Radha and the space-time illusion

Rohit Gupta | Updated on January 19, 2018
Before sunrise: The night sky in this 1650 painting betrays the artist’s ignorance of astronomy

Before sunrise: The night sky in this 1650 painting betrays the artist’s ignorance of astronomy   -  Wikimedia Commons

Rohit Gupta

Rohit Gupta   -  Business Line

The history of perspective in art, engineering and architecture

This miniature painting (right) from circa 1650, by an unknown artist, shows Lord Krishna’s lover Radha in an elegant pose at night with the stars looking down. From just this single mythological image, one may extrapolate a modest sketch of science in the 17th century.

Since the pigments don’t seem to have faded or changed much in over 360 years, it shows a good knowledge of materials, if not their actual chemistry. The night sky betrays the painter’s ignorance of astronomy; to depict stars as points distributed evenly in the upper sky, instead of irregular clusters and constellations, is wrong. The ornate water vessels are testament to the Mughal mastery of metallurgy, but their proportions against the little crane show that geometric perspective has not yet been discovered in this culture; or perhaps the exotic bird is now extinct like Emperor Jahangir’s dodo.

Although the moon is full, it casts no shadows on the ground — as if the painter is unsure how they should fall. It may seem that the lonely milkmaid is waiting for Krishna at the upper edge of the Earth’s atmosphere, the moon visible directly through the vacuum of outer space. The twisted, rhombic frame of Radha’s square seat, however, shows an amateur attempt at three-dimensional illusion; an affine transformation in today’s vocabulary.

The craft of mimicking three dimensions of space on a two-dimensional surface was significantly more advanced at this time in faraway Europe, where Renaissance artists such as Filippo Brunelleschi (AD 1377-1446) had inherited and re-invented Greco-Islamic geometry. It gave to their architects and mechanical engineers the modern equivalent of software — a perspective drawing with depth that could be reproduced and printed. More importantly, it transformed the way they designed these buildings and machines themselves. Mechanical and architectural drawing may have served a similar purpose in the Renaissance, as computer simulations of complex physical systems, such as aircraft or galaxies, do for the modern scientist.

These methods entered popular entertainment as well, in the hands of innovative stage-designers such as Nicola Sabbatini. Inspired by Perspectivae Libri VI (1600 AD), a book written by mathematician and astronomer Guidobaldo del Monte (a friend of Galileo’s), Sabbatini created new kinds of machinery for dramatic effects in theatre: A wave machine to show the turbulence of sea, hidden mechanisms for storms, lightning, flying gods and blazing fires of hell. If perspective drawing was like software for the Renaissance artists, Sabbatini was creating the equivalent of computer graphics in movies.

In an unexpected turn of events, this new science of perspective was to lay the foundations of a revolution in geometry. What if different curves like lines, circles, ellipses, parabolas and hyperbolas were actually the same when viewed from different points of view? Even more profound was the realisation that not only did this field of projective geometry contain new theorems, it contained theorems about theorems. Simply by interchanging the usage of ‘points’ with ‘lines’, one theorem could be transformed into another — a phenomenon called the Duality Principle.

Despite a foundational work of 1639 by Girard Desargues being lost for over 200 years, this force of unifying ideas was profound; and it grew slowly in minds such as Pascal and Monge, Poncelet , Gergonne, all of whom came later. Towards the end of the 19th century, Arthur Cayley (1821-1895) was led to exclaim that “’projective geometry is all geometry”; in 1925, Felix Klein concurred by calling it “the royal road” to geometry.

As the 20th century raised its curtain, Einstein’s field equations of gravity hinted at a spherical or hyperbolic shape of the universe. In the opposite direction, Paul Dirac used projective geometry to build his quantum mechanics. Could it be that these two discordant sciences had an underlying symmetry? Space-time had become the theatre’s stage, quantum particles its actors and the laws of physics its play. And yet these three pieces do not fit together into a coherent whole until this day.

Some theoretical physicists such as Juan Maldacena have now proposed that the three dimensions of space, and one of time are possibly the four-dimensional projection of information that exists in only two dimensions. This ‘holographic principle’ is like an echo of those Renaissance artists who wanted to bewitch the beholder with their virtual conjurings on a sheet of paper, or like maya in Hindu cosmology.

In the painting we have, if Radha were to look up toward the night sky, she would notice in some time that the stars are not drawing great, concentric circles in the sky with Polaris at the centre, as she expected. These equidistant, identical points cannot be traced, even against the blackboard of night. They look like slow tidal waves, or Moiré patterns. There are no shadows because the moonlight has been subdued by light from these dense stars. And this strange world she would know to be maya, the illusion that Krishna keeps talking about.

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

Published on February 12, 2016

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