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Āryabhata & Chamravattam New Light on Āryabhata & Chamravattam K. CHANDRA HARI K. Chandra Hari, 17 Feb 2011, Cochin University of Science & Technology 17 Feb 2011 K. Chandra Hari, 17 Feb 2011, Cochin University of Science & Technology Dr KV Sarma (1919-2005) I am to gratefully acknowledge the love, affection and inspiration given by Dr KV Sarma and Mrs Lakshmi Sharma. He was one of the few ‘truly’ qualified people to do work in history of science, especially astronomy and mathematics Kerala legacy we speak of today could survive only because of his arrival at the right time if not late… ('Contributions to the study of the Kerala School of Hindu Astronomy and Mathematics' (1977) ) K. Chandra Hari, 17 Feb 2011, Cochin University of Science & Technology K. Chandra Hari, 17 Feb 2011, Cochin University of Science & Technology Kerala legacy of Astronomy & Mathematics Pre-historic epochs seen recorded in the alpha-numeric chronograms These chronograms combine both mathematical and astronomical information and attests for an antiquity that finds little support in the known historical details. Most of these chronograms specify a day count, i.e. the kalidinam expired and had implicit in them the epoch of ‘Kaliyugadi’ i.e. midnight /sunrise of 17-18 February – 3101 CE when the siddhāntic planetary means had a computational super-conjunction at 0 degree. Such dates can be traced as far back as 29 April -58 CE, 13 November -26 CE etc. th In the 4 century after Christ, these chronograms make us meet with a legendary astronomer Vararuci and he is succeeded by Aryabhata-I in Kali 3623 (Giritunga) K. Chandra Hari, 17 Feb 2011, Cochin University of Science & Technology Epoch of Vararuchi th 20 March 403 CE apogee conjunction of moon can be shown to be the epoch of the Girnasreyadi vakyas Udayagiri epoch of Indian astronomy can be identified as 20 March 402 CE (K3503 i.e. 120 years prior to K3623) Studies today lack an audience that can understand and appreciate the astronomical evidence Vararuchi of Kerala known through the Chandravakyas had the epoch of his Vakyas related to the Udayagiri of Chandragupta-II Vikramaditya. In Kerala, the chronogram yajnasthanamsamrakshyam puts his son’s epoch as 14 Feb 378 CE. Aryabhata epoch Kali 3623 (elapsed) is 120 years after the Udayagiri epoch K. Chandra Hari, 17 Feb 2011, Cochin University of Science & Technology Āryabhata Āryabhata stands renowned even in modern times for the scientific treatise he presented on Astronomy and Mathematics. Knowledge that won him praise in Kusumapura in his own life time continues to win him praise even in the 21st century. Apart from his astronomical and mathematical precepts, his advent is looked upon as a turning point in the history of exact sciences in India. He not only set forth the right background by drawing the best of the scientific tradition that preceded him but also chose to create a break with the paradigm by enunciating such revolutionary principles like the rotation of earth and a wholesome revision of mathematical astronomy based on observations. We are in dark about his observational innovations as the Āryārdhrātrasiddhānta is lost and is known only through brief extracts in texts like those of Bhāskara-I. K. Chandra Hari, 17 Feb 2011, Cochin University of Science & Technology Legacy of Āryabhata Kerala legacy of Astronomy and Mathematics begins with Aryabhata (522 CE) – ‘practically every astronomical text produced in the land base itself on the teachings of Aryabhata’ Ref: Sarma, KV., Tradition of Aryabhatiya in Kerala, Revision of Planetary Parameters A vast body of astronomical and mathematical literature in such illustrious names as Bhaskara-I, Haridatta, Madhava, Paramesvara, Nilakantha, Achyuta etc. Modern researchers, Dr. KV Sarma, Kuppanna Sastri, RC Gupta, KS Shukla, CT Rajagopal etc. Revision of the older siddhantas was an outcome of the realization of data misfit between prediction and observations of the astronomical phenomena and successive astronomer- mathematicians have been very critical of even the most astute of their predecessors as we see with Brahmagupta and Vatesvara. K. Chandra Hari, 17 Feb 2011, Cochin University of Science & Technology Āryabhata, Brahmagupta, Vatesvara Brahmagupta minced no words to criticize Aryabhata and Vatesvara followed on the lines of the “lotus-born” (Brahmagupta) : “The longitude of a planet obtained from its forged revolution number cannot be the same as that obtained from its real revolution number…. The revolution number for Mars (for example) may be forged by taking the first four figures as 8522, 0635, 7552 or 9292..” (I:20-22) and “On account of forged revolution numbers, forged civil days and forged positions of apogees and due to ignorance of the epicycles, the longitude of the planets disagree with observations and so they are not true”. (I:27) With Vatesvara airing such criticism on Brahmagupta, one can imagine the plight of the lesser folks if anybody were