Measures of Fuzziness and Information: some challenges from reflections on aesthetic experience

Abstract

Evaluating aesthetic in arts is, by sheer consensus, a daunting task. Even when all the social, historic and politic considerations are stripped from the living flesh of the piece – and with them most of what differentiates creation from description – the folk concept that beauty stems from some sort of order/chaos relationship, formalized by G. D. Birkhoff as the aesthetic measure, requires an adequate and consistent quantification of both factors. Old and new approaches to the problem generally resort to classical definitions of information and entropy (Shannon entropy, Kolmogorov-Solomonoff complexity) and their derivatives, neglecting the fact that compactness and repetition have a different value in arts than in information theory, a “confusion of our languages” already noted by R. Arnheim. In this paper we discuss a possible, fruitful interaction among such different topics as fuzziness and art, dealing with similarities and differences in measuring fuzziness and information, and the relationship between the informal notion of information and the measures of fuzziness.