Michael Wettstein

Statement

Michi Wettstein is a musician, artist, and researcher based in Vienna, Austria. He investigates connections between physics, mathematics, and art. While researching the evolution of stars, in particular nucleosynthesis, Michi was intrigued by the instabilities of certain elements. For example, there exist no stable elements with mass number 5 and 8, or with 19 neutrons. On the other hand, elements with 2, 8, and 20 neutrons, the “magic numbers”, are known to be especially stable. Michi wondered how this behavior is reflected in the arrangement of fundamental particles. The force field of a nucleus holds the nucleons (protons and neutrons) together. In a simplified model, the nucleons behave like repellent spheres on a spherical surface. After initial experiments with magnets on a sphere, Michi started enumerating configurations of points on the unit sphere to find optimal configurations. In this way, up to 42 candidate solutions for up to 24 points were constructed and 3D printed.

Films

The problem of finding the configuration of n points on a sphere that maximize the minimal distance, or equivalently, finding the location of n non-intersecting circles on a sphere with maximal radius, is known as the Tammes problem. This problem is named after the botanist L. Tammes who studied the distribution of pores on pollen grains in 1930. Explicit solutions are known only for a limited number of points. Through enumerating possible vertex locations, Michi searched for solutions and verified them with Laszlo Hars’ numerical results. Surprisingly, the vertices of two platonic solids, namely the cube and dodecahedron, are not necessarily arranged in an optimal way. The short film “Kugeln um Kugel“ shows constructions of the optimal configurations for n = 1 to n = 20. The conversions of the cube, dodecahedron, and cuboctahedron to the optimal configurations are visualized. The music was developed in the project Megaboom – a remix of the track “Allkugeltrain” by Rio.