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

Clemency Montelle
Johns Hopkins
Publication Date: 
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[Reviewed by
John McCleary
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Eclipses are among the most spectacular natural phenomena. Anyone who has experienced a total solar eclipse will testify to the effect it has, making eclipse watchers of us all. This fact has been true for all of recorded history; the earliest records of eclipses are found in the omen literature of the ancient Near East, from the Old Babylonian Period (ca. 2000–1600 B.C.E.).

The belief that solar and lunar eclipses were portents of significant phenomena led early skywatchers to record their occurrences. Beyond their frequency, date and time, it was important to know the color of the sun’s disk and the direction of impact of the moon on the disk. The many observations led them to discover a periodicity that allows prediction. The Mesopotamian cultures focused on arithmetic periodicities deduced from previous observations, together with some sophisticated uses of what we would recognize as zigzag and step functions.

It was more prudent to predict eclipses that might not happen than miss one predicted by their model. The methods of the astrologer-scribes suggested a minimal period of 5 months between lunar eclipses, which helped make sure non-predictions were correct.

Greek astronomers in the 5th century B.C.E. were not as advanced in eclipse prediction as their neighbors in the Near East, but their intellectual impulse was to seek explanations that distinguished between apparent phenomena and their underlying causes. This philosophical turn led to the development of geometric models, principally based on spheres. In this context an eclipse is an alignment of spheres, which represents a major step forward in understanding eclipses.

In the 2nd century B.C.E., in order to match theory to the Mesopotamian arithmetical procedures, numerical relations were brought into spherical mathematics in order to produce predictions. With further development, and especially the development of trigonometry, the mixture of numerical patterns with a powerful geometric model led to pinnacle of theoretical astronomy in the ancient world, Ptolemy’s Almagest.

The most extensive chapter of Montelle’s book is the chapter on Indian astronomy. “Premodern” India includes the whole period from ancient times up to the nineteenth century, when European science replaced Indian ideas. Many features distinguish Indian science: It was preserved in a kind of “scientific poetry” whose metrical requirements sometimes forced the composer to eliminate necessary material in order to conform to the meter. This poetry reflects and fosters an oral tradition, but it was eventually written down, and the historian has to face some three million such scientific texts.

The reliance on oral tradition and the belief that basic texts came from gods held Indian astronomy fixed. Change did come, however, from external sources. Five major “intrusions” have been identified: Mesopotamia via Iran (5th century B.C.E.), Mesopotamia via Greece (2nd and 3rd centuries C.E.), Greece (4th century C.E.), Iran (10th to 18th centuries C.E.), and Europe (18th to 20th centuries C.E.). Montelle discusses the important foundational texts regarding eclipses from each era, together with their methods, noting methods shared with external sources.

The final culture to be considered is Islamic (700–1500 C.E.). It was an empire at times and many disparate nations at others, and at its peak spread from Spain to India and into central Asia. With a strong respect for scholarship, Islamic astronomers acquired, studied, critiqued, and developed astronomical texts from India and Greece. By the beginning of the second millennium, the astronomy of the Islamic Near East had attained a character of its own and that spread across the Islamic nations. Astronomers attained a command over observation and theory that set the standard for the modern West.

The book focuses on eclipses and the ideas that ancient cultures grappled with in order to understand and predict their occurrence. The story is set in the context of the progress of astronomy across millennia. The challenges set by such scholarship are manifold — few documents/too many documents, ancient languages, unfamiliar mathematics, incorrect observations, etc. Montelle has overcome these obstacles and contributed a significant addition to our understanding of premodern mathematical astronomy. The book sets a high standard for scholarship, and is written in compelling prose. It will be the standard reference for the history of eclipses.

John McCleary ( is Professor of Mathematics at Vassar College.

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