The Dancing Wu Li Masters by Gary Zukav

Author:Gary Zukav [Zukav, Gary]
Language: eng
Format: epub
ISBN: 9780553249149
Amazon: 0553249142
Publisher: Bantam
Published: 1984-09-01T14:00:00+00:00

It is not possible for us actually to see the geometry of the space-time continuum because it is four-dimensional and our sensory experience is limited to three dimensions. For that reason, it is not even possible to picture it.

For example, suppose that there existed a world of two-dimensional people. Such a world would look like a picture on a television or a movie screen. The people and the objects in a two-dimensional world would have height and width, but not depth. If these two-dimensional figures had a life and an intelligence of their own, their world would appear quite different to them than our world appears to us, for they could not experience the third dimension.

A straight line drawn between two of these people would appear to them as a wall. They would be able to walk around either end of it, but they would not be able to “step over” it, because their physical existence is limited to two dimensions. They cannot step off the screen into the third dimension. They would know what a circle is, but there is no way that they could know what a sphere is. In fact, a sphere would appear to them as a circle.

If they like to explore, they soon would discover that their world is flat and infinite. If two of them went off in opposite directions, they would never meet.

They also could create a simple geometry. Sooner or later they would generalize their experiences into abstractions to help them do and build the things that they want to do and build in their physical world. For example, they would discover that whenever three straight metal bars form a triangle, the angles of the triangle always total 180 degrees. Sooner or later, the more perceptive among them would substitute mental idealizations (straight lines) for the metal bars. That would allow them to arrive at the abstract conclusion that a triangle, which by definition is formed by three straight lines, always contains 180 degrees. To learn more about triangles, they no longer would need actually to construct them.

The geometry that such a two-dimensional people would create is the same geometry that we studied in school. It is called Euclidean geometry, in honor of the Greek, Euclid, whose thoughts on the subject were so thorough that no one expanded on them for nearly two thousand years. (The content of most high-school geometry books is about two millennia old.)

Now let us suppose that someone, unbeknownst to them, transported these two-dimensional people from their flat world onto the surface of an enormously large sphere. This means that instead of being perfectly flat, their physical world now would be somewhat curved. At first, no one would notice the difference. However, if their technology improved enough to allow them to begin to travel and to communicate over great distances, these people eventually would make a remarkable discovery. They would discover that their geometry could not be verified in their physical world.

For example, they would discover that if

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