Interdisciplinary Application of Symmetry Phenomena

This chapter gives a short overview of a few possible contributions of interdisciplinarity to aesthetics, as the latter appears in the sciences. Symmetry phenomena play an important role in these considerations. Therefore, the chapter first introduces the most modern interpretation of symmetry. In this course there is discussed what is the common in the different geometric appearances of symmetry (e.g., mirror reflection, rotation, translation, similitude, etc.), and how do they appear in decorative arts. Symmetry, perfection and beauty were considered in close relation to each other since the ancient times. Then the title theme is exemplified by interdisciplinary applications of symmetry phenomena. At first, symmetry operations in decorative arts are presented in one dimension (frieze patterns), in two dimensions (wallpapers or tiling), with just a short reference to the beauty of crystals (three dimensions), then extended to the even coverage of surfaces (sphere and symmetric flat-faced polyhedra). At second, there is mentioned that symmetry operations appear in algebra and arithmetic as well. The paper presents how the translation of the natural numbers and their sequences appear in aesthetic representations. This leads the reader over to the discussion of the so-called golden section in aesthetic terms. Then, we turn back to the perfect (Platonic) polyhedra as reflected in the so called golden section kaleidoscope. We explore step by step how the perfect proportions appear in the perfect bodies. We give also a short historical overview how the study of beauty of the symmetrically perfect bodies led to interdisciplinary applications in the sciences. At third, examples are presented, how the discussed aesthetically outstanding proportions, shapes, are embodied not only in artworks, but also in recent scientific achievements. First of all, the discovery of quasicrystals is treated—that represent the so far “missing” golden proportional fivefold symmetry in concrete material structures. Then there are shortly mentioned also such successful new molecules—like the fullerene and the graphene—which is so important in nanoscience. These discoveries cited from the recent decades demonstrate productivity of interdisciplinarity, in terms of science-art relations. They led from aesthetic considerations (based on different appearances of symmetries) to realized scientific ideas.