in understanding the
multi-dimensional properties of “Platonic Solid geometry,” as we have seen on
the Earth. To recap, our term “consciousness units” (consciousness unit)
CUrefers to an area
where the energetic, conscious “aether” or zero-point energy bleeds through
into our physical space and time, taking up the form of a luminous sphere of
electromagnetic energy that has a hole through the middle, which forms a
north-south rotational axis. From the last two chapters, we now know that
these spherical energy formations are seen to have within
them as well. This information comes from scientific investigations of
planetary behaviors as well as a straightforward mathematical analysis of
the “tetrahedral” angles and ratios between the various objects located in
geometric vortexes, which appear to be artificially created. the Cydonia area of MarsStraight-lined formations like these are usually thought to be manmade objects only, certainly not a part of nature, and thus for most of us the information in this chapter will be very unique. We have never tried to insinuate that any of the planets have gigantic, physical crystals in them, only that this is a shape that is formed by energy as it flows through the
CU, which in turn forms the planet. We are not accustomed to thinking of
sound or color as having hidden geometric shapes in their vibration, and yet
this is exactly what our research has now led us to conclude.
” octmeans the number eight. In an octave there
are seven fundamental "" of vibration followed by an eighth. The eighth
note has two purposes, in that it not only completes one octave but it also
begins the next. nodesGreek mathematician and philosopher Pythagoras, through a straightforward
process of repeatedly dividing a frequency by five, is credited as being the
first to devise these eight “pure” tones of the octave, known as the
. He started by taking a single-stringed “monochord”
instrument and measured its exact lengths when different notes were played.
Diatonic scale
Then, just like playing a guitar, he pressed his finger down on different
lengths of the string and strummed it to get different notes. Each note that
he played would divide the string into two different sections, and the
relative lengths of the two sections would then be measured and written down
for each note. We can see the Diatonic scale on a piano as the white keys, providing that the beginning note in our octave is a C. The piano has black keys as well, and when they are included, there are a total of thirteen notes in the Octave, with the thirteenth note also being the first note in the next octave. These thirteen notes are known as the , and most of
the world’s music will consist only of notes that fit somewhere within this
scale; therefore almost all possible songs can be played on a piano. (As one
exception, Indian music will use notes that do not fit in a chromatic scale,
called Chromatic scalequartertones or microtones.)
Mathematics aside, the most basic reason why the number eight was chosen
instead of thirteen for the “octave” grouping of musical notes is that all
they
will be harmonic. You can play a song on the white keys of the piano and it
will always sound like music, regardless of what notes you play. However, if
you experiment with the without knowing what you are doing,
painful dissonance is most likely soon to follow and anyone else in the room
will quickly ask you to stop. chromatic scaleMathematically, the highest note in an Octave has a vibration speed or frequency that is twice as fast as the lowest note, and that is the most basic way to see how an Octave organizes one full group of sound vibrations.
Every note, whether A, B, C, D, E, F or G, will be doubled in its value in
the next octave. Since the octaves are continually doubling in their vibration, there are only a handful of octaves within the range of human hearing. Above a certain point the vibrations will become too fast for human ears to detect, even though they will still exist all around us.
, is simply
on a higher octave of vibration than the frequencies of sound in the musical
octave. To put it more simply, you could take the numerical ratios between
each note in the fluidlike aetheric energy and double them many times over, and
eventually you would find the same, musical Diatonic scaleidentical ratios between the vibrational
speeds of the light spectrum. The only difference between them is sound is vibrating much more slowly, whereas light is vibrating
much more quickly. the
magnitude;
From
Geometry completes the basic triad of our perception of the fundamental
building blocks of vibration in the Universe – that triad being
and sound. With the geometries that we have already been discussing, the
sounds of music and the colors of the rainbow suddenly spring into physical
form. Suddenly, the abstract concepts of harmony and color reveal structures
composed of straight and curving lines that we can then make models with and
build things out of. Although we can see color and hear sound, we do not
normally think of a physical geometric shape in two or three dimensions that
would precisely represent these vibrations. However, numerous researchers
such as geometryGerald Hawkins, Buckminster Fuller and Hans Jenny have shown that
sound vibrations will form specific geometric patterns, providing that what
you are vibrating is visible instead of air, which is normally not visible.
Gerald Hawkins did not actually arrive at his findings through studying
vibration. In his case, he was led to make his discoveries after spending
years investigating the ""
crop circle, where complex geometric
patterns would show up overnight in various grain crops around the world,
usually visible only from the air. After studying hundreds of these
formations, phenomenonHawkins realized that certain patterns were repeating
themselves, and the underlying unity among these patterns was expressed by
taking simple two-dimensional geometric shapes such as a triangle, square
and hexagon and fitting them precisely inside of a circle, so that all tips
of the shape perfectly touched the circle’s edge. To his amazement, the
surface area of the inner geometries, when divided against the area of their
outer circles, showed the exact same relationships responsible for the
vibrations of music in the Octave – the "diatonic ratios" that we mentioned
above. This is exactly what Pythagoras demonstrated with his one-stringed
“monochord” instrument, only now instead of a ratio of string lengths, we
have a ratio of geometry that indicates the same thing. He realized that
this was a totally new and unrecognized set of theorems in geometry, and not
a single academic authority who he consulted with was familiar with these
concepts. So in two dimensions, we can understand sound as being a "flat"
geometric vibration, such as a triangle, that emerges within a "flat"
circle.
(and
therefore light vibrations on a higher magnitude as well) can be seen in
both two and three dimensions, and the two-dimensional forms such as the
triangle, square and hexagon discussed by sound vibrationsHawkins are probably more familiar
to us than the three-dimensional forms revealed by Fuller and Jenny, though
we have now seen these geometries at work in the planets. Very importantly,
these can also grow and contract in size, and simple,
visible geometric structures organize and control these movements as well.
