On Mathematical Contents of Jaina Prakrit Texts

Author(s): L C Jain
Publisher: Z_Yatindrasuri_Diksha_Shatabdi_Smarak_Granth_012036.pdf
Catalog link: https://jainqq.org/explore/250230/1

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On Mathematical Contents of Jaina Prakrit Texts A Brief Survey Prof Padmavathamma, H.O.D. Mathematics, Mysore University Prof. L.C. Jain Hon. Director A.V.R.I.above Diksha Jewelers, 554, Sarafa, jabalpur (M.P.) INDIA (NORTH) ABSTRACT the Jaina Karma philosophy in the symbolic forms, Certain mathematical contents of the Prakrit akrit arithmetical, algebraical and geometrical.? texts are simply described here in view of the sym Mahaviracharya', the author of the Ganitasara bolic mathematic used in Karnataka Vritti of the samaraha, did collect the mathematical material from Gommatasara and the Labdhisara as elaborated the Jaina source material and he goes beyond in by Pt. Todaramala. This consolidates the Karma stating that whatever is more to be said may be theory in the Jaina School. The cosmological seen in the Agama. Sridharacharya is still contheory contains the astronomical and geographi- troversial, however, in the history of mathematics. cal mathematics which is quite simple for study yet deeper in approach to setting of mathematical Still now we do not have the Jyotisapatala of background of a model. Mahaviracharya, nor the Parikarma text or com mentary work of Kundkundacarya. Similarly the 1. INTRODUCTION commentaries of Tumbucluracarya and Samantabhadracarya are not available which Let us start with a quotaton of the philosopher could have told and traced the algebraic symbolscientist Albert Einstein, regarding mathematical ism of the Karnataka Vritti of Kesava Varni. achievements of the Greeks round about the Christain era, "We reverence Greece as the cra There are several problems in the history of dle of western science. Here for the first time the mathematics and science which could be solved world witnessed the miracle of logical system which regarding the source in India if we could channelize proceeded from step to step with such precision the talents of brilliant scholars of Jainism and that every single one of its propositions was abso. Prakrit towards this end in our universities. Bhopal lutely indubitable - I refer to Euclid's geometry. This university has opened such a course in the departadmirable truimph of reasoning gave the human ment of religion and culture recently. The problems intellect the necessary confidence in itself for its are regarding the origination of and motivation of subsequent achievements. If Eculid failed to kin a paradigm shift in the terminology and usage of dle your youthful enthusiasm, then you were not symbols. In the Prakrit texts, we find the logical born to be a scientific thinker." and philosophical co-mathematical terms, no doubt as in other philosophies, but the mathematical If we go through the Jaina technical terms in manipulation through symbols is a peculiarity of the Prakrit texts of the Karananuyoga or the the Digambara Jaina School. There is also no Dravyanuyoga, we find that most of the terms are doubt that this was the achievement in the south importing mathematical significance. Philosophy perhaps round about the period of here is tinged with mathematics as Bertrand Russell Kundkundacarya, when writing of the scripture puts it, it is a beginning of a mathematical philoso- might have been in full swing, after the compilaphy. His work, Introduction to Mathematical Philoso- tion of the Satkhandgama' and the Kasayaphuda phy' is worth reading. If one reads the Karnataka texts. Round about this period we find certain revoVritti of the Gommatasara, one can carry the same lutionary events which speak of the mathematical impression, for it carries the mathematical details of talents of some genius. inimoimimaritionin rintosiominciano 14 incontinction infinitionsintrininin

