... " Perhaps All the Dragons in Our Lives Are Princesses Who are only waiting to See Us Act, Just Once, With Beauty and Courage. Perhaps Everything that Frightens us Is In Its Deepest Essence Something Helpless That Wants Our Love." Rainer Maria Rilke
Einstein's Formula: "The everything and Nothing Continuum" or Universal Consciousness with thousands of given names, (here are only some examples as bows around the graphic), Causes all form out of nothing by means of Rhythmic compression-decompression sequences at the speed of light squared.
There is not one point of balance, nor are there two; there are actually three:
- One point of Stable balance
- Two points of Unstable balance
The easiest way to visualize this concept is a pendulum.
A still pendulum is in stable balance. Stable balance means rest. Once the pendulum is set in motion, stable balance is lost. All motion, except the initial push, is returning to rest. Despite the pendulum moving through the point of rest in midst of every swing, stable balance can only be found when rest is reestablished.
A moving pendulum moves in two opposite directions through the point of stable balance because the imbalance of the inicial push owes to the balanced system by momentum stored in inercia. In consequence the pendulum swings through towards another point of imbalance at 180º to the inicial push. These two points of imbalance, at the amplitude of the swing, are the points of unstable balance, because motion ceases for an instant before turning to the opposite direction.
In order to translate the Pendulum concept into Universal Geometry, instead of our pendulum, wich does not change shape during its journey, we need to imagine it as the cube-sphere: one half of the swing, at the point of unstable balance, becoming a tiny sphere and the other half an enormous cube, more like in-breath and out-breath sequences. The sphere is either a sun or an atom, the cube is the surrounding space that balances the motion by expansion versus compression.
All perpetual motion, vibration and cycles are compression-decompression sequences, where the only variation consists in frequency, wavelength, amplitude and velocity.
(The position of Carbon in the wave field is closest to the compression point of unstable balance.
inert gases are not elements, because their position is stable balanced. please refer to the Periodic Table)
Cube and Sphere are the two points of unstable balance aka equilibrium.
The TRUNCATED OCTAHEDRON that can be inscribed half way between the cube and the sphere is the
zero point of STABLE BALANCE.
Two points of unstable balance are called STATIC CONDITIONS.
forth and back vs. in- and outward motion between static conditions, are the two DYNAMIC CONDITIONS.
On the page "Universal Geometry" I explained the four alchemical elements and their meaning.
The elements Air and Earth are the STATIC elements of eternal stillness and momentous form
The elements Water and Fire are the DYNAMIC elements of perpetual vibratory motion, and of spontaneous change.
white light - toneless
formless (the cube)
magenta cyan yellow
(masculine > feminine)
red blue green
change and time
(feminine > masculine)
form and matter
Translated to the breathing process,
Water and Fire are out-breathing and in-breathing. Action - the verbs - (predicate).
Air is the stillness after the out-breath and before the in-breath . Expansion - The Subject.
Earth is the still point after the in-breath and before the out-breath. Compression - The Object.
In and out-breath are happening simultaneously in perfect balance.
- the IMBALANCED sphere of compression is the magenta line, or Z axis of depth and equals the visual axis, it creates the illusion called perspective or centripetal motion. It is the focal point centred on the observed object.
also referred to as the UNDERWORLD
- The UNSTABLE BALANCED TRUNCATED OCTAHEDRON of Equilibrium equals the second dimension, this plane is formed by adding the X axis, or the cyan line of width. Width and depth create the plane of pressure equilibrium, also called Horizon, the sum of infinite focus points.
also referred to as the EARTH PLANE
- The IMBALANCED expansion cube is the result of adding the third dimension, yellow line, or Y axis, of height. It creates the illusion called space or centrifugal motion. The sum of infinite planes., The subject.
also referred to as the HEAVENS.
The three dimensions form the Wave Field. The geometric position within the field determines the length-frequency duality, amplitude, and velocity of the wave.
Just one single cubic wave field contains all possible combinations of wave characteristics.
The combined unity of all vibration and frequency, the WAVE, is the observing SELF, or universal consciousness.
“You are not a drop in the ocean. You are the vastness of the ocean in a drop.”
― Jalaluddin Rumi
The dynamic conditions of time are all rotating horizontally around the Y axis or yellow line.
- The red vertical plane defined by Y and Z, is the past in time.
- The blue horizontal plane defined by X and Z, is the present moment in time.
- The green vertical plane defined by X and Y, is the future in time.
