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Mahåvira : The Systematizer
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three dimensionally (in payaya or ghana), in the elongated form also one dimensionally (in sedhi). 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 Mahâvîra's. The frequency of their occurence 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 it. But this certainly asked for a wider knowledge of mathematics than Mahâvîra had, if we are allowed to judge by the favourite ideas he presumably cherished. Nor is the astronomy of the Jains, as, above all, it is offered to us by Surapannatti, 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 polemics. As to the aspect of the world, however, it bears Mahâvîra's stamping by his doubling the widths of geographical units a geometrical line with the quotient. This, perhaps, accounts for the contention that there are two suns and moons over Jambuddiva, which then leads up to the doubling of further stars. The arithmetical line is applied in Mahâvîra's teaching to the sums. Of a sum (jumma or rasi or rasijumma) continuously diminished by 4 there remains 4 (or O), 3,2 or 1, and it is called accordingly by the terms used at diceplaying kada-jumma teoya, davara or kali-oya (Viy. 744b), and even khuddaga may be placed at the head of these names of khudda-jumma (Viy. 948b). They are called small “sums” as against the “large” ones, maha-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. These calculations to be found in the last passages of the Viy.-are applied in the most different connexions, though even Abhayadeva fails to know what to do with the latter.
Other speculations related to permutations 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 (Viy. 686), with the result that each of these four passions occur with all beings, with all minus 1, with several ones and with
