Birkhoff’s aesthetics, Arnheim’s entropy. Some remarks on complexity and fuzzy entropy in arts

A judgement of aesthetic in arts is, by sheer consensus, a daunting task that requires evaluation of a whole host of endogenous and exogenous cultural factors. A few of them can actually provide very useful hints in tackling foundational problems in Information Science in a more natural setting than what is usually provided by a typical engineering stance. This interaction can however work the other way about, as instruments from the Information and Computer Science toolkit may help in focusing the less explored features of art and its evaluation. When all the social, historical, hermeneutical and political considerations are stripped from the living flesh of the piece, we lose most of what differentiates creation from description. This notwithstanding, or maybe exactly for this reason, measuring structures is still an important element of artistic judgement, and 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 tiny fragment of the general and wide mesh of interactions between information sciences and humanities: 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.