The blue horizontal plane of the present moment is un-perceivable directly by the senses, because it has zero height and is always at ninety degrees to the observer.
The red vertical plane of Past and the green vertical plane of the future are of limited perceptibility by the senses, because the red has zero width , and the green zero depth always at 180 degrees to the observer. The observer's position is always at centre, where either axes or planes intersect.
This point is still White Light of pure consciousness.
Planes and Axes of the wave field.
There are NINE PLANES that define the cube, three dimensional planes at 90° in the centre, plus six planes equidistant and parallel to them, defining the cube of time. The distance, and therefor the size of the cube defines the Change in wavelength and frequency of the single wave, The illusion of differentiation is an effect of Time. ... just as volume, change, movement, aggregation, mass, weight, density, energy ... and any physical property.
Nine planes plus the zero point are the numbers:
ten sephiroth, vowels or decimal system.
There are EIGHT CUBES inside the inicial cube, as result of the separating dimensional planes, also eight vertices. They are the origin of sound and represent the
octave. or the heavens.
There are TWENTY FOUR SEGMENTS as result of the intersection between three dimensional planes. Every plane being divided by four on each side. The segments are the origin of the alphabet and all other duodecimal systems and constellations.
Number, Sound and Letter are the only ingredients imagination uses to create reality from thought in time.
10+22 = 8+24 = 4x8 = 32
"By thirty-two mysterious paths of wisdom Jah (1) has engraved [all things], the Lord of hosts (2), the God of Israel (3), the living God (4), the Almighty God (5), He that is uplifted (6) and exalted (7), He that Dwells forever (8), and whose Name is holy; (9 names) created His world by three of sefar : namely, sefer (book), sefor (number) and sippur (words), along with ten calibrations of empty space, twenty-two letters of alephbet [of which] three are mothers ( א מ ש), seven are doubles (בג"ד כפר"ת) and twelve are ordinary ( ה ו ז ח ט י ל נ ס ע צ ק)." Sepher Yezirah
Creation in doubling sequences: from sphere, through tetrahedron, octahedron towards cube.
first image, first step:
consciousness thinking creates through her center of still light two opposing pressure conditions. Atziluth, Light emanation, space.
Each of the opposed conditions split into another two pressures creating the first two of the Sefiroth: Kether and Malkuth, and three dimensional planes aleph, mem and shin.
opposites are again split into opposing pressures of light. between the four spots of maximum/minimum pressures the next four Sefiroth emerge:
next image, fourth step:
The four pressure conditions split up again and create the cube. The last four sefiroth are created.
"Around the throne, and on each side of the throne, are four living creatures, full of eyes in front and behind: the first living creature like a LION (AIN = wrath-anger), the second living creature like an OX (ZAIN = walk-manners), the third living creature with a face like a HUMAN face (HEH = speech-conversation), and the fourth living creature like a flying EAGLE (VAV = thought-contemplation). And the four living creatures, each of them with six wings, are full of eyes all around and inside ..."
... see the third graph for a complete image.
Creation in nature takes place in simple steps of...
The triplet of divisions from the sphere through the tetra to the cube is called TRINITY and is repeated in all of formation.
from the fourth phase of cell division onward the geometry alternates between 5cube-10tetra and simple cubic 7axis geometries.
.... "In proof of these things, and witnessing faithfully are the Universe, the Year of time, and Man himself, the Microcosm. He fixed these as testimonies of the TRIAD, the HEPTAD, and the DODECAD; the twelve constellations rulers of the world, the Dragon (THELE) Tali which environs the universe, and the microcosm, man."
From the Sefer Yetzirah
Any Cube of edge length 1x is formed by eight cubes of edge length ½x
This is how the octave is formed. doubling the edge length adds seven times the volume to an expanding cube, As we have already learned in Universal Geometry, by expanding a central cube of edge length ½ we pass through four locked positions, where pairs of tessellating geometries form a homogeneous lattice. These four groups of geometry are defining the Universal Ratio which equals a five time doubling sequence, cubed. [x2^5]^3 = x2^15 = x32,768, Thirty two thousand seven hundred sixty eight, being the compression /decompression ratio from Zero of balanced stillness to either point of equilibrium (unstable balance). The universal constant of minimal compression to maximal expansion is:
1 / 262,144 - (or 2^18)
the complete octave sequence being: 1/0 - 1/1 - 1/2 - 1/8 - 1/64 - 1/512 - 1/4,096 - 1/32,768 - 1/262,144 also known as frequency ranges of the Electromagnetic Spectrum.
