The last eclipse of kaliyuga

Rohit Gupta | Updated on July 15, 2019 Published on February 09, 2018

Shape of things: Dandelin spheres touching a cone. Why do they look like the optical geometry of a total solar eclipse?   -  Wikimedia Commons

The planets hanging like pendulums, and the machinations of a demon called Kali

One of the more exotic models for the movement of planets came from the French astronomer Ismaël Bullialdus (1605-1694). He imagined an invisible cone in the heavens, whose various elliptical slices gave rise to orbits — as if god were gently swinging the Earth around the sun like a pendulum. Like the equivalence later shown by Isaac Newton in the falling of a cannonball and the moon, here, too, there was “no distinction between terrestrial and celestial motion”.

The theory of ‘conic sections’ goes back to antiquity, and indeed to the very birth of geometry, if one assumes that to be the discovery of the Pythagorean theorem (this could have happened independently in several ancient cultures).

Take any right triangle and spin it around its apex, the solid shape generated by this revolution is a cone. When this cone is sliced at different angles one obtains circles, parabolas, hyperbolas and ellipses. If this is how geometers found these figures with their hands, ruler and a compass, why could the heavens not operate on the same mechanical principle?

Bullialdus speculated further about gravity in Astronomia Philolaica (1645), to ponder its role in making these orbits: “As for the power by which the Sun seizes or holds the planets, and which, being corporeal, functions in the manner of hands, it is emitted in straight lines throughout the whole extent of the world, and like the species of the Sun, it turns with the body of the Sun; now, seeing that it is corporeal, it becomes weaker and attenuated at a greater distance or interval, and the ratio of its decrease in strength is the same as in the case of light, namely, the duplicate proportion, but inversely, of the distances [that is, 1/d^2].”

Common to all of the above is the presence of quadratic terms — that is, squared or inverse squared (also known as terms of “degree 2”). From the geometry of the Pythagorean theorem, to the conic sections, and to a host of physical phenomenon (such as atmospheric pressure), which all involve equations of degree 2, all of this would have seemed connected in the 17th century.

When Archimedes (225 BC) had imagined a sphere ensconced inside a cylinder, was he imagining something more “corporeal” in the universe than abstract shapes?

Could it be envisaged that the universe itself was born from the Pythagorean theorem; a cosmic triangle starts tearing up the ethereal void and its gentle revolution around an axis mundi making the invisible cone that Bullialdus imagined?

There is an esoteric theorem from 1822 named after the Belgian mathematician Germinal Pierre Dandelin (see figure), where two spheres are sandwiched inside a cone, with a tangent plane between them. If the apex of the cone were a sun, this becomes the picture of a total solar eclipse by the moon, with the cone representing the shadow. The moon’s optimal size and distance from the Earth to cause such a perfect cover is a confounding mystery, but often cast aside as a strange coincidence. Like the imaginary cone of Bullialdus, the Dandelin construction suggests that eclipses, too, are a product of some celestial cone.

The occurrence of eclipses and planetary conjunctions has been a focal point of astronomy for thousands of years, and within the Indian tradition it finds its proper apocalyptic place. In the Brahma Vaivarta Purana, Lord Krishna describes this horrifying state of affairs thus, “For 10,000 years of (the demon, not the Goddess) Kali such devotees of Mine will be present on earth. After the departure of My devotees there will be only one varna (caste), Outcaste.”

The astronomical treatise Aryabhatiya of Aryabhata mentions a conjunction (a meeting, or passing) of all the planets and the moon — a celestial super-alignment at the start of the Kaliyuga epoch, which he gives to be 18th February, 3102 BC. This fantastical description led John Playfair, in 1790, to remark that, “There is reason to suspect, that some superstitious notions, concerning the beginning of the Calyougham, and the signs by which nature must have distinguished so great an epoch, has in this instance at least, perverted the astronomy of the Brahmins”.

The modern ‘light cones’ often seen alongside descriptions of Einstein’s general relativity have the same hourglass shape as that of a symmetric cone. Its two opposite lobes represent the causal past and the future, with the point of intersection being the present moment. It has an uncanny resemblance to a musical drum carried by Shaivaites and certain Buddhist sects in the Indian subcontinent — the damaru, which symbolises the birth of universe by the gentle beating of this cone-shaped drum, its animal-skinned space-time reverberating with light-years of gravitational waves.

Rohit Gupta explores the history of science as Compasswallah; @fadesingh

Published on February 09, 2018
This article is closed for comments.
Please Email the Editor