Imagined Civilizations: China, the West, and Their First Encounters by Roger Hart (review)

Moral and intellectual refinement distinguished the inhabitants of the Zhou (1045–770 BCE), Tang (618–907 CE), and Song (960–1279 CE) dynasties from their surrounding uncivilized neighbors. Chinese historiography largely concludes that sages invented scripture and painting, thus enabling elites to form identity through the recording of traditions. Carpentry, pottery and textile production, medicine, music, and archery all contributed to the building of social order and the unification of the territory. Among all these knowledge fields and techniques, Roger Hart inquires into the role of mathematics as a measure of civilization, examining the decline of late Ming mathematics around the advent of Western learning (xixue). Imagined Civilizations critically reviews the historical binary of “East” versus “West,” concluding that world history of science prior to the scientific revolution needs to be rethought (p. 262).

This book is about prerogatives of interpretation around mathematics and modernity, development narratives and hero stories in the historical study of knowledge, truth, and systematic learning. Inspired by Benedict Anderson’s 1991 discourse on nationalism, Imagined Communities, Hart looks at “civilization” as an imagined sense of belonging, illustrating how individuals therein employed, repeated, and generalized notions of superiority in skills and knowledge for political and social aims. Carlo Ginzburg inspired Hart’s view of world history as one venerating small details—what Hart calls a story best told in the exemplary study of emergent conflicts or “local collaboration between the members of a small group of Chinese scholar-officials and Jesuit missionaries” (pp. 28–29). A thorough reenactment of the fangcheng practices in linear algebra (pp. 134–58) and related recordings thereof in early-thirteenth-century Italian and seventeenth-century Chinese mathematical treatises (pp. 173–91) divulges the existence of mathematics, numeracy, and calculation beyond scholarly realms, and reveals Xu Guangqi (1562–1633) (chapters 5 and 6) as a talented compiler of memoranda rather than a grand scientist-mathematician collaborating with Jesuits from the West, the more-often-told story.

Reenactment also marks the book as a whole. Six of the seven chapters build on Hart’s previous publications. In chapter 2, his “Beyond Science and Civilization: A Post-Needham Critique,” East Asian Science, Technology, and Medicine 16 (1999): 88–114 is expanded to include extensive reviews of twentieth-century history debates on science being the measure of civilization. Chapter 3 on language and translation was “Translating Worlds: Incommensurability and Problems of Existence in Seventeenth-Century China,” Positions: East Asia Cultures Critique 7, no. 1 (spring 1999): 95–128. The analysis of mathematical textual traditions (chapter 4) and practices of mathematics during the sixteenth and seventeenth centuries (chapter 5) both synergize and aggrandize Hart’s decade-long study of Ming mathematics, in particular his 2010 work on linear algebra, The Chinese Roots of Linear Algebra.

Chapters 5 and 6, which focus increasingly on Xu Guangqi, highlight Hart’s current preoccupation that mathematical practices and texts show how “scholars often recorded practices that they did not fully understand.” When he asserts that “17th century texts provide a good enough basis for the reconstruction of mathematical practice” because they are “unlikely to have been tampered with” (p. 29), he also refers to Zhu Zaiyu’s New Theory of Calculation which, though compiled by 1581, was only engraved in 1604, and thus long remained exclusive to the court. Elite writings are Hart’s source to develop the premise of an earlier study—that much of higher mathematics ultimately had a non-literate origin. Chronologically, erroneous texts indicate how scholars may have misunderstood things, yet whether false recording verifies the genuine mastery of such techniques by contemporary practitioners or is simply the ultimate loss of such knowledge requires further scrutiny.

Hart’s thoughtful arrangement frames his past and current research into a step-by-step guide to the intricacies of studying China and its mathematical sciences. His very personal reflection on his own education and formation as a historian of both subjects provides ample evidence of...