Mathematical Aspects of Jambudvipa
Summary
This article analyzes the numerical and geometrical features of the Jain cosmological model of Jambūdvīpa and Mount Meru. Jain scriptures describe the universe as a series of concentric continents and oceans centered on Jambūdvīpa with Mount Meru rising at its centre. The author explains that Jain cosmographers used several units of measurement—including pramāṇa, āṭmā, and utsedha yojanas—and that later commentators introduced the Tīrthaṅkara-pramāṇa (TP) yojana and a Buddhistic yojana. By systematically converting between these units, the article derives modern equivalents for cosmographical dimensions. According to Jain texts, the radius of Jambūdvīpa is 50 000 yojanas, and Mount Meru is 5 000 yojanas high. The author shows that in TP yojanas, one yojana equals about 6.37 miles, so the radius of Jambūdvīpa is roughly 318 500 miles, a value comparable to the circumference of the Earth when interpreted symbolically. He further notes that the Sun’s orbit is 800 TP yojanas above the earth and that the Moon is 80 yojanas higher. By analyzing the obliquity of the ecliptic implied by these heights, the article argues that Jain cosmography implicitly acknowledges the tilt of the celestial sphere. The author also compares the TP yojana to Buddhist and Purāṇic yojanas, deriving that one Buddhist yojana equals about 8.2 miles and one Purāṇic yojana about 9 miles. He uses these conversions to propose corrected values for the dimensions of Jambūdvīpa and Mount Meru and to reconcile textual discrepancies. Although some of the measurements yield implausibly large sizes, the author suggests that the cosmographical numbers are symbolic and encode astronomical ratios rather than literal distances. The article thus demonstrates that Jain scholars engaged in sophisticated mathematical reasoning to interpret their cosmological scriptures. By translating ancient units into modern terms and analyzing the structure of the Jain universe, the author shows how religious cosmology stimulated mathematical inquiry.
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Conclusion
The article concludes that the Jain cosmological model of Jambūdvīpa combines mythic imagery with precise numerical schemes. By carefully converting ancient units into miles, the author illustrates that Jain scholars developed a coherent measurement system and that their figures for the heights of the Sun and Moon correspond to an understanding of celestial mechanics. The analysis of obliquity suggests that the cosmographers recognized the tilt of the ecliptic. While the dimensions exceed modern physical values, the author argues that they are intended to convey cosmic harmony rather than physical geography. The study thus highlights the intersection of mathematical analysis and religious cosmology in Jain tradition.