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The Genesis of Geometry

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(Graphics by Robert W. Gray)

A Message from The Pattern's Midwife:

For almost a decade I've been sharing the story of The Pattern with anyone who would listen, illustrating The Pattern with sketches that are, at best, kindergarten art. Suffice it to say, attempting to draw what I see so clearly in my mind's eye while working with leading scientists, educators, and researchers has been a humbling experience.

So it is, that those who have worked with me for years and individuals new to this geo-matrix will fully understand my deep gratitude to Bob Gray, mathematician/physicist and recognized expert in the geometry of Buckminster Fuller. In addition to other significant contributions as a member of the Sequoia team, Bob created the magnificent storyboard graphics and the animation of The Pattern you are about to see.

In November 1999, Bob continued his labor of love by taking a nosedive into my head in order to create in 3D what I have described all these years and can still see very clearly. What he estimated as a two week project turned into a three month (and counting) exhilarating and exhausting quest! Believe me, Bob now has a deep appreciation of what my thirteen year journey has been for me.

As a scientist and researcher, Bob's sole focus was to graphically map the geometrical connection that I see bridge the 144 hyper-diamond octahedron and the 120 faceted Icosahedral bubble. This would be the first step toward a more complete understanding of the mathematics of the "language of knotted light" we call The Pattern. We were persuaded that this step was imperative in order to engage other researchers in the adventure and unfold the implications and understand possible physical applications of The Pattern.

So welcome to the quest! We are excited to share this work with you and look forward to hearing your thoughts and responses to this evolving work. As you encounter The Pattern please consider the following:

Most of us have been looking for answers to our questions: Who am I? Why am I here? Does my life mean something? Can I make a difference? Why do I feel so different? You now have The Answer: YOU are the Answer.

Before proceeding, there is one remaining question you must answer:
Are you willing to stop living the Question, repeating your story that has left you riddled with doubt and unresolved despair and be The Answer?
Answer "Yes" and your world will change.


The Genesis of the Geometry


Formation of the Geometry

There are two "objects" which can be seen. They seem to be "lines" or "cylinders".

Observe from a distance and you see two objects that appear to be a line above a point.
Change your point of view and it looks like a line under a point.
Move yet again and it appears to be a point beside a line.
Change your perspective once more and what you originally thought was a "line" above a "point" appears to be an "X."
You will soon realize that the entire point of The Pattern is fully manifest in this first sequence of its developing structure!

The "point" and the "line" are actually two planar geometries that evolve simultaneously and become embedded spheroids.

The larger, "top" object eventually defines itself as a 120 Icosahedron Bubble. I describe this structure as "feminine," for reasons that will soon become clear. It grows downward and eventually circumscribes the "bottom" object that is growing upward. This second structure will soon define itself as a, 144 polyhedron, which I describe as "masculine, which will also become clear shortly.
The simpler but much larger Icosa structure completes first, closing at the South completely surrounding the 144 Octa that is still forming.
As the final edges of the Icosa meet, an "upward" rushing force akin to a breath blows, hitting the 144 Octa, centering it within the vacuum of the 120 Polyhedron.
As the 144 polyhedron grows, there is an energetic intensity building inside the bowl that I liken to a cauldera of a volcano. As the final edges come into contact, a tone is emitted that sounds like two different tuning forks have been struck together. The 144 hyper-diamond closes at its "North." Just as when two rocks are struck together, this contact causes an imploding spark. As the spark rolls inward it ignites the pent up energy that grew during its formation. The "bottom/inner" object completes its formation ("closes") into the 144 polyhedron.

Note: In the Genesis Account of creation we read: "God created Heaven and Earth." This is followed by "And God said, "Let there be light." In The Pattern we see a heaven, the 120 Polyhedra enclosing a solid "earth," the 144 Polyhedra. It is important to notice that only when there is sound, does the intentionality of being -- Light/The Pattern -- begin to come into full existence.