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YATEENDRASURI SMARAK GRANTH 2. Mathematical Terms, Symbols, And Events sion of calendar. Success in building up various Round About the Christian Era. programmes in the Karma theory will depend on how we are able to form states, input and outputs We shall relate the events and not go into their from the mathematical data furnished in the comcontroversial details. Then it is upto the scholars mentaries of the Gommata sara and the Labdhisara, to solve the problem of their source on the basis of oblem of their source on the basis of the through C** language. an indispensable necessity. Zero in the place value system was needed by the Jaina School. We also Let us have a look at the mathematical mate. find the place value system used in addition of the rial in these texts which could be helpful in comtactor as well as in their subtraction, in the puterization. The simile and the number measures Karnataka Vritti. Zero was used in the writing of (upama and samkhya pramana) are finite and the Mahabandha to fill up the gaps and so on. transfinite cardinals and ordinals of various types of sets (rasis). There are fourteen types of seThe Jain calender records a precession in the quences (dharas) in the Trilokasara" which locate Vedamga Jyotisa calender during this period, and several types of sets and their measures. Every the Vikrama Samvat is established in India. Per topic in the Karma theory deals with the minimum haps this was the era when various texts quoted (jaghanya) and the maximum (utkrishta) fixing the by Virsenacarya were compilled for mathematical domains and ranges between which the computer imports of the Karma philosophy. For example, the is to work. The eight operations called the Varganasutra Vedanaksetravidhana, the parikarmasataka not only deal with the finite Khottaniogaddara, Pariyamma, Kalavihano, and quntities but also transfinite quantities as well as so on were some of the mathematical texts which the fixed and variable sets. The trikona-yantra (tricould survive against the time.! angular matrix) can be given several programmes The cosmological texts including astronomy for the variability of the measures of the mass and geography, e.g., the Tiloyapannatti, the number (pradesas), configurations (prakrtis), en. Suryaprajnapti, the Candapannatti, and so on, did ergy levels (anubhagas) and the life-times (sthitis) not only depict calendrical details as the Vedamga of the Karma ultimate particles (paramanus). The Jyotisa but there was also a unified astronomical Labdhisara depicts these variations in a symbolic theory, set in a mathematical universe. When sev way of mathematics. 12 The equations and inequaleral processes are depicted through a single 'ma ity relations given in this way may pave the way to nipulation it becomes a unified theory which is re more complex manipulation of the problems posed garded as simple. The Greeks splitted it through in the modern set up of the Karmic data, the epicycles for finer calculations. Einstein gave Before we give the measureable terms it will a unified theory. Now there is an attempt for a theory not be out of place to suggest that the vast mathof every thing (TOE) in physics. The Jaina School ematical data could be arranged in a computer file tried to give such a theory of every thing for the in a graded manner. From the lowest value we go biological phenomena through the mathematical to the largest value in a certain programme and theory of karma. 10 The question is whether we could these could be coded in one of the computer's high computerize such a theory and prepare files in the level languages such as Fortran Mathematica or software to execute programmes as is happening C++. The contiollable and observable situations even in astrology. What could be the resluts in the are defined in terms of the control (guna) and reachbenefit of a society or a nation? Astronomical pro able (margana) stations (sthanas). Thus the comgrammes will be found to be simpler. Rogers Duter could be helpful in showing the time dependBillard has already computerized the Yuga sys- ent and time-independent phenomenology of the tem of Indian astronomy leaving the Prakrit ver- Karma theory of the Prakit texts referred above.

