The Emergence of Symbolic Notation and Data Visualization in Algebra and Chemistry

This award supports doctoral dissertation research in history of science that focuses on the use of mathematical and chemical symbolism. Such notation is currently regarded as essential to scientific work. By contrast, for much of Western European history, the use of symbols in science was not regarded as a suitable approach. However, by the nineteenth century, symbolic notation had become ubiquitous. This project's objective is to explain why European scientists came to see symbolic notation as credible during the early modern period. To identify when and how scientists used symbolic notations, the researcher will study scientific manuscripts, where the exigencies of publishing did not constrain the use of symbols. These include mathematicians' and chemists' notebooks, apothecaries' inventories, doctors' records, and manuscript textbooks, all of which are unique and un-digitized. The results of this project will shape how symbolic notation and visual thinking are understood by historians of science and more broadly. They will show the limits of historical methodologies that invest too heavily in a distinction between language and image; symbolic notations were powerful precisely because they blurred the line between these two domains. More broadly, they will show how effective design can be improved through consideration of visual objects that are not admitted under a strict definition of data visualization. Finally, they will be disseminated to secondary students through lesson plans and classroom tools created by the researcher, a former high school instructor, to provide another means by which teachers can provoke interest in STEM fields, and to show students that the union of the sciences and humanities can lead to productive thinking.

By examining how symbolic notations came to be seen as credible during the early modern period, this project presents a deeper historical understanding of how 'visual thinking' and data visualization developed. Today, diagrams, drawings, charts, and pictures are indispensable tools for displaying data and identifying patterns within that data. However, the ancient and medieval methods of scientific reasoning that early modern scientists inherited were fundamentally verbal, and some scientific traditions distrusted images altogether. The epistemological validity of visual thinking therefore had to be proved. This project posits that symbolic notations played a crucial role in that process during the early modern period. Because symbolic notations could be seen as either linguistic or pictorial, they gave scientists a way of experimenting with visual thinking while still being able to characterize it as verbal thinking. Symbolic notations, in other words, served as a conduit through which the validity of visual proof could be established by means of an appeal to verbal proof. Moreover, it is argued that, over time, as scientists became accustomed to the advantages of visual thinking afforded by symbolic notations, they became bolder in their experiments with other visual tools like diagrams, charts, and graphs. This project thus demonstrates an underappreciated legacy of the Scientific Revolution: namely, that the legitimization of visual thinking in science was predicated upon the development and application of symbolic notations.