Saturday, January 25, 2014

Building the Unsolvable Maze

I came across a tweet via Simon Singh, famous writer of books based on math-topics. I've read a couple of them: 'Fermat's last theorem' and 'The code book'. His tweet points to a picture of an amazing maze hand-drawn over 30 years ago in Japan. Although it is supposed to be 'unsolvable', some comments there claim that it could be solved very quickly if it was made publicly available. Among the very first papers I read after coming to the U.S to study traffic engineering (to understand the reasons for India's chaotic, maze like traffic) was about Moore's algorithm entitled "shortest path through a maze". Mathematically, the shortest path problem formulation has a couple of properties of small interest in the context of this discussion. It has no duality gap, and is totally unimodular: It is sufficient to solve the continuous 'relaxation' to recover an integral optimal solution to the primal or dual formulation. Wikipedia has a page on maze-solving algorithms.  Interesting as the optimization problem of finding an 'optimal route' to 'escape' this maze is, a more interesting question to me personally was: why would someone hand-build such an intricate maze over years; and then why not claim any credit for it? I have tried to interpret this based on my understanding of the Indian way.

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The intense concentration required for such a task is surely daunting: to at once elevate one's consciousness while also dissolving one's aham (ego) that hinders the mind from systematically growing a complex maze whose paths increase rapidly over time as more forks and merges are constructed. Paths that stop even as they begin, paths that ultimately lead nowhere, paths where you travel for a while, only to discover that you are back where you were before... and then after a lot of calm, refined, and introspective searching (not suffering), finding a path that leads one to satya (ultimate reality/truth) that transcends the maya of the maze that held us in its thrall. A path that dissolves the noisy duality between the world within the maze and without, uniting them harmoniously into a unified whole, even as the space enclosed within the maze maintains a provisional identity within this overall unity. And then perhaps a realization that there could be a pluralism of such (alternative optimal) transcendental paths to satya. A harmonious unity within multiplicity that celebrates its diversity, rather than a synthesized unity derived by optimizing the goal of orderly sameness. The latter produces an efficient monoculture, but one that invariably regards pluralism as a seed of chaos. The former, integral unity best represents the nature of the underlying philosophical unity of India that has continually preserved and refined its dharma civilization over several thousand years. This forms the dharmic basis for any reasonable 'idea of India'. I look forward to reading Rajiv Malhotra's new book on this subject.

Journeys that traverse such a path have led to amazing discoveries that enlightened the world, and will continue to do so. Perhaps it produced this captivating art that simultaneously appeals to the casual observer, the artist, the seeker, and the analyst alike; yet each of us seeing only a partial facet of its underlying truth. A work of art to which its 'creator' deliberately did not append a signature to, and claim ownership of, perhaps unwilling to disturb it's harmony. That is the way of the Yogi.

Dedicated to Rajiv Malhotra on the occasion of India's 65th republic day.Thank you.

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