Understanding without words: visual representations in math, science and artistic research

As knowledge can be condensed in different non-verbal ways of representation, the integration of graphic and visual representations and design in research output helps to expand insight and understanding. Layers of visual charts, maps, diagrams not only aim at synergizing the complexity of a topic with visual simplicity, but also to guide a personal search for and insights into knowledge. However, from research over graphic representation to interpretation and understanding implies a move that is scientific, epistemic, artistic and, last but not least, ethical. This article will consider these four aspects from both the side of the researcher and the receiver/interpreter from three different perspectives. The first perspective will consider the importance of visual representations in science and its recent developments. As a second perspective, we will analyse the discussion concerning the use of diagrams in the philosophy of mathematics. A third perspective will be from an artistic perspective on diagrams, where the visual tells us (sometimes) more than the verbal.