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The snake and the lotus

Rohit Gupta | Updated on March 10, 2018 Published on March 10, 2017
Life in squares: Game of Heaven and Hell (Jnana Bagi), snakes and ladders in Jain cosmology

Life in squares: Game of Heaven and Hell (Jnana Bagi), snakes and ladders in Jain cosmology   -  Wikipedia

Rohit Gupta

Rohit Gupta

From the ancient game of snakes and ladders to modern string theory

The ancient game of “snakes and ladders” is a metaphor for learning, among other things, either morality or, in some cases, the worldly circumstance of the human being. Like a photon emerging from the sun’s womb, or a billiard ball, the player’s journey ricochets from and falls into unexpected detours on the perfect Cartesian geometry of the board.

Mathematically speaking, the snake and the staircase are no different from each other. They are mere placeholders for transport from one point on the board to another via a subterranean path. This is a journey that happens in a different dimension, through a topological hole in the fabric of the board game’s universe. There is a point of entry and an exit, like an algorithm which takes input and gives output. Only in the serpent’s depiction as Ouroboros, the snake eating its own tail, does the output go back as input, creating an infinite feedback loop.

When August Kekulé discovered the circular symmetry of the benzene molecule, he claimed to have dreamt of a snake devouring its own tail (a claim which may have been manufactured for dramatic effect). However, it was not so much benzene but organic chemistry, the molecules of life, which underwent a revolution. In order for life to be self-sustaining, there must be a chemistry (autocatalytic reactions) that could trigger itself without external stimulus. The infinite feedback loop, the self-generating automata, the instantaneous rebirth became a metaphor for life itself.

In a 2003 paper on the subject, Barry M Trost observes that “Kekulé establishing that carbon has four valences and Jacobus Henricus van’t Hoff and Joseph Achille Le Bel arranging these valences in a tetrahedral fashion set the stage for one of the most profound features of organic molecules — their ability to exist in mirror-image forms. The implications of this fundamental feature of organic molecules are immense. Undoubtedly, the richness of the biological world would not exist without this structural feature. Indeed, the very existence of the biological world is likely to have become possible only because of its exquisite use of this phenomenon.”

This solves the problem of creating a cyclical time, but can a single snake of any length fill up a given space without crossing itself even once? The mathematical study of space-filling curves is one such family, enumerating all the ways in which this is possible. (“Drawing —” once remarked Paul Klee, “... is taking a line for a walk.”)

In physics, a theory is considered incomplete if it assumes the prior existence of space and time, and does not suggest a mechanism by which they are created before the particles that play within it. In a sense, the rules of the game must generate the board on which it is played. Certain flavours of modern string theory (and there are far too many) suggest that such a cosmological physics can be generated by space-filling curves in higher dimensions. Perhaps while taking a snake for a walk in nine dimensions, it gets knotted with itself at a vast number of points, and these knots are what we perceive as fundamental particles. What if space-time is the fabric created by the body of one snake that stretches and folds from the origin to infinity? Such a snake would be one-dimensional, and yet create the illusion of multiple dimensions that we see.

Although the study of knots goes back to prehistory, especially among sailors, “in the 1860s, Lord Kelvin’s theory that atoms were knots in the aether led to Peter Guthrie Tait’s creation of the first knot tables for complete classification. Tait, in 1885, published a table of knots with up to 10 crossings, and what came to be known as the Tait conjectures. This record motivated the early knot theorists, but knot theory eventually became part of the emerging subject of topology.” (Wikipedia)

Topology is the study of space where such things as distance and deformation do not matter, so long as certain other things, such as connectedness, are preserved. There is no difference between a child’s marble and the Earth in space, or a wedding ring and a cyclotron (or torus, a knot with one hole in it). Some of these topological knots in space may also mirror each other across vast distances and scales, creating a fractalised universe.

Brahmajala Sutra (Brahma’s Net), translated in AD 406 by Mahayana Buddhists, narrates a similar vision: “Now, I, Vairocana Buddha, am sitting atop a lotus pedestal; on a thousand flowers surrounding me are a thousand Sakyamuni Buddhas. Each flower supports a hundred million worlds; in each world a Sakyamuni Buddha appears. All are seated beneath a Bodhi-tree, all simultaneously attain Buddhahood. All these innumerable Buddhas have Vairocana as their original body.”

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

Published on March 10, 2017
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