SYBILLE KRÄMER The Productivity of Blanks: On the Mathematical Zero and the Vanishing Point in Central Perspective. Remarks on the Convergences between Science and Art in the Early Modern Period 1. Instruments as Symbol-Technical Hybrids We usually associate ‘instruments’ with man-made products such as tools, appliances, machines, or devices. Ranging from the screwdriver to the piano, up to the telescope and computer, we create objects which are then put to use to achieve particular goals. Speaking concretely, such an instrumentality makes up the core of our technical relation to the world. This rests on a further conviction: if the technical is fundamen- tally related to the instrumental, then the symbolic, that is, the use of signs, is not instrumental but should be understood as oriented towards understanding and interpretation. The materiality and sensual thing-ness, which is also part of the sign, is not then articulated in the termini of opaque objecthood, but on the foil of a transparent, transitory mediality. Here our understanding of instrumentality seems to establish a dividing line: the technical relates to the symbolic as production to representa- tion (Herstellen to Darstellen), construction to interpretation, and as in- strument to medium. Technical and symbolic procedures embody, there- fore, two distinct domains of human poiesis, each with its own procedural and developmental logics. Nevertheless, there are quite a few artefacts that block this schema of a disjunctive sorting into the technical or semiotic. Phonetic writing is a mechanism for setting down oral language – but is writing a techni- cal or symbolic system? The decimal position system together with cal- culative algorithms allows a human calculator to ‘mechanically’ solve all the tasks of elementary arithmetic – so is the decimal system a cal- culating instrument or a numerical language? Is software, for example a Helmar Schramm, Ludger Schwarte and Jan Lazardzig - 9783110971910 Downloaded from De Gruyter Online at 09/22/2016 12:31:19PM via Freie Universität Berlin