martes, 2 de marzo de 2010
Flatland is a two dimensional world whose inhabitans are all geometrical figures. The protagonist is a square. One day the square is visited by a sphere from a tree-dimensional world called Spaceland. When a sphere visits Flatland, however. all that is visible to Flatlanders is the part of the sphere that lies in their place -in other words, a circle. The square is astonished that the circle is able to grow or shrink at will (by rising or sinking into the place of Flatland) and even to dissapear and reappear in a different place (by leaving the plane, and then re-entering it). The sphere tries to explain the concept of the third dimension to the two-dimensional square, but the square doesn´t get it. He cannot understand what it means to have thickness, in addiction to height and breadth, nor can he understand that the circle came from up above him, where "up" does not mean from the North. The sphere presents analogies and geometrical demonstrations of how to move from one dimension to two, and then from two to three, but the square still finds the idea of moving "up" out of the plane of Flatland ridiculous. In desesperation, the sphere yanks the square up out of Flatland and into the third dimension, so that the square can look down on his world and see it all at once. He can see the inside of all the houses and the guts (insides) of all the inhabitants. The square recalls the experience:
An unspekeable horror seized me. There was darkness; then a dizzy, sickening sensation of sight that was not like seeing; I saw space that was not space: I was myself, and not myself. When I could find voice, I shrieked aloud in agony, "Either this is madness or it is Hell". "It is neither", calmly replied the voice of the sphere, "it is knowdledge; it is Three Dimensions: open your eye once again and try to look steadily." I looked, and, behild, a new world!
The square is awestruck. He prostrates himself before the sphere and becomes the sphere´s disciple. Upon his return to Flatland, he struggles to preach the "Gospel of Three Dimensions" to his fellow two-dimensional creatures -but in vain.