (as illustrated in Figure 04). The book will be on the fiction shelves and the author's name will appear in alphabetical order. In the catalogue, the book is given a unique decimal number. There is only one possible way in which "War and Peace" can be arranged in relation to all the other books. Indeed, there is only one possible way in which the contents of the entire library can be arranged. But then imagine a second library, in which by some quirk of the rules, books are arranged on the
Imperfect Cataloging shelves according to the color of their bindings (Figure 06). There may be a thousand red books grouped together in one section of the shelves. This arrangement contains a certain amount of order and conveys some information, but not as much as in the first library. Since there are no rules governing the ordering of books on the shelves by title and author within the red section, the number of possible ways of arranging the books is much greater. If the borrower knows that "War and Peace" has a red binding, he will proceed to the right section, but then he will have to examine each book in turn until he chances upon the one he is looking for. Then imagine a third library, in which all the rules have broken down. The books are strewn at random on any shelf or on a desk (as the case in Figure 03). "War and Peace" could be anywhere in the building. There is no denying that the books are in a certain sequence, but the sequence is a "noise," not a message. It is only one of a truly immense number of possible ways of arranging the books, and there is no telling which one, because all are equally probable. A borrower's ignorance of the actual arrangement is great in proportion to the quantity of these possible, equally probable ways.

Figure 06 Imperfect Cataloging [view large image]

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