The Birth of Three and FourEver

This increased energy cannot be contained within the hyper-diamond so the excess is expelled, "pushed out" through the forty-eight vertices of the 144, like a series of volcanoes that erupt equally and simultaneously. This light, "seeds" emitted from the masculine 144 Octa, are contained within the feminine "womb" of the expanding and contracting 120 Icosa bubble, gestating there to become The Pattern, the third structure.


The Energy Beams Emitted from the 144 Poly

The forty-eight energy beams emitted from the forty-eight vertices of the 144 Polyhedron are bundled into eight groups, each comprised of six beams.

The clustered beams move radially out from the 144 Poly. They are straight with an internal "Y" structure that is seen in the cross section.

Once the luminous energy leaves the 144 Polyhedron it begins to spin. This action combined with the eruption of light causes a "virtual" shell of energetic pressure to arise, located midway between the inner and outer structures. We have called this energetic horizon "the Focusing Sphere."


Energy Beams out of the Focusing Sphere

The "Focusing Sphere" is unlike the 120 and 144 Polyhedron in that it does not have a polyhedral structure, that is, it does not have faces or vertices. It is a sphere. I believe that further investigation into this particular, evenly forced "field" will give rise to some interesting dialogues on the subject of gravity.

As the forty-eight energy beams pass through the Focusing Sphere, they are bent, refocused due to the spin of the 144 polyhedron.

As the energy beams are bent, they retain their original straight shape with the "Y" structured cross section.

The bending occurs such that each of the eight groups of six beams converge into a different vertex of the 120 Polyhedron. The 120 Poly is a "mixed" polyhedron, being both concave and convex, its surface having "hills" and "valleys."

The vertices that these eight bundles are focused into correspond to eight of the twelve vertices of the Icosahedron (The base polyhedron forming the 120 Polyhedron).
The specific grouping of these six energy beams can be identified by referring back to the 144 Polyhedron; a group is identified below by yellow dots. It is significant that there are three different grouping of six possible in the 144. However, it turns out that the grouping I drew several years ago is the only one that "works" in the geometry you will see evolve into The Pattern.
For years I have said that when the light emerges from the 144 to the 120, four vertices of the Icosahedron do not have energy beams focused into them and those would somehow define an equator. This was confirmed. These four vertices turn out to be in the same plane and do form an "equator" around the same great circle.


From the 120 Poly Back to the Focusing Sphere

The six arrays that make each of the eight energy beams meld when they come together at the vertex of the Icosahedron, so we now have eight singular beams, each of which retain their "Y" cross section. The energy beams get bounced back from the 120 Poly (from the 8 Icosahedon vertices) back to the Focusing sphere. At the focusing sphere, the energy beams do a small loop and ricochet off the focusing sphere. The little loop is like a cursive "e."
As these eight beams catch "inside the Mother" they are then bounced straight back to the Focusing Sphere and seem to hit the Focusing sphere at approximately the same point. These arrays cannot penetrate the Focusing Sphere. As the arrays of energy hit the focusing sphere, they bounce off, each making a small loop as it ricochets off the focusing sphere. The loop looks is like a cursive "e" with a corkscrew shape. This is the first curvature of the light seen in the evolutionary dynamic.

Note: It seems that somehow this action reflects how many of us must have felt at birth or any kind of "rebirth" for that matter. For nine months or so we're snuggled up in a warm and cozy space, then suddenly find ourselves being pushed and pulled, unceremoniously hauled out into a cold world and smacked on the backside.

In a similar way, this "child," says, "Whoa! What's going on? No way! I'm outta here! I'm going back to my father!"

But, like a child at birth, this luminous structure cannot reverse its journey. It is unable to penetrate the Focusing Sphere and thus, cannot return to the "father," the 144 Octa.

So it is, that our cosmic child of light begins a long journey within the "mother," a trip that will eventually return the child to its starting place, itself, at which time the three become One.

