Notion of Declination Implied in the Concept of Mandala (Diurnal Circle) in Jaina School of Astronomy
Summary
This article by Sajjan Singh Lishk investigates a curious aspect of ancient Jain cosmology: the notion of declination, or the north‑south displacement of the Sun and Moon relative to the equator, implied in the concept of mandala or diurnal circle. Jain texts postulate an idealised geography with two Suns and two Moons moving in concentric circles around Mount Meru, the axial mountain at the centre of the flat earth; these circles of light, called solar or lunar mandalas, are described as bands encircling Jambudvipa and Lavanasamudra. Lishk draws on canonical works such as Jambudvipa Prajnapti and Sūrya Prajnapti to enumerate 184 solar mandalas and 182 lunar mandalas and examines how Jain astronomers linked these circles to the Sun’s annual course. One text states that the Sun traverses all 366 solar mandalas during its 366‑day year by moving outward through each circle on the summer solstice and inward on the winter solstice. The author interprets this as an implicit recognition of the Sun’s varying declination: by occupying different mandalas at different times of the year, the Sun appears north or south of the terrestrial centre. The article then quantifies distances between the solar mandalas and Mount Meru. Using units like yojanas and yūti, the texts specify that the innermost solar mandala lies 44 820 yojanas from Meru and that each subsequent mandala is 1 1⁄6 yojana further south or north, leading to an outermost solar mandala 45 330 yojanas distant. By analysing these figures, Lishk reconstructs a geometric model in which the Sun progresses across latitudes (mandalas) at a steady rate, implying knowledge of solar declination. He also compares solar and lunar mandala systems, noting that the distance between the extreme solar and lunar mandalas corresponds to the diameter of the lunar disc. The paper concludes with a diagram illustrating the north‑south distances between the extreme solar and lunar mandalas and notes that Jain scholars conceptualised declination as a shift between mandalas rather than as angular latitude. Lishk argues that this cosmology predates the development of spherical trigonometry and reflects an indigenous understanding of celestial motion.
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Conclusion
By dissecting the mandala concept in Jain cosmology, the author shows that ancient Indian thinkers embedded observations about the Sun’s seasonal motion within mythological models of concentric discs. Although the model assumes a flat earth and multiple Suns and Moons, the systematic progression through 184 mandalas to complete an annual cycle mirrors the modern idea of declination. The article highlights the sophisticated numerical and geometric reasoning found in Jain canonical texts and invites scholars to reassess the contribution of Jain astronomy to the history of science.