Astronomers and their reasons: Working paper on Jyotihśāstra

Journal of Indian Philosophy

Volumn 30, Issue 5, 2002, Pages 495-514

  Minkowski, Christopher ^a  

^a 388 Rockefeller Hall ^*  (United States)

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[No Author keywords available]

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EID: 51349160301     PISSN: 00221791     EISSN: 15730395     Source Type: Journal    
DOI: 10.1023/A:1022870103341     Document Type: Article

References (77)

1. A version of this paper was presented as part of a panel on "Sanskrit Knowledge Systems on the Eve of Colonialism" at the Association for Asian Studies in Washington, D.C., in April '02.
2. For discussion of this list of disciplines and terms, see the NEH proposal written by Sheldon Pollock, and posted on the Sanskrit Knowledge Systems Website at the following URL address: http://dsal.uchicago.edu/sanskrit/ proposal.html. The last category of dharmaśāstra has the closest overlap, since the timing of dharmic performances is in the later period determined according to calendrical systems developed by the Jyotisīs.
3. See especially his Census of the Exact Sciences in Sanskrit (henceforth CESS) published in five volumes by the American Philosophical Society in Philadelphia, 1970-1994. My thanks to David Pingree and to Kim Plofker for reading a draft of this paper, though they are not at fault for any errors made. As will become evident, I have relied throughout on Pingree's findings, though I have organized them into a form that responds to the questions of the group project. Some sections are based on the results of my own research.
4. Randall Collins, The Sociology of Philosophies (Cambridge: Harvard University Press, 1998), 543-556; partial in two different ways.
5. Collins, The Sociology of Philosophies op. cit. 551.
6. In fact Collins makes his judgments based on Pingree, "History of mathematical astronomy in India," Dictionary of Scientific Biography 15 (New York, 1978), 533-633.
7. Johannes Bronkhorst has already remarked on this point, "Pānini and Euclid: Reflections on Indian Geometry," JIP 29.1-2 (April 2001): 64.
8. David Pingree, Jyotihśāstra: Astral and mathematical Literature (Wiesbaden: Otto Harrassowitz, 1981), 10, 12, etc.
9. See for example D. Pingree, "The Greek Influence on Early Islamic Mathematical Astronomy," JAOS 93 (1973): 32-43.
10. For the rationale of the periodization, see the proposal at the website as listed above in note 2.
11. CESS III 75-76; IV 100; V 122-123. For a family tree see Jyotihśāstra 124. Pārthapura probably lay in the region of the Ahmadnagar kingdom.
12. Jñānarāja and his son(s) made a similar resumption of mathematical literature, which had received its authoritative formulation in Bhāskara's Līlāvatī, though in that case there had been another important mathematician a century and a half earlier (Nārāyana Pandita).
13. CESS II pp. 94-107; III 27-28; IV 72-75; V 69-74. Pingree Jyotihśāstra 126. Ganeśa gives the credit for his innovation to his astronomer father, Keśava, the date of whose Grahakautuka (1496) is closely contemporary with Jñānarāja's work, but Ganeśa would appear to be the greater innovator. S. B. Dikshit, History of Indian Astronomy, Translated by R. V. Vaidya. 2 vols. (Delhi: Director General of Observatories, 1969) 2: 128-130.
14. Grahalāghava - "The Planets Made Easy." On karanas see Pingree, Jyotihśāstra 13-14.
15. One reason for this would be that the Grahalāghava, as its name might suggest, does away with the need for Siddhāntic treatises with their full geometric models and calculations reckoned from the distant beginning of long ages. For this reason the Grahalāghava has an alternative name, the Siddhāntarahasya. Dikshit, History of Indian Astronomy 130-139.
16. His approach, which features a boldly approximative stance, is unique enough that Pingree identifies his system as a paksa or school of thought in its own right. "History of mathematical astronomy in India," 624-625. Plofker [personal communication] suggests that it is in a way a recapitulation of the Babylonian, non-geometric method of positional astronomy by mathematical/arithmetical functions alone.
17. It is not an easy matter to reconstruct how Ganesa evolved his systems; see now K. Plofker and S. Ikeyama, "The Tithicintāmani of Ganeśa, a medieval Indian treatise on astronomical tables," SCIAMVS 2 (2001), 251-289.
18. Pingree, Jyotihśāstra 120.
19. CESS II 65-74; III 24; IV 64-66; V 56-59.
20. Pingree, Jyotihśāstra 49.
21. Pingree devotes a separate section to their treatment in Jyotihśāstra 47-50.
