Colorful, flexible seven-fold model of the evolving universe. The torus, or donut shape, is the latest physicists' conception of the shape of the universe. This same mathematical form occurs everywhere in the natural world, from electromagnetic fields to galaxies, from atoms to apples. The seven-fold principle, which can be found throughout the world of science, art, myth and music, is built into the HYPERSPHERE.

 What is a HYPERSPHERE? In mathematics, a HYPERSPHERE is a sphere having more than three dimensions. Since the early twentieth century, physicists have used this idea of a higher-dimensional sphere to describe a universe in which time is the fourth dimension.* Why is the HYPERSPHERE shaped like a donut? Today, cosmologists say that the universe of relativity and quantum physics can best be understood when seen as a torus, or donut shape. A universe containing black holes, white holes and "wormholes" conforms best to this model. And a torus has the same formula (2pi2r3) as the HYPERSPHERE. As a model of the universe, the HYPERSPHERE shows how things emerge in time and are enfolded back into fabric of the universe. You can experience this by rotating your HYPERSPHERE through its center. The HYPERSPHERE also shows how all things in the universe are interconnected, even when they appear to be separate from one another. If you isolate point a from point b in this diagram with cut c, the two points can still be connected--without crossing the cut--by going through the center: Where does the HYPERSPHERE occur in nature? Almost everywhere! The vortex, which is a section of the torus, occurs throughout the natural world-from tornados, whirlpools and electromagnetic fields to the formation of galaxies. And the torus shape is not limited to vortices. An apple, a tree, even a human being all share this same "toroidal" topology. Why does the HYPERSPHERE have seven colors? This is perhaps the most interesting part of the story. For hundreds of years, mathematicians have known that it is impossible to construct a map on a plane surface or a sphere that requires more than four colors to distinguish all adjacent areas: On a torus, it's possible to create a map that requires seven colors, and this is what we have done. If you look closely at the HYPERSPHERE, you will see that every color is touching every other color. Why is the seven-ness of the HYPERSPHERE significant? Since the HYPERSPHERE is a model of the universe, we can say that seven-ness is a basic feature of the natural world. We know this innately. This is why the seven note musical scale is naturally harmonious; why we have seven days in our week; why there are seven colors in the rainbow. Our myths and legends are full of stories where seven is the most important number, representing the completion of a mystical journey or mythical task. And this is no accident. The seven stage process is a feature of the universe itself. This has been shown by writers since time immemorial, but perhaps by none more elegantly than philosopher Arthur M. Young in The Reflexive Universe. In this simple model, which he calls the "Arc," he draws a seven-fold picture of universal evolution, the descent of spirit (light) into matter and the ascent back to our spiritual potential: *The formula for the volume of a regular sphere is 4/3pi(r3)The formula for a HYPERSPHERE is 2pi2r3. The extra pi in the HYPERSPHERE formula represents rotation in an additional dimension.