March 19-20, 2015 – 9.30 am- 1 pm
University Paris Diderot,Condorcet Building, 4 rue Elsa Morante or 10 rue Alice Domon et Léonie Duquet 75013 Paris, Building Condorcet, Room 483A. Maps and directions can be found here.
The exploratory workshop is organised by Karine Chemla (Sphère, CNRS & University Paris Diderot, SAW Project), Sho Hirose (Sphère, CNRS & University Paris Diderot, SAW Project), Agathe Keller (Sphère, CNRS & University Paris Diderot, SAW Project) and Daniel P. Morgan (Sphère, CNRS & University Paris Diderot, SAW Project)
Ritual is a science of precision. Like any proper performance or game, ritual choreographs action to the beat and bounds of time, and it manipulates symbols with rigorous rules of accounting. The calendar, the timepiece, the tokens, the altars, the counts—to mathematics and the astral sciences are owed the rigor of ritual, one might say, and to ritual, one of the very meanings of these sciences. In this workshop, we will reflect upon the interdependence of ritual, mathematics, and astronomy in the ancient world, giving special attention to the question of astronomical and computational practices unique to the context of ritual.
What textual resources could help us in this reflection? Chinese sources suggest that this question is worth asking. Indeed, as Zhu Yiwen has established in the context of the SAW project, many ancient commentaries on Confucian Classics develop computations precisely in relation to questions of rituals. Moreover, a 6th century mathematical Classic dealing with the mathematical knowledge required for Confucian canons gives rituals pride of place. Why and what for? How can the articulation of mathematics and ritual in this context be understood?
Were there specific mathematical computations developed for ritual? In India a Kerala tradition of astrologers using cauri shells both for computations and for casting horoscopes is known—how localized are such practices? Have they developed specific ways of computing or casting horoscopes?
What were the relations between astral sciences and mathematics in the context of ritual? In the Indian subcontinent, for example, the very first texts on astral science (jyotiṣa) and mathematics (ganita) are related to Vedic ritual, while being wholly distinct in terms of aims and textual genre. When and how then are mathematics or astral science involved in “Vedic” rituals? What are their connections in this context? How different is this from the situation of “Hindu” rituals? Are there Hindu ritual texts containing references to astral science and/or requiring mathematical activities? What about Jain texts?
Further, how did developments in astronomical knowledge affect the timing, contents, or performance of rituals? For example, in early imperial China, the state astronomical office was a subsidiary of the Ministry of Rites, its task being to “observe the phenomena/signs and grant the seasons” according to the sacrosanct precedent of the Sage Kings of old. In practice, this translated to the operation of an observatory for the purposes of observation, testing, record-keeping, omen-interpretation, and briefing as well as a staff of computers, whose job it was to produce a calendar that would realize the synchronization of humanity, the spirits, and Heaven above. Later detached from the Ministry of Rites, how much of this office’s activities went into state ritual per se? What other than symbolism was the substance of debate as concerns the role of the astral sciences in ritual? Equally important, what was the situation like beyond the state ritual apparatus, in the performance of personal and popular rites, or in the great religions of Buddhism and Daoism? In the Indian subcontinent, how much did the introduction of horoscopes affect the assessment of “auspicious days” for rituals?
We also need to better understand how different sub-topics within the astral sciences (e.g. astronomy, horoscopy, divination, …) could be related to rituals, and in which circumstances they involved computations. For instance, what elements of the Indian almanach, the pañcāṅga, are specifically required for the performance of ritual?
How were technologies like water clocks, calendars, and ephemerides used to regulate ritual time? What sort of empirical questions were raised about these technologies in the context of ritual, and how were they resolved?
The realm is very large according to the definition given to “ritual”, and taking into account the long historical span of both India and China, papers then will be on specific case studies addressing some of these questions.
List of Speakers
March 19, 2015
YANO Michio (Kyoto Sangyo University, Japan)
Astral sciences and rituals in India with reference to ayana
Bill Mak (Kyoto University, Japan)
Ritualistic cyclicity in Indo-Greek astral science – Expressions for various modes of time measurement in the Yavanajātaka
March 20, 2015
ZHU Yiwen (Sun Yatsen University, China)
Commentaries on ritual numbers through different mathematical knowledges in 7th century China
IKEYAMA Setsuro (Kyoto Sangyo University, Japan)
The calculation of Vyatipata, an astrological phenomenon in Indian astrologygy