22. See Pingree, "Nīlakantha's Planetary Models," 29.1-2 (April 2001): 192-193. A reconfiguration of the arrangement of the deferent circles and the epicycles of each planet. For sun and moon the manda epicycle is made concentric about the earth, and the center of the deferent is made to move on the manda. For other planets the center of the manda circle is in turn placed on the śīghra epicycle, which is made concentric with the earth at center. Pingree argues that though significantly new, pace Ramasubramaniam, etc., this is not a quasi-Tychonian reformation.
23. See Bronkhorst on this text and the math/philosophy divide, "Pānini and Euclid," 61-64.
24. Pingree, "Nīlakantha's Planetary Models," 187.
25. Tantravārttika on JMS 1.3.2.
26. Pingree, Jyotihśāstra 51. K.V. Sarma, ed. Jyotirmīmāmsā: Investigations on Astronomical Theories (Hoshiarpur: VVRI, 1977), xi-xiii, xix-xx.
27. Jyotirmīmāmsā, xv, and 1-2. In fact the extant manuscripts do not preserve the text's beginning.
28. Pingree, Jyotihśāstra 49-51.
29. Note that Pingree's most recent history of Indian astronomy, "Astronomy," forthcoming in the volume of the Enciclopedia Italiana on the History of Indian Science, approaches the descriptive problem by making regional variation of the organizing principle for describing historical developments from approximately the 12th to the 18th Centuries: South India, Kerala, West and Central India, Rājasthān, Kāśī, etc.
30. S.B. Dikshit, History of Indian Astronomy, 2: 134-137.
31. S.B. Dikshit, History of Indian Astronomy, 2: 129-130.
32. See S.R. Sarma, "Astronomical Instruments in Brahmagupta's Brahmasphutasiddhānta," Indian Historical Review 13 (1986-1987): 68-69;
33. Pingree, "History of Mathematical Astronomy," 629-630.
34. Pingree, "Bīja-corrections in Indian Astronomy" JHA 27 (1996), 161-172. Bīja-corrections had been in use for a long time. The authority of observation was sometimes invoked in earlier bīja texts as the basis for making the corrections. In fact most early bīja tables were designed to approximate all of the parameters of one astronomical paksa to the parameters of another. There is little evidence that observation played anything but a secondary role until the work of Keśava, who is also at variance with the older bīja-correction tradition in his eclectic choice of parameters.
35. At about the same time as Keśava, another astronomer, perhaps named Rāma, appears to have been working independently in the same fashion, combining observation with bīja-corrections to adjust existing parameters. It is further possible that, relying on observations, Rāma, and another astronomer Rāmacandra (fl. 1599) "may well have introduced entirely new corrections unconnected with other paksas as well." Pingree, "Bīja-corrections," 168-171.
36. That of the Saurapaksa. Pingree, "Nīlakantha's Planetary Models," 189, 191, also n. 10 on p. 194.
37. See Pingree, "Islamic Astronomy in Sanskrit," 315-316.
38. On the typical contents of an ilm al hay'a text, see for example F.J. Ragep, Nasīr al-Dīn al-Tūsī's Memoir on Astronomy (al-Tadhkira fi 'ilm al-hay'a) 2 vols. (Springer Verlag, 1993). On the use of observations in relation to theory, see especially Book Two, chapter 11.
39. Pingree - personal communication. The astrolabe had been introduced into India from Arabic/Persian sources. Various Sanskrit texts about their construction and use date from the mid-14th Century onward.
40. Tājikapaddhati, also called Varsaphalapaddhati. On this form of astrology and its explicitly Arabic/Persian terminology, see Pingree, "Tājika: Persian Astrology in Sanskrit," in From Astral Omens to Astrology; From Babylon to Bikaner (Roma: Istituto Italiano per L'Africa e L'Oriente, 1997), 79-90.
41. S.R. Sarma, "Indian Astronomical and Time-measuring instruments," IJHS 29(4) (1994): 515-516. Its first description in Sanskrit occurs in Rāmacandra's Yantraprakāśa of 1428. Ganeśa is the author of three texts on instruments - the Cābukayantra, Pratodayantra, and Sudhīrañjanayantra. CESS references given above in note 13. 'Cābuka' is a Persian word meaning whip, i.e. 'pratoda' in Sanskrit. Though he might have been influenced in his interest in the use of instruments and the taking of observational measurements, Ganeśa's astronomical mathematical method is not discernibly influenced by the contents of Arabic/Persian astronomy.
42. CESS III pp. 75-76; IV pp. 100; V pp. 122-123.
43. For a family tree see Pingree, Jyotihśāstra 124.
44. Some of the examples and arguments of this section are drawn from a more detailed discussion that appears in a separate article, "Competing Cosmologies in Early Modern Indian Astronomy," forthcoming.