The geometries are listed below with their percentage of occupation inside the complete 8-cube wave field. Three of the four planes, the octahedra's faces, form the holographic canvas where reality is perceived 1/512 (+1 infrared) - 1/4,096 (+2 light) - 1/32,768 (+3 ultraviolet) is the IN-breath, and 1/32,768 (-3 infra sound - matter) - 1/4,096 (-2 bass) - 1/512 (+1 treble sound) the OUT-breath.
+ 4 + position: - equilibrium - (unstable balance)
+ 1 sphere 300 PHz - 33 EHz (x-gamma ray) = unison - nucleus - sun (sphere 0) = 0.003051757 %
+ 1 cube 0 - 0,33 Hz ELF = octave - space - void (cube 8) = 99.996948243 %
+ 3 - position:
+ 1/8 octahedron 3 PHz - 33 PHz (ultraviolet) = second - atomic shell = 0.02441406 %
- 1/8 truncated cube 0.33 - 33 Hz ELF (infra sound)= seventh -gravity = 99,97558594 %
+ 2 - position:
+ 1/3 octahedron 30 THz - 900 THz (visible light) = third = 0.1953125 %
- regular truncated cube 33 - 330 Hz SLF (bass) = sixth = 99.8046875 %
+ 1 - position:
+ 1/2 octahedron 300 GHz - 30 THz (infrared) = perfect fourth = 1.5625 %
- cuboctahedron 330 Hz - 33 KHz (sound)= perfect fifth = 98.4375 %
- 0 - position: - zero balance - (stable balance)
- 1 regular truncated octahedron 300 KHz - 33 GHz = tritone = 12.5 % (micro waves)
- 87.5 % (radio waves)
"every imaginable thing is real"
Pablo Ruiz Picasso
The image to the left shows an approximation to the geometric proportions in cubic volume.
-1- (violet), -2- (pink) and +3- (orange) are the frequency bandwidths of sound and light our senses are tuned to emit and receive. From all the infinite spectra of frequency to wavelength, these are the only three planes, our senses are resonating with. They define the octaves of perceivable reality.
The +2 position is just one single octave of visible light, an octahedron buffered towards -1+ (sound) by a barrier of four octaves of infrared, and towards -3+ (infra-sound or matter) by a barrier of four octaves of ultraviolet blue.
The +2 position is surrounded by infrared and ultraviolet, both occult to the senses, the -1 to -3 positions of sound and matter are open towards their neighboring cubic wave field sections, The individual ranges are formed by nine octaves each:
-1- and -2- nine octaves of Sound..
Nine octaves of Light. thereof
+2- One octave of visible light.
-3- Nine octaves of chemical Elements (infra sound).
The image to the left shows in cubes of different size, the approximate volume and proportions of the nine geometric solids in the single wave field. From the infinite of -4- through 100% of the -3- position, through balance of -0- towards the tiny 0.003%, the volume of the +4+ position, where it joins the -4- position of infinity, completing the cycle.
All together there are Nine frequency Ranges, including -zero- of micro and radio waves. They cover a range of 36 octaves, (2¹⁸ and 2‾¹⁸, in doubling and halving sequences). The Tritone at Zero position adds 27 additional octaves of radio- and microwaves, which are the geometric equivalent to the isotopes on the periodic table of elements, (one pair per face of the truncated octahedron).
The I Ching
Universal Ratios - Cubic Proportions:
6.62607004 × 10‾³⁴ m²kg/s (2,384185 x 10‾⁷ volume)
128/1 ratio - x+gamma - edge: 1.0 x 5,0398*
5.3008 x 10‾³⁰ (3,0517 x 10‾⁵ volume)
64/1 ratio - UV - edge: 5,0398 x 4,0*
1.40471 x 10‾²⁴ (1,953 x 10‾³ volume)
32/1 ratio - visible - edge: 20.1592 x 3.174*
5.95597 x 10‾¹⁸ (6,250 x 10‾² volume)
16/1 ratio - heat IR - edge: 64'945 x 2.5*
2.02026 x 10‾¹² (1 volume)
8/1 ratio - micro+radio - edge: 162'362.7 x 2*
5.08629711 x 10‾⁴ (143,481,600 volume) - 4.23/1 ratio - sound treble - edge: 324'725.4 x ³√4*
696,278542 (286,963,200 volume) - 2.038/1 ratio - sound bass - edge: 515'339.212 x ³√.2*
299'792'458 x m/s (464,316,070 volume) - Ф/1 ratio - long radio. - edge: 649'275.8735 x ³√Ф*
8.987554787 x 10 ¹⁶ (m/s)² (574,892,963) volume - 1 x ratio - infinite. - edge: 760'236.89 x 1.0*
*(volume ratios and cubic edge lengths are relative to the higher compression just one position above).
