History of Science in South Asia
A journal for the history of all forms of scientific thought and action, ancient and modern, in all regions of South Asia
B O O K R E V I E W
MLA style citation form: Clemency Montelle, Book Review. History of Science in South Asia  (): –.
Online version available at: http://hssa.sayahna.org/.
HISTORY OF SCIENCE IN SOUTH ASIA
A journal for the history of all forms of scientific thought and action, ancient and modern, in all
regions of South Asia, published online at http://hssa.sayahna.org
Editorial Board:
. Dominik Wujastyk, University of Vienna, Vienna, Austria
. Kim Plofker, Union College, Schenectady, United States
. Dhruv Raina, Jawaharlal Nehru University, New Delhi, India
. Sreeramula Rajeswara Sarma, formerly Aligarh Muslim University, Düsseldorf, Germany
. Fabrizio Speziale, Université Sorbonne Nouvelle – CNRS, Paris, France
. Michio Yano, Kyoto Sangyo University, Kyoto, Japan
Principal Contact:
Dominik Wujastyk, Editor, University of Vienna
Email: ⟨hssa@sayahna.org⟩
Mailing Address:
Krishna GS, Editorial Support, History of Science in South Asia
Sayahna, , Jagathy, Trivandrum , Kerala, India
This journal provides immediate open access to its content on the principle that making research
freely available to the public supports a greater global exchange of knowledge.
Copyrights of all the articles rest with the respective authors and published under the provisions
of Creative Commons Attribution- ShareAlike . Unported License.
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SAYAHNA FOUNDATION
  • Jagathy • Trivandrum •  •  • ⟨info@sayahna.org⟩ • www.sayahna.org
B O O K R E V I E W
J. M. Delire (ed.), Astronomy and Mathematics In Ancient India. Actes de la journée
d’études organisée le  avril  à l’Université Libre de Bruxelles, (Leuven, Paris,
Walpole : Peeters, ),  pp. Lettres Orientales et Classiques, volume .
 ----. € .
A
stronomy and Mathematics In Ancient India is an edited volume of collected
scholarly articles on various topics in the history of astronomical and mathematical sciences in India. With contributions in both French and English, this
book covers a variety of themes that were presented at a day-long colloquium in
Brussels by an impressive group of international participants. The group, led by
J. M. Delire, included P.–S. Filliozat, K. Mahesh, R. Mercier, F. Patte, K. Ramasubramanian, S. R. Sarma, and Venketeswara Pai R. The contributions are diverse
in their range; from infinite series to instruments, mean motions to music theory
to manda epicycles.
The book opens with a short editorial preface followed by seven contributions, each with their own reference section. The first contribution is by Mercier,
who continues to tackle important issues surrounding the origins and generation
of planetary period relations. His approach, inspired and guided by Billard, is
to employ modern statistical tests and retrodictions of planetary positions to explore ancient parameters. “It is commonplace to test an ancient astronomical
work by a recalculation from modern parameters of the state of the sky at that
time,” he clarifies, “indeed how else would one hope to date an ancient work?”
(pp. –). It is true that modern mathematical analysis can be useful in recovering historical information that is otherwise unavailable through conventional
approaches. However, fully understanding the circumstances and details of ancient astronomical systems requires a multifaceted approach that harmonizes
textual readings, contextual circumstances, as well as the inferences drawn from
modern mathematical analyses. Caution must be exercised with respect to the
conclusions made when one of these lines of inquiry is prioritised at the expense
of the others. This point has been the focus of many recent historiographical
reflections.
 For instance, in the context of tabular
texts, Robson () enumerates six conditions
that she considers crucial: historical sensitivity,
cultural consistency, calculational plausibility,
       () –
 B R
Furthermore, the use of mean motions to attest to observable physical phenomena is a delicate matter. Modern scholars who invoke modern comparisons
to explore ancient data must make explicit all assumptions used in their reconstructions and comparisons to present a lucid and convincing case. Recent work,
such as that done by Duke () has made important contributions to this issue
too.
Delire considers the construction of tables of sines, their features, and the
various interpolation procedures that were developed to compute intermediary values. He situates such activity at the intersection of mathematics and
astronomy and reconsiders important familiar passages from Āryabhaṭa to
Nilākaṇṭha. Filliozat explores a work entitled Haricarita by Parameśvara Bhaṭṭa
which incorporates the vākyas (or short statements which encode astronomical
data) by Vararuci. He presents a small selection of verses to reveal the double
reading that can be made of the text; the first reading reveals a verse relating
episodes in the childhood of Kṛṣṇa, and the second reading which focuses on the
the beginning of each verse, uncovers the true longitude of the moon, encoded
using an alphanumeric coding scheme, known as kaṭapayādi. He notes that this
type of literary form falls between astronomical, mythological, devotional, and
philosophical genres.
