Talk – Understanding by Doing: Theorems and Construction Problems in Chinese Translations of Euclid’s Elements

In this talk I will analyze how deductive structure and modalities of proof were communicated through language by the translators of Euclid’s Elements into Chinese and framed in new and local conceptual terms. Far from being a literal translation of the original, the Chinese versions reflect how the co-translators, each with their own cultural and philosophical backgrounds, made sense of a canonical text. “Understanding by Doing” in the title of this contribution is not simply a pun to “learning by doing”. Neither Matteo Ricci nor Xu Guangxi was a professional translator and their Chinese Elements (1607) was the first translation of Western mathematical writings in a series to come. “Understanding by Doing” in the title also hints to Gadamer’s point “that the experience (Erfahrung) of meaning that takes place in understanding always includes application” even if “this whole process is verbal” (Gardemer, Truth and Method). Through a close reading and linguistic analysis of key propositions in the Elements and their Chinese translations, I shall question the relevance of the aspect of “application” in understanding: how to detangle this aspect of understanding a text in a foreign language from the constructivist and algorithmic formulation adopted in the stylistic code to translate the logical deduction of theorems and the construction of geometrical objects?