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YATEENDRASURI SMARAK GRANTH We now relate only the terms of the Prakrit Various terms of the Labdhisara have been texts which denote a measure which could be cal- defined by Todaramala in the Arthasamdrsti culated to give a rough or fine gradation or topol- Adhikara of his samyakinana Candrika commenogy. One should note that a variable measure is tary. These terms like the Apakarsana, Utkarsana, given in an algebraic way, set theoretic in approach. etc. give operational details in the theory of Karma. Its measure is therefore given between its minimum. suitable value. This could be approximate also as The relations between various entities have is found in several places of the Labdhisara or the been given through several formulae, both in the Suryaprajnapti, Tiloyapannatti or the texts on the Karma theory and the Cosmological theory. These Ganitanuyoga. Surely, this is based on probability. formulae can be seen in a collected form in the project work on the Labdhisara assigned by the . Datta had collected some terms and tried to Indian National Science Academy, New Delhi.8 give their interpretation admitting that his attempt For Astronomy, published Doctoral thesis of Lishk.9 was premature. The Dhavala texts and the For Cosmological formulae, one can see the Karnataka Vrtti were not before him. However, his Mathematics of the Tiloyapannatti."10 point of view was only historical. yet one has to dewive deep into the theory also for showing the 3. Concluding Remarks definitions and their historical importance. Dr. A.N. The appearance of the Ganitasara samgraha Singh also atempted the same way while he con of Mahaviracarya in 1912, gave the first indication tributed articles on the mathematics of the Dhavala of the existance of the Jaina School of Mathematcs and other texts. 14 However a study of the hierar in the South India. It was a full book on practical chy of various topics is needed for fruitful results mathematics. He was the first mathematician in the and recognition. world to recognize the imaginary quantities. Most In this brief article we give certain mathemati of his formulae may be seen in other forms in the cal terms out of which the asterisk marked will be Digambara Jaina texts on the Karma theory. Forthose whose measure could be rather ascertained mulae given in the commentary of the Suryaprajnapti (translated into Hindi from their Prakrit version) deserve special attention. The mathematics of the Parikkarma (eight operations-pratyutpanna, medieval period may also be seen in the works on bhagahara, varga, vargamula, ghana, ghanmula, astronomy and astrology which still await Hindi and sankalita and vyutkalita); jiva rasi*; Ajiva rasi"; English translation. These may be found in the salaka (counting rod); samkhyata*; asamkhyata*, Digambara and Svetambara Grantha Bhandaras. Muhurta*; Antarmuthurta*: Samaya*; Pradesa*; The Bhandara-keepers have to realize in right earVarga*; Vargana*: Spardhaka"; Gunahani"; Nana nest that it is their prime duty to engage Panditas Gunahani*; Anyanyabhyasta rasit; to translate the still unpublished scientific works Samayaprabaddha*: pudgala paramanu rasit: into Hindi, rather than repeating publication of the Akasa pradesa rasi*: kala samaya rasi : published works. In this respect we must acknowlKevalajnana rasi"; Kalpa"; Avali*; Rajju*: Yojana: edge our indebtendness to the foreign scholars Kalasavarna; Yavat-tavat; Addha; Uddhara; who took interest in such affairs. Now the circumVyavahara; Ardhaccheda; Trikaccheda; stances have changed and now we have to de. Vargasalaka; Vargita-samvargita; Vikalpa; pend on our own attempts, attitude and choice, in Bhanga; Samdrsti; Ganana Sthana; Oja and the larger interest of the culture. Yugma rasis; Gunasreni; Sarvadhana; Gaccha; Mukha; Madhyadhana; Adidhana; Uttaradhana: References And Notes Dharas; Alpabahutva; Utsedha; Dhanusa; Bana; 1. Albert Einstein, Ideas and opinions, Calcutta, Viskambha; Ksetraphala; and so on. 1979. p. 271.

