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The medieval period is still sometimes dismissed in general surveys of the history of science as a time when science was of little importance to a society dominated by theology. Part of the basis for this view are the rather confused and fragmentary scientific and mathematical texts that have come down to us. Sometimes it appears as though the author was copying something that he or she barely understood. Arianna Borrelli takes on this problem, looking at treatises on the astrolabe, which begin to appear in Latin Europe in the tenth century. She explains that we are looking at summary notes intended to accompany more detailed oral explanations. Recipe-style instructions ("If you would understand this," or "Do this") indicate that readers were meant to learn by doing, actually constructing diagrams or models for themselves. The same analysis she holds to be true for early geometry texts, which placed most of their emphasis on the diagrams and gave short shrift to Euclid's rational-deductive process.
Ptolemy himself was thought to have invented the astrolabe in the second century, and "The Planisphaerium," a work attributed to him, was the basis for most medieval collections of astrolabe-related materials. The Arab world was familiar with the instrument by the eighth century, and it was introduced into Latin Europe in the tenth. Along with the physical object came a collection of texts, explaining how to make and use the astrolabe. The principal technical problem was the projection of the sphere of the heavens onto the plane surface of the front of the astrolabe. Carefully made diagrams usually accompanied the instructions for this process, and Borrelli asserts that these were crucial to understanding. The reader needed to draw the diagrams himself in order to internalize the knowledge they contained. Some of the treatises seem to have been notes from lecture-demonstrations, where the note-taker exhorts himself to commit various points to memory. In the later Middle Ages, the written word became more dominant as a transmitter of knowledge, and the earlier texts were replaced by more literary, narrative ones. Already in the eleventh century Hermann of Reichenau had composed a treatise on the construction of the astrolabe, because, he said, those in existence were "muddled, obscure, and sometimes mutilated" (p. 89). Borrelli thinks that his treatise, long assumed to be based on a lost original, was probably derived from practice more than from the abovementioned texts.
What was the use of the astrolabe, and why was it considered such a significant invention? Modern scholars have puzzled over the seemingly useless or non-functional exercises that were part of astrolabe treatises. As a tool for celestial observation, it was too small for precision; as a timekeeper [End Page 776] it could measure only very large units of time, and yet the manuscripts are full of experiments designed for these purposes. For determining the depth of a lake, for example, Borrelli imagines the difficulty of the practitioner balancing his astrolabe while bobbing up and down in a small boat and trying to determine time lapses of a few minutes as the weighted plumb bob descends to the bottom and, shedding its load, rises again to the top. Other, more effective methods of marking time were available but were not considered so prestigious.
Borrelli argues that the astrolabe was not so much a working tool as a model of the heavens. It may not have been very useful for actual time-keeping, but what it could demonstrate was how time itself was created by the marvelous revolutions of the celestial spheres. "Thanks to the astrolabe," she writes, "as a structure to be understood and as a tool to be used, the human mind could grasp the 'architectonica ratio,' according to which the Divine Artifex had created the world" (pp. 25–26).
The core of the book is a close analysis of an eleventh-century astrolabe manuscript in the Bibliothèque Nationale in Paris (MS lat. 7412). General readers may want to pass over this section, but...