Patterns In Nature – A Case For Intelligent Design

‘Nature geometrizes universally in all her manifestations.’ – H.P. Blavatsky

Humans have always looked upon the beauty, majesty, and ingenuity of the world around them with reverent wonder. The grandeur of the heavens, the regular rhythms of the sun and moon, the myriads of living creatures in all their splendid diversity, the magnificence of a rose flower, a butterfly’s wings or a snow crystal – the idea that all this might be the product of a mindless accident strikes many people as far-fetched. The ancient Greeks aptly called the universe kosmos, a word denoting order and harmony. This underlying order is reflected in many intriguing patterns in nature.

1. Phi and Fibonacci

Consider the line ABC in the following diagram:

Fig. 1.1

Point B divides the line in such a way that the ratio between the longer segment (AB) and the shorter segment (BC) is the same as that between the whole line (AC) and the longer segment (AB). This proportion is known by various names: the golden section, the golden mean, the golden ratio, the extreme and mean ratio, the divine proportion, or phi (φ). If the distance AB equals 1 unit, then BC = 0.6180339887… and AC = 1.6180339887… . The second of these two numbers is the golden section, or phi (sometimes this name is also given to the first number). Many designs in nature are related to the golden section, and it has been widely used in sacred architecture and artwork throughout the ages.

The golden section is an irrational, or transcendental, number, meaning that it never repeats and never ends. It is unique in that its square is produced by adding the number 1 (φ² = φ+1), and its reciprocal by subtracting the number 1 (1/φ = φ-1). (Phi equals (√5+1)/2, the positive root of x² = x+1.) The golden section is the only irrational number that approaches more closely to rationality the higher the power to which it is raised. For instance, φ3000 = 1.0000000000 x 10500.

The golden section is part of an endless series of numbers in which any number multiplied by 1.618 gives the next higher number, and any number multiplied by 0.618 gives the next lower number:

0.090 0.146 0.236 0.382 0.618 1.000 1.618 2.618 4.236 6.854 11.090
φ-5 φ-4 φ-3 φ-2 φ-1 φ0 φ1 φ2 φ3 φ4 φ5

Like phi itself, this series of numbers has many interesting properties:
•  each number is equal to the sum of the two preceding numbers;
•  the square of any number is equal to the product of any two numbers at equal distances to the left and right (e.g. 1.618² = 0.618 x 4.236);
•  the reciprocal of any number to the left of 1.000 is equal to the number the same distance to the right of 1.000 (e.g. 1/0.382 = 2.618).
(To obtain perfectly exact results, the numbers would have to be extended to an infinite number of decimals.)

The large rectangle below is a golden rectangle, meaning that its sides are in the proportion 1.000:1.618. If a square is removed from this rectangle, the remaining rectangle is also a golden rectangle. Continuing this process produces a series of nested golden rectangles. Connecting the successive points where the ‘whirling squares’ divide the sides of the rectangles in golden ratios produces a logarithmic spiral, which is found in many natural forms (see next section). A similar spiral can be generated from a golden triangle (an isosceles triangle whose sides are in the golden ratio), by repeatedly bisecting one of the angles to generate a smaller golden triangle.

Fig. 1.2

Fig. 1.3

    A number series closely related to the golden section is the Fibonacci sequence: it begins with 0 and 1, and each subsequent number is generated by adding the two preceding numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 …

If we take these numbers two at a time, and divide the larger one by the smaller one, the value will oscillate alternately above and below the golden section, while gradually converging on it. If we divide the smaller number by the larger number, the value converges on 1/φ (0.618). (Note that in any series of numbers in which we start with any two ascending numbers and add each consecutive pair to produce the next term, the ratio of successive terms will always tend towards φ.)

1/1 2/1 3/2 5/3 8/5 13/8 21/13 34/21 55/34 89/55 144/89
1.0 2.0 1.5 1.666 1.600 1.625 1.615385 1.619048 1.617647 1.618182 1.617978

    The Fibonacci sequence has many curious features. For example, the sum of any 10 consecutive Fibonacci numbers is always divisible by 11, being equal in fact to 11 times the seventh number. The sum of all Fibonacci numbers from the first to the nth is equal to the (n+2)th number minus 1. Thus the sum of the first 15 numbers (986) is equal to the 17th number (987) minus 1. The square of any term differs by 1 from the product of the two adjacent terms in the sequence: e.g. 3² = 9, 2×5 = 10; 13² = 169, 8×21 = 168. The last digit of any number in the sequence repeats itself with a periodicity of 60: e.g. the 14th number and the 74th number both end in 7. The last two digits (01, 01, 02, 03, 05, 08, 13, 21, etc.) repeat in the sequence with a periodicity of 300. For any number of last digits from three upwards, the periodicity is 15 times ten to a power that is one less than the number of digits, (e.g. for 7 digits it is 15 x 106, or 15 million).

2. Nature’s numbers

Many of nature’s patterns are related to the golden section and the Fibonacci numbers. For instance, the golden spiral is a logarithmic or equiangular spiral – a type of spiral found in unicellular foraminifera, sunflowers, seashells, animal horns and tusks, beaks and claws, whirlpools, hurricanes, and spiral galaxies. An equiangular spiral does not alter its shape as its size increases. Because of this remarkable property (known as self-similarity),* it was known in earlier times as the ‘miraculous spiral’.

*Shapes and forms that look similar under any magnification are known as fractals. Numerous apparently irregular natural phenomena display approximate self-similarity, meaning that similar patterns and details recur at smaller and smaller scales. This applies, for example, to the branching of lightning, rivers, trees, and human lungs. Other fractal objects include the chambered nautilus, a head of cauliflower, coastlines, clouds, snowflakes, and rocks (a magnified rock can look like an entire mountain).

Fig. 2.1 The Whirlpool Galaxy (M51).

Fig. 2.2 Each increment in the length of the nautilus shell is accompanied by a proportional increase in its radius, so that the nautilus does not need to adjust its balance as it matures.

Fig. 2.3 A ram’s heavy corkscrewed horns keep a stable centre of gravity as they grow.

Fig. 2.4 Owing to the structure of their compound eyes, insects such as moths follow an equiangular spiral when drawn towards a candle flame. Peregrine falcons, which have eyes on either side of their heads, follow a similar spiral path when flying at their prey.

Phi can be found in the proportions of the bodies of humans and other creatures, including birds, flying insects, frogs, fish, and horses. The height of a newborn child is divided by the navel into two equal parts (1:1), whereas in adults, the division of the body’s height at the navel yields two parts in the ratio 1:φ, though the navel is usually a little higher in females and a little lower in males. Phi is found in the proportion between the hand and the forearm, and between the upper arm and the hand plus forearm.

Fig. 2.5 Each section of an index finger, from the tip to the base of the wrist, is larger than the preceding one by about 1.618, fitting the Fibonacci numbers 2, 3, 5 and 8.

The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of the double helix spiral. 34 and 21 are Fibonacci numbers and their ratio closely approximates phi. DNA has two grooves in its spirals, with a phi ratio between the major groove and the minor groove (roughly 21 angstroms to 13 angstroms).

Fig. 2.6

    The Fibonacci numbers and golden section are widely found in the plant kingdom. In nearly all flowers, the number of petals is a Fibonacci number. For instance, lilies have 3 petals, buttercups have 5, many delphiniums have 8, marigolds have 13, asters have 21, and daisies commonly have 13, 21, 34, 55 or 89. Non-Fibonacci numbers don’t occur anything like as often. For instance, very few plants have 4 petals, an exception being the fuchsia. Some plant species are very precise about the number of petals they have, e.g. buttercups, but with others only the average number of petals is a Fibonacci number.

Fig. 2.7 Shasta daisy with 21 petals.

    Fibonacci numbers are often found in the arrangement of branches, leaves, and seeds (phyllotaxis). If we look at a plant from above, the leaves are not arranged directly above one another, but in a way that optimizes their exposure to sun and rain. The Fibonacci numbers occur when counting both the number of times we go around the stem from one leaf to the next, and when counting the number of leaves we meet until we encounter one directly above the starting one. The number of turns in each direction and the number of leaves are usually three consecutive Fibonacci numbers.

In the diagram below, to get from the topmost leaf to the last of the 5 leaves of the plant on the left takes 2 anticlockwise turns or 3 clockwise turns. 2, 3 and 5 are three consecutive Fibonacci numbers. For the plant on the right, it takes 3 anticlockwise rotations or 5 clockwise rotations to pass 8 leaves. Again, 3, 5 and 8 are consecutive Fibonacci numbers. An estimated 90% of all plants display this pattern.

Apple, cherry, apricot,
oak, cypress, poplar
Holly, pear, spruce,
various beans

Fig. 2.8 (by Michael S. Schneider from A Beginner’s Guide To Constructing The Universe)

    Similar arrangements can be found in the scales of a pinecone or the seeds of a sunflower. The florets in the head of a sunflower form two intersecting sets of spirals, one winding clockwise, the other anticlockwise. In some species the number of clockwise spirals is 34, and the number of counterclockwise spirals is 55. Other possibilities are 55 and 89, or 89 and 144. Pineapples have 8 rows of scales sloping to the left, and 13 to the right. Again, these are successive Fibonacci numbers.

