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 awhole host of endogenous and exogenous cultural factors. A few of them can actually provide veryuseful hints in tackling foundational problems in Information Science in a more natural setting than whatis usually provided by a typical engineering stance. This interaction can however work the other wayabout, as instruments from the Information and Computer Science toolkit may help in focusing the lessexplored features of art and its evaluation. When all the social, historical, hermeneutical and politicalconsiderations are stripped from the living flesh of the piece, we lose most of what differentiates creationfrom description. This notwithstanding, or maybe exactly for this reason, measuring structures is stillan important element of artistic judgement, and the folk concept that beauty stems from some sort oforder/chaos relationship, formalized by G. D. Birkhoff as the aesthetic measure, requires an adequateand consistent quantification of both factors. Old and new approaches to the problem generally resort toclassical 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 artsthan in information theory, a “confusion of our languages” already noted by R. Arnheim. In this paperwe discuss a tiny fragment of the general and wide mesh of interactions between information sciencesand humanities: a possible, fruitful interaction among such different topics as fuzziness and art, dealingwith similarities and differences in measuring fuzziness and information, and the relationship betweenthe informal notion of information and the measures of fuzziness.