BMCR 2006.03.21

Re-Inventions: Essays on Hellenistic and Early Roman Science. Apeiron 37.4

, Re-inventions : essays on hellenistic & early Roman science. Apeiron, v. 37, no. 4. Kelowna, BC: Academic Print. and Pub, [2005]. 153 pages ; 24 cm.. ISBN 0920980880 $22.95 (pb).

What’s new in the past? The past that we study is largely a human production of words and deeds, thoughts and theories, and thus the human past, like the present and future, contains almost boundless potential to elicit reflection and reaction. A few years ago I was in the audience at Emory when speakers in a conference entitled Reinventions propounded some novelties in the history of Hellenistic science. The five papers of this volume include three of those papers, joined with two new contributions. The goal was to open up the discussion on ancient science by looking at the relatively neglected period that followed Aristotle and preceded Ptolemy and Galen, and by recasting the questions to produce new results. Conference proceedings, like Festschriften, because heterogeneous, can remain under-appreciated — I hope that the papers of this volume will be more widely and deeply received, especially the far-reaching and innovative contribution of G. E. R. Lloyd.

The keynote address by Lloyd appears here as the lead paper, “New Issues in the History of Science” pp. 9-27), presenting his call for an “ecumenical” history of science. Even in the best of circumstances, the past provides a narrative without a causal account, which upon reflection elicits from those studying the narrative a desire to create such an account. It is all too easy to read the narrative as inevitable. Lloyd offers an exciting alternative by challenging historians of science to discover how things developed in other places as the best way to test their explanations of how things developed in the place under study. That is probably the closest one can come to a control experiment in the study of history — so long as such comparison is possible. If we are to study the past or other people at all, we must assume some commensurability, and Lloyd makes good use of several points of contact. His chosen comparanda here are ancient Greece and ancient China, within the fields of mathematics, astronomy, and harmonics. Chinese mathematics have been contrasted with Greek mathematics by describing the Chinese system as less axiomatic and more practical. Lloyd (12-15) accepts the former and rejects the latter: Chinese mathematicians sought to develop a systematic method to analyze and solve problems that went far beyond the practical. Not only did they calculate pi using inscribed polygons of hundreds of sides, they in general sought to establish connections between categories of problems, an approach that was “not deductive, but analogical” (15). Such analogic moves are highly productive in modern mathematics and mathematical sciences, and were probably an important ingredient in ancient Greek medical and biological practice as well. In the study of nature, whereas Greeks had a concept of phusis, the Chinese did not (15-16); moreover, they did not seek the ultimate constituents of things, and instead sought an understanding of the processes of change without postulating a radical separation between perception and reality (17-18). The material to observe was the same, but the style of inquiry differed (18). As in mathematics, so in astronomy — Greeks sought a deductive explanation validated by prediction, whereas Chinese sought to determine patterns (e.g., eclipse cycles) in order to facilitate prediction: in both cases astrology provided a key impetus (19). In harmonics too there were common concerns, such as to elucidate the regularities of scales, but Chinese omitted the methodological debate over perception versus reason as tools of harmonic analysis (20). Science, as Lloyd would define it, is a matter of aims — to comprehend and explain natural phenomena — and that common ground of commensurability allows analysis (22). Moreover, although lacking an explicit concept analogous to phusis, it is clear that the Chinese saw themselves as studying a world of “natural” phenomena, in contrast to the phenomena of spirits and deities, and that too provides a ground of commensurability. As Lloyd argues, the primary referents of natural phenomena themselves provide a shared reality — but do not wholly determine the mode of inquiry (23). We as students should be limited neither to our own perspective nor to an ancient perspective, whether purely Greek or purely Chinese (24-25). It is to be hoped that the ecumenism advocated by Lloyd will continue to bear fruit, and that others will take up the task of learning Chinese (or Sanskrit), so as to read the texts with a wider vision.

Karin Tybjerg’s paper, “Hero of Alexandria’s Mechanical Geometry” (29-56) substitutes for her conference contribution “Texts and Machines: Hellenistic and Early Roman Mechanical Treatises”; she here reconsiders the mathematics of this neglected author, whose five Teubner volumes are rarely read or translated. The works offer a view of geometry and mechanics interacting in ways seen in few Greek texts: Hero’s demonstrations combine numerical examples with mechanical methods and instruments, resulting in a melding of geometry and mechanics (34, 36), in a manner seemingly opposed to Aristotle, who insisted on a radical distinction (Physics 2.2 [193b32-194a13]). Hero transforms Archimedes’ solutions into mechanical systems and describes physical procedures for performing numerical integration of surface areas or volumes of irregular shapes (40-41). When doubling cubes or other solids, various forms of “slide rule”, analogous to Eratosthenes’ device, are employed (41-43). Hero is dealing with the irregularity and complexity of the world within which Plato and Euclid sought to find an underlying regularity and simplicity — or as Tybjerg puts it, Hero “prioritizes completeness over purity of method” (43). In other treatises, Hero performs the converse, and geometrizes his devices, describing their construction as if describing the construction of a diagram (46-51).