Sarma gives a detailed description of the earliest extant Sanskrit astrolabe.
In order to settle existing controversy surrounding its date and authenticity, he
compares the instrument with passages from an early work on astrolabe construction, the Yantrarāja by Mahendra Sūri (with the text and a translation given
in an appendix to the chapter). His account connects specific recommendations
set out by Mahendra Sūri regarding the construction and detailing on astrolabes with the actual physical features of this particular instrument and the quality of the workmanship. His interpretations are supported by ample photographic evidence which is magnified enough for Sanskritists to read and appreciate themselves.
K. Ramasubramanian discusses the traditional Indian planetary model as
outlined by Nīlakaṇṭha in his commentary on the Āryabhaṭīya. He carefully describes Nīlakaṇṭha’s modifications to the tradition model that entailed, among
other things, that the equation of centre for the interior planets should be applied
to the mean heliocentric planet (and not to the mean sun). Such modifications
raise a number of fascinating questions, the most compelling being what motivated these proposals? Ramasubramanian notes the observations made by Kerala
astronomer Parameśvara in the early fifteenth century may have prompted a reconsideration of the model, however the precise ways in which these (and other)
physical reality, textual completeness, and tabular order (p. ). This point is also discussed
more fully in Brummelen, Husson, and Montelle (forthcoming).
       () –
C M 
observational records inspired revisions of the behaviour of celestial phenomena
still remain to be clarified.
Patte explores a sequence of numbers that was originally inspired by a combinatorial rule given by Bhaskara II, and developed by later commentators, including Gaṅgādhara and Śārṅgadeva the author of the Saṅgītaratnākara (Ocean
of Music) for the enumeration of various rhythmical patterns. His account gives
a glimpse into the methods employed by Indian scholars for resolving complex
problems which were generated in fields outside of mathematics. His contributions, like others in the book, remind contemporary historians of mathematics that much critical mathematical activity can be found outside traditional
domains of mathematics.
K. Mahesh, Venketesvara Pai, and K. Ramasubramanian spell out various
‘Madhāva’ series for the computation of π, and some of the ingenious correction terms that were introduced to improve the convergence of these series. One
marvels at these corrections, which are justified to the modern eye with recourse
to some serious algebraic manipulation, but were somehow arrived at without
symbolic styles of reasoning. Nīlakaṇṭha’s reflections on the ‘irrationality’ of
π are captivating. Again, the question of motivation immediately arises. What
was the incentive for developing these extremely precise articulations of π. Were
they actually used by working astronomers? Or were they developed largely for
supra-ultilitarian purposes?
As Delire notes, the history of the astral sciences on the Indian subcontinent
is seriously understudied. Many key works still need to be edited and translated
and their contents analyzed, for specialists and non-specialists alike. Overall this
book is a welcome addition that showcases ongoing research in this field. For
those who are interested in specific topics, a detailed index would have been
helpful and as would a general bibliography. Certainly given the wide range of
topics covered, a way to further ramify the coherency between the contributions
could have been to draw out and develop the common themes raised throughout the book, perhaps in an introductory chapter. In addition, editorial finesse
could have been applied at certain points in the book to ensure a constructive
and dispassionate scholarly tone throughout. However, all in all, this book is
a testament to the dedication and expertise of scholars who are working in this
field and will be an encouragement and inspiration for others.
REFERENCES
Brummelen, Glen van, Matthieu Husson, and Clemency Montelle (forthcoming).
“Tools of the Table Crackers: Using Quantitative Methods to Analyze Historical Numerical Tables”. In: The History of Numerical Tables. Ed. by Dominique
Tournès. Berlin: Springer.
       () –
 B R
Duke, Dennis W. (). “Mean Motions and Longitudes in Indian Astronomy”.
In: Archive for History of Exact Sciences ., pp. –.
Robson, Eleanor (). “Neither Sherlock Holmes nor Babylon: A Reassessment
of Plimpton ”. In: Historia Mathematica , pp. –.
Dr Clemency Montelle
University of Canterbury
New Zealand
       () –