Fig. 2.9 Sunflower head.

Fig. 2.10 This pine cone has 13 spirals to the right and 8 to the left.

    The fact that in the arrangement of seeds on flower heads, the numbers of spirals in each direction are nearly always neighbouring Fibonacci numbers means that each seed is roughly 0.618 of a turn from the last one, i.e. there are roughly 1.618 seeds per turn. This results in optimal packing of the seeds, because no matter how big the seed head gets, the seeds are always equally spaced. Similarly, trees and plants tend to have 0.618 leaves or petals per turn. In terms of degrees this is 0.618034 of 360°, which is 222.5°. If we measure the angle going in the opposite direction around the circle, we get: 360 – 222.5 = 137.5°, which is known as the golden angle. The Fibonacci numbers appear in leaf arrangements and the number of spirals on seedheads because they form the best whole-number approximations to the golden section. The higher the numbers are on the Fibonacci sequence, the more closely the golden ratio and the golden angle are approached and the more complex the plant.

3. Pentads and hexads

Fig. 3.1 Each successive pair of heavy lines in this pentagram is in the golden ratio.

    The golden ratio appears in pentagonal forms of symmetry, notably in the five-pointed star (or pentagram), which was the emblem of the Pythagorean brotherhood. Pentagonal symmetry abounds in living organisms, especially plants and marine animals (e.g. starfishes, jellyfishes, sea urchins). Flowers with 5 petals (or multiples of 5) include all fruit blossoms, water lilies, roses, honeysuckles, carnations, geraniums, primroses, orchids, and passionflowers.

Fig. 3.2 Left: Sea cucumber (cross section). Right: Sand dollar (sea urchin).
(by Michael S. Schneider from A Beginner’s Guide To Constructing The Universe)

Fig. 3.3 Pentagonal diatom.

Fig. 3.4 Apple blossoms have five petals, pentagonal indentations are seen at the bottom of the fruit, and cutting an apple in half reveals a star pattern of seeds.

Fig. 3.5 The human body clearly expresses the pentad’s symmetry in its five senses and five extensions from the torso, each limb ending in five fingers or toes. (by Michael S. Schneider from A Beginner’s Guide To Constructing The Universe)

While pentagonal patterns abound in living forms, the mineral world favours twofold, threefold, fourfold, and sixfold symmetry. The hexagon is a ‘close-packing’ shape that allows for maximum structural efficiency. It is very common in the realm of molecules and crystals, in which pentagonal forms are almost never found. Steroids, cholesterol, benzene, TNT, vitamins C and D, aspirin, sugar, graphite – all show sixfold symmetry. The most famous hexagonal architecture is built by bees, wasps, and hornets.

Fig. 3.6 Six water molecules form the core of each snow crystal.

Fig. 3.7 Snow crystals (courtesy of Kenneth G. Libbrecht).

Fig. 3.8 Benzene (C6H6).

Fig. 3.9 Honeycomb.

Fig. 3.10 The facets of a fly’s eyes form a close-packed hexagonal arrangement.

Fig. 3.11 A hexagonal lattice, or honeycomb, of convection
cells (Bénard cells) in a heated liquid.

    The atmosphere of Saturn, one of the four gas giants, circulates around its axis in striped bands. Seen from the poles, the bands generally appear to be circular. But the band nearest the north pole is hexagonal, with sides about 13,800 km long. Unlike other clouds in its atmosphere, it rotates slowly, if at all, relative to the planet. It is one of Saturn’s most enigmatic features.

Fig. 3.12 Saturn’s northernmost hexagonal cloud band. The dark radial lines are artefacts of the way the above images were produced.

4. Platonic solids

A regular polyhedron is a three-dimensional shape whose edges are all of equal length, whose faces are all identical and equilateral, and whose corners all touch the surface of a circumscribing sphere. There are only five regular polyhedra: the tetrahedron (4 triangular faces, 4 vertices, 6 edges); the cube/hexahedron (6 square faces, 8 vertices, 12 edges); the octahedron (8 triangular faces, 6 vertices, 12 edges); the dodecahedron (12 pentagonal faces, 20 vertices, 30 edges); and the icosahedron (20 triangular faces, 12 vertices, 30 edges). In each case, the number of faces plus corners equals the number of edges plus 2. These five polyhedra are also known as the platonic or pythagorean solids, and are intimately connected with the golden section. Their striking beauty is derived from the symmetries and equalities in their relations.

Fig. 4.1 The five platonic solids. The ancients considered the tetrahedron to represent the element of fire; the octahedron, air; the icosahedron, water; and the cube, earth. The dodecahedron symbolized the harmony of the entire cosmos.

Fig. 4.2 An icosahedron’s 12 vertices are defined by three perpendicular golden rectangles. With an edge length of one unit, its volume is 5φ5/6.

The symmetry of the platonic solids leads to other interesting properties. For instance, the cube and octahedron both have 12 edges, but the numbers of their faces and vertices are interchanged (cube: 6 faces and 8 vertices; octahedron: 8 faces and 6 vertices). Similarly, the dodecahedron and icosahedron both have 30 edges, but the dodecahedron has 12 faces and 20 vertices, while for the icosahedron it is the other way round. This allows one solid to be mapped into its dual or reciprocal solid. If we connect the centres of all the faces of a cube, we obtain an octahedron, and if we connect the centres of the faces of an octahedron, we obtain a cube. The same procedure can be used to map an icosahedron into a dodecahedron, and vice versa. (In the Hindu tradition, the icosahedron represents purusha, the male, spiritual principle, and generates the dodecahedron, representing prakriti, the female, material principle.) The tetrahedron is self-dual – joining the four centres of its faces produces another, inverted tetrahedron.


Fig. 4.3

    There are two other ways of passing from dodecahedron to icosahedron, and icosahedron to dodecahedron. If we join interiorly all the vertices of an icosahedron, the lines will intersect at 20 points defining the vertices of a dodecahedron. If we then do the same with the resulting dodecahedron, a smaller icosahedron is generated within it, and so on, ad infinitum. Likewise, if we lengthen the sides of an icosahedron, an enveloping dodecahedron will be formed. Lengthening the sides of the dodecahedron will generate an enveloping icosahedron. Again, this operation can be repeated indefinitely – a fitting symbol of the theosophical teaching of worlds within worlds.

The sum of the angles of the platonic solids is 3600 degrees for the icosahedron, 6480 for the dodecahedron, 1440 for the octahedron, 2160 for the cube, and 720 for the tetrahedron. Each of these numbers is divisible by 9, which means that the sum of the digits is 9 (e.g. 6+4+8=18, 1+8=9). They are also divisible by the canonical numbers 12, 60, 72 and 360. As we shall see, the numerical elements of the five regular polyhedra frequently recur in nature’s cycles.

The platonic solids (especially the tetrahedron, octahedron, and cube) form the basis for the orderly arrangement of atoms in crystals, though the regular dodecahedron and icosahedron are never found.

Fig. 4.4 In salt crystals, the sodium chloride atoms tightly pack along cubic lines of force.

    Tetrahedral geometry commonly occurs in organic and inorganic chemistry and in submicroscopic structures. For example, the methane molecule (CH4) is a tetrahedron, with a carbon atom at its centre and a hydrogen atom at each of its four corners.

Carbon exists in three pure forms. In graphite crystals, the carbon atoms lie in hexagonal sheets, which readily slide off a pencil as we write. In diamond, the hardest substance known, each carbon atom is bonded to four others in a super-strong tetrahedral arrangement. Buckminsterfullerene, the third, highly stable allotrope of carbon, consists of 60 carbon atoms, arranged at the vertices of a truncated icosahedron (i.e. one with its corners cut off).


Fig. 4.5 Graphite; diamond; buckminsterfullerene.

    The great majority of viruses are icosahedral, including the polio virus and the 200 kinds of viruses responsible for the common cold. Icosahedral symmetry is believed to allow for the lowest-energy configuration of particles interacting on the surface of a sphere. The five platonic solids are also found in radiolarian skeletons.

Fig. 4.6 The platonic solids have been found living in the sea. The tetrahedron, somewhat rounded as if from internal pressure, is embodied in a protozoan called Callimitra agnesae, the cube is Lithocubus geometricus, the octahedron Circoporus octahedrus, the dodecahedron Circorrhegma dodecahedrus, and the icosahedron Circognia icosahedrus.

5. Precession and yugas

Due to a slow gyration of the earth’s axis, the spring equinox occurs about 20 minutes earlier each year, when the earth is still about 1/72 of a degree (50 arc-seconds) from the point in its orbit where the previous spring equinox occurred. The vernal equinoctial point therefore moves slowly through the constellations of the zodiac. This key astronomical cycle is known as the precession of the equinoxes. The ancients called it the ‘great year’.

At the average rate of 1/72 of a degree per year, the earth enters a new constellation about every 2160 years, and takes 25,920 years to make a complete circuit of the zodiac. The entry into each new constellation marks the beginning of what is called in theosophy the Messianic cycle, which is said to be marked by the appearance on earth of a spiritual teacher or avatar (lit. a ‘descent’ of divinity); for instance, the commencement of the Piscean age was marked by the appearance of Christ. Interestingly, 2160 is the total number of degrees in the angles of a cube, and if a cube is opened out it forms the shape of a cross, a universal symbol representing the descent of spirit into matter, or the ‘crucifixion’ of spirit in the ‘tomb’ of matter.