45. Siddhāntasundara (henceforth SSJ), II.1.30.
46. SSJ II.1.22.
47. Grahaganitacintāmani (henceforth GGC) on SSJ II.1.22 f. 13v 11. 2-6.
48. GGC on SSJ II.1.22 f. 14r 11. 4-7.
49. A pala is a unit of time, a 60th of a 60th of a day, or 24 seconds.
50. C/10 = 3600/7 1/5. C = 10·3600/36/5 = 5000 yojanas GGC on SSJ n.1.26, f. 16r 11. 8-10. CintāmanI acknowledges, again via his imaginary interlocutor, that there is no sapaksa for this inference, which should invalidate it as a proof, but does not do so because the hetu pervades the sādhya in places other than the paksa, and so on.
51. GGC on SSJ II.1.26, f. 16r 11.2-4.
52. GGC on SSJ II. 1.32 f. 22r 11 6-7; and GGC on SSJ II.1.37, f. 23v 11 8-10. In the first case the experiment is done with slab of rock and an areca nut.
53. GGC on SSJ 31 f. 21r 11. 1-4. The argument is about the inference of the existence of air because of the many small things that are seen to be supported by it, since non-falling implies support. The passage cited is found on p. 58 of the Gaekwad oriental Series edition, in the commentary on Praś astapāda 54.
54. GGC on SSJ 31 f. 21r 11. 10-11. This discussion is found in Kusumāñjali 5.4. My thanks to Phyllis Granoff for this reference.
55. For the most complete list of his works, see Sarma, "Siddhā nta-samhitā-sārasamuccaya."
56. See also Dikshit, History of Indian Astronomy 144-145;
57. Dvivedi Ganakataranginī 65-67.
58. There is a commentary on the SŚB attributed to him, which unfortunately was not available to me at the time of this writing. Sūryadāsa is a figure worthy of a great deal more study, especially for the particular nature of his polymathia, which combined the fields of kāvya and astronomy.
59. A reference in the last chapter appears to indicate a date of composition in 1583. The text is as yet unpublished; a copy of one flawed manuscript was made available to me (courtesy of David Pingree) (Jaipur Khasmohor 5026). My synopsis in the following is provisional, pending the creation of a proper edition.
60. Pingree has written several articles outlining the history of the awareness of the Muslim astronomy among the Sanskrit jyotisīs, ("Islamic Astronomy in Sanskrit," Journal for the History of Arabic Science 2 (1978): 315-330;
61. and "Indian Reception of Muslim Versions of Ptolemaic Astronomy," in eds. F.J. and S.P. Ragep, Tradition, Transmission, Transformation (Leiden: 1996), 471-485), but did not describe this chapter by Sūrya. I plan to provide a more detailed description of the chapter in a forthcoming study.
62. Pingree "Islamic Astronomy in Sanskrit," 318.
63. Pingree "Tajika: Persian Astrology in Sanskrit," note 37.
64. Pingree, "Indian Reception of Muslim Versions of Ptolemaic Astronomy," 474-475.
65. The Risalah Dar Hay'ah of 'Alī al-Qūshjī, composed ca. 1460. Pingree, "Islamic Astronomy in Sanskrit," 327-328;
66. "Indian Reception of Muslim Versions of Ptolemaic Astronomy," 475-476.
67. The Sanskrit translation was published as Hayata, ed. Vibhūtibhūsan Bhattācārya, Sarasvatibhavana Granthamālā 96 (Vārānasī: 1967).
68. Pingree, "The Sarvasiddhāntarāja of Nityānanda, " forthcoming.
69. Also "Islamic Astronomy in Sanskrit," pp. 323-326,
70. and "Indian Reception of Muslim Versions of Ptolemaic Astronomy," 476-480.
71. Pingree, "Amrtalaharī of Nityānanda," SCIAMVS 1 (2000), 209-217.
72. This debate has been described by Pingree in "Islamic Astronomy in Sanskrit," 320-323.
73. See most recently D. Pingree, "An Astronomer's Progress," Proceedings of the American Philosophical Society 143 (1999), pp. 73-85.
74. Subsequent encounters with European, Copernican astronomy are described in Richard F. Young, "Receding from Antiquity: Indian Responses to Science and Christianity on the Margins of Empire," Kokusaigaku-Kenkyu 16 (Meiji Gakuin Ronso 595), 1997 pp. 241-274;
75. C. Minkowski, "The Pandit as Public Intellectual: The Controversy over virodha or Inconsistency in the Astronomical Sciences," in ed. Axel Michaels, The Pandit: Traditional Sanskrit Scholarship in India (Festschrift P. Aithal). Heidelberg South Asian Studies XXXIX (New Delhi: Manohar Publications, 2001), pp. 83-102;
76. Kim Plofker, "Derivation and revelation: the legitimacy of mathematical models in Indian cosmology," in ed. Teun Koetsier, Mathematics and the Divine (Amsterdam: forthcoming);
77. and Michael Dodson, "Re-Presented for the Pandits: James Ballantyne, 'Useful Knowledge,' and Sanskrit Scholarship in Benares College during the Mid-Nineteenth Century," Modern Asian Studies 36.2 (2002): 257-298.