Friday, October 13, 2006

An Ever Increasing Circle

Imagine for example, a two-dimensional surface such as a plane. This plane extends off to infinity in every direction. To a being living in the plane, there is nothing beyond the plane, and indeed the notion of a third dimension is inconceivable. A mathematician of the University of Squash or theologian amongst the First Flat Church of Christ, Polygon, might be able to imagine the idea of a third dimension, by simple extrapolation. They may see the two dimensions of their own universe, and speculate a third. But they are incapable of truly imagining the reality of a third dimension, as we are incapable of imagining a fourth or a fifth dimension. We can say, "Oh, another dimension, what an excellent and original idea!" But we are incapable of imagining what life would truly be like in a universe of four dimensions.

Suddenly, to the inhabitants of the plane, a strange and unusual apparition appears. At first a point, then an ever increasing circle, then a diminishing circle, then a point again. Then the apparition vanishes. Truly they have never seen anything like this before. A creature which changes shape, and vanishes into nothing? And then they tell their family and friends, but the other Planers merely laugh. "There is no room for your crazy beliefs," they say. "They are not rational!" And so only the memory remains, kept alive by those poor Planers who had the misfortune of witnessing the miraculous: the passing of the almighty Sphere through the plane.

We are as tiny scratches of ink upon a piece of paper. Once in an age, a Sphere of great worth passes through the page. And we scoff. And we laugh. The page is all there is, we say. Black ink on white paper. Color is a thing of three dimensions. We scoff. We go about our lives. And inside our black outlines, all is white. All is empty.

The Sphere floats on. Floats on to other realms, and other pages, where we cannot follow.

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