Sunday, July 12, 2020

Flatland: A Romance of Many Dimensions

Flatland: A Romance of Many Dimensions
By Edwin A. Abbott
Read in 9th grade

Square lives in Flatland, a two dimensional world with height and width. Their world has all four cardinal directions, but no up or down, and its subjects could not possibly comprehend such a thing. In this world, all women are lines, with varying lengths based on age. The lowest class of men are isosceles triangles, with vertex angle measures depending on their status. These shapes can eventually get into the class of equilateral triangles by increasing angle measures every generation. After that, every generation results in an increased number of sides by one, until a shape is Polygonal, and eventually has so many sides as to be called a circle. One day, Square has a dream where he visits Lineland, a one dimensional world that is, quite literally, a line. Just as Flatlanders cannot conceive the possibility of three dimensions, the king of Lineland does not comprehend the Square when he attempts to show the king that Lineland is not the entire universe. Then, the next day, he is visited by a Sphere. At first, Square is astonished, believing that a perfect circle has graced his home. But in fact, the Sphere has arrived to preach the Gospel of Three Dimensions. He attempts to make the Square understand the concept of up, the dimension of height, but the Square falls to the conclusion that the Sphere is a lunatic, and tries to kill him with a sharp corner. But he cannot, for the Sphere has passed out of Flatland, and as he goes up, Square can see all the circular cross-sections of him, getting smaller and smaller, then increasing again as he returns. The Square, however, believes the Sphere is a magician, so as a last resort, the Sphere lifts him out of Flatland entirely and takes him into Space to look down on his two dimensional work from above. He can see into the homes, the hearts, the thoughts of all those in Flatland. It also turns out that a visitor from Spaceland comes to try to preach the Third Dimension. The Chief Circle outlaws the discussion of such things, and the Square sees what his fate shall be. Still, he is unable to contain what he has seen, and is imprisoned for speaking of three dimensions.

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