Συμμετρiα – Symmetria – Symmetry

Abstract

The idea of the triennial congresses “Symmetry: Art and Science” is going back to the late 1980s, with a desire that the “Two Cultures” should have some bridges. Our goal was to provide a regular forum where representatives of different disciplines from East and West may come together for interdisciplinary exchange of ideas and shaping new forms of co-operations. We reached already five continents, and now we pay tribute to “Portuguese symmetries”. We survey the development of the concept symmetry, starting from zoo- and ethno-mathematics (Platonic solids). We also discuss the related terminology of συμμετρία – symmetria – symmetry. We suggest that the Greek concept of συμμετρία (commensurability) vs. ἀσυμμετρία (incommensurability) played a relevant role at the be- ginnings of mathematics, then reached aesthetics (due proportion), and became a central concept in Vitruvius’ theory of architecture. The term also appeared in the Greek Bible, but later disappeared in the translations. We present our view on how symmetry “returned” to the mainstream of art and then of science and gained a new meaning-family (bilateral, rotational, translatory symmetries, and invariances). Parallel with this, we present an “anti-golden-sectionism” because in some “well- known” cases the Golden Section (GS) had no role at all. On the other hand, the GS gained some importance in other cases that are less known. We discuss the Pacioli – Leonardo connection, adding that “Leonardo’s code” in the case of his reconstruction of the “Vitruvian man” was not the GS, but perhaps the simple ratio 1/3. Finally, we turn to future tasks, including interdisciplinary education.