Thursday, October 24, 2013

Cross-referencing an Eclipse

Diagram of an eclipse from a modern translation of Hipparchus
It is not always easy to figure out dates from classical or medieval writings. Chroniclers did not necessarily strive for the kind of historical accuracy which 21st-century audiences expect. When they wanted to be precise, they often expressed themselves in ways that do not provide a proper context for the modern scholar.

Consider, for instance, Pappus of Alexandria, whom the Encyclopedia Britannica calls "the most important mathematical author writing in Greek during the later Roman Empire." [source] He wrote many important texts, but we knew little of his life.

I mentioned the other day how Suidas' Lexicon gives us data on works and events otherwise lost to history. The entry for Pappus reads:
Alexandrian, philosopher, born in the time of the elder emperor Theodosius, when the philosopher Theon also flourished, the one who wrote about Ptolemy’s Canon. His books [are] Description of the Inhabited World; Commentary on the 4 Books of the Great Syntaxis of Ptolemy; The Rivers in Libya; Dream-Interpretations. [source]
We know that Theodosius reigned from 372-395 CE, so it gives us a time frame for Pappus. This creates a small head-scratcher, however. Pappus claims to have calculated and observed an eclipse in the month of Tybi (the fifth month of the Coptic calendar). There is a problem with this dating: no eclipse occurred during the month of Tybi during the reign of Theodosius that Pappus could have observed! Could the Suidas be wrong? Certainly. But then... what is right?

There is, as it turns out, a 10th century copy of a work by Theon of Alexandria (the one mentioned in the Suidas entry) that has a marginal note next to an entry on the Emperor Diocletian (who reigned from 284-305 CE), stating "at that time wrote Pappus." Is it possible that the composer of Suidas had access to that work and assumed that it meant Pappus flourished when Theon did? If we look closer to the reign of Diocletian, we discover that there was an eclipse in the month of Tybi which would place it (using the modern method of dating) on 18 October 320 CE. If Pappus observed it himself in 320, it isn't likely that he was flourishing over 50 years later. This places him firmly in the earlier part of the 4th century.

Pappus is far more important than as an example of the care with which modern historians must date historical events. Some of his eight-volume work on mathematics is extant; and deals with many facets of geometry and carefully lays out the mathematical findings of his predecessors and how their work builds on each other over time. He also worked on several problems such as inscribing regular polyhedrons inside a sphere, conic sections, trisecting an angle, and many more. He has a theorem named after him, as well as the Pappus chain, the Pappus configuration, and the Pappus graph.

His commentary on Ptolemy provides us with insight into some lost works of classical astronomy, such as an astronomical work by Hipparchus on eclipses (illustrated in the above figure).

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