to forge astronomical works without taking into account the data misfit of his times. (Vatesvara siddhanta, translated by Prof. KS Shukla) K. Chandra Hari, 17 Feb 2011, Cochin University of Science & Technology Controversy about place… "Aryabhata I or Aryabhata the Elder to distinguish him from a 10th-century Indian mathematician of the same name, he flourished in Kusumapura—near Patalipurta (Patna), then the capital of the Gupta dynasty—where he composed at least two works, Aryabhatiya (c. 499) and the now lost Aryabhatasiddhanta. Aryabhatasiddhanta circulated mainly in the northwest of India and, through the Sasanian dynasty (224–651) of Iran, had a profound influence on the development of Islamic astronomy. Its contents are preserved to some extent in the works of Varahamihira (flourished c. 550), Bhaskara I (flourished c. 629), Brahmagupta (598–c. 665), and others. It is one of the earliest astronomical works to assign the start of each day to midnight. Aryabhatiya was particularly popular in South India, where numerous mathematicians over the ensuing millennium wrote commentaries" (sic) (Encyclopedia Brittanica) K. Chandra Hari, 17 Feb 2011, Cochin University of Science & Technology Controversy contd. "A veritable pioneer of Indian Astronomy, Āryabhata is without doubt one of the most original, significant and prolific scholars in the history of Indian science. He was long known by Arabic Muslim scholars as Arjabhad and later in Europe in the middle Ages by the Latinized name of Ardubarius. He lived at the end of the 5th century and the beginning of the sixth century CE, in the town of Kusumapura..." (Georges Ifra, The Universal History of Numbers) "As far as astronomical works are concerned, it seems that the Kerala country was the seat of its development in the South. It is all based on the Āryabhatīya, with or without corrections called the bījas... How Āryabhata came to be connected with the Kerala country is yet to be explained. He is called Aśmaka (i.e. one born in the Āśmaka region) and some say that an early name of the erstwhile princely state of Travancore was Āśmaka (Apte's Dictionary). But many say that the region near the Vindhyās was called the Āśmaka country...“ (TS Kuppanna Sastri) K. Chandra Hari, 17 Feb 2011, Cochin University of Science & Technology Āryabhatstviha nigadati kusumapurebhyarcitam jnānam, 'Āryabhatstviha nigadati kusumapureƒbhyasitam jnānam‘ "...scholars have thought for a long time that Āryabhata was either born in Kusumapura or lived and taught in that great city of ancient India. Such a view now appears untenable in the light of recent studies on the works of Bhaskara-I and his commentators and also of the medieval commentators of Āryabhata. In these works, Āryabhata is frequently referred to as an aśmaka, that is one belonging to the Aśmaka country which is the name of a country in the south, possibly Kerala....the fact that commentaries of and works based on Āryabhatīya have come largely from South India, from Kerala in particular certainly constitute a strong argument in fvaour of Kerala being the main place of his life and activity" ('A Concise History of Science in India‘, INSA) SB Dikshit to Dr KV Sarma (1977/2001) K. Chandra Hari, 17 Feb 2011, Cochin University of Science & Technology (Dr KV Sarma, IJHS, 2001) K. Chandra Hari, 17 Feb 2011, Cochin University of Science & Technology Astronomical Evidence Conflict of the latitude of Ujjayinī ºlɱÉVɱɨÉvªÉɱ±ÉÆEòÉ ¦ÉÚEòIªÉɪÉÉ ¦É´ÉäSSÉiÉÖ¦ÉÉÇMÉä* =VVÉʪÉxÉÒ ±ÉÆEòɪÉÉ& iÉSSÉiÉÖ®Æú¶Éä ºÉ¨ÉÉäkÉ®úiÉ&*14* Verse spells out that on the prime meridian, Ujjayinī is located at one-sixteenth of the earth's circumference North of Laňkā and thus the latitude of Ujjayinī turns out to be 3600/16 = 220N30'. 0 "...This makes the latitude of Ujjayinī equal to 22 30'N. This is in agreement with the teachings of the earlier followers of Āryabhata, such as Bhāskara-I (AD 629), Deva (AD 689) and Lalla and the interpretations of the commentators Someśvara, Sūryadeva (b. AD 1191) and Parameśvara (AD 1431). Even the celebrated Bhāskara-II (AD1150) has chosen to adopt it. Brahmagupta (AD628) differed from this view. He takes Ujjayinī at a distance of one-fifteenth of the earth's circumference from Laňkā and the likewise the latitude of Ujjayinī as equal to 240N K. Chandra Hari, 17 Feb 2011, Cochin University of Science & Technology 0 Āryabhata gave the latitude of Ujjayinī as 360 /16 North of Laňka and it had acceptance among only his followers. Brahmagupta and a host of others like Varāhamihira did not agree with Āryabhata and had given rise to an alternate school of thought and tradition. Bhāskara-II apparently had agreement with Āryabhata but some followers of Āryabhata like Sūryadeva could not find any rationale underlying the Āryabhata's notion and they did tacitly accept Brahmagupta as correct. Apart from what Shukla and Sarma have discussed, we can see that the Sūryasiddhānta also did not agree with Āryabhata in the matter.
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