Replicating Mathematical Inventions: Galileo’s Compass, Its Instructions, Its Students

Questions about how closure is achieved in disputes involving new observational or experimental claims have highlighted the role of bodily knowledge possibly irreducible to written experimental protocols and instructions how to build and operate instruments. This essay asks similar questions about a scenario that is both related and significantly different: the replication of an invention, not of an observation or the instrument through which it produced. Furthermore, the machine considered here—Galileo’s compass or sector—was not a typical industrial invention, but a mathematical invention, that is, a machine that produces numbers, not yarn. This case study describes some of the similarities and differences between replicating experiments, traditional machines producing material outputs, and mathematical inventions yielding calculations or information. This comparison indicates that, as in other kinds of replication, the replication of mathematical inventions involves texts but that in this case bodily knowledge cannot be properly described as either tacit or explicit. It rather takes the shape of memory—muscle memory—that may be recalled from reading the instructions.