The important role of mathematical representations in scientific thinking has received little attention from cognitive scientists. This study argues that neglect of this issue is unwarranted, given existing cognitive theories and laws, together with promising results from the cognitive historical analysis of several important scientists. In particular, while the mathematical wizardry of James Clerk Maxwell differed dramatically from the experimental approaches favored by Michael Faraday, Maxwell himself recognized Faraday as “in reality a mathematician of a very high order,” and his (...) own work as in some respects a re‐representation of Faraday’s field theory in analytic terms. The implications of the similarities and differences between the two figures open new perspectives on the cognitive role of mathematics as a learned mode of representation in science. (shrink)

The sciences use a wide range of visual devices, practices, and imaging technologies. This diversity points to an important repertoire of visual methods that scientists use to adapt representations to meet the varied demands that their work places on cognitive processes. This paper identifies key features of the use of visualization in a range of scientific domains and considers the implications of this repertoire for understanding scientists as cognitive agents.

: In 1856, Michael Faraday (1791–1867) conducted nearly a year's worth of research on the optical properties of gold, in the course of which he discovered the first metallic colloids. Following our own discovery of hundreds of the specimens prepared by Faraday for this research, the present paper describes the cognitive role of these "epistemic artifacts" in the dynamics of Faraday's research practices. Analysis of the specimens, Faraday's Diary records, and replications of selected procedures (partly to replace missing kinds of (...) specimens and partly to understand the "tacit knowledge" implicated in Faraday's research) are outlined, and a reconstruction of the events surrounding the initial discovery of metallic colloids is presented. (shrink)

: Faraday is often described as an experimentalist, but his work is a dialectical interplay of concrete objects, visual images, abstract, theoretically-informed visual models and metaphysical precepts. From phenomena described in terms of patterns formed by lines of force he created a general explanation of space-filling systems of force which obey both empirical laws and principles of conservation and economy. I argue that Faraday's articulation of situated experience via visual models into a theory capable of verbal expression owed much to (...) his strategy of moving—via conjectural visual models—between the phenomenology of particulars (often displayed as patterns) and the general features of dynamical phenomena which he depicted as structures. (shrink)