The energy beams on "opposite" sides, coming in from opposite vertices, seem to hit the Focusing sphere at approximately the same point, but actually pass by each other.

The loop is like a cork screw.


Back to 120 Poly and Other Ricochets

The eight energy beams now begin a complex dance ricocheting around to hit the other vertices of the 120 polyhedra. The energy beams remain straight during this repetitive bouncing phase, save where they change course, and curve as they bounce off the Focusing Sphere. When the eight beams finally come back to their starting point, the synchronization is complete and The Pattern of knotted energy forms in the "open" position of 19.5 degrees.
These images document the discovery Bob Gray made several weeks ago using the 3D program he wrote. On 11/14/1999, I sent him a fax which contained a drawing of The Pattern using twelve straight edges, a drawing I have drawn for Sequoia researchers many times. This is the exact, corresponding image that showed up in Bob's 3D program. He labels the vertices exactly as I had them. Bob writes, "It was really cool to see this using the program." Bob and others are working to determine how it matches with the vertices and common parts of the "bubble."
Because the 120 Polyhedron is "dimpled in" at the twenty vertices corresponding to the Icosahedron's face centers, the interior surface of the 120 Polyhedron is not smooth. The inward bumps of the 120 Poly channel the energy beams into the straight edge pattern formation. Perhaps in the same manner that a lens refracts light. The Pattern knot at this point consists of eight straight energy beams. Note that the eight vertices of the straight edge Pattern Knot are not all at the same distance from the center of volume. This is because four out of the eight vertices of the straight edge Pattern Knot are at the "dimpled in" Icosahedron face centers.
The other four vertices of the straight edge Pattern Knot are at four vertices of the 120 Poly corresponding to mid-edges of the Icosahedron. Note that these four vertices (mid-edge points of the Icosahedron) are all in the same plane. They, therefore, are on the same great circle equator of the 120 Poly.


Formation of The Vesica Pisces

Note: The Vesica Pisces is an elliptical figure made by the intersection of two arcs, an ancient symbol found in many cultures to designate a "unity consciousness," a place or being radiating an energy that inspires unconditional compassion and harmony.

As The Pattern "breathes," expanding and contracting, it causes the 120 Icosahedral bubble to go from spherical to elliptical. Here we see the continuum of luminous energy squashed flat as the 120 Icosahedron is elliptical. It simply looks like a line.
Yet as we rotate it, we see that from another orientation this same line looks exactly like the Vesica Pisces.
The 120 Polyhedron is distorted into an ellipse at this time.
Here we see the genesis of the geometries present all the way through the Vesica Pisces.
When we first placed this image beside the Hubble Telescope's photograph of the Hourglass Nebula, everyone heard a collective audible gasp.
As The Pattern breathes, changing the structure of the 120 Polyhedron, the Pent vertices of the 120 open. (Note: The pentagon like face is outlined in orange. Notice how the vertex at the center of this pentagon is opened slightly.)
The triangles making up the surface of the 120 Polyhedron can also be grouped into diamonds.
They can also be grouped into triangles.

19.5-Degree Pattern

It is interesting to note that the Vesica Pisces picture of The Pattern, when "opened" to 19.5-degree's, forms The Pattern Knot first as first remembered drawn on February 14, 1991.

There is an inherent 720-degree (3/2) twist to the "Y" cross sectioned energy beam once The Pattern knot forms. Picture it as if someone cut the "ribbon," gave it a 720 degree twist, and glued it back together. This structure immediately brings to mind the double helix of DNA. Be sure to visit Dr. Louis Kauffman's site via the links listed, and see how The Pattern forms as two double helices intersect. The 120 Polyhedron is spherical (and concave/convex) again The 120 Poly starts to spin as it returns to a spherical shape. The Pattern Knot rotates internally on an asymmetric axis, at a 22.5-degree angle of asymmetry. This luminous energy flows in one direction only. Also, the Pattern appears to be conspicuously absent two distinct colors: what I call stoplight red and green.

