Conceptualizing Birkhoff's Aesthetic Measure Using Shannon Entropy and Kolmogorov Complexity

Abstract

In 1928, George D. Birkhoff introduced the Aesthetic Measure, defined as the ratio between order and complexity, and, in 1965, Max Bense analyzed Birkhoff s measure from an information theory point of view. In this paper, the concepts of order and complexity in an image (in our case, a painting) are analyzed in the light of Shannon entropy and Kolmogorov complexity. We also present a new vision of the creative process: the initial uncertainty, obtained from the Shannon entropy of the repertoire (palette), is transformed into algorithmic information content, defined by the Kolmogorov complexity of the image. From this perspective, the Birkhoff s Aesthetic Measure is presented as the ratio between the algorithmic reduction of uncertainty (order) and the initial uncertainty (complexity). The measures proposed are applied to several works of Mondrian, Pollock, and van Gogh.