The work of Roger Billard
The year 2012 marked the 40th anniversary of the publication of L'Astronomie Indienne. Investigation des textes sanskrits et des données numériques by the French Sanskritist Roger Billard (1922-2000), published in Paris in 1971 by the École française d'Extrême-Orient.
The Program Deviations
Billard's approach depends on a carefully controlled comparison between the mean longitudes of the Indian canons and those known from modern celestial mechanics. Such a comparison is not, of course, very novel, but it was done in such a systematic way, and coupled with a statistical analysis, that it amounts to a new strategy. The program made available here is simply a Windows App which makes this available in a clear and immediate form. Not only does it show the results for the Indian canons (so reproducing Billard's results) but it also shows the application to a very wide range of canons from other sources.
The program Deviations may be downloaded here:
This program serves as a laboratory for the exploration of mean longitudes, and to some extent also the true longitudes. The wide range of data on which it is incorporated is based on an exploration of astronomical canons from all periods, both manuscripts and printed sources, which I have explored over the years.
An example of the display of deviations curves is shown here here, in the famous instance of the deviation curves of the Āryabhaṭīya (ca A.D. 500).
The reception of Billard's work
Billard's work has met with a strange reception over the decades since its publication in 1971. The publication came at the time when David Pingree was advancing his views about the origin of Indian astronomy, particularly for the period just prior to Āryabhaṭa. In particular he insisted that the parameters of mean longitudes employed by Āryabhaṭa had been derived somehow from Greek sources, such as Ptolemy's Almagest. Billard's demonstration that the mean longitudes of the Āryabhaṭīya were in striking agreement with the true state of the Sun, Moon and planets just around A.D.510, and must therefore have been founded on observations by Āryabhaṭa, was therefore in plain contradiction with Pingree's views. There were as well a number of other beliefs of Pingree that were destroyed by Billard's discoveries. From that time Pingree continued to pour abuse on Billard's work, beginning with a review in the J. Roy. Asiatic Soc.
I have little doubt that if Billard's discovery had been made by Neugebauer, or by Pingree himself, it would have been splashed across the front pages and hailed as a great discovery by the Brown school. As things went, its rejection by Pingree and his followers is nothing but naked politics.
Over the decades since that time Pingree's influence has been felt in a wide circle of his disciples, who have uncritically repeated his views. This is seen clearly, for example, in Kim Plofker's Mathematics in India, 2009, as far as it refers to Indian astronomy, where on the one hand she recites uncritically Pingree's narrative of the origins of the Indian canons, and on the other does her best to rubbish Billard's results.
The failure to appreciate Billard's work arises from a multiplicity of factors. Many who support him are, in my view, simply swayed by a misplaced loyalty to a fellow American scholar, together with a resistance to a work written by a French intellectual. I am reminded of a dispute in a very different subject, the decipherment of the Mayan script. As we read in Michael Coe's Breaking the Maya Code (Penguin, 1994, p. 156) "Why did the Maya decipherment take so very long as compared to, say, the Egyptian or the cuneiform scripts or Hieroglyphic Hittite ? I am sorry to say that the major reason was that almost the entire Mayanist field was in willing thrall to one very dominant scholar, Eric Thompson, who by the force of his personality, his access to the resources of the Carnegie Institution of Washington, his vast learning, and his acerbic - even cruel - wit, was able to stem the Russian tide until his demise in 1975." This subservience to Pingree's views has somehow induced people in the community to ignore the obligation to read his work in a critical spirit. For example one key paper of his, ‘The recovery of early Greek astronomy from India’, D. Pingree, Journal for History of Astronomy vii (1976), 109-123, presents a demonstrably fallacious argument in favour of the dependence of the parameters of mean longitudes on Greek sources.
Further details will be found in my paper ‘The reality of Indian astronomy’, in Astronomy and Mathematics in Ancient India. Actes de la journée d’études organisée le 24 avril 2009 à l’Université Libre de Bruxelles, ed. J.M. Delire, Peeters, Lettres Orientales et Classiques 17, 2012.
The program Deviations (devplo.exe), which you can download, will show the real usefulness of Billard's approach, an approach which applies not only to Indian canons but to any system whatever.