Chasing Shadows: Mathematics, Astronomy, and the Early History of Eclipse Reckoning

CHAPTER FOUR: Beyond the Appearances: Greek Eclipse Reckoning

CHAPTER FOUR  Beyond the Appearances Greek Eclipse Reckoning 4.1 Overview Theon of Smyrna says that Babylonian astronomers using arithmetical methods, succeeded in confirming the observed facts and in predicting future phenomena, but that, nevertheless, their methods were imperfect, for they were not based on a sufficient understanding of nature, and one must also examine these matters physically. —As paraphrased by Evans (1998) p. 214, from Theon of Smyrna, Mathematical Knowledge Useful for Reading Plato (III, 30). Scrupulous accuracy about such a small amount is a sign of vain conceit rather than love of truth. —Ptolemy, Almagest VI, 7, as translated by Toomer. In the fifth century BCE, methods to predict eclipses as developed by Mesopotamians were far more advanced than those of their Greek contemporaries. There is no evidence to suggest that the early Greek astronomers were experimenting with numerical patterns in any way comparable to the Mesopotamians at this time. However, as was even recognized in their own times, as in Theon of Smyrna’s account centuries later, ancient Greek thinkers were engaged with the celestial phenomena, and in ways that were new and unprecedented. Astronomical alignments beckoned to them in ways that drew them beyond the surface appearances to considerations beyond what they observed directly. With such aspirations, these early thinkers thus initiated for the first time theoretical dimensions for the investigations concerning eclipses. 99 CHASING SHADOWS Nascent philosophical reflections had set the groundwork for thinkers to be mindful of the distinction between facts as they might manifest themselves apparently and what they might be really. Explanation emerged as an ambition, as increasing attention was paid to conditions not within the appearances but able to be inferred from them. Greek ambitions reveal that once theory begins to direct people’s consideration of celestial appearances then the functions that astronomical observations can serve are soon deepened. Those inquirers who first dealt with empirical considerations by theoretical modes of questioning and reflection, initially experienced countervailing pressures to their efforts, but in time encountered richly compounding inducements to further that new mode of investigation. Among the earliest astronomical questions posed by Greek inquirers were those that concerned the calendar, and the connection between the structuring of the year and the rising, setting, and general patterns of movement of the stars and planets. Such a focus was common to many early cultures. However, what set the Greek inquirers apart from all other peoples at the time was the emergence of questions about the physical structure of the earth and the heavens, and their relation to these calendrical questions. When calendar problems were combined with concurrent cosmological speculations, such as the proposal that the heavens are rotating concentric spheres, first articulated by Eudoxus of Cnidus in the fourth century BCE, an entirely new mode of investigation in astronomical research was unleashed. Investigations into when and where the stars and planets rise, set, and move across the sky, were addressed primarily by a qualitative study in celestial spherics—a search beyond the appearances. Accordingly, early sources reveal attempts by the Greeks to comprehend, on a cosmographical level, the physical causes that brought about eclipses, something that their Mesopotamian contemporaries (as far as the extant evidence suggests) were not doing. In fact, as emphasized in the previous section, the sophisticated arithmetical patterns of the Mesopotamians are an example of the limits to which astronomy can progress without the existence of any suppositions about the shape and dimensions of the earth and the celestial realm. It was the cosmographical proposals of the early Greek astronomers considering that the earth and the luminaries are spherical in shape, their relative positions , their illuminations and so on, that gave direction to early astronomical researches. With such propositions in hand, the Greeks began to experiment with geometrical models to describe the movements and patterns of the heavenly phenomena—those very features that the Mesopotamians had advanced by means of numerical accountancy. These geometrical conceptions were able to emulate the general qualitative patterns of the celestial motions, but a further step was needed to make 100 BEYOND THE APPEARANCES these models truly replicate the astronomical phenomena. This was to apply numbers and magnitudes to these models so that sizes, distances, and timings were consistent and reflected what was being observed. Perhaps surprisingly, Greek thinkers were slow to seek such quantitative potential for the models. Inspiration came from afar. With no significant sources...