Let us begin with the seed of fore-knowledge. It is a simple tetrahedron that casts the shadow of a square. This is fore-knowledge because we see three things here: 1) the tetrahedron in 3-space, 2) the square in 2-space, and 3) the light above the tetrahedron that passes through it to cast the shadow of the square below it. Thus, by the light of fore-knowledge are we naturally gifted, to see through the moment to other times. Just as in the beginning must have been the seed, so will the fruit inevitably enhouse around the seed.
So we see the fruit of knowledge is a sphere that becomes a new sphere, even if apparently unchanged, over time. Thus to say, a sphere containing itself like a fruit contains its seeds. The shadow of a hypersphere on paper appears somewhat like a Gordian knot or a Moebius strip. It is one line that loops to form a bigger circle surrounding a smaller circle. This form of shape is in 4-space. The shadow of the "hypersphere" is the sphere.
If we examine the fruits of fore-knowledge of future events, we see the depiction of seven generations of immortal Nefilim and the five of the mortal Sethites. This is "the fruit without its skin," a skeleton-key to unlocking the mysteries of 7 and of 12 to follow. Here we see the 2-space Gordian knot or Moebius strip-like shape unravel to reveal its true components in 3-space above, casting down the linear shadow of the sphere-within-a-sphere onto 2-space below. We see they are two positions of the same model, a circle around a central axis point.
This is what existence was like in the un-differentiated mono-elemental quantum foam a Planck-time following the "big bang;" "before the fall," so to speak, when the 4 elements separated and our 3-dimensions expanded. I tell you, it is like that still in the furthest depths of space now. The local universe of 3-space and 4 elements exists within the original, un-"banged," singularity. This is simply a higher dimensional vibrational world, and such was known to all in silence "before the fall."
Just as around the seeds the fruit forms a container, before the fruit desicates to release the seeds to find fertile soil, so, too, after the seeds take root, follows the sapling from the seeded soil. All of this we see clearly occuring in nature, before our own eyes. So let is continue to make models that flesh out time.
As we saw that the tetrahedron cast the shadow of the square, now let us look at two tetrahedrons (one over time) that cast in 3-space the shadow of a cube. We see the one above and the one below connect to form the hexagonal shadow of the cube, but that, if left apart, they remain two tetrahedra casting the shadow of a square above and one below. All this occurs because the stelloctahedron, that is comprised of two tetrahedra sharing a common central point, the thus representing the "hyper-tetrahedron" (one over time), has eight corner points, just like the cube has eight corner points. A "hyper-tetrahedron" or "stelloctahedron" casts the shadow of a cube.
Likewise, examining the "hyper," or "sphere-within," version of a sphere, we begin by looking at the outlines of its shadow in 2-space. We must look down to study what is above. We look down to see the shadow cast below us to ascertain the source of the light above. The first three seeds - the object in 3-space, the shadow in 2-space, and the light source above - form three circles over time, two within one. The knotted outline of this shape contains at its core therefore a unique overlap or alignment between past hypothesis and future antithesis, central within the synthesis of these as the present. The friction between time flowing from future to past against space moving past to future causes change over time.
Thus, the synthesis is at the core of the present material reality of both its past and its future. This can be depicted using unique overlaps and alignments that constitute the "magic" art of optical illusions. These occur when the angle or position of the object and the light source align such that it casts a regular shaped pattern. Another example is the tetrahedron above and tetrahedron below casting the 3-space shadow of the cube, the cube's hexagonal shadow, and the square shadow of the single tetrahedron. The example here is the doughnut-shaped torus, or "hypersphere," whose distorted topology depicts the closed geometry of a temporal cycle.
The alignment of the torus as a synthesis of future and past within the present itself is simply an ellipse around a central axis again, but instead of it being a shadow in 2-space it is a doughnut shape in 3-space. The ellipse and axis also aligned as the circle and origin point. The torus can also appear thus as a doughnut looking down on its middle hole. However, because thedoughnut-torus is a shape in 3-space, it also has width, and can therefore also be viwed from the side. Representing the movement of a sphere in a circular pattern over time, we depict these alignments thus as minimum-packing space arrangements of circles. From above we see ten circles form a torus when they overlap, and that from the side seven do so.
Now, let us return to the depiction of creation from the perspective of an angel standing outside of it and observing, looking in. We see from the point of view of Raziel, fallen so Enoch could become Metatron, the ten above and the seven beklow. To this is added behind it the 4-torus and above it the light. So did the ancients and as do the QBLHists of today reckon all these alignments as interior to the prsent material reality.