Ian Mueller’s wide-ranging paper, “Remarks on Physics and Mathematical Astronomy and Optics in Epicurus, Sextus Empiricus, and some Stoics” (57-87), is also a substitute for the paper given at Emory, “Stars and the Weather” (p. 2 offers an explanation). His aim is to elucidate how mathematics and physics were distinguished in the Hellenistic era, using astronomy and optics as examples. Epicurus’ rejection of the possibility of conclusive demonstration regarding “things on high” (58-61), and the rejection by both Epicurus and Sextus of most of the topics of paideia (61-64), serve to open a larger discussion of mathematics and physics in several Stoic texts by or related to Poseidonios/ Geminus (64-85). Mueller reads the difficult passage in Simplicius In Phys. 2.2 (pp. 292-293) in a way consonant with that of Bowen and Todd, Cleomedes’ Lectures (2004) 193-204: Poseidonios/ Geminus associates causal explanation with “physics” and denies it to “astronomy”, because there the hypothesized causes (geometrical models) are not better known than the observed effect (66-69). Here there is an interesting opportunity for resonance with Lloyd’s work: is it possible that an analogous (but implicit?) epistemological move lies behind the Chinese preference for pattern-recognition over hidden causes in physical explanation? Passages in Strabo (2.5.2) and Proclus that may go back to Poseidonios/ Geminus seem to disclose a similar point of view (72-82), whereas a neglected extract on optics may attribute causal explanation to hypothesis-based geometrical optics (82-85).

James Allen’s subtle paper, “Experience as a Source and Ground of Theory in Epicureanism” (89-106), given at Emory, aims to use texts showing how the medical Empiricists viewed experience to elucidate the view of experience among Epicureans. The Empiricists distinguished peira from empeiria as knowledge based on a single observation from knowledge or memory of repeated observations. This “generous … conception of experience” nonetheless confines experience to knowing that phenomena occur, and does not include any causal account (89-92). Allen notes that this is consistent with the Aristotelian framework in Metaphysics A.1 (980-981), and then argues that Epicureans took a position in consistent with that framework (92-93). The Epicurean method by which theories are falsified or supported involves the “evident”, or ways of grasping it (93-96). For Epicurus, to reject any theory that could explain the phenomena is in effect to reject the phenomena (96-98). That is because the grasp of the evident is ipso facto a (partial) grasp of how even non-evident things can and must occur (98-99). Epicurean epilogismos proceeds from phenomena to other phenomena — unlike the empiricist epilogismos which proceeds to the non -evident (101-104). Again, a possible resonance with Lloyd’s work: could it be that Chinese thinkers analogously eschewed epilogismos to the non-evident?

Finally, the editor’s own paper, “Medical and Ethnic Identities in Hellenistic Egypt” (107-131), studies how Greek medicine plays a role in expressing Greek identity among bicultural residents of Ptolemaic Egypt, and how they perceived medicine. Several points of contrast between Greek and Egyptian medicine are surveyed: Egyptian medicine in all its practices was strongly tied to the civil and religious apparatus of the state, and valued “continuity and authority”, against the “competitive renovation” of Greek medicine (108-112). Egyptian medicine did not conceive a radical distinction between the activities of gods and spirits, on the one hand, and forces of nature, on the other (112-113). Lang argues that the lack of such a distinction contributed to the absence of elaborate medical theory and apparent avoidance of surgery (113-117). Lang studies taxation policy of the Ptolemies in three aspects: (i) residents categorized as “Hellenes”, and thus exempt from the obol-tax, (ii) exemptions from the salt-tax, and (iii) levying of the “medical” ( iatrikon) tax, from 310-175 BCE (pp. 117-125). From this she elicits conclusions about the role of Greek doctors in the Egyptian countryside: the Greek doctors paid from the iatrikon receipts formed part of the civil definition of Hellenicity. Nonetheless, the drugs, amulets, and incantations of Greek and Egyptian practice would likely often have overlapped, rendering rigid distinction impossible (125-130).

Rigid distinctions are rarely possible in history, for no practice or people is an island cut off from the world. The history of scholarship, modern or ancient, shows that fields of study are often defined by their early practitioners, and thus exclude material whose irrelevance they assumed but never established. Just as Lang does with Egyptian and Greek medicine, or Allen does with Epicurus and Empiricists, or Mueller does with mathematics and physics, or Tybjerg does with mathematics and mechanics, so too does Lloyd with Greek science and Chinese science. Hybrid scholarship, like hybrid plants and animals, is the more vigorous and fertile.