Tuesday, March 22, 2011

The Great Square Within the Torus

The other morning we were reading Verse 41 in the Tao Te Ching and came across this puzzling line:
"The Great Square has no corners"

which the Simple Explanation might tranlate as

"Ideal Squareness lacks corners"

Naturally, I began wondering about the Great Square with no corners and how Ideal Squareness would arise from the toroidal shape. After a couple of weeks of passive pondering and mental modeling, this is what I've come up with.

Since I'm accustomed to working with a 3-D mental model, I upped the square to a cube.

Then I imagined this cube suspended at its eight corner points against the inner walls of a spherical torus. 

Here's an animated blue cube rotating inside a sphere I found on Google images. This will help to visualize what I'm talking about. The other Platonic shapes are rotating in there, too, but we will try to disregard them for now.

Of course, we want to imagine the sphere in the above link is a torus.

The center point of the cube would also be the center point of the torus. Now remove any lines, walls, or corners you may have imagined for the cube and just sense its pure Form suspended there, framed by the torus. This would be an Ideal Cube precisely placed in the only position a cube can occupy within the Ideal Torus. Perhaps this is the Great Square of the universal UC.

Now consider the following chalk drawings where I build the square and cube from two essential elements of the torus: the pole and the plane of the equator. This will give us another way of conceptualizing the Perfect Square and Perfect Cube.
This is a cross section of a torus. In the Simple Explanation, the white star at the middle is the transdimensional zero-point field from which creation springs forth.

Torus with pole. There is only one line that goes straight up through the middle of a singularity or zero-point at the center of the torus without touching any curved sides.

Torus with pole and plane of equator. There is only one plane of the equator, which runs perpendicular to the pole and from side to side along the widest part of the torus, dividing the torus into top and bottom.

Torus with parallel poles, perpendicular to the equatorial plane, bisecting the toroidal tube.

Torus with perfect cube. The lines of the square/walls of the cube are precisely placed relative to the pole and equatorial plane. Once this shape is achieved within the torus, the Platonic shapes and all regular geometry are possible.
The chalk drawings below are the same series as the drawings above, but from a cutaway, topside view, looking straight down on the bottom half of the toroidal sphere from above.
Pardon my free-hand drawing. This is supposed to be a square touching the inside edge of the circle at four points, or a cube touching the inside edge of the torus at eight points. The center of the cube is the same as the center of the torus. All planes of the cube are either parallel or perpendicular to the pole and equatorial plane, thereby making the placement of this cube quite precise.

This is both a top-side cutaway view of the top and bottom planes of the perfect cube, and a side cutaway view of the perfect cube sitting in center of the toroidal tube.

This is also a view from the top of the plane of the equator radiating out from the center point until it bumps up against the inner walls of the confining toroidal space.

Here is the topside view of the torus, not cutaway. You can still see the white star at the middle from outside the torus looking down the funnel. The outside of this torus is white, just like the star at the middle, and the skin of the torus is feeding upward and wrapping over the lip of the funnel, then condensing toward the middle. At the middle, the outside metaversal energies turn inside out and push into the blue toroidal interior space, where material instantiates from energy and form.The funnel is barely visible; the white exterior is pouring up over the lip of the top of the torus and down into the funnel toward the ananada/joy zero point at the center.