When we start fitting these shapes inside of each other, they indeed form a
“nested” appearance, with each successive shape growing harmonically larger
than the one before it. We will show more of this as we go along. This
“vibrational geometries” sphere within sphere has already been seen in various
experiments, and now we can expect the various geometric harmonies to exist
inside these expanding spheres as well.geometryThe simplest way to model the geometric expansionfrom one shape to another
is by tracing out how the nodes move relative to each other. We remember
that on Earth, the expanding geometric movements have been called “radial”
or “spiraling” by Spilhaus and others. The simplest way to chart the
movement from node to node between two different shapes would be with a
spiraling line, which Ra calls “.” These spirals
include the the spiraling line of lightFibonacci or “" as well as the spirals created by the
square roots of two, three and five. We will now show that these spirals are
directly related to musical frequencies through mathematics.
Golden Mean
referred to straight and curved
lines as the two apparent opposites in the Universe, even though they are
actually unified as vibration. Ultimately we feel that in one way of
thinking, the straight lines and geometries can represent space, and the
curved lines and spirals can represent time. But for now we will put it in
more familiar terms and say that straight lines create form, and curved
lines create the movement and growth of that form. In other words, straight
lines form the geometric structures of the vibrations themselves, and curved
lines form the pathways for these structured frequencies to expand and
contract. Although we normally don’t think of curving geometry with sound
and light, we know that these spirals govern the movement between one note
in the octave and the next higher note, or one color in the spectrum and the
next higher color. the AncientsTo put all this in a more spiritual context, in many ancient mystical traditions the straight line was thought of as the , and the curved line was thought of as the
masculine force,
associated with the Sun. These masculine-feminine associations are
quite easy to intuitively work out in our own minds. At rest, the sperm cell
forms a straight line, whereas the egg is a rounded structure. Men’s bodies
are harder and more straight-lined in construction and women’s bodies are
more smooth and curvaceous. Men’s minds tend to think in more linear, rigid,
mathematical "left brain" patterns and women’s minds tend to think in more
curving, fluid, emotional "right brain" patterns. Primitive men hunted and
built by the light of the Sun, using straight spears and arrows to catch
prey – or more recently, straight boards, hammers and nails to build
structures, whereas women cooked and served food in smooth, curved bowls of
pottery or wood and nurtured their young with smooth, curved breasts in the
secluded darkness of the cave, igloo, teepee or longhouse, nestled away from
the light of day where predators and villains once roamed. Furthermore,
women are directly connected with the Moon in ways that men could never be,
through their menstrual cycle, showing another level of why the Ancients
associated the feminine spirit with our own Midnight Sun. feminine
force, associated with the Moon13.7 SACRED GEOMETRY AND LIFEThe study of these various geometric forms and spirals, including their
spiritual connections to humankind as partially illustrated above, is known
as "," and
sacred geometryRobert Lawlor’s book of the same title is arguably
the best existing reference on the subject. Many of history’s greatest
scholars studied the principles of sacred geometry in extensive detail, as
they were fascinated to discover that lifeforms of every possible variety on
Earth demonstrated these musical, vibrational principles involving the
interplay of space and time – straight and curving lines. Simple seashells
provided perfect representations of the , as did the growth
pattern of plants, the fingerprints, the horn of an ox, the interior of a
sunflower or lotus and many, many different proportions in the skeletal
structures of animals and human beings. There are obviously no limits to how
far these principles will go, providing that someone is willing to
mathematically study each plant or organism separately in search of these
connections. Fibonacci spiralSince our current scientists give us no reason to believe that such harmonic
principles are necessary in the growth of lifeforms, then why do they exist?
If these proportions were not important, then why do we see them so
repetitively? Indeed, are we simply ignoring the evidence that is all around
us – evidence that proves that everything in the Universe is a product of
vibration? If the fundamental energy that constructs all of reality is
vibrating in harmonic resonance, would it be possible for anything not to
have a harmonic foundation?13.8 Just so that we can conclusively demonstrate that spirals connect all the
SPIRAL RATIOS IN PLATONIC SOLIDS together, we will pull a chart excerpt from Platonic Solids
that makes our point. In The Shift of the
AgesRobert Lawlor’s quintessential book
Sacred
Geometry, we learn that the resolved the HindusPlatonic Solid geometriesinto an octave structure like we see for sound and light, and in the next
table we have listed this geometry in order. This gives us a complete,
unified view of how the various vibrations work together, which we will see
in the next chapter. For now, we should just be aware of what this graph
represents. This is formed by assigning a length of “1” to the edges of the
cube, and then comparing how larger or smaller the edges of the other forms
are in relation to it. We remember that in the , every face
is the same shape, every angle is identical, every node is evenly spaced
from the others and every line is the same length.Platonic Solids
In the next chapter we will make a very compelling case that the ancient
Hindus knew everything that we have discussed about these energy fields so
far, and more. We were fortunate enough to locate a rare reprint of Prasad’s book should be
nothing short of dazzling, as almost every key aspect of the
that we have covered so far is contained in the pages of this book in one
form or another. We will also take a closer look at how the aetheric modelancient aetheric
conceptof an “octave” of dimensions correlates with modern scientific
studies, and show that there is a lot less difficulty in rectifying the two
opinions together than we may have thought. Furthermore, by understanding
how geometry intersects with higher dimensions, as we have already seen on
the planets, the idea of “hyperdimensional physics” moves out of the realm
of theoretical speculation and into the arena of an applied science. And
once we can apply these concepts, we open up a door to the Universe… |