BMCR 2004.03.47

Science and Mathematics in Ancient Greek Culture

, , Science and mathematics in ancient Greek culture. Oxford: Oxford University Press, 2002. xvi, 379 pages : illustrations ; 24 cm. ISBN 0198152485. $85.00.

The excellent collection of essays edited by Tuplin and Rihll (hereafter TR) reflects two major changes that the history of ancient science has experienced in the last thirty years. First is the great broadening of materials considered relevant to the field. Whereas in the not so distant past scholarship would concentrate on a few great works by a few great men, the modern historian of ancient science takes advantage of a much wider range of sources, including, for instance, materials documenting connections between magic and medicine or astrology and astronomy. The second major development has been an increased attention paid to the broader social context out of which scientific practices emerged. Economic and political forces have come to be recognized as important determinants of scientific activities, as have the close connections between practical achievements and theoretical innovation.

Both developments are central to the aims and achievements of TR’s anthology. Its sixteen papers (and a substantial introduction) arise from a 1996 conference in Liverpool that sought to bring together scholars working in diverse areas of ancient science, including mathematics, astronomy, mechanics, chemistry, medicine, and technology. The aim was not just for participating scholars to share their findings with one another but to demonstrate the relevance and value of historical studies of ancient science to what the editors term “mainstream” classicists and ancient historians. On the whole, the papers succeed in doing this by emphasizing precisely the two trends that have transformed the field. Because so many different and complex papers cannot be adequately treated in a limited review, I shall highlight what seem to me the contributions of greatest interest to the readers for whom the collection is intended.

Several essays offer new insights by crossing old, restrictive borders. Andrew Barker’s “Words for Sounds” succeeds brilliantly in showing how scientific terminology in Greek acoustic theory never fully loses metaphorical connotations that go back to Homer. As early as the first efforts to treat sound scientifically in Archytas and Aristotle, and as late as Ptolemy, key acoustic terms surrounding concepts of such as those of pitch ( ὀξύς) always carried connotations of what is perceived as physically piercing.

In a practical-pedagogical vein, J. L. Berggren shows how an instructor may go beyond the usual reliance on texts and use “Ptolemy’s Maps as an Introduction to Ancient Science.” Beginning with maps drawn according to Ptolemy’s directions, Berggren shows how details that might appear to be of marginal importance can in fact reveal the Greek geometrical model of the cosmos and be used to measure the earth’s circumference and to determine locations of cities by their maximum length of daylight. This approach offers fresh insights into how ancient Greeks viewed the world and their place in it.

Liba Taub’s “Instruments of Alexandrian Astronomy” shows what can be gained when ancient astrological interests are taken into account by historians of astronomy. Taub attacks the mystery surrounding the Alexandrian equinoctial rings, instruments mentioned dismissively by Ptolemy, and not well understood by modern historians. She locates their function in astrological predictions used in areas of daily life ranging from weather forecasting and agriculture to medicine, throwing welcome light on neglected aspects of Alexandrian astronomical interests and practices. A similar practical grounding is found by R. Hannah for “Euctemon’s Parapegma,”an early solar calendar in use in Athens. After finding its origins in the official need to regulate Athenian religious festivals, he goes on to suggest that non-scientific needs and interests may lie behind early Greek astronomy generally.

In another major paper dealing with astronomy, Alan Bowen asks when Graeco-Latin astronomy became predictive in its intent as opposed to the explanatory emphasis of its earlier history, taking as his focus the predicting of solar and lunar eclipses. Bowen finds the motivation for the shift to prediction not in any technical scientific or mathematical problem but in a literary trope progressively elaborated by a series of Roman authors, none of whom was an astronomer.

Editor Rihll and J. V. Tucker deliver a bravura survey of ancient technical knowledge in “Practice Makes Perfect: Knowledge of Materials in Classical Athens.” Concentrating on the vast silver industry at Laurium in Attica, the authors identify a body of complex practical knowledge that was formed and maintained in almost complete isolation from theory. After exploring the technical, economic, and social dimensions of the mines, they conclude with a careful seven point comparison between practical knowledge on the one hand and theoretical knowledge on the other. The paper offers illuminating insights to practitioners in many areas of ancient studies.

