Hermann von Helmholtz-Zentrum für Kulturtechnik

Zentralinstitut der Humboldt-Universität zu Berlin

Showing and Referring. The Diagram as a Cultural Technique

Jochen Brüning, Gloria Meynen

Project funded by the Fritz Thyssen Foundation

Deductive mathematics essentially owes its emergence to an innovation in the form of a cultural technique that combined letters and lines – the labelled diagram. Labelled diagrams first appear around 440 BC in the lunes used by Hippocrates of Chios to square the circle. Since the mid-fifth century BC, the labelled diagram has enabled numbers, letters and lines to be translated into each other, and visuality to be produced without images by recourse to letters. This new form of visuality is no longer purely based on vision and arithmetical knowledge, and it enables a technique of showing and referring that is closely linked to the earliest books in mathematical instruction, the format of Euclid’s »Elements« (Stoicheia).

This project studies the visual production of abstraction and ideality. Taking the cultural history of the process of providing mathematical proofs as our starting point, we will examine how deductive truth is produced on the image surfaces of geometry. The project therefore focuses on the relationship between visuality and imagelessness and on the question of how evidence and truth were able to become so evidently one of the functions of the image in deductive proofs.

Back to top