‘Yavana’ and ‘Indian’: Transmission and Foreign Identity in the Exact Sciences

Summary

The Sanskrit term ‘Yavana’, originally a transliteration of ‘Ionian (Greek)’ but later applied to other foreigners as well, was used throughout the common era to designate various foreign importations in the exact sciences. Likewise, the name ‘Indian’ was attached to several mathematical concepts and techniques in the Islamic world (as well as Europe) from about the seventh century onward. However, not all innovations adopted from or into the Indian tradition were labeled ‘Indian’ or ‘Yavana’ respectively. This paper examines the question of what characteristics marked some borrowed techniques and concepts as ‘foreign’ and stamped them with their outlandish origin, while others were quietly assimilated into ‘indigenous’ learning.

Acknowledgements

The author would like to acknowledge the detailed and helpful comments provided by thereferees of this paper.

Notes

¹A related paper on the same theme, focusing primarily on ancient and medieval scientific transmissions from Indian to European sources, is K. Plofker, ‘“Indian” rules, “Yavana” rules: foreign identity and the transmission of mathematics’, in Proceedings of the International Congress of Mathematicians 2010, edited by Rajendra Bhatia et al. (Hackensack NJ, USA, 2011).

²Julius Eggeling, trans., The Satapatha Brahmana, Part II (Oxford, 1885), 30–2. Here and elsewhere, quotes from published translations of Sanskrit texts retain the transliterations found in the original publica-tions, while bracketed comments within the quotes use the same standard transliterations as in the rest of the paper.

³Julius Jolly, trans., The Institutes of Visnu (Oxford, 1880), 94–5.

⁵G. Bühler, trans., The Laws of Manu (Oxford, 1886), 412.

⁴J. Jolly (note 3), 255.

⁶H. H. Wilson, trans., The Vishnu Purana (London, 1840), 375.

⁷These early omen texts, along with arguments for the hypothesis that their predictive associations were ultimately derived from Mesopotamian celestial omens in the Achaemenid period, are described in D. Pin gree, Jyotiḥsāstra (Wiesbaden, 1981), 67–71.

⁸See the overview of these developments in D. Pingree, ‘The Recovery of Early Greek Astronomy from India’, Journal for the History of Astronomy, 20 (1976), 109–22.

⁹G. Cardona, ‘On Attitudes towards Language in Ancient India’, Sino-Platonic Papers, 15 (1990), 2–19.

¹⁰D. Pingree, From Astral Omens to Astronomy, from Babylon to Bīkāner (Rome, 1997), 31–8.

¹¹H. Kern, trans., The Bṛhat Sanhitá of Varáha-Mihira (Calcutta, 1865), 8.

¹²K. Plofker, Mathematics in India (Princeton, 2009), 49–52.

¹³D. Pingree (note 10), 34–5.

¹⁴Pingree (note 10), 34–8.

¹⁵Pingree (note 10), 79–90.

¹⁶Pingree (note 10), 80–9.

¹⁷K. Plofker, ‘The Astrolabe and Spherical Trigonometry in Medieval India’, Journal for the History of Astronomy, 31 (2000), 37–54.

¹⁸V. B. Bhattacarya, ed., Hayata (Varanasi, 1967), 1. This description, transliterating into Sanskrit script the Arabic words ishāra ‘sign’, ḥissī ‘perceptible’, and nuqta ‘point’, evidently attempts to render a typical Arabic presentation of Euclidean entities (compare, e.g., F. J. Ragep, ed., Naṣīr al-Dīn al-ṭusī's Memoir on Astronomy, 2 vols (New York, 1993), I, 92–3).

¹⁹V. B. Bhattacarya, ed., Ukarā (Varanasi, 1978), 1. Except for the garbling of the names, Nayanasukha's Sanskrit account squares fairly well with the story that the translation of the Sphairika (Arabic al-ukar, ‘spheres’) by the 9th-century scholar Qusṭā ibn Luqā al-Balabakkī was commissioned by his patron Aḥmad (often identified with Abu 'l-‘ Abbās Aḥmad), and revised by the 13th-century astronomer Naṣīr al-Dīn al-ṭusī. The reference to a “correction” by Thābit suggests confusion with Thābit ibn Qurra's 9th-century Arabic recension of a different translated Greek treatise, the Sphere and Cylinder of Archimedes. (See D. Gutas, Greek Thought, Arabic Culture (Oxford, 1998), 125–6; Ragep (note 18), II, 377–8; and R. Lorch, ‘Archimedes’, in Medieval Science, Technology, and Medicine: An Encyclopedia, edited by Thomas F. Glick et al. (New York, 2005), 40–2 (40).

²⁰M. Levey and M. Petruck, trans., Principles of Hindu Reckoning (Madison WI, USA, 1965).

²¹M. Yano, ‘Knowledge of Astronomy in Sanskrit Texts of Architecture’, Indo-Iranian Journal, 29 (1986), 17–29 (17–8).

²²See, for example, E. S. Kennedy, ed., The Exhaustive Treatise on Shadows, 2 vols (Aleppo, 1976), II, 80–90; and Ragep (note 18), I, 306–7.

²³An early version of the Indian approach was described by Bhāskara I in the 7th century: T. S. Kuppanna Sastri, ed., Mahābhāskarīya (Madras, 1957), 275–82. For Ptolemy's technique see G. J. Toomer, Ptolemy's Almagest (Princeton, 1998), 311–3.

²⁴See E. S. Kennedy and W. R. Transue, ‘A Medieval Iterative Algorism’, American Mathematical Monthly, 63 (1956), 80–3; E. S. Kennedy, ‘Parallax Theory in Islamic Astronomy’, Isis, 47 (1956), 33–53; and C. Montelle, Chasing Shadows: Eclipse Theory in the Ancient World (Baltimore, 2011). The ‘hybridization’ of Hellenistic exact and Indian iterative methods for parallax sometimes extends even to the methods’ application, where a calculation is iterated only for a prescribed number of repetitions rather than continuing until the value becomes fixed.

²⁵See Plofker (note 12), 257, quoting a claim by the 11th-century Muslim scientist (and Indologist) al-Bīrūnī that Indian mathematics uses only the sines or half-chords.