Abnormality (information theory)

The conspicuousness is a measure of the contribution of a sign to the overall entropy of a system that was introduced around 1965 by the German cyberneticist Helmar Frank .

definition

The function ${\displaystyle A_{z}=-p_{z}\cdot \log _{2}{p_{z}}}$

When investigating the entropy introduced by Shannon , Frank focused on the term that provides the contribution of individual probabilities to the total entropy. This contribution is the product of the probability of an event and its information content (surprise value) : ${\displaystyle p}$ ${\displaystyle I(p)=-\log _{2}p}$

${\displaystyle A(z)=-p_{z}\cdot \log _{2}{p_{z}}}$

The maximum of this function is approximately at: ${\displaystyle 0{,}530\,737\,8}$

${\displaystyle p_{\text{max}}={\tfrac {1}{\mathrm {e} }}\approx 0{,}367\,879\,44}$.

(e - Euler's number )

When investigating the importance of this function, Frank drew parallels to human perception based on the work of Wilhelm Fucks . He defined the conspicuousness of a sign as its contribution to the overall uncertainty of the system (entropy).

interpretation

${\displaystyle A_{z}=-p_{z}\cdot \log _{2}{p_{z}}}$with golden ratio

Frank and other scientists drew parallels between the relationships that result from the maximum of conspicuity and the golden ratio :

Maximum of conspicuity:

${\displaystyle p_{\text{max}}\approx 0{,}367}$

Ratio of the shorter distance to the total distance in the golden section:

${\displaystyle b\approx 0{,}382}$

From this they concluded that the conspicuousness is an information-theoretical explanation for an aspect of aesthetic perception.

Individual evidence

1. ^ Helmar G. Frank, Brigitte S. Meder: Introduction to cybernetic pedagogy , DTV German paperback, 1984, ISBN 3423041080
2. ↑ Horst Völz : Reproduction 11/11/2006: . Computers and art series accent 87. 2nd ed Urania-Verlag Leipzig Jena - Berlin 1990 67 pages, definition of entropy P. 11 - 14 The surprise value p 14; accessed on August 13, 2018
3. ^ André Frank Zimpel: The counting person. What emotions have to do with mathematics , page 170 ff. Vandenhoeck & Ruprecht, 2008, ISBN 3525315422

literature

• Helmar G. Frank, Herbert W. Franke : Aesthetic information. Estetika informacio. An introduction to cybernetic aesthetics , Kopäd Verlag, 2002, ISBN 3929061821