On Geometry Of Jambudvipa - Book Summary

Here is a comprehensive summary of the provided Jain text, "On Geometry of Jambudvipa" by Dr. S. S. Lishk:

This scholarly article by Dr. S. S. Lishk delves into the geometrical and astronomical concepts presented in Jain canonical literature, particularly concerning the structure of Jambudvipa and the celestial bodies within it. The author employs mathematical analysis to interpret these ancient descriptions, suggesting they imply sophisticated astronomical understandings, including the obliquity of the ecliptic and celestial latitude.

Key Concepts and Mathematical Interpretations:

Jambudvipa and Mount Meru: Jain cosmology describes the earth as a series of concentric land and ocean rings, with Jambudvipa being the central island. Mount Meru is situated at its center. According to Tiloya Pannattia, Meru is depicted as a frustum of cones. Lishk's analysis of Meru's dimensions suggests that its concept implies the obliquity of the ecliptic. The Earth's true axis, according to this interpretation, aligns with the hypotenuse of Meru's cone, not its central axis. This leads to the calculation of Jambudvipa's "true radius" being 45,000 yojanas (50,000 yojanas apparent radius minus Meru's base radius of 5,000 yojanas). This true radius aligns with the parallel of maximum solar declination (23.5° North).
Samatala Bhumi (Flat Land): Surya Prajñapti states that the Sun moves at a height of 800 Yojanas above the samatala bhumi. Mathematical analysis of this data suggests that samatala bhumi represents a plane parallel to the plane of the ecliptic, bounded by a parallel of celestial latitude of 73.7°. Its center coincides with the projection of the pole of the ecliptic onto the Earth. The radius of samatala bhumi is calculated as 160.3 yojanas (900 yojanas minus 73.7 yojanas). This concept helps explain the Jain notion that the Moon is 89 yojanas higher than the Sun, implying a concept of celestial latitude for the Moon. Lishk also notes a consistency: the radius of Meru (5000 yojanas) is equivalent to the height difference between the Moon and the Sun above the samatala bhumi (80 yojanas, with a conversion where 1 yojana = 500 Yojanas), which is an intriguing observation linking the structural elements of the cosmos.
Solar Mandalas and Declination: The text discusses the Sun's southward journey from the sarvābhyantara mandala (innermost circle, representing the Sun's path on the summer solstice) to the sarvabāhya mandala (outermost circle). This journey is measured in earth distances of 510 yojanas. Jambudvipa Prajñapti states there are 65 solar mandalas stretching over 180 yojanas of Jambudvipa, after which the lavana samudra (salt ocean) begins. Equating 510 yojanas with 47° (double the maximum declination of 23.5°) leads to the conclusion that 180 yojanas corresponds to 16.6° (23.5° - 60.9°). This suggests that the north-south extent of mandalas in Jambudvipa is from the Sun's extreme northern position (23.5° North) down to 60.9° North latitude. This range is interpreted as covering the southern limit of ancient India, including modern Sri Lanka.
Evolution of Jambudvipa's Limits: The author proposes that the concept of solar mandalas, derived from gnomonic experiments (using a sundial), implies that the outermost limit of Jambudvipa aligns with the terrestrial latitude of 60.9° North. The article acknowledges that the apparent geometry of a flat earth is confirmed by these Jainian notions, but actual observations fit the "real geometry of earth." Lishk speculates about shifts in the conceptualization of Jambudvipa's limits over time. Initially, the apparent radius might have been taken as the true radius, shifting the limit southwards by 80 yojanas. Later, the development of the mandala concept through gnomonic experiments shifted it further south by 180 yojanas. The concept of "Jagat" might have been introduced to account for discrepancies or errors in these measurements.

Conclusion:

Dr. S. S. Lishk's research highlights the remarkable sophistication of Jain astronomical thought. By applying mathematical analysis to canonical texts, he argues that Jain cosmology implies an understanding of celestial phenomena like the obliquity of the ecliptic and celestial latitude. The consistent figures and interrelationships observed between elements like Meru, samatala bhumi, and the solar mandalas suggest a detailed and interconnected cosmological model. The study opens new avenues for research into Hindu astronomy and the significant contributions of Jain acharyas to these fields.