Compression from the "zero point" has edge length 1 in the graph and volume of eight composite cubes of edge length ½.
In order to achieve a compression ratio of the volume in halving sequences, the edge length ratio has a sequence of:
2 - 2.5 - 3.174 - 4 - 5.0398.
In order to achieve an expansion ratio of the volume in opposite potential, the edge length ratio has a sequence of:
2 - ³√4 - ³√2 - ³√Ф - 1.
each sequence is the equivalent of just one octave of five tones. the Pentatonic Scale.
+4+ = Planck Unit
+4- = speed of light squared
- Compression = doubles (4 octaves)
- Expansion = halves (one Ф divided octave.)
This expansion sequence in nature forms different intervals that are either PHI fractions, or close to PHI values based on:
- 1.587401… (³√4) - the cubic root of four*
- 1.61199… (cubic root of the volume of a sphere with r=1) - ³√(4π/3)**
- 1.618034… (Ф phi) - (½√5+½) - the mathematical value of phi***
* 1.5874, the cubic root of four, is the ratio of a cube's edge length to get four times the volume. Half of the doubling sequence of an octave, harmonically the tritone (f#).
** 1.61199 is the actual Ф value found in all of nature,, the cube to sphere proportion where a sphere fills the cube with its radius being 1 and the edge length of the cube having the value of 2.
*** 1.618034… Ф phi is an irrational number and can only be approximated through the Fibonacci sequence or the cube-sphere.
Ф phi can never be reached.
To find out all about PHI and Fibonacci please refer to my page: Design Principles.
Wave length is a bad term, because it supposes the wave to be bi-directional. Waves are spherical compression and decompression sequences, therefor we should better speak about wave-volume, or cubic volume of waves. Wavelength is the volume an emitted compressed pulse expands spherically, before the next one is being emitted. Frequency is the time-span* between two pulses of compression expansion compression expansion and back to compression. If an octave is half the length of a linear string, it is actually the eighth part of the wave volume. Doubling the volume of the sphere gives the seven times doubling sequence of the octave.
As mentioned, the relation between the Spherical Wave and its cubic Wave Field is the basis for Phi proportions and the harmonic division of the octave, and, as all phenomena manifest three dimensional, the actual value is Ф³, or phi cubed 4.2360 or 2+√5.
The volume for Cubing the Sphere is 4.18879 or 4π/3 (99% of Ф³)
Fibonacci is a sequence of volumes, not of edge lengths.
Around -zero- (micro and radio-waves), the pressure conditions are always balanced pairs of opposites, equal in potential, different in volume:
-0+ micro << RADIO -0-
+ 1+ infrared << TREBLE -1-
+ 2+ visible light << BASS -2-
+ 3+ ultraviolet << INFRASOUND -3-
+ 4+ x and gamma << SPACE +4-
The illusion of Motion (water) manifests inside of the initial cube in form of concentric Spheres,
The illusion of Movement (fire) manifests inside every one of the eight segments of the initial cube in form of double vortexes (just like shown in the image on top of this article.)
Double vortexes are the geometries of extending spheres of light, reflecting at the six mirror planes of the cube, as well as projections through the octahedral face lenses, at all 14 wave field boundaries.
the image above shows, at two vertices of the cube, the triangular faces of the four octahedral geometries forming five locked positions from tessellation. The first one is located at the cube's vertices, the remaining four are: Yellow-green-turquoise-blue triangles at the expanding half of the cycle, and red-orange-yellow triangles, at the compressing half.
four octaves of compression form concentric cones, from the blue horizontal plane of present towards the cube's vertex at centre of the red vertical plane from the past. Simultaneously, in order to balance the motion, four octave cones of expansion form at centre of blue (plane of present) towards the rim of red (plane of past). Only one pair of cones reaches all the way from maximum compression (+4 / centre of planes) to maximum expansion (-4 / rim of planes). The rest of the cones form double vortexes, with their focal points at the locked positions of the wave. (little white dots or suns).