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The Plan of a Square

Published online by Cambridge University Press:  01 January 2020

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Amidst many discussions on super-valuational algebras and their philosophical applications - on which I was writing my dissertation - Hans and I once paused to ponder the mystical experience of the square. I mean A Square, the hero of Flatland. I mean that perfectly two-dimensional being, with no depth whatsoever, citizen of an equally two-dimensional depthless world, who one day had the good fortune of receiving a visit from a Sphere. What's more, he had the fortune of being able to visit, albeit briefly, the undreamt-of three-dimensional world his guest came from - which is to say, our threedimensional world. He visited and experienced our world before falling back for all eternity into the total flatness of his: Flatland, the plane world, the world with no aboves and no belows, the world in which cars and airplanes alike, so to speak, belong to the same category, and everything, literally everything, is reduced to fragile shadows on an enormous and eternally illuminated floor.

Type
Research Article
Copyright
Copyright © The Authors 2008

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