The Genesis of GeometryRead What's New!!
(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 "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
||Observe from a
distance and you see two objects that appear to be a line above a
||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. |
perspective once more and what you originally thought was a "line"
above a "point" appears to be an "X." |
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
||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.
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
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
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
||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.
|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
||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
||They can also be
grouped into triangles. |
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
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
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
||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
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]