# Information

Chapter

## Abstract

In chapter 3 the term
was introduced. (8.1) can be used to describe natural and artifical systems.

*information*was introduced which describes the very often used word*information*in an exact way. Strictly speaking, this term represents a measure of the width of a statistical distribution function. In particular, an increase of the width of a distribution function leads to an increase of the value of information (see example (3.2)-(3.5)). Due to the fact that such an increase means that the considered system contains more information (in the ordinary sense of the word), it is obvious that the term*information*can be used to put the often used word*information*in concrete terms. As it was discussed, such a distribution function can describe both stochastic and deterministic systems. For example, if a*Brownian*motion is observed, it makes sense to use a statistical distribution function, in which case such a process represents a stochastic process. By contrast, if a written text is considered, a distribution function can be used to describe the probability to find a special word. Such a system represents a typical deterministic system. Both the*Brownian*motion and the written text contain information (in the ordinary sense of the word). Instead of a written text the human genetic code can be taken as a basis. Then instead of words special molecular configurations occur which represent hereditary information (in the ordinary sense of this word). In order to put the word*information*in concrete terms, the expression$$\boxed{{I_m} = - \int_m {\rho \left( \Omega \right)\ln \left[ {\rho \left( \Omega \right)d\Omega } \right]d\Omega } } $$

(8.1)

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## Copyright information

© Springer Fachmedien Wiesbaden 1993