The invisible Atlas

Rohit Gupta | Updated on January 20, 2018

Arthur Eddington showed that light from the star cluster Pleiades curved near the Sun. Pleiades by Max Ernst (above) seems to evoke the mythical Pleaides, the seven daughters of the titan Atlas   -  WikiArt

Does geometry underlie strength and awareness in the universe?

Anaximander of Miletus had proposed around 700 BC that the Earth was a cylindrical drum that floated all by itself in the infinite void. Theoretical physicist Carlo Rovelli calls him ‘the first scientist’ because after Anaximander, “...up and down become notions relative to the Earth.” Another writer, Dirk Couprie observed that “When Anaximander looked at the heaven, he imagined, for the first time in history (…) space.”

Even though Eratosthenes measured the circumference of the Earth using sundials as far back as 200 BC, it did not prove that the planet is a sphere. If the difference of solar shadows had been measured on the curved side of a cylinder instead, the result might have been the same — depending on the position of the Sun. One might wonder if the shape and size of the Earth could have been discovered at all without reference to an extraterrestrial entity.

According to the analytical geometry of René Descartes, all points, lines, curves, surfaces and solids are measured against an origin at (0, 0, 0) for three dimensions. Is it possible for tiny beings living on a giant spherical rock to discover its true shape without the help of any external vantage point? Perhaps on a planet whose suns stay on the same side for millennia, never rising — casting upon its inhabitants an eternal night; or a planet like Pluto... so far away from its parent star that sundials cast no tell-tale shadows.

The distance travelled on Earth was measured as far back as Alexander by specially appointed ‘bematists’ — soldiers who counted their own steps (this method would see a revival in British India, when spies of the Great Trigonometrical Survey, disguised as Buddhist monks — made forbidden maps of Tibet). From the time of the Yellow Emperor Huangdi (2600 BC) to the polymath Zhang Heng (100 AD), Chinese legends speak of mechanical ‘odometers’ invented to measure distance.

A careful observer would notice that while turning, the two wheels of a carriage traverse different distances. A mechanism of gears evolved to measure this differential; it provided information not only about how far a vehicle had travelled, but also in which direction. The Chinese south-pointing chariot was a mechanical compass that always pointed south on a flat surface — no matter which way one turned the chariot. Since the Earth was not a flat surface, errors in the chariot would have hinted at a spherical shape. And this global information would be gained without any assistance from external viewpoints, from local geometry alone.

Sailors, in particular, realised that a straight line on the oceans was actually curved in space, and that following a fixed compass direction could send them spiralling from pole to pole (along loxodromes or ‘rhumb lines’). Unless they sailed along the Equator, of course — since ‘great circles’ are the equivalent of straight lines on a sphere. In 1919, the astronomer Arthur Eddington observed a total solar eclipse during an expedition to the island of Principe, off the coast of west Africa. He proved Einstein right by showing that light from the star cluster Pleiades curved as it passed near the Sun before reaching the Earth. In fact the light wasn’t bending at all — it was merely following a straight line (or geodesic) in a space-time fabric that itself was curved due to the Sun’s gravity.

The idea that information about large-scale structure was embedded in local geometry was finally proved by Gauss in 1826, who called it his theorema egregium — or ‘remarkable theorem’. Gauss went further and defined ‘Gaussian curvature’ for all surfaces, a quantity which was always conserved like energy. If the surface was bent without stretching — such as a morsel of Indian bread ( roti), leaves from a plant, or a piece of paper — a soft, flat surface would become stiff when pinched in one direction. A rolled newspaper is almost as hard as a stick, for example. Change of curvature in one direction is compensated in the other direction, to keep the overall Gaussian constant. This phenomenon can be seen throughout nature, and seems to be the very basis of structural mechanics in the universe — including the tactile sense of plants.

In the tradition of Anaximander, today we think of the universe more like a drum than a cylinder. The dark circle of tuning paste (syahi) applied on Indian percussion instruments such as the tabla and the mridangam resembles a gravitationally dense black hole, whose vibrations send out waves into space. The taut skin of a dead camel undulates in response to these messages, its own geometry being the local awareness of something beyond the ordinary senses of an animal.

One might even say that intelligence has less to do with life, and more to do with structure. The intrinsic geometry of things, like an invisible Atlas, holding the world on its shoulders for eternity.

Rohit Gupta explores the history of science as Compasswallah

Follow and tweet to him @fadesingh

Published on May 06, 2016

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