Sean O'Neil

Across the arts and sciences, symbolic notation is essential for transcribing and disseminating technical information. Many symbolic notations that are still used today were first devised in western Europe during the early modern period. Algebra, music, chemistry, dance—whole fields of knowledge were quite literally being rewritten. This dissertation argues that the broad appeal of notations derived from the fact that they enabled powerful techniques of visual thinking. Early modern people routinely described notations as allowing them to “see” things that they had not previously recognized. However, because established methods of reasoning were predominantly verbal, symbolic notations and the visual thinking that they entailed necessarily challenged received ideas about how knowledge ought to be represented and discovered. In demonstrating how symbolic notations’ credibility was established, this project also argues that their increased use brought on an epistemological rupture that remains an underappreciated legacy of the scientific revolution.