Hermann von Helmholtz-Zentrum für Kulturtechnik

Zentralinstitut der Humboldt-Universität zu Berlin

The Alphabetisation of Mathematics. Elements of the Cultural History of the Diagram

Jochen Brüning, Gloria Meynen

Deductive mathematics essentially owes its emergence to an innovation in the form of a cultural technique that combined letters and lines – the labelled diagram. Since the mid-fifth century BC, the labelled diagram has made it possible to translate numbers, letters and images into each other. This enables a technique of showing and referring that achieves an exemplary formalisation in Euclid’s »Elements«. Taking Euclid’s »Elements« as its case study, the project explores the media conditions of deductive mathematics. Its focus is the technique of referring in Euclidean diagrams and the implied relationships between image, script and number. Our central focus is the techniques of providing proof. Two aspects are therefore of interest:

1. Firstly, the surfaces used for writing and images in geometry. This is an aspect that Euclid’s »Elements« mask completely, just as they obscure the question of the materiality of mathematical proofs.

2. We assume that the materiality of image surfaces fundamentally determines the operations performed by the diagram. Therefore, the second focus of our investigations shifts from the media of the diagram to its tools: lines and letters.

The diagram combines elements of arithmetics and geometry. It is the product of manifold translation processes between Egyptian astronomy, the processes of geometrically sketching and setting out in Ionian temple construction and the Pythagoreans’ theory of music. The project is concerned with transfers between geometry and arithmetics. We believe that the emergence of the new cultural technique of the labelled diagram coincides with cultural and technological fractures.