He began to preach, spreading news of the revealed Truth, but alas, the world he described was so different from his own that he was declared a lunatic and interred for life. In a short book, he ruthlessly described the narrow, two- dimensional vision of his fellow citizens, while trying to evoke a fuller, deeper comprehension of the universe. That visionary was known simply as A. Square, and the religious nature of his teachings was no accident. He was invented by Edwin Abbott Abbott, a double-named preacher who was also a teacher, social reformer and authority on the works of Pope and Shakespeare. For the uninitiated, it may help to point out that the original world of A. Square is literally two-dimensional.
All residents live on a flat, infinitely large plane.
Each is a regular polygon, a triangle or square or pentagon or figures with too many sides to count. But then a three-dimensional Sphere reveals himself to A. Square by passing through Flatland's plane. He magically appears first as a point, and then grows into a larger circle as the plane passes through his equator, until he then shrinks to a point once again. Since it is impossible for Flatlanders to imagine any higher dimension, the Sphere lifts A. Square out of Flatland, providing a glimpse of Spaceland. And we, as complacent three-dimensional beings, are invited, by analogy, to imagine similarly unimaginable realms.