Thinking and Acting with Diagrams

In 1303 Wang Zhen published the agricultural treatise Nongshu 農書, in which he included in tabular form instructions for, amongst others, the best period for sowing different kinds of crop. These tables were accompanied by further textual explanations with the obvious goal of guiding the reader to agricultural improvements (Bray, this issue). In 1996, the Bank of England produced fan charts in its inflation report showing the range of uncertainty in its inflation forecasts. These charts were accompanied by an explanatory text intended to guide the reader in understanding the diagram (Boumans, this issue). When the famous ancient mathematical text Zuobi Suanjing 周髀算經 (The Gnomen of the Zhou) was re-edited for the Complete Library of the Four Treasures, the restructuring of textual elements added another layer of interpretation to a fundamental text explaining how to perform mathematical calculations (Chemla, this issue). Imperially commissioned in the early 1770s, this edition appeared around the same time Benjamin Franklin was jotting down dots into a tabular system to keep track of his moral improvements, a system he explained in his Autobiography first published, in French, in 1793 (Maas, this issue).

These four cases, together with two other articles by Hsiang-Ke Chao and Mary Morgan, and a field review by Chiara Ambrosio, constitute this special issue, "Thinking and Acting with Diagrams." Diagrammatic reasoning has been an important topic in recent studies in the history and philosophy of science and technology. This special issue contributes to the discussion by offering the studies that treat the questions of how to think and act with diagrams in the history and philosophy of science and technology from widely different time periods and geographical areas. Diagrammatic reasoning is (at least) two-dimensional; reasoning with diagrams is a form of visual reasoning that takes place in space. This common feature of diagrams is prominently present in the six original research papers as well as the field survey article in this special issue, covering historical and contemporary examples and comparative studies of East and West.

Space is of central importance in Hsiang-Ke Chao's comparative essay on economic geography. Chao examines different diagram-based modeling strategies of nineteenth-and twentieth-century economists and sociologists to discover regularities in the geographical distribution of towns and villages in Germany, the United States and China. By going through a wide range of examples from different scientific disciplines, especially economics, Mary Morgan provides an in-depth discussion of the cognitive and inferential work done by and with diagrams. The importance of diagrams as a form of spatial reasoning springs out as an overarching theme in Chiara Ambrosio's historicophilosophical reflection on diagrammatic reasoning in science and technology. In this short introduction to this special issue, we would like to highlight the importance of space in diagrammatic reasoning, and how this may challenge longstanding distinctions between image and text, inductive and deductive reasoning, and the meaning of what diagrams are. Before we do so, we say a few words about the origin and gestation of this special issue.

The original impetus for this issue came from the increased and still increasing interest of historians, philosophers, and sociologists of science and technology in the role of visual artifacts in the formation and transmission of scientific and technological knowledge. To examine one of these artifacts more in depth, and also to see if new insights could be gained from a combination of scholarship on Chinese and Western science and technology, Hsiang-Ke Chao and Hsien-chun Wang organized a conference on diagrammatic reasoning at National Tsing Hua University in Taiwan from which the present collection of essays, after the normal review process, was retained. There were two important reasons to focus on diagrams and diagrammatic reasoning. The first was inscribed in recent scholarship on model-based reasoning, as can be found in the work of Michael Weisberg, Marcel Boumans, Mary Morgan, and many others (see, for example, Morgan 2012; Boumans 2004; Weisberg 2007; Matthewson and Weisberg 2009). The second, in the already-mentioned wish for a treatment of diagrammatic reasoning that would extend beyond the confines of the history of Western...