In spite of their practical importance, the connections between technology and mathematics have not received much scholarly attention. This article begins by outlining how the technology–mathematics relationship has developed, from the use of simple aide-mémoires for counting and arithmetic, via the use of mathematics in weaving, building and other trades, and the introduction of calculus to solve technological problems, to the modern use of computers to solve both technological and mathematical problems. Three important philosophical issues emerge from this historical résumé: (...) how mathematical knowledge depends on technology, the definition of the hybrid concept of a computation, and the usefulness of mathematics in technology. Each of these issues is briefly discussed, and it is shown that in order to analyze them, we need to combine tools and ideas from both the philosophy of technology and the philosophy of mathematics. In conclusion, it is argued that much more of interest can be found in the historically and philosophically unexplored terrains of the technology–mathematics relationship. (shrink)

Farmers all over the world perform experiments, and have done so since long before modern experimental science and its recognized forerunners. There is a rich anthropological literature on these experiments, but the philosophical issues that they give rise to have not received much attention. Based on the anthropological literature, this study investigates methodological and philosophical issues pertaining to farmers’ experiments, including the choice of interventions to be tested, the planning of experiments, and the use of control fields and other means (...) to deal with confounding factors. Farmers’ experiments have some advantages over the field trials of agricultural scientists, but also some comparative disadvantages. The two experimental traditions are complementary, and neither of them can replace the other. Several aspects of farmers’ experiments are shown to have a direct bearing on central topics in the philosophy of science. (shrink)