The ancient chronological charts of the Brahmans refer to four great cycles or yugas. The krita- or satya-yuga lasts 4000 divine years, the treta-yuga 3000, the dvapara-yuga 2000, and the kali-yuga 1000, a ‘divine year’ being equal to 360 earth-years. Each yuga is introduced by a ‘dawn’ and concluded by a ‘twilight’, each equal to one-tenth of the period of the yuga. The total length of the four yugas in earth-years is therefore 1,728,000 for the satya-yuga, 1,296,000 for the treta-yuga, 864,000 for the dvapara-yuga, and 432,000 for the kali-yuga. The lengths of these four yugas are related in the ratio 4:3:2:1, i.e. they are all multiples of 432,000. If the individual digits of each yuga are added together, the result is always 9 (e.g. 1+2+9+6=18, 1+8=9).

The four yugas together make up one maha-yuga, lasting 4,320,000 years, which in theosophy is said to equal half the evolutionary period of a root-race or ‘humanity’, of which we are now in the fifth. The total life-period of earth, or a day of Brahma, is said to last 1000 maha-yugas or 4,320,000,000 years, and is followed by a rest period, or night of Brahma, of the same length, making a total of 8,640,000,000 years. 360 days and nights make up one year of Brahma, equal to 3,110,400,000,000 ordinary years. 100 years of Brahma make up an age of Brahma, this being the total life-period of our universal solar system, equal to 311,040,000,000,000 years. If we take the precessional cycle of 25,920 years and add to it a dawn and a twilight equal to one-tenth of its length, we get 31,104 – the initial digits of a year and age of Brahma.

4320 is twice 2160, the total number of degrees in a cube, the length of the Messianic cycle, and the average time it takes the equinoctial point to pass through one constellation of the zodiac. 432,000 is equal to 4 x 108,000, and 108,000 years is the average length of an astronomical cycle known as the revolution of the line of apsides. The line of apsides is the line joining that point in the earth’s elliptical orbit where it is closest to the sun (perihelion) and that point where it is furthest from the sun (aphelion). This line turns extremely slowly – by an average of 12 arc-seconds a year – from west to east, and therefore rotates through the whole zodiac in 108,000 years.

The sun has a radius of approximately 432,000 miles (432,475) and a diameter of about 864,000 miles, while the moon has a radius of 1080 miles and a diameter of 2160 miles. Silver, the metal associated with the moon, has an atomic weight of 107.9. In addition, 108 is roughly the average distance between the sun and earth in terms of solar diameters, the average distance between the surfaces of the moon and earth in terms of lunar diameters, and the diameter of the sun in terms of earth diameters (actual figures: 107.5, 108.3, and 109.1 respectively). As a result of these remarkable ‘coincidences’, the moon has the same apparent size as the sun, as seen from earth, and almost exactly covers the disk of the sun during a total solar eclipse.

Fig. 5.1

    According to conventional astronomy, in each precessional cycle the earth’s north pole slowly traces an approximate circle, with an average radius of about 23.5 degrees (the current inclination of its axis), around the north pole of the ecliptic – a point in the constellation Draco perpendicular to the plane of the earth’s orbit around the sun. (According to theosophy, the earth’s axis does not trace a circle but a spiral around the ecliptic poles, as the tilt of the earth’s axis is said to change by four degrees every precessional cycle.)

The ‘circle’ traced by the earth’s axis around the north ecliptic pole is not smooth but wavy, as the moon’s gravitational pull causes the earth to ‘nod’ about once every 18 years (currently 18.6 years), a movement known as nutation. The circle therefore contains about 1440 waves, since 18 x 1440 = 25,920. Note that the average human heartbeat is equal to 72 beats a minute, and on average we breathe about 18 times a minute. 72 years (= 6+60+6 or 6×12) is said to be the ‘ideal’ lifespan of a human being, during which time the sun moves through one degree of the zodiac in the precessional cycle. A human breathes 72 times in 4 minutes, the time required for the earth to turn 1 degree on its axis. In 24 hours (86,400 seconds) we breathe 18 x 1440 = 25,920 times, equal to the number of years in the precessional cycle.

Each human heartbeat takes about 8 tenths of a second. The time-periods occupied by each of the five cardiac phases, reckoned on the basis of one hour, are as follows: auricular systole, 432 seconds; ventricular systole, 1296 seconds; repose of the entire heart, 1728 seconds; diastole, 3024 seconds; and ventricular diastole, 2160 seconds. There are on average 4320 heartbeats in one hour, 8640 beats in 2 hours, 12,960 beats in 3 hours, 17,280 beats in 4 hours, 21,600 beats in 5 hours, and 25,920 beats in 6 hours.* In these figures we can recognize the digits of the four yugas, the Messianic cycle, and the precessional cycle (whose lengths are all multiples of 12, 60, 72, and 360). Thus, again and again we find correspondences between what takes place in the small (the microcosm) and what takes place in the great (the macrocosm) – as above, so below.

*G. de Purucker, Esoteric Teachings, San Diego, California, Point Loma Publications, 1987, 7:20-1.

6. Formative power of sound

In the late 18th century, German physicist Ernst Chladni demonstrated the organizing power of sound and vibration in a visually striking manner. He showed that when sand is scattered on metal plates, and a violin bow is drawn across them, the resulting vibrations cause the particles to move to the places where the plate is almost motionless, producing a variety of beautiful, regular, intricate patterns.*

*Joscelyn Godwin makes an interesting comment on this phenomenon: ‘Once, passing by a crowded dance hall where rock was being played, I could not help perceiving the floor of the hall in terms of a Chladni plate, and the dancers appeared for all the world like the jumping, helplessly manipulated grains of sand’ (1995, p. 246).


Fig. 6.1 Chladni figures. For a video, click here.

    A century after Chladni, Margaret Watts-Hughes created images by placing a powder or liquid on a disk then letting it vibrate to the sound of a sustained musical note. She experimented with several musical instruments but had most success using her voice. The particles arranged themselves into geometric shapes, flower patterns (such as pansies, primroses, geraniums, and roses), or the shape of a fern or a tree. The higher the pitch, the more complex the patterns produced; a powerful sustained note produced an imprint of a head of wheat.

Fig. 6.2 Figures generated by the voice of Margaret Watts-Hughes.

    In the 1950s the study of wave phenomena was continued by Swiss scientist and anthroposophist Hans Jenny (1904-1972), who named the field ‘cymatics’. Using crystal oscillators (which allow precise frequencies and amplitudes to be used), he vibrated various powders, pastes, and liquids, and succeeded in making visible the three-dimensional effects of sound. He produced an astonishing variety of awe-inspiring geometrical and harmonic shapes, including life-like flowing patterns, which he documented in photographs and films.

Jenny, too, found that higher frequencies produced more complex shapes. A low frequency produced a simple central circle surrounded by rings, while a higher frequency increased the number of concentric rings. Even higher frequencies created shapes resembling petals, butterflies, or crustaceans, zebra patterns, mandala-like patterns, and images of the five platonic solids. As the frequency rises, the dissolution of one pattern may be followed by a short chaotic phase before a new, more intricate, stable structure emerges. If the amplitude is increased, the motions become all the more rapid and turbulent, sometimes producing small eruptions. Under certain conditions Jenny was able to make the shapes change continuously, despite altering neither frequency nor amplitude.

Fig. 6.3 Hexagonal pattern produced by light refracting through a small sample of water (about 1.5 cm in diameter) under the influence of vibration. The figure is in constant dynamic motion. (Jenny, 2001, p. 112; courtesy of Jeff Volk)

Fig. 6.4 A round heap of lycopodium powder (4 cm in diameter) is made to circulate by vibration. At the same time two centres of eruption rotate at diametrically opposed points. (Jenny, 2001, p. 108; courtesy of Jeff Volk)

Fig. 6.5 Jenny built a tonoscope to translate the human voice into visual patterns in sand.
Left to right: ‘oh’ sound, ‘ah’ sound, ‘oo’ sound. (Jenny, 2001, p. 65; courtesy of Jeff Volk)

    More recently, Peter Guy Manners found that an acoustic recording of the Crab Nebula caused sand to form a pattern strikingly like the nebula itself. As the near-infrasonic sound was played, the two swirling arms pulled in, forming a tight ball. Towards the end of the audiotape, the sand became very highly compacted and then suddenly exploded, throwing sand off the table.

