I'm A Little Square

The book: “Flatland: A Romance Of Many Dimensions,” was written in 1884 by Edwin Abbott, and is still popular among mathematics and computer science students. The story is that Flatland was a two-dimensional world and seeing and knowing could only be seen and known in that plane; there was nothing above it or below it. Flatland was populated by a large number of Squares and Circles, with a subculture of Triangles and a occasional Parallelogram. In the book there is a story of one Square and how he is awakened one day. It begins:

One sunny day in Flatland a little Square saw a Circle coming toward him. He carried on with his usual activities, but it soon became obvious that this Circle was not like any he had seen before. This Circle just kept getting larger and larger until it was clearly not just a Circle, but a Sphere. Square had heard about Spheres before, but he had always believed that they were just fairy tales or children’s myths. This one, however, looked very real indeed. Frightened, Square began to run. “Don’t be afraid,” called the Sphere, “I won’t hurt you!” The Square stopped and turned toward the stranger. Slowly backing away, he asked, “What are you, anyway?” “I’m a Sphere.”

“But there are no Spheres in Flatland,” Squared challenged.

“That may be so,” gently replied the Sphere, but Flatland is not all there is to life. There is more to life than the two dimensions with which you are familiar- much, much more, indeed. There is actually another dimension of which most of the citizens of Flatland are not aware at all: Spaceland. Spaceland is a wonderful world with so much more freedom to see and move and play! But you cannot enjoy it because all of you in Flatland have gotten used to looking only forward, back, and to the sides. Hardly anyone in Flatland ever looks up! If you did, you would see many wondrous forms far more exciting and fascinating than you have found in Flatland.”

“How can I see these lovely sights?” young Square wondered aloud.
“Simply look up and you will see the whole picture,” the Sphere explained. “In fact,” Sphere went on, “you will be surprised to know that what you see in Flatland is actually a part of the third dimension. Those you see as Circles are actually Spheres, but because you see only in two dimensions, all you see is one plane of a much greater reality!”

“You will be happy yo know that you and your friends are not just Squares, but you are actually facets of a marvelous and very practical form called a “Cube.” The Triangles belong to a mystical design called “Pyramid,” and that funny-looking family down the street that you laugh at, Mr. and Mrs. Ellipse, are actually components of a most important configuration called “Egg.”
“Alas, but you see none of these rich aspects of your life because you are so preoccupied with what is behind and in front of you- Oh Square if you only knew how much, much more there is to life, you would dance with joy!”

Sphere paused for a moment. She realized this was a lot for a little Square to absorb so quickly, and she wanted to give him time to awaken.

“My dear Square, the universe is so much greater than you have imagined- and now you are seeing things as they truly are, and indeed have always been. I am very happy for you.”

The Square was astounded; yet somehow it made sense. Into his mind flashed some memories of having seen unusual shapes when he was just a few points old. He remembered seeing beautiful, dazzling configurations just before going to sleep or while traveling through the park of Diamonds. Then he recalled that when he had told his mother about them that she patted him on one of his sides and told him he had a vivid imagination. Eventually he stopped seeing them- he didn’t want to be different from his friends.

The Sphere, shimmering before the young one, sensed he was ready to see more.
“Would you like to see your true self?” she asked.

The Square hesitated. He wasn’t quite sure about his true self. It seemed that most of the inhabitants of Flatland were rather fearful of looking at their true self. Whenever someone would bring up the idea of their true self at a party, for example, someone would quickly make a joke or change the subject. Why were the Flatlanders so afraid of their own being? Even the Square could not understand why hardly anyone in Flatland loved himself.

“Yes,” Square answered, “Yes I would like to see my true self.” The moment he said those words his fear went away.

“Very well, then- Look up!” Sphere commanded. “Look up and you will see who you really are!”

Square looked up and he could hardly believe his eyes. What a wondrous sight he did see! He saw that he was not just a small Polygon with four sides of equal length, as he had read in his Geometric Geneology textbook. He saw that his square self was just one part of his being, the part that could be seen in Flatland. Square saw that he was actually a great, glowing Cube, of which the lines that he thought limited him were but one aspect. How exciting to find that he was a whole! So that was why he had felt so strangely incomplete as a little Square! Now he realized that there was nothing to be afraid of, nothing in his real self that could harm him. In fact, nothing had ever made him as happy as looking upon his real self and seeing all that he was.

That was just the beginning. As the Square became more and more comfortable looking up, he could see the real identity of everyone in Flatland! They were so beautiful! He saw marvelous Cones, sparkling Cylinders, and even a Great Sphere made up of triangles. His guide told him this was a “Geodesic Dome”(but hardly anyone in Flatland was ready for that one). Square saw that what was happening in Flatland was such a little part of the whole picture. And he was afraid no more.

I live in a three dimensional world and I am scared to see and feel the other dimensions that surround me. By looking within I am able to see my true self; I am able to feel whole, and just like the Square, I’m not afraid anymore.

I'm A Little Square