The Doctrine of the Jainas, Described after the Old Sources c6.103

Language: English

c6.103.1

§21. Even individual traits borrowed from nature have been incorporated into the total conception by Mahāvīra, the systematizer, as is shown by many passages of the Viy. Thus his explanation for a hot spring he must have visited near Rāyagiha (§ 94), his theory of the wind (§ 110), and the life-community of fire and wind (§ 105). The fact that the movement of a flying object slows down (Viy. 176 b; Jiv. 374b) was probably concluded by Mahāvīra from the effect of gravitation. Nor should we omit the wind kavvadaya (Viy. 499b) arising between the heart and the liver and causing within a galloping horse the sound of khu khu. Above all, however, the most versatile thinker we know of in ancient India had a liking for figures and arithmetic, that characterizes his speeches most extraordinarily. In most cases we are not able to prove which considerations are his own and which are of others, but he calls himself the author of a theory of the 7 possible lines (evam khalu, Goyama, mae satta seḍhio paṇṇattāo, Viy. 954b). Acc. to Viy. 866b such a line is either straight (ujjuya-āyaya), has 1 break (egao-vamka), 2 breaks (duhao-v.), forms an open rectangle on one side (egao-khaha), forms a rectangular Z (duhao-kh.)¹, is circular (cakkavāla) or semicircular (addha-c.). As a general principle there is neither a beginning nor an end to a line, whereas either is the case within the world since the world is finite.

c6.103.2

In the infinite non-world (§ 103) this applies to the tangential straight lines that touches a border plane² of the world. A line leading from the non-world and meeting with the world border has no beginning, a line leading from the latter into the non-world is without an end, and a line leading all around the world in one way or other has neither beginning nor end (Viy. 866a with comm.). As to geometrical forms (samṭhāna)³—to add them in this connexion—Viy. 860a refers to orbicular (paṭṭa), triangular, rectangular, elongated ones (āyaya), and to the ring (parimaṇḍala)⁴, and in them the atoms are arranged either two-or three-dimensionally (in payara or ghaṇa), in the elongated form also one-dimensionally (in seḍhi). In referring to them the minimum and maximum numbers of the atoms and space units are being discussed, and this leads us up to the calculative reflections. In them a certain family likeness seems to become apparent, and where it goes together with a special liking for applying it we are probably confronted with an original idea of Mahāvīra’s. The frequency of their occurrence alone is not decisive, or else it would be he, too, who had come to find the root of 10 and to apply it in the sense of the figure of π⁵. But this certainly asked for a wider knowledge of mathematics than Mahāvīra had, if we are allowed to judge by the favourite ideas he presumably cherished.

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Nor is the astronomy of the Jains, as, above all, it is offered to us by the Sūrapannatti, a creation of his own, but it rather reflects the thinking of generations. This becomes equally clear by the usage of "we" instead of "I" and by the absence of polemics¹. As to the aspect of the world, however, it bears Mahāvīra's stamping by his doubling the widths of geographical units, a geometrical line with the quotient 2 (§ 122). This, perhaps, accounts for the contention that there are two suns and moons over Jambuddīva, which then leads up to the doubling of further stars (§ 128). The arithmetical line is applied in Mahāvīra's teaching to the sums. Of a sum (*jumma* or *rāsi* or *rāsi-jumma*)² continuously diminished by 4 there remains 4 (or 0), 3, 2 or 1, and it is called accordingly by the terms used at dice-playing *kaḍa-jumma*, *teoya*, *dāvara* or *kali-oya* (Viy. 744b)³, and even *khuddāga* may be paced at the head of these names of *khudda-jumma* (Viy. 948b). They are called small "sums" as against the "large" ones, *mahā-j.* (Viy. 964b). They are sums expressing by their name not only the final remainder but also the number of the factors, the latter always preceding in the bipartite names of *kaḍa-jumma-kaḍajumma*, *k.-teoya*, etc.⁴. These calculations—to be found in the last passages of the Viy.—are applied in the most different connexions⁵, though even Abhayadeva fails to know what to do with the latter¹.

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Other speculations related to permutations² are arrived at by crossing different lines of conceptions. Thus, for instance, it is being examined how many beings occupying one and the same hell exercise one of the 4 main passions, i.e. anger, pride, fraud, and greed (§ 167) (Viy. 68b), with the result that each of these four passions occurs with all beings, with all minus 1, with several ones and with a single one. Or, it is being demonstrated in which way 1-10 hell-beings (§ 109) divide among the 7 regions (Viy. 439b ff.). In order to give a characteristic example of the calculatory intelligence we here refer to the statements made on the maximum and minimum (*jahanneṇam* and *ukkoseṇam*) of most of the figures of the system, to the qualification of being both the first and not the first, both the last and not the last of one's like (*paḍhama* and *apaḍhama*, *carima* and *acarima*) (Viy. 731b), to which the Carama-paya Pannav. 10 goes back, to the discrimination made between the beginning and the continuation of a certain condition (a. o. *aṇantara-siddha* and *paramparas.*, Viy. 877a, also-*neraiya* Ṭhāṇ. 513b), and finally to the teaching of the relative number (T. 1, 8: *alpa-bahutva*). It answers the question of *kayarā kayarehimto appā vā bahugā vā tullā vā visesāhiyā vā*? Such statements (in the Viy. first 235b) are comprised in Pannav. 3, the Bahuvattavvaya-paya.

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An object exists in proportionally a smallest number (*savva-tthovā*), others in either undecidedly, uncountably, or infinitely as many numbers (*samkhejja-guṇā*, *asaṃkhejja-guṇā*, *aṇantaguṇā*). The terms mentioned here—and to be represented in this book by the figures of *x*, *i*, ∞—are very frequent. In this connexion *aṇanta* specifically means nothing else but any other high figure. It is applied in a similarly naive way as the idea of time, which, at least within the cosmography, means a quality among others, and which, as such a one, may be either attributed or denied to a region (§ 128).