At this point, therefore, we are on already familiar ground. That sapling planeted by the desicating fruit into fertile soil has grown from a sapling cube into a "hypercube," or cube over cube, tree. We sit and bask beneath its shade here in Eden every day. It is only the familiar "tree of life" diagram, showing the hypercube at "antipode." The reason the central pillar is "fallen" is that this is not two cubes, one above one below, but only one cube over time.
Now, the shifting of the middle pillar of the "tree of life" represents the alignment of one shape with another as object and shadow, and so we see, again, if we map the outline of the "tree of life" from a different angle, its shape will be that of a Gordian-type knot with seven twists. Here we see the middle pillar assumes the central, "gold" or "heart" chakra of the basic seven spinal pressure points. These seven are the same as the seven overlapping circles of the torus from the side's shadow.
If we look at the middle of the torus, again we see the ellipse around an axis shape nested at the central core. It is, however, twisted at either end. This represents that we are seeing the elliptical circle around the axial central point from exactly above its side. Instead of seeing only a flat plane, however, we are seeing an ellipse with two twists in it.
If we look at the basic shape of the orbit of earth around the sun, for example, we find it has been divided into twleve surrounding seven - twelve constellations in the zodiac behind seven visible planets. The circle around the central point we see when we look at the ellipse of our orbit from above the axial central point has become a new shape, and this is its shadow: twelve around seven, the double twisted ellipse of twelve around the axial central point of seven. This symbol of the Alchemist Henry Agrippa is nothing but the 2-space shadow of the 3-space shape of a double twisted ellipse around an axis. Knowing of the 2-space shadow, then, let us study the 3-space shape itself.
But first, we should return to our basic cosmology of the universe and take note of what, from outside the speed of light, the 4-worlds model appears "before the fall," and the middle pillar has not descended, that from beneath the speed of light, our local universe of twleve and seven appears "after the fall," the so-called "shattering of the shells" or the quantum information units comprising all our universe's karma. The result of this is that the QBLHistic worlds of Yetzirah, realm of the Sefirot, and Beriah, realm of Eden, appear to switch places. Let us also remember the rebellion of Lucifer and the fall of man correspond to the Kherubim with the "flaming sword" and the explusion from paradise, and that these in turn refer to the "tree of life" and to the realm of Eden. Likewise all these refer to various vibrational frequencies in and around our universe, and us as well, right now.
Now we can return from physical cosmologies to pure geometry. The combined "tree of life" (antipode hypercube) and "tree of death" (antipode hypertetrahedron) is the tesseract at antipode. A tesseract is another form of depiction of the hypercube, just as is the torus of the hypersphere. When the tesseract is seen from above one of its faces, it forms the shape of the cube within-within-a-cube, or hypercube, of a cube over time. When the tesseract is seen from above one of its edges, it appears at "antipode" as the combined trees of life and death, whose fruits are longevity and fore-knowledge. When the tesseract is seen from above one of its corners, it appears as a 3-dimensional form of a Moebius strip or Gordian knot, where, by the Pythagorean theorem, a flat, 2-d pattern can be twisted into a 3-dimensional shape. The shadow itself becomes an object.
Therefore, just like the alignment between two tetrahedrons casting a cube shaped shadow, that between the cube and its hexagonal shadow, or the square shadow of the single tetrahedron, or even between the corner of the tesseract and the Pythagorean, "phi" spiral in 3-d, so is the alignment we see here between two tori (doughnuts). The center of a torus' interior, however, is not the central axis point for the elliptical orbit around it. It rotates around one edge because an ellipse has two foci points.
Essentially, however, we are still only looking at a twelve over or around seven based system. Symbollically, if we wanted to depict this great, mysterious shape that casts off all these alignments, that is the highest source of light, and that is the pattern causing all patterns and cycles in our whole universe, we could simply enough depict it in flat-space like a seven-pointed star inside a circle of twelve parts. This type of pattern can be found dating very late back into antiquity and is used in "magick" today. Here we see the seven attributes of Greek vowels arrayed within the twelve Greek consonants.
Next I will describe the minimum-packing space shape represented by this "symbollic" array, and describe in greater detail the cosmology it describes, but before we delve into that let us back at how all of this "twelve around seven" pattern fits into where our species is in the history of our evolution in this present material reality.
We have a unique oppurtunity to observe the seven planets and twleve constellations at this moment in time. on May fifth, 2000 AD, the seven planets of classical study all aligned in the constellation of Taurus, representing the predatory Apis bull. On December twnety-first, 2012 AD, the sun, earth and galactic core will all align in Saggitarius.
this information is all © 2007 Jonathan Barlow Gee