NOTE: I believe the directionality of the light's flow will lead to serious dialogues about The Pattern's intimate relationship to time, the circular and cyclical nature of past, present, and the ever pending future.

The directional arrow of this streaming thread also leads me to believe that inner darkness and emotional shadows are illusions, merely states that we experience when we are unwilling to move in and with the Light. That is, darkness, be it ignorance, evil, "burn out" or depression, is the result of closing our eyes, a self-induced blindness caused by vainly attempting to go into the light rather than allowing it to illumine our way. In the same way, shadows, doubt, mistrust, and skepticism are what I call the "Picasso Effect," the result of an individual's resisting the flow by sidestepping or stalling. It happens when one is turned ninety degrees off the path. Then one eye is closed off from looking into the Light and the other eye is open, following the Light. Since they can never make up their mind, they are always seeing the world through one eye or the other. Imagine what their world looks like when they try to superimpose these two images. Hello, Mr. Picasso! When you look at The Pattern's "path," you will instantly realize why it is that if you're stuck in this position of indecision you always have the sense that you are about to fall into the abyss.


The Reformation of Vesica Pisces

Every time The Pattern Knot is in the Vesica Pisces position, the 120 Icosahedron is in its elliptical form and the vertices open up slightly.
In every instance of opening, a single energy beam emerges through each of the twelve openings.

Each beam retains the tetrahedral structure of the original One. The 120 and 144 Polyhedron continue their antipodal rotation.


Curve Back to the 120 Poly

In the epilogue to their book, The Living Energy Universe ( 1999 Hampton Roads Publishing), Gary E. R. Schwartz, Ph.D. and Linda G. S. Russek, Ph.D say:

"The continued accumulation of information and energy can only occur to the extent that the system is not "too open." This applies to info-energy systems as well as material systems. If the system is too open, the systemic memory will 'fall out.' The logic is straightforward. However, all systems, material and non-material, have functional boundaries that theoretically continue even after the info-energy systems 'leave' the scaffolds of the physical structures that helped shape them. Hence, logic dictates that once initiated, the systemic info-energy memory process can continue to function to various degrees in a stabile yet dynamic manner."

So it is with The Pattern.

The twelve luminous energy beams then bend around and return to the 120 Polyhedron.
During this "loop back," there is a "crossing over," and each of the twelve loops spawns a bubble. Again, just as in the knotted light of The Pattern, there is a helical "twisting" inherent within this loop (due to the limitations of the software we are unable to show this helical aspect.)
These twelve energy beams are drawn up and stabilize over the diamond, and after spawning a new bubble, reenter the 120 Poly as it becomes spherical, entering through the face center of the Icosahedron's triangular vertices found in our 120 Polyhedron. There are twelve energy beams and twenty Icosa face centers. So there are (20 - 12) = 8 Icosa face centers, which do not have energy beams returning into them. These eight Icosa face centers can be grouped into two groups of four face centers. There is one group of four at each "end" of the 120 Poly ellipsoid. Therefore, the energy beams do not return into the ellipsoid ends.
A group of four face centers can be identified as follows (using the Icosahedron)

And a similar grouping on the reverse side of the Icosa. This grouping results in an edge-bond connected band of twelve triangles around the Icosa. This "band" of triangles is then around the ellipsoid "equator", although the band oscillates from being a little below to a little above the "equator." Note that the major axis of the ellipsoid is not through two Icosa face centers but through two Icosa edges.


The "triangular vertices" (Icosa face centers) become dimpled as the 120 Poly becomes spherical resulting in the 120 Poly becoming a mixed convex/concave polyhedron.

Progression of Bubbles

The twelve bubbles spheres each produce another twelve spheres, beginning its intentional destiny to eternally create in order to regenerate Itself. In the time that it takes The Pattern to breathe through three "cycles," the bubble spheres multiply and give new meaning to exponential growth. Its growth is:

One plus twelve times 13 to the 5th. [(1+12)*13^5]