Targeting Zero

This project deals with the development of mathematical understanding in Western Europe and its ramifications on literary vernacular texts. The main research question concentrates on the importance of the evolution and establishment of zero as a number, as an intellectual paradigm, and as a means of calculation in the Late Middle Ages and the Early Modern Period. The zero as a means of broadening our mathematical horizon and therefore gaining a new approach to the empirical understanding of the world can be seen as the beginning of a paradigmatic shift towards scientific thinking. This is accompanied by the development of a specialised, scientific German language that slowly emerged as a result of the translation of Latin texts. Therefore I will focus on the connection between literature and the development of science by looking at the traceable development of the inclusion of i.e. the words ziffer and nulla figura (Null) in the German word pool. A first goal of this research project is to create a database that includes a cross-referenced and annotated list of references relevant for German-language texts. Keywords- and phrases of different genres will also be included to prove the transmission and transformation of mathematical thinking via linguistic and hermeneutical means. In a second step the project will expand the collection of references and will concentrate on the contextualization within the texts itself and the literary genres they are attributed to. This will provide first findings within certain frames of references which will be connected to each other in a third step that concentrates on combining the findings and placing them within a larger context. Identifying fields of discourse within and beyond genres as well as their transformation over time will be part of this last step. An important result of this research project is to develop and provide a method to examine literary vernacular texts with regard to their relevance to the transmission, incorporation and processing of academic information. This will provide a tool to make the linguistic signs of an intellectual discourse evident and to help to better understand the complexity of literary texts. Looking at the establishment of zero in Western Europe means to understand the underlying important change in mathematics and natural philosophy. The findings of this project as well as the developed method will contribute to a better perception of underlying processes of exchange and interdependencies of different disciplines. The importance of literature to mirror academic progress will be of particular interest to show that already at that time literature can be seen as a catalyst that jumpstarts, accompanies, and triggers scientific ideas.

This project aimed to understand how Hindu-Arabic numerals, particularly the zero, were introduced into the German-speaking world. The terminology for zero underwent significant changes over time: initially, it was known as a "cipher" or "figure of nothingness" and only gradually established itself with the introduction of the positional numeral system. This raised questions such as: Is zero a number? Is it compatible with the Christian worldview? Is it resistant to forgery? Consequently, the project also sought to determine when and how zero was integrated into the intellectual framework. The algorism, as the genre of text that widely introduced Hindu-Arabic numerals in Europe, was studied in connection with land surveying and literature. It was shown that the use and knowledge of Hindu-Arabic numerals in German-speaking regions occurred much earlier than previously assumed. The term "cipher" was analyzed in a separate study, which revealed that, contrary to general belief, early uses of the term did not refer to the zero but to the Hindu-Arabic numeral symbols. This finding is particularly significant for early mathematical literature, where "cipher" means zero. The simultaneous use of the term for both zero and numerals reflects terminological uncertainty, which persisted even in Luther's time. In addition to these studies, the symbolic use of zero in literature was also examined. In Fortunatus, a popular tale addressing early capitalism, zero is associated with the female reproductive organ and its fertility. Similar to the allegory of fortune, depicted as a woman who multiplies wealth with her magical pouch, the zero functions as a wealth multiplier when appended to a number. In the text, the pouch acts as a decimal calculating machine and a cornucopia embodying the properties of zero. Mystical interpretations used zero as a precursor to existence. Rulman Merswin, in his Book of the Nine Rocks, imagines a "null level" as a point of departure where things merge. From this level, both ascent to God and descent into hell are possible. A study of numeration in 15th-century manuscripts from Klosterneuburg Abbey demonstrated that Hindu-Arabic and Roman numerals did not compete but complemented one another in the art of numeratio. However, zero remained a challenge even in the late Middle Ages, especially with tens and hundreds, where numbers were often written out to avoid using it. Clear differences were found between the learned Latin culture and the practical German context, which included trade, crafts, and literature. Ultimately, the project highlighted the relevance of zero in German cultural and intellectual history, emphasizing its significance in mathematics, literature, and mysticism.