Other worthwhile papers must receive more limited mention. Serafina Cuomo begins with a neat logical analysis of the argument of Hero of Alexandria’s Belopoeica (War Machines) in “The Machine and the City,” before linking this neglected work to the very practical concerns of a city’s survival in the period of Roman expansion, expressed rhetorically in terms of the Hellenistic philosopher’s pursuit of ataraxia. Reviel Netz imagines the faces that might be included in “Greek Mathematics: A Group Portrait.” Combining careful combing of sources with a good deal of plausible speculation, Netz finds an exceedingly small group of amateurish autodidacts working in a tenuous network extending over the centuries. In doing so, he provides a model for considering the place of the intellectual in a world of limited literacy and higher learning. J. R. Milton considers “The Limitations of Ancient Atomism.” He attributes the theory’s limited appeal in the ancient world in part to the status of Epicureanism as an almost secular religion, which one joined as one would join a sect, and in part to the limitations imposed by a rigid distinction between the full and the empty. As for its equivocal reception in modern science, the major factor is found in a contrast between the aims of ancient vs. modern atomism: ancient atomists, as part of their opposition to the Stoics, resisted reducing nature to a machine as an artifact of a creator, while their modern counterparts (Boyle and Newton, for instance) sought precisely to provide testimony for the existence of a creative deity which worked through a mechanized nature. Vivian Nutton devotes his essay to a survey of the revival of interest in ancient medicine in recent decades. He asks in particular why so many once standard assumptions about the field have been discarded, and answers by tracing a broadening of the subject that has made post-Hippocratic physicians, and Galen in particular, emerge into new importance. In “Galen on the Seat of the Intellect,” Tuen Tieleman considers the theoretical aspects behind Galen’s experiments to locate the bodily organ in which the soul was located. While using the philosophical tradition in at times innovative ways, Galen was also a captive of the tradition, ending up as a kind of empirical Platonist. Rihll’s excellent introduction, “Ancient Science in Context,” should also be mentioned. It is a concise overview of how Greek scientific accomplishments have come to be “not only admired, but also studied, analysed, criticized, and contextualized” (p. 21). One is reminded of her very fine Greek Science (Oxford, 1999), which is perhaps the most accessible up-to-date survey of the field available.

Other papers, while reflecting the aims of the collection, seem likely to have more limited appeal. Harry Hine surveys a wide variety of sources to determine whether a coherent scientific interest in seismology and vulcanology can be detected — poetry, history, letters, philosophical and scientific works are all considered. While Hine does show clearly the extent to which ancient philosopher-scientists relied on popular reports for their data, he resists giving a definite conclusion to his main question. J. J. Coulton describes Hero of Alexandria’s dioptra as a rather impractical surveying instrument inspired more by theoretical issues in mathematics than by practical surveying. C. Anne Wilson traces a knowledge of chemical techniques useful for “Distilling, Sublimation, and the Four Elements” to Pythagorean cultic practices.

A few papers are more narrowly, which is to say traditionally, focused, despite the aims of the conference and the volume. E. Hussey’s treatment of “Aristotle and Mathematics” is not without interest — Hussey argues that Aristotle is at once philosopher, scientist, and mathematician, and surveys Aristotelian ideas of applied mathematics in the area of force and motion along with more theoretical questions of demonstration and scientific principles. A ‘mainstream’ classicist curious about these topics will find Hussey clear and comprehensive. But he or she will not find much that reflects the new trends in history of ancient science that provide the focus for other articles in the collection. Similarly, C.M. Taisbak, in “Euclid’s Elements 9.14 and the Fundamental Theorem of Arithmetic,” speculates as to why neither Euclid nor any other Greek mathematician attempted to formulate let alone prove the theorem that every number is either prime or a product of primes in one way only, limiting his explanation to factors internal to Greek mathematics.

The collection is made more useful by several features. Footnotes give full bibliographic citations, sparing the reader the need to flip back and forth from an article to the end of the book. But all citations are also gathered in a comprehensive bibliography at the end as well. An index locorum and an extensive general index further add to the usefulness of the volume. In short, a collection with much to offer to a variety of readers.