Towards the Use of Aesthetics in Decision Making: Kolmogorov Complexity Formalizes Birkhoff's Idea
Decision making is traditionally based on utilitarian criteria such as cost, efficiency, time, etc. These criteria are reasonably easy to formalize; hence, for such criteria, we can select the best decision by solving the corresponding well-defined optimization problem. In many engineering projects, however, e.g., in designing cars, building, airplanes, etc., an important additional criterion which needs to be satisfied is that the designed object should be good looking. This additional criterion is difficult to formalize and, because of that, it is rarely taken into consideration in formal decision making. In the 1930s, the famous mathematician G. D. Birkhoff has proposed a formula that described beauty in terms of "order" and "complexity". In the simplest cases, he formalized these notions and showed that his formula is indeed working. However, since there was no general notion of complexity, he was unable to formalize his idea in the general case. In this paper, we show that the existing computer-based general notion of object complexity (called Kolmogorov complexity) leads to a reasonable formalization of Birkhoff's idea and thus, leads to a possibility to take aesthetic criteria into consideration in decision making.
Technical Report: UTEP-CS-98-11