{"content":[{"text":"Cross-disciplinary entities: An interaction model illustrated by works combining \n mathematics and arts (Milena Damrau, Martin Skrodzki) \n The 2020 annual meeting of the German Mathematical Society saw the first minisymposium \n on Mathematics and Arts. This introductory article presents a classification scheme for \n interaction between these two disciplines. In the following collection, each article \n exemplifies the different cases of the scheme via a contribution presented at the \n minisymposium. \n Since 1998, the Bridges Conference promotes the interdisciplinary presentation and \n publication of mathematical connections in art, music, architecture, education and culture \n (Fenyvesi 2016). Douglas G. Burkholder characterises these interactions between \n mathematics and arts in terms of two extremes: “mathematics [used] to create artwork and \n artwork that is used to explain mathematics” (Burkholder 2019, 289). While this can serve \n as a starting point, the connections between these two disciplines are more subtle and \n complex. To investigate these facets further, we first relate them to the broader \n interdisciplinary context. \n Science philosopher Michael Jungert presents a hierarchy of concepts with an increasing \n degree of integration of two disciplines (Jungert 2010). Burkholder’s characterisation of the \n interaction between mathematics and arts best corresponds to the middle ground of Cross- \n Disciplinarity, discussed by Jungert, which is identified by the usage of methods or research \n paradigms of one discipline within the other without trying to blend the disciplines \n (Jungert 2010, 3). Alternatively, Heinz Heckhausen subdivides interaction between two \n disciplines into six sub-types (Heckhausen 1972). Heckhausen’s third subtype Auxiliary \n Interdisciplinarity best reflects the observation by Burkholder. It is denoted by one \n discipline making use “of a method borrowed from another discipline” \n (Heckhausen 1972, 88). Both classifications have in common that the notion of method is of \n central importance. \n A method is “a way of proceeding or doing something, esp a systematic or regular one” and \n denotes “the techniques or arrangement of work for a particular field or subject” (Collins). \n In this sense, a method is applied to some situation or input entity in order to reach an end or \n an output entity, where neither entity has to be materially realised, but can remain abstract or \n ideal. Burkholder’s classification identifies both mathematics as a method to reach an artistic \n outcome and art as a method to reach the outcome of an explanation of mathematics. \n However, it neglects the input entity, the starting point to which to apply the method. \n Expanding Burkholder’s scheme and considering the two disciplines (mathematics and arts) \n as possibilities for the input entity, the method, and the output entity, respectively, provides \n the complete scheme as given in Figure 1. This expanded scheme contains eight cases. It \n does include Burkholder’s “artwork that is used to explain mathematics” (case 2) as well as \n his “mathematics [used] to create artwork” (case 3). The cases 5 and 6 are non- \n interdisciplinary and therefore only given for the sake of completeness here. Furthermore, \n cases 7 and 8 challenge this classification as they propose that applying a method from one \n discipline to an input entity of the same discipline could give rise to an outcome in another \n discipline, which raises a rather philosophical question not to be settled in the article. This \n leaves cases 1 and 4 as new additions to Burkholder’s classification. The articles in this \n collection exemplify all cases 1 to 4. Thereby, they validate this generalised scheme.","bbox":{"left":0.128674,"top":0.086125,"width":0.749061,"height":0.825392}}],"images_bbox":[],"images_bbox_not_text_overlap":[]}