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2. 5. 6. -YATEENDRASURI SMARAK GRANTH Commatasara of Namicandra and he must have compiled the work as a Jaina. It Siddhantacakravarti, vols. 1-4, Bhartiya also seems possible that under certain circumJnana Pitha, New Delhi, 1978-81. stances he might have adopted Saivism but whether he wrote two such manuscripts after his The Ganitasara samgraha of Mahaviracarya, conversion is doubtful. Thus looking into the needs ed, and trans. by L.C. Jain, Sholapur, 1963. of the Digambara Jaina School of Mathematics in A hecent article short in the Ganita Bharati, the South, and both were Jainas in the Digambara vol. 9 (1987), numbers 1-4 P. 54-56, by Jaina Schools of Mathematics For this purpose of Ganitanand, Ranchi, has appeared on the convincing argument one may see the project work date of Sridhara. His remarks are worth men on the Labdhisara of Namicandra tioning here, S.B. Dixit (1896) had found a Siddhantackaravarti, Indian National Science reference to sridhara by name in an old Academy, 1984-87, by L.C. jain. manuscript of Mahavira's Ganitasara Mention has been made by N.C. Jain while samgraha (ca. 85), and so put the former he was at Arrah Jaina Siddhanta Bhavana, before the later. .... Royal Asiatic Society, and this manuscript is not available now. Bombay Rs. 230 of GSS also ends with the words (ABORI? Vo. 31, p. 268) Vide The Section of Mathematics in the Sci ence and Civilization in China vol.3., by J. The similarity of several rules and of many Needham and W. Ling, Cambridge, 1959. other features between the works of sridhara and mahavira is accepted by scholars. Both may have These texts are in several volumes and have drawn from a third and common source which is gone out of print. New editions of the former not known nor likely to be known. But most of the are now coming out of the press scholars considered Mahavira as borrower (he him Sathaandgama of Acarya Puspadanta and self named his work as a collection"). Bhutabali, Books 1-16, Amaroti, Vidisha, 1939-1959. Cf. Also, Kasaya Pahuda of The date circa 799 A.D. was assigned to Gunabhadracharya, alongwith the Sridhara by N.C. Jain, by equating him to the Jaina Jayadhavala commentary of Virsenacarya author of Jyotirhnanavidhi (799). And to reconcile and Jinasenacarya, vol. 1-13, and the followsalutations 'Sivam' and 'Jinam' of the different ing Mathura, 1944.. manuscripts it has been suggested that the same Sridhara, after writing mathematical works, may 8. For the texts of the Svetambara Jaina School, have turned a Jaina toward the end of his life. cf. the exhaustive article, The Jaina School of Mathematics, by B.B. Dutta, Bul. Cal. Math. The above note also gives the opinion of B. Soc., vol. xxi, no. 2, 1929, pp. 115-145. Dutta and A.N. Singh as 750 A.D. as the probable date of Sridhara. It appears that the common source 9. For details, see the Jaina Astronomy' by Dr. material for both of the above mathematicians have S.S. Lishk, (1978), Doctoral Thesis approved been the Kasayapahuda and the Satkhandagama by the (Patiala) Punjabi University, 1987, and their commentaries which might have been Vidyasagara Publications, Delhi. Cf. also before them. As the modieval Jaina writers have Jain, L.C., (1976). On the Spira-elliptic Mobeen writing Jina and Siva for the same daity, some tion of the Sun implicit in the Tiloyapannatti, scribe might have got it changed under certain IJHS, vol. 13, no. 1, 1978, pp. 42-49. unknown circumstances. It does not seem possible that Sridhara could have availed the opportu 10. Jain, L.C. System Theory in Jaina School of nity of the Jaina source material as a non-Jaina, Mathematics, IJHS, Vol. 14, no. 1, 1979, pp. 29-63 iniinimoomiminindinimo romano 1,7 snor firinonnointivitis

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YATEENDRASURI SMARAK GRANTH11. Trilokasara . of Nemicandra History of Hindu Matiematics, Bombay, 1962. Siddhantackravarti, Sri. Mahavirji, 1976. Cf. also Jain, L.C. Divergent squences locating 15. Cf. ref. 4 for details. Transfinite sets in trilokasara, IJHS, vol. 12, 16. Cf. Jain, G.R. Cosmology, old and new, no. 1, 1977, pp. 57-75. Gwalior, 1942. 12. Cf. the project referred in 4. 17. Cf. re. 4 for the project on the Labdhisara. 13. Cf. the ref. 8. 18. Cf. ref. 9. 14. Singh; A.N. Mathematics of Dhavala, 19. Ct. Jain, L.C., Tiloyapannatti ka Ganita, in inSathkandagama, book 4 loc., citl., Amaroti, troduction to the Jambudiva pannatti 1942, pp. i-xxiv. Datta, B.B., and Singh, A.N., Samgaho, Sholapur, 1958, pp. 1-109. microcarrer oncino onvon woman wawancara vivir