John’s Gospel begins: ‘In the beginning was the Word, and the Word was with God, and the Word was God.’ The Egyptian Book of the Dead, contains a parallel passage: ‘I am the Eternal, I am Ra … I am that which created the Word … I am the Word …’ The Hindu tradition teaches that ‘Nada Brahma’ (the world is sound). The underlying idea is that everything we see is a divine word – or vibration – that has solidified and become manifest, the vibrations originating in the inner, more ethereal realms. All of nature is essentially rhythmic vibration. Everything from subatomic particles to the most intricate lifeforms, from planets to galaxies, comprises resonating fields of pulsating energy in constant interaction. In the poetic words of Cathie Guzzetta:

The forms of snowflakes and faces of flowers may take on their shape because they are responding to some sounds in nature. Likewise, it is possible that crystals, plants, and human beings may be, in some way, music that has taken on visible form. (D. Campbell, ed., Music: Physician for times to come, Quest, 1991, p. 149)

7. Planets and geometry

If we draw a circle representing the earth – which has a mean radius (in round numbers) of 3960 miles – and then draw a square around it, the square will have a perimeter equivalent to 31,680 miles. If we then draw a second circle with a circumference equal to the perimeter of the square, its radius will be 5040 miles (using 22/7 as a good approximation to pi (π), as the ancients often did) – or 1080 miles more than the smaller circle. Just as 3960 miles is the radius of the earth, 1080 miles is the radius of the moon. In other words, the relative dimensions of the earth and moon square the circle!

Fig. 7.1 Earth and moon square the circle. Note that 5040 (the radius of the outer circle) = 1x2x3x4x5x6x7 (known as ‘factorial 7’, also written: 7!) = 7x8x9x10 (or 10!/6!). A quarter of its circumference (also equal to the diameter of the earth-circle) = 7920 = 8x9x10x11 (or 11!/7!), and the area of each semicircle = 11!.

Exactly the same proportions and digits (expressed in feet rather than miles) can be found at Stonehenge (see Michell, 1995, 2001). The outer (sarsen) circle has a mean radius of 50.4 ft and a circumference of 316.8 ft. This is equal to the perimeter of a square drawn round the smaller (bluestone) circle, which has a radius of 39.6 ft. This radius is also equal to the diameter of the circle defined by the inner U-shaped structure. This is clear evidence that the ‘English’ foot and mile are at least as ancient as Stonehenge and, like many other ancient systems of measures, are closely related to the dimensions of earth, moon, and sun.

Fig. 7.2 Ground plan of Stonehenge. The lintels on top of the stones of the outer (sarsen) circle were mortised to the uprights and jointed at their ends, forming what was once a precision-made, perfectly level platform.

Fig. 7.3 Given its slope angle of 51.83°, the Great Pyramid, too, squares the circle. The length of each base side divided by the height equals π/2. In addition, the apothem divided by half the base side equals φ.

Fig. 7.4

    If a tetrahedron is inscribed in a sphere with the apex placed at either pole, the three corners of the base will touch the sphere at a latitude of 19.47 degrees in the opposite hemisphere. This latitude marks the approximate location of major vorticular upwellings of planetary and solar energy. The primary focus of sunspot activity is about 19.5° N and S. On Venus, there are volcanic regions at 19.5° N and 25.0° S. Mauna Loa and Kilauea (Hawaii), Earth’s largest volcanoes, are located at 19.5° and 19.4° N respectively. On the moon there is a mare-like lava extrusion at 19.6° S. On Mars, Olympus Mons, possibly the largest volcano in the solar system, is located at 19.3° N. The Great Red Spot of Jupiter is located at 21.0° S. On Saturn there are storm belts at 20.0° N and S. On Uranus, there are upwellings causing cooler temperatures at 20.0° N and S, and a dark spot at about 22.5° S. The Great Dark Spot of Neptune, photographed by Voyager 2 in 1989, was located at 20.0° S, but when the Hubble Space Telescope viewed the planet in 1994, the spot had vanished – only to be replaced by a dark spot at a similar location in the northern hemisphere.

Fig. 7.5 Jupiter’s Great Red Spot.

8. Planetary distances

Are the planets of our solar system located at random distances from the sun? The Titius-Bode law, discovered 1766, suggests they are not. The law is obtained by writing down first 0, then 3, and then doubling the previous number: 6, 12, 24, etc. If 4 is added to each number and the sum divided by 10, the resulting numbers give the mean distances of the orbits of the planets in astronomical units (1 AU = the earth’s mean distance from the sun). Uranus, discovered in 1781, fitted the law, as did Ceres, the largest asteroid between Mars and Jupiter, discovered in 1801. However, the law breaks down completely for Neptune and Pluto, which were discovered later. Various efforts have been made to modify the Titius-Bode law to make it more accurate.*

*William R. Corliss, The Sun and Solar System Debris, Sourcebook Project, 1986, pp. 34-42.

What the Titius-Bode law essentially means is that planetary orbits become progressively greater by a ratio of approximately 2:1 (the ratio of the octave) with increasing distance from sun. This is brought out in columns 3 and 4 of the table below, in which half the distance between Mercury and Earth is taken as the unit of measurement. Uranus and Pluto have mean orbits close to the exact distances necessary to complete two further octaves. Neptune is located almost exactly half-way between Uranus and Pluto, as though to fill in the half-octave position. This may indicate that it was not an original member of the solar system (theosophy says it was captured from outside our solar system). Likewise, the Titius-Bode law works for Pluto if we ignore Neptune.

Mean distance of the planets from the sun
Planet Calculated
according to
Titius-Bode law
(in AU)
(in AU)
Perfect octaves
in units of
distance from
Actual units
of distance
from Mercury
Mercury 0.4 0.387 0 0
Venus 0.7 0.723 1 1.1
Earth 1.0 1.000 2 2
Mars 1.6 1.524 4 3.7
Asteroid belt
2.8 2.767 8 7.8
Jupiter 5.2 5.203 16 15.7
Saturn 10.0 9.539 32 29.9
Uranus 19.6 19.191 64 61.4
Neptune 38.8 30.061 (64×1.5=96) (96.8)
Pluto 77.2 39.529 128 127.7

Due to its ad-hoc nature, the Titius-Bode law is usually dismissed as a numerical coincidence that has no physical basis. However, the fact that the planets’ distances from the sun follow a pattern can easily be demonstrated by plotting the logarithm of the mean distance of the planets (including the asteroid belt) against their sequential number (1 to 10). The fact that all the points lie very nearly on a straight line proves that gravitation is ‘quantized’. However, there is currently no detailed mainstream theory that explains how gravity works and why it should be quantized. The orbits of satellites around moons show the same quantized spacing, as do the orbits of electrons around an atomic nucleus (in the Bohr model of the atom).

Fig. 8.1
Figs. 8.1 to 8.6 courtesy of John Martineau (A Little Book of CoincidenceWooden Books, 2001)

    Curiously, the mean orbital radii of the four inner and four outer planets reflect about the asteroid belt. For instance, if we multiply together the orbital radii of Venus, Mars, Jupiter, and Uranus, we get virtually the same value as multiplying the orbital radii of Mercury, Earth, Saturn, and Neptune (5.51 x 1034 km as against 5.56 x 1034 km).

The spacing of the planets shows many geometrical regularities. For example:

Fig. 8.2 Three circles touching: if Mercury’s mean orbit passes through the centres of the three circles, Venus’ orbit encloses the figure (99.86% accuracy).


Fig. 8.3 Left: The mean orbits of Mars and Jupiter can be drawn from four touching circles or a square (99.995%). Right: A related pattern spaces Earth’s and Mars’ orbits (99.8%).

Fig. 8.4 In this diagram, the smaller and larger circles represent not only the relative sizes but also the orbits of Mercury and Earth; they are related by a pentagram (99.1%).

Fig. 8.5 This diagram shows Earth’s and Saturn’s relative sizes and orbits;
they are related by a 15-pointed star (99.3%).


Fig. 8.6 Earth’s and Jupiter’s mean orbits can be created by spherically nesting three cubes, or three octahedra, or any threefold combination of them (99.89%).

9. Solar system harmonies

The 17th-century astronomer Johannes Kepler discovered a remarkable relationship between a planet’s mean distance from the sun and the time it takes to orbit the sun: the ratio of the square of a planet’s period of revolution (T) to the cube of its mean distance (r) from the sun is always the same number (T²/r³ = constant). For instance, measuring T in earth-years and r in astronomical units, we get:

 = 1.0002
 = 1.0000
 = 1.0000
 = 0.9991

Orthodox science has no real explanation for this, or for the many ‘resonances’ in solar system dynamics. For instance, the periods of Jupiter and Saturn show a 2:5 ratio. The periods of Uranus, Neptune, and Pluto stand in a 1:2:3 ratio. Mars and Jupiter are locked into a 1:12 resonance, Saturn and Uranus are in a 3:1 resonance, and there is a 2:3 resonance between Mercury’s rotational and orbital periods.

What is the nature of such ‘resonances’? Abstract mathematical concepts such as ‘curved spacetime’ shed no light on the matter. A concrete explanation must be sought in the behaviour of the dynamic ether filling space, whose vorticular motions cause the planets and stars to rotate and carry them along in their respective orbits. According to the ether-science model known as aetherometry, T²/r³ is a constant for all the planets because it refers to the constant flux of energy that the solar system as a whole extracts by its primary gravitational interaction with the ether, entailing a nearly constant energy supply for each of its members.

The speeds of the planets in their orbits represent their pitch-frequencies. Cosmic ‘chords’ are produced when planets come into conjunction (or ‘kiss’), i.e. stand in a straight line with the earth and sun. A certain number of regular planetary conjunctions occur over particular periods of time, and the ratios between these numbers reflect with considerable accuracy the length ratios necessary to produce the diatonic notes of an octave, i.e. the seven notes of a musical scale.

Fig. 9.1 Planetary conjunctions as ‘chords’ (Tame, 1984, p. 239).
The line in this diagram represents an octave, divided into seven intervals by eight notes. The line could represent the string of a one-stringed musical instrument. The numbers above the line are the numbers of conjunctions of each planet with the sun and earth, and those below the line are the numbers of years involved.

The planets’ orbits are ellipses with the sun at one of their foci. Their speeds are therefore variable: they speed up as they approach perihelion (the point in their orbit nearest the sun) and slow down as they approach aphelion (their greatest distance from the sun). Following Kepler, Francis Warrain expressed the ratio between the minimum and maximum speeds of one planet and those of different planets as a musical interval. The results (only those for the inner planets are given below) rule out chance altogether, and constitute ‘a powerful argument for the harmonic arrangement of the solar system’ (Godwin, 1995, pp. 132-6). Of 74 tones, as many as 58 belong to the major triad CEG.

Harmonies of the planets’ angular velocities, as seen from the sun
Harmonic number
1 9 5 3 25 27 15 2
Mars aphelion (l)
perihelion (m)
l:m = 2:3
l:n = 9:20
l:o = 5:12
m:n = 2:3
m:o = 3:5






Earth aphelion (n)
perihelion (o)
n:o = 15:16
n:p = 3:5
n:q = 3:5
o:p = 5:8
o:q = 5:8
B C’


Venus aphelion (p)
perihelion (q)
p:q = 24:25
p:r = 5:9
p:s = 1:4


D E G G#


Mercury aphelion (r)
perihelion (s)
q:r = 16:27
q:s = 81:320
r:s = 9:20



The time taken by Venus to seemingly orbit the Earth (i.e. a Venus synod) is currently 584 days, so that 5 Venus synods are equivalent to 8 ‘practical’ earth-years (of 365 days). Venus has a sidereal orbital period of 225 days, and 13 of these periods equal 8 practical earth-years. In both cases, the numbers composing these ratios are consecutive Fibonacci numbers, and therefore give approximations to the golden section: 8/5 = 1.6, and 13/8 = 1.625. Venus rotates extremely slowly on its axis: its day lasts 243 earth-days, or 2/3 of an earth-year (the same ratio as a musical fifth). Every time Venus and earth ‘kiss’, Venus does so with the same face looking at earth. Over the 8 years of the 5 kisses, Venus will have spun on its own axis 12 times in 13 of its years.

Thus, in 8 years Venus has 5 inferior conjunctions (when it lies between earth and sun) and 5 superior conjunctions (when it lies on the opposite side of the sun). Plotting either of these sets of 5 conjunctions in relation to the zodiac produces a five-pointed star or pentagram, the segments of the constituent lines being related according to the golden section. There is a slight irregularity, for the pentagram is not completely closed, there being a difference of two days at the top. This irregularity generates a further cycle, as it means that the pentagram will rotate through the whole zodiac in a period of about 1200 years. It is interesting to note that the pentagram was associated with the Babylonian goddess Ishtar-Venus, and that depictions of Venus as a five-pointed star have also been found at Teotihuacan in Mexico. In theosophy, Venus is said to be closely connected with our higher mind (manas), the fifth principle of the septenary human constitution.

Fig. 9.2 Teotihuacan: stellar symbol of Venus dispensing its influence
downwards towards the earth.

Fig. 9.3 The Venus pentagram.

    According to theosophy, the key numbers to the solar system lie in a combination of the year of Saturn and the year of Jupiter, expressed in earth-years (Purucker, 1973, pp. 3-15). About 12 earth-years (11.86) make 1 year of Jupiter, and about 30 earth-years (29.46) make 1 year of Saturn: 12 x 30 = 360, the number of degrees in a circle and the number of days in an ideal earth-year. (Theosophy says that an earth-year oscillates above and below 360 days over very long periods of time.)

The whole process of evolution can be summed up as a descent of divine consciousness-centres or monads into matter, and their subsequent re-ascent to spirit, enriched by the experience gained on their aeons-long evolutionary journey. This process can be symbolized by two interlaced triangles, known as Solomon’s seal or the sign of Vishnu, the upward-pointing triangle representing spirit, and the downward-pointing triangle representing matter. Significantly, as Saturn and Jupiter revolve around the sun, they mark out two interlaced triangles around us every 60 years! The upward triangle is formed by their conjunctions and the downward triangle by their oppositions. Once again, there is a slight irregularity: after 60 years the conjunction does not take place at exactly the same point; there is a gap of 8 degrees, so that the interlaced triangles slowly rotate through the entire zodiac in a period of 2640 years. There are 432 of these 60-year Jupiter/Saturn cycles in a precessional cycle of 25,920 years.

Fig. 9.4 Conjunctions and oppositions of Jupiter and Saturn.

    The sun is the heart and brain of the solar kingdom and the regular sunspot cycle is akin to a solar heartbeat. The sunspot cycle has a major impact on earth, especially terrestrial magnetism and the climate. Over the past 250 years its length has varied irregularly between 9 and 14 years, averaging 11.05 years. Sunspots peak shortly after Jupiter passes the point in its orbit closest to the sun. (The ‘ideal’ sunspot cycle is said in theosophy to be 12 years, so there would be one such cycle for each year of Jupiter.) The sunspot maximum does not occur exactly in the middle of the sunspot cycle. The ascending part of the cycle has a mean length of 4.3 years – very close to the figure of 4.22 years that would divide the 11.05-year cycle exactly according to the golden section.*

*Theodor Landscheidt, ‘Solar activity: a dominant factor in climate dynamics’,

10. Intelligent habits

To attribute the order, harmonious proportions, and marvellous recurring patterns in nature to pure chance is absurd. The pagan philosopher Cicero wrote:

If anyone cannot feel the power of God when he looks upon the stars, then I doubt whether he is capable of feeling at all. From the enduring wonder of the heavens flows all grace and power. If anyone thinks it is mindless then he himself must be out of his mind. (On the Nature of the Gods, Penguin Classics, 1972, 2.55)

However, the traditional theological picture of ‘God’ as a supreme selfconscious being who thinks, plans, and creates – even managing to make the entire universe out of nothing – is untenable. If ‘he’ is a being, he must be finite and limited, and have a relative beginning and end. Whereas if the divine is infinite, it cannot be a thinking being, separate from the universe, but must be one with it, as taught by pantheism. The divine essence would then be synonymous with boundless space, or infinite consciousness-life-substance. And since nothing can come from nothing, it must always have existed.

Materialistic scientists prefer to attribute the patterned order of the cosmos to ‘laws of nature’, with new ones emerging ‘spontaneously’ as evolution proceeds. But this explains nothing, for the word ‘law’ simply denotes the regular operations of nature – the very regularities that the term is supposed to explain! Patterns in the living world are sometimes attributed to genetic programmes, but this is merely a declaration of faith, since all that genes are known to do is provide the code for making proteins – not for arranging them into complex structures. Moreover, it is hard to swallow the conventional claim that genetic programmes themselves originated by chance.

If some patterns arose through random genetic mutations and natural selection, it would mean, for example, that the reason the golden angle is widely found in leaf arrangements throughout the plant kingdom is because it contributed to their survival. This implies that at one time most plant species did not embody the golden angle – but such a claim can never be tested. What we do know is that life emerged on earth incredibly quickly, that new and fully functional types of organisms have tended to appear on earth incredibly quickly, and that there is no evidence whatsoever for vast periods of trial-and-error experimentation along darwinian lines.

The theosophic tradition, or ancient wisdom, teaches that nature’s patterns and regularities are better seen as habits, an expression of its ingrained instinctual behaviour, of the tendency for natural processes to follow grooves of action carved in countless past cycles of evolution. For it teaches that all worlds, on every conceivable scale, reembody again and again. And behind these habits lies an all-pervading consciousness, the universe being composed of interworking hierarchies of intelligent and semi-intelligent ‘beings’ or energy-forms, from elemental to relatively divine. The order of nature also reflects the essential interconnectedness of all things, and the fact that the same basic patterns and processes recur on widely different scales.

All monads, or units of consciousness, are said to progress through a series of kingdoms towards a state of relative perfection in the system of worlds in which they are then evolving, before passing, after a long rest, into other world systems, on other planes. Humans, in their present stage of rebellious selfconsciousness, often succumb to the temptation to misuse their free will for selfish and shortsighted ends, creating discord and suffering. But it lies within our power to attune ourselves to the fundamental harmony of our inner, spiritual selves – sparks of the universal ‘Self’ – and to become voluntary coworkers with nature in the great cosmic adventure of evolution.

3, 6, 9. – Tesla & Divine Numerology

Why did Tesla say that 3,6,9 was the key to the universe?

If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe.

– Nikola Tesla


Excerpt from the New York World

Telegram, July 11, 1935

Nikola Tesla revealed that an earthquake which drew police and ambulances to the region of his laboratory at 48 E. Houston St., New York, in 1898, was the result of a little machine he was experimenting with at the time which”you could put in your overcoat pocket.” The bewildered newspapermen pounced upon this as at least one thing they could understand and Nikola Tesla, “the father of modern electricity” told what had happened as follows:
Tesla stated, “I was experimenting with vibrations. I had one of my machines going and I wanted to see if I could get it in tune with the vibration of the building. I put it up notch after notch. There was a peculiar cracking sound. I asked my assistants where did the sound come from. They did not know. I put the machine up a few more notches. There was a louder cracking sound. I knew I was approaching the vibration of the steel building. I pushed the machine a little higher. “Suddenly all the heavy machinery in the place was flying around. I grabbed a hammer and broke the machine. The building would have been about our ears in another few minutes. Outside in the street there was pandemonium. The police and ambulances arrived. I told my assistants to say nothing. We told the police it must have been an earthquake. That’s all they ever knew about it.”

Some shrewd reporter asked Dr. Tesla at this point what he would need to destroy the Empire State Building and the doctor replied: “Vibration will do anything. It would only be necessary to step up the vibrations of the machine to fit the natural vibration of the building and the building would come crashing down. That’s why soldiers break step crossing a bridge.”

“On the occasion of his annual birthday celebration interview by the press on July 10, 1935 in his suite at the Hotel New Yorker, Tesla announced a method of transmitting mechanical energy accurately with minimal loss over any terrestrial distance, including a related new means of communication and a method, he claimed, which would facilitate the unerring location of underground mineral deposits. At that time he recalled the earth-trembling “quake” that brought police and ambulances rushing to the scene of his Houston Street laboratory while an experiment was in progress with one of his mechanical oscillators…”


From My Inventions: The Autobiography of Nikola Tesla

Chapter 5—The Influences That Shape Our Destiny

As I review the events of my past life I realize how subtle are the influences that shape our destinies. An incident of my youth may serve to illustrate. One winter’s day I managed to climb a steep mountain, in company with other boys. The snow was quite deep and a warm southerly wind made it just suitable for our purpose. We amused ourselves by throwing balls which would roll down a certain distance, gathering more or less snow, and we tried to outdo one another in this sport. Suddenly a ball was seen to go beyond the limit, swelling to enormous proportions until it became as big as a house and plunged thundering into the valley below with a force that made the ground tremble. I looked on spellbound incapable of understanding what had happened. For weeks afterward the picture of the avalanche was before my eyes and I wondered how anything so small could grow to such an immense size.

Ever since that time the magnification of feeble actions fascinated me, and when, years later, I took up the experimental study of mechanical and electrical resonance, I was keenly interested from the very start.

Nikola Tesla WAITED 37 YEARS to brag of the earthquake incident in 1898, but THE VERY NEXT YEAR in 1899 he dropped everything an went out west to Colorado Springs. IN A TRANSATLANTIC RACE TO BROADCAST AND RECEIVE RADIO SIGNAL, ON THE WORLD STAGE, HE DROPPED EVERYTHING THE NEXT YEAR…AFTER MAKING EARTHQUAKES AND WENT WEST?
What are the chances it would be decision # 3 – 6 – 9 ?
At least one in three hundred an sixty nine. RIGHT?
Nikola Tesla caused the September 1899 Cape Yakataga and Yakutat Bay earthquakes in Alaska from Colorado Springs.
September 3, 1899 [ 9, 3,   9]
September 6, 1899 [ 9, 6,   9]
September 9, 1899 [ 9, 9,   9]
“If you only knew the magnificence of the three, the six and the nine… then you would have a key to the universe.”  -Nikola Tesla


Perhaps selecting 3, 6, 9 for the dates was just to pay respect to the 3, 6, 9 Rule…
Please Read below


A recently discovered set of original Nikola Tesla drawings reveal a map to multiplication that contains all numbers in a simple to use system. The drawings were discovered at an antique shop in central Phoenix Arizona by local artist, Abe Zucca. They are believed to have been created during the last years of Tesla’s Free Energy lab, Wardenclyffe. The manuscript is thought to contain many solutions to unanswered questions about mathematics.

The Sketches were hidden in a small trunk with numerous other drawings and manuscripts ranging from hand-held technological devices to free-energy systems, many with notes scrawled all over them. Some of the pieces are already familiar to the public, but a few others are not. Most notably is the Map to Multiplication or the Math Spiral. Zucca made a few copies and showed the drawings around to different thinkers, dreamers, and mathematicians.

A few days later a Local High School Mathematics Instructor, Joey Grether, had been working on deciphering the system and had a few breakthroughs. Grether suggests that the Spiral not only explores Multiplication as an interwoven web, but that it, “offers a comprehensive visual understanding of how all numbers are self-organized into 12 positions of composability.”

“This device allows us to see numbers as patterns, the formation of prime numbers, twin primes, Highly composite numbers, multiplication and division, as well as few other systems, I imagine, that are yet to be discovered.”

The diagram itself is very intuitive, allowing students to see how numbers all work together based on a spiral with 12 positions. 12, or 12x (multiples of 12) is the most highly composite system, which is why we have 12 months in a year, 12 inches in a foot, 24 hours in a day, etc. 12 can be divided by 2, 3, 4, and 6. So can all multiples of 12. For every 12 numbers there is a chance of 4 numbers being prime. They happen to fall in positions (think clock positions) 5, 7, 11, and 1.

Tesla is known for the quote “If you only knew the magnificence of the 3, 6 and 9, then you would have the key to the universe.” It turns out that when the device is examined, the digital roots of the numbers in positions 3, 6, 9, and 12 constantly repeat the same sequence 3, 6, 9! Is this what Tesla was referring too? The self-organization of numbers and their digital roots?

Its hard to say, but Grether seems to think so. “This breakthrough is phenomenal. If we could get students all over the globe to use this technique, to play with it, and help figure out how to use it, we could overcome our cultural aversion to Mathematics. Instead of memorizing the multiplication table, we could learn the positions of numbers and have a better understanding of how they work.”

Juan Zapata, One of Mr. G’s students believes so as well… “I used to say I’m bad at Math… because that’s what everyone says, but now, I’m like, dude, this is too easy.”

There’s one other fact about the Tesla Spiral that make it interesting. The diagram is dated 12/12/12! 1912. Grether and his students want to turn December 12 into a national holiday. So grab a 12 pack, get a dozen donuts, and celebrate the power of 12x ( via ).

Thanks to Disclose for this article

PS2 The Ten Emanations of God

With the zero being regarded as Heaven and the all or nothing this now leaves us 9 numbers within our base-ten system. 1, 2, 3, 4, 5, 6, 7, 8 and 9. These nine gods were celebrated by the Greeks and Egyptians in the Ennead. The Ennead was nine gods that represented the archetypal principles that regulated and ruled the cosmos through the laws of number. This company of nine has shown its face many times throughout the world. In Norse mythology, the god Odin hung on the Yggradsil tree for nine days. Benjamin Franklin was Grand Master of the charitable Nine Sisters Lodge. In the European Middle ages we see the Nine-Worthies, semi-legendary figures who personified the ideas of chivalry. We have all heard of Cloud Nine, being dressed to the nines, the nine lives of a feline and a stitch in time saves nine. The Christian’s mythologized the power of these nine numbers in the Christian Angelic hierarchy with those angels being the (9) Seraphim, (8) Cherubim, (7) Thrones, (6) Dominions, (5) Virtues, (4) Powers, (3) Principalities, (2) Archangels and (1) Angels. Even the ancient Mayan venerated the principles of nine. One of the most well-known Mayan pyramids is the pyramid at Chichen Itza. Chichen Itza is nine-level pyramid with a celestial observatory at the top. For a few moments on the solstices and equinoxes, the light and shadows on this pyramid forms a snake that travels down the side of the pyramid to the base, where the head of this great snake, called Quetzacoatal or Kukulcan is carved into stone. The Hebrew letter “Teth”, transcribed as a “T”, meant serpent, or the secret intelligence of all spiritual activities, and was designated by the number nine. The number 9 shows up quite often in the metrology of our universal architecture as well. The diameters of the Moon, the Sun and the Earth using decimal parity all reduce down to this number of spirit.


ZERO, ONE, TWO, THREE, FOUR, FIVE, SIX, SEVEN, EIGHT and NINE: These ten principles united represent completion, the perfection of all being and the harmony that exists within the demiurgic word of the creator, once again, apparent on the two hands that lay right before you. These ten principles are the living thoughts of a great creator being, a great mystery or grand architect who is within all things and without which, all things would cease to exist.

The ancient Vedic peoples, responsible for the oldest of Hindu scriptures, reiterated the supremacy of this base-ten system by placing nine numbers around a circle/zero and performing their math in this way. By placing 9 at the top and moving clockwise around the circle, these 9 digits encased the wholly / holy zero with the zero performing its magic as the placeholder for the rest of the digits (We will see the use of this mathematical template again later on in the text).


Read the Source Article >>

PS 3 Vortex Based Mathematics: Numerically Conceptualizing Reality


There is more to numbers than the mere quantities we assign them.  Numbers are alive.  They structure our waking reality.  All the great mystics and philosophers throughout the ages understood this numeric universe.  It won’t be long until we are able to manufacture energy and reshape our world the way nature intended, through implosion rather than explosion.

The principles of Vortex Math and the underlying ideologies of this forgotten science are resurfacing.   This lost numerical art is a portal to understanding the nature of reality, and the psychological implications gained from such introspection are paramount to the evolution of the world soul.



– – –

Dark Matter, the vibratory essence of all that exists, is no longer on its elusive hide and seek trip — it has been found! With the introduction of Vortex-Based Mathematics you will be able to see how energy is expressing itself mathematically. This math has no anomalies and shows the dimensional shape and function of the universe as being a toroid or donut-shaped black hole. This is the template for the universe and it is all within our base ten decimal system!

You have entered a place where Numbers are Real and Alive not merely symbols for other things. You will discover that the relationships between numbers are not random or man-made but that numbers are actually elementary particles of which everything is composed. This lost knowledge was well known to our ancients and is now being uncovered for us today. Gradually you will come to see numbers in a simple yet profoundly perfect three-dimensional matrix grid pattern that forms the shape of a torus. The number grid reveals the calibration and timing for an engine that can take us throughout the universe and solve mankind’s energy needs. Interested? Delve in…


Want to find the answers to the unknown?
Want to see a man-made black hole?

Using a new math that shows that numbers are not man-made symbols, but are actually real, you will see and understand the answers to these questions.

Learn about:

  • A particle that does not bend, but causes everything in the universe to curve around it.
  • The three toroidal number patterns that are the basis to all mathematics (the pattern of numbers traversing the toroidal surface in, out, and around).
  • The universe as an ecological system of renewal.
  • Your body being made out of countless stars of the past.
  • Proof of an omniscient supreme being.
  • Making a coil that produces unlimited free energy.
  • A number grid that shows the underpinning geometry of the universe.
  • How everything is a torus.
  • Making a propulsion source that can take you anywhere in the universe.
  • Artificial Intelligence based on a binary triplet.
  • The Aetheric Template in DNA that guides evolution.
  • The repeating number pattern that solves pi and demonstrates it to be a whole number.
  • A mathematics in which numbers do not move, but the functions move instead.
  • How numbers form a 3D solid geometric object.
  • The secret of a gyroscope — why it vertically lifts itself upright.
  • Wormholes, nested vertices, portals, and doorways.
  • Why Dimensions are a result of how things move through space.
  • The preferred frame of reference to the universe is based upon the fixed constant number 9.
  • Number crunching and encription compression done through cross addition.
  • The labrynth maze of the Doubling Circuits where they invert in the center.
  • World boundary conditions and inversion seams of nested vortices.
  • The bilateral symmetry of the decimal system resulting in polar number pairs having parity by being perfect mirrors of one another.
  • The zero is always in the center in the form of the vortex hole.
  • Multiplication series are unbroken rings from cross sections of the torus.
  • A number cannot be created or destroyed and zero does not exist on a number line or in any multiplication series.
  • The number 9 is the node and represents Spirit.
  • The numbers 3 and 6 represent the Yin and Yang in the form of magnetism and the number 9 is the S curve.
  • The base ten numerical counting system is triangulated.
  • Infinity has an epicenter.
  • The powers of ten occur by halfing.
  • The torus skin models harmonic cascadence.

Our base-ten decimal system is not man made, rather it is created by this flow of energy. Amazingly, after twenty years of working with this symbol and collaborating with engineers and scientists, Marko discovered that the 1,2,4,8,7,5 was a doubling circuit for a very efficient electrical coil.


There was still one more very important number pattern to be realized. On the MATHEMATICAL FINGER PRINT OF GODnotice how the 3, 9, and 6 is in red and does not connect at the base. That is because it is a vector. The 1,2,4,8,7,5 is the third dimension while the oscillation between the 3 and 6 demonstrates the fourth dimension, which is the higher dimensional magnetic field of an electrical coil. The 3, 9, and 6 always occur together with the 9 as the control. In fact, the Yin/Yang is not a duality but rather a trinary. This is because the 3 and 6 represent each side of the Yin/Yang and the 9 is the “S” curve between them. Everything is based on thirds. We think that the universe is based on dualities because we see the effects not the cause.





PS 4 Physicists Prove Surprising Rule of Threes

In 1970, Vitaly Efimov was manipulating the equations of quantum mechanics in an attempt to calculate the behavior of sets of three particles, such as the protons and neutrons that populate atomic nuclei, when he discovered a law that pertained not only to nuclear ingredients but also, under the right conditions, to any trio of particles in nature.

While most forces act between pairs, such as the north and south poles of a magnet or a planet and its sun, Efimov identified an effect that requires three components to spring into action. Together, the components form a state of matter similar to Borromean rings, an ancient symbol of three interconnected circles in which no two are directly linked. The so-called Efimov “trimer” could consist of a trio of protons, a triatomic molecule or any other set of three particles, as long as their properties were tuned to the right values. And in a surprising flourish, this hypothetical state of matter exhibited an unheard-of feature: the ability to range in size from practically infinitesimal to infinite.

Efimov had shown that when three particles come together, a special confluence of their forces creates the Borromean rings effect: Though one is not enough, the effects of two particles can conspire to bind a third. The nesting-doll feature — called discrete scale invariance — arose from a symmetry in the equation describing the forces between three particles. If the particles satisfied the equation when spaced a certain distance apart, then the same particles spaced 22.7 times farther apart were also a solution. This number, called a “scaling factor,” emerged from the mathematics as inexplicably as pi, the ratio between a circle’s circumference and diameter.

“It’s like layers of an onion,” Hulet said. “You see molecules at one layer. Peel the layer away, and you see that there’s a molecule there 22.7 times smaller. Every time you peel away a layer, you find another molecule.”

Efimov trimers are states of matter that theoretically come in an infinite range of sizes. Experimentalists recently observed consecutive trimers, verifying the strange theory.

Read the entire article at the source:

PS5  The Borromean Rings

In mathematics, the Borromean rings consist of three topological circles which are linked and form a Brunnian link (i.e., removing any ring results in two unlinked rings). In other words, no two of the three rings are linked with each other as a Hopf link, but nonetheless all three are linked.


The mystery of the Christian Trinity is expressed in the Athanasian Creed: we worship one God in Trinity, and Trinity in unity; neither confounding the Persons, nor dividing the substance. Trying to depict this triune nature without leaving oneself open to attacks of polytheism was problematic, and geometrical symbols became popular. The equilateral triangle, consisting of three equal parts, equally joined, was used as an early symbol of the Trinity. It was often inscribed in a circle, a symbol used to stand for God for many centuries. For the Greeks, the circle symbolised perfection; its never-ending form also encapsulates the idea of eternity.


Today, the Borromean rings are commonly used as a symbol of the Trinity. The earliest source for this that we are aware of was a thirteenth-century manuscript in the Municipal Library at Chartres. It contained four diagrams, one of which is shown above. In the centre, inside all the circles, is the word `unitas’; the three syllables of `tri-ni-tas’ are distributed in the outer sectors. Unfortunately, the manuscript was destroyed in a fire in 1944. The copy shown here was reproduced in a manual of Christian iconography [Didron-Didron], along with descriptions of the other three. The labels on these other figures are shown below. They are:



  • “God is Life” surrounded by “Father”, “Son” and “Holy Spirit”;
  • “God is” surrounded by “Word”, “Light” and “Life”;
  • the phrases “Trinitas Unitate” (three in one) and “Unitas Trinitate” (one in three) distributed over the diagram.

Gematria & Numerology Insights Part 2


If you take the square root of the fist 7 prime numbers :

2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 + 17^2 = 666

Take the 6th power of the first 3 digits, and subtract the first from the second, and add that to the 3rd :

1^6 – 2^6 + 3^6 = 666

1+2+3+4+567+89 = 666
123+456+78+9 = 666

loose the + sign, and notice the sequence : 123456789

reversed :

9+87+6+543+21 = 666

sequence= 987654321

There are many other connections with 666, like for instance by calculating them as ‘degrees’ with sin and cos functions, but for the sake of simplicity, we will only mention this fact. Take a calculator and play with those functions, Mr. Anderson, to find them for yourself.

666^6 = 872 660 613 456 236 16

There are 6 6’s in the result. No 9 in the result.

6×6=36=9 -> the 3, the 6 and the 9

If you then take the other digits from the result, and reduce them, the result is 36, or 9.

-> the 3, the 6 and the 9.

123+876= 999
123+543= 666
123+210= 333

Notice the middle sequence is 876 543 210.
Vertically you also see the sequence 147258 once more. The sequence of life within the Matrix.
(see our previous post about parity where we explain this sequence in more depth)

The result is 999 666 333, and vertically it reads 369 throughout…

999-876= 123
876-333= 456
543-456= 78
210-111= 99

Again we see the sequence 147258 progressing within, with 369 RIGHT NEXT TO IT, but hidden from view because it is 1 level off the axis of sequence 147258. Here you see that with the 0, knocking the 369 sequence 1 level up.
The entire sequence occurs within the start and end of 9, and the result reads 123 456 789. Vertically in the result you see again 147258 369

Taking the last result of the previous sequence, 78 :

78 + 9 = 87

87 + 123 = 210
87 + 234 = 321
87 + 345 = 432
87 + 456 = 543
87 + 567 = 654
87 + 678 = 765
87 + 789 = 876
87 + 890 +10 = 987 -10

Again, perfect symmetry.

Middle sequence:
horizontal -> 123 234 345 456 567 789 890
vertical -> 12345678 23456789 34567890

horizontal -> reversed it is 987 876 765 654 543 432 321 210
vertical -> column 1 : 23456789 column 2: 12345678 column 3 : 01234567

Notice there are only 8 steps within the sequence. The same symmetry within a sequence only reaches up to 8 steps. Beyond it, other symmetries are formed, still containing the original symmetry, but additional symmetries are added to form a higher complexity.
8×8=64, is one unit of symmetry. In other words 7×9 digits is 63, and upon 64 additional complexity is added to the original symmetry by normalisation (the higher you go, the more difficult it gets to ‘see’ the symmetry.
(notice the +10 -10 in the last step of the sequence. That is the normalisation we talked about in earlier posts).

Another sequence reveals fibonacci numbers. We will not be showing the + and – normalisation happening because it would look to complicated to understand. Our goal here is only to reveal the numbers within :

[Image: iq2uHv5.png]

Do you see the fibonacci numbers, Mr. Anderson ?

There are many steps in between, repeating each number several times, and more times as you go up. We are showing only some, all having fibonacci numbers as the building block for the result.

The finonacci sequence is in the middle vertical column of the results.
Beyond 999 we go to 1332 (the next unit), which is 1 level up from 333 (1+332 -> 1332)

1875 is 1 level up from 876 (1+875 -> 1875)

2196 is 2 levels from 999 (1+998, 2+996 -> 2+1+96 -> 2196)

etc…you see Mr. Anderson, no matter how complicated it seems at first, when looking underneath, we ALWAYS find the same simplicity, AND the same symmetry.

Another nice one for the Neo that calls himself ‘BackFromTheFuture’ :

3.33×6.66×7.77×11.11×14.44 = 27645.263

Distance to the centre of the galaxy is roughly 27000 light years.
The exact distance is notoriously unknown to science, and they estimate it at 27-28000ly. It’s exact centre, the big loophole, should be very close to 27645.

Star system Sirius is estimated little over 27000 AU from the Sun.
The average temperature on Sirius B is about 27000K.
We would bet they are very close to 27645.

The problem with science is that it doesn’t accept such non-traditional methods for calculations…allthough they always work when used correctly.

Tonight we will reveal lots of hidden code within the number PI, the number of the ONE. More specifically translated into BASE-26, revealing the letters asigned to the numbers.
We will be looking more at the SCRAMBLED words deep within this undefinable matrix within the Matrix, and showing many connections in the between the words that go far beyond coincidence, as we will be showing it all from within a few thousand letters, so only a little snapshot…

CyberCyrus  Wrote: (02-28-2013 02:03 AM)

Considering the 147258 circuit, it is every digit except 3, 6 and 9.

Incorporating both to comprise the complete system of 9 digits, we find more clues to the symmetry portrayed within The Matrix :

So we have 3 pairs of 3, forming a 3×3 matrix :


Allready we are seeing something :
Notice the vertical symmetry (123 456 789)…

We can verify the symmetry over and over, in all directions :


[Image: UnEGpvq.png]

147+258 = 405
369-147 = 222

369+36 = 405
258-36 = 222

258-147 = 111
369-111 = 258

147-36 = 111
222+36 = 258

258+111 = 369
111+36 = 147

147+222 = 369
369-222 = 147

Vertically :

[Image: jU1ZwEX.png]

789-456 = 333
456-123 = 333
654-321 = 333
987-654 = 333

789-123 = 666
987-321 = 666

Also diagonally, the symmetry is still retained :

[Image: UOUU0Hr.png][Image: XCM4BX2.png]

357-159 = 198
456-258 = 198

951-753 = 198
852-654 = 198

357+159 = (0)516
456+258 = (0)714

(notice vertically in the result: leftside is 5+2->7; rightside is 6-2=4)

654+852 = 1506
753+951 = 1704

(notice vertically in the result: same symmetry, only 1 and 0 have switched places)

456×258 = 117648
357×159 = 56763 = 11 76 48 (56=11; 3=48)

Going even further, we verify the symmetry in other ways :

[Image: jF43Yxr.png][Image: SNem9BR.png]

248+268 = 516
359+157 = 516

248-157 = 91
359-268 = 91

[Image: AREv8WM.png]

987-963 = 24

[Image: PS6QHFe.png]

369-321 = 48

[Image: WXWAKre.png]

684+624 = 1308
957+351 = 1308

684-351 = 333
957-684 = 333

We are showing here how 1308 and 333 are connected. Remember the movie 1308, Mr. Anderson ? How they showed reality shifting upon that number ?

It is the 333 guardians working together with 666…

642×2 = 1284

1284 + 24 = 1308

If you split 1308 into 13 and 08, subtract, and we have 5.

5 is at the centre of our matrix :


13-8 = 5
13×8 = 104 = 5

104-5 = 99

13+8 = 21
13×99 = 1287

1287+21 = 1308

1308 / 666 = 1.963 963 963 963 963…

1308-963 = 345
1308-639 = 669
1308-396 = 939

1308+333 = 1641
1308-333 = 975

1308+666 = 1974
1308-666 = 642

1308-975 = 333
1641-975 = 666
1974-975 = 999

975-642 = 333

1308 is an interlock within the Matrix, defined by 3’s and 6’s working around a centre-point. Together they form other patterns in between a FIXED pattern of 369…


Quote:0 is the overlap. That happens twice per cycle.
The overlap of maximum volume (5.26) was reached on 12-21-12.

We will show you how it is connected.
And thanks to your 333 / 11.11 thread, Neo, we spotted something else :

Regarding 1776.
Not gonna spoil with too much words this time, Neo.

Very interesting correlations though. The year 2057 popped up, and we will briefly explain why…

111 +333 =
444 +333 =
777 + 333 =
1110 + 333 =
1443 + 333 =
(Vertically, 147 is repeated…)

5 x 333 = 1665

[Image: EVNZS6Y.png]

[Image: TuDtufj.png]

[Image: VrrSUs7.png]
(Vertically : doubling and halving…)

[Image: lJJeDfC.png]

(After the 8th step, the level always increases by 1 level: to the left, 0 becomes 1, then 1 becomes 2,etc… )

[Image: VQPwfCi.png]

[Image: MQhCu72.png]

(Vertical: Fibonacci…Only divison of 444 and 111 do not result in a Fibonacci number…)

[Image: I6j67pt.png]

Notice the symmetry in the divisions…
Again, after every 8th step, upon the 9th, complexity increases with 1 digit to the left.
4.111…, 41, and 444 are the only results that are not a Fibonacci integer.

Between 4.111… and 32.888… are also 8 steps.
Between first and second recurring 142857 are also 8 steps.

142857 occurs every last step before the level increases.
142857 occurs exactly 2 steps before and after 197.333…

1776 / 14400 = 1233.333…

About 1233, 12.21.12 and 11.11.11 :


[Image: N8rvHvW.png]

We can tell you for certain that 2057 will be an important date, Neo…

After a google search :

[Image: yesKJ1v.png]

The next double solar eclipse in the same year will be 01/12/2252 and 12/31/2252…rd_century

We will now show you that those dates are correct…

First thing to notice : 2252 = 11

01.12 an 12/31

14400 / 112 = 128.57142857142857… = 20.57 142857 142857 (12+8=20)

20 / 57 = 0.3508 77 19298 245 614 = 0.7 77 11 11 11 (3+5+0+8=7; 1+9+2+9+8=11; 2+4+5=11: 6+1+4=11)

11.11.11 represents the point of overlap. We are on the right track…

Now that we have determined the right sequence, we incorporate the correct year :

2252.7 77 111111 x 7 = 15769.439 777777 = 15769.7 777777 (4+3+9=16=7)

15769.439 777777 – 0.432 = 15769.00 7777777

15769.7 777777 / 112 = 140.801587 3008 92 857142 = 140.11 11 11 857142 = 140.12 (0)1 11 857142 (0=neutral)
15769.439 777777 / 112 = 140.798569 444 4375 = 140. 8 12 (0)[b]1[/b] (0=neutral)
15769.00 7777777 / 112 = 140.7947 12301 580357142857… = 140.9 1231 1 142857…

Also notice :
2252 x 7 = 15769
15769 – 14400 = 1369
15769 / 1369 = 11.29 5845272206303 724 92 83 667 621 78 = 11.11 11 4 11 11 7
4+7=11, and 4/7=0.57 142857 142857

CyberCyrus  Wrote: (03-02-2013 05:11 AM)

If we look again at the pattern of the doubling and halving sequence :

[Image: OeN9iZe.png]

We allready mentioned it is the symbol of infinity aswel. But there is much more, Mr. Anderson :

Look at the ancient symbol of the cross

[Image: rYht7V7.png]

If you still think they got this symbol only from the so-called “crucifiction”, then think again :

Follow the path from the “father” to the “son”, to the “holy spirit”, to “amen”, to the “father” again, etc…

[Image: x29