Practical Geometry and Operative Knowledge

Knowing and Doing

There is much more to be said about the history of natural knowledge, and of such related technical skills as mathematics, than can be contained within accounts of discoveries, explanations, ideas, schools of thought, and philosophical argument. With the current acceptance of a wider cultural engagement for the history of science and a richer, more inclusive narrative comes an acknowledgment that attitudes toward primary evidence also need to be broadly based. Books and manuscripts are augmented by instruments, collections, maps, and buildings, and even by reconstructions and replications. One spur to greater inclusiveness is the realization that the general tendency to impose irrelevant relationships and distinctions onto the past is particularly problematic in the history of science. The realization is far from new, but the refinement of sensibility it creates shows no sign of having reached its limit. Such is the result of building a discipline on writing the history since ancient times of a category of learning and practice—namely, “science” in the sense understood today—that was created only in the nineteenth century.

Historians of science are thus increasingly concerned with the evidence offered by instruments, or at least are increasingly engaged in instrument studies. The caveat needs to be added, because this development in the discipline has not always been acknowledged by those who care for the collections of instruments—namely, the museum curators, much less the private collectors. Complaints from instrument specialists about the lack of interest in their collections among the historians are almost as commonly heard now as they were in former years, when they might have been justified. This is at first surprising and frustrating, and might temptingly be attributed to mere lack of awareness on the part of curators, but the two approaches to instruments can seem so distinct as to have little to say to each other. This is both mistaken and injurious to either side. Historians have much to learn from the inclusive picture of the surviving corpus of instruments, as well as from selected categories or examples; while curators need to extend their interpretive skills beyond technical competence and connoisseurship.

This paper contains two parallel proposals, both of which are further attempts to avoid foisting inappropriate assumptions on the past: one concerns disciplinary boundaries, the other the motives of practitioners. In the first case we need—the evidence demands—a more inclusive view of the instruments of the period of the Scientific Revolution, and of the disciplinary area associated with most of them, namely practical geometry. In the second case, this can be achieved only in parallel with yet another disavowal of intruded assumptions, namely, that knowledge is the principal object and commodity of the practitioners.

The former focus on “a radical transformation of scientific ideas” as the “canonical” account of the Scientific Revolution ¹ made it difficult to accommodate certain historical figures without awkwardness and embarrassment. As one example, concerning a figure of pivotal importance, we were told by the Dictionary of Scientific Biography that Leon Battista Alberti

shared the preoccupation of a great number of fifteenth-century scholars, considering mathematics as a tool rather than an independent science. . . . Thus, geometry was used to calculate the height of a tower, the depth of a well, the area of a field. . . . In all of this work [machines, instruments, surveying, navigation, hydrography] he manifested more interest in manual crafts than in true science. . . . he seems to have regarded science as a means for action rather than as a system of organized knowledge. On many occasions he admitted his interest in knowledge, but more for reasons of efficiency than as an abstract science, as power rather than as intellectuality. ²

The disapproving tone reflects a tension between the received historiography and the author’s sensitivity to Alberti’s program and, we note, that of “a great number” of his contemporaries. This is not a complaint that Alberti spent too much time on practical matters when he might have followed a higher calling in mathematical theory, but rather that he imagined mathematics to be a matter of practice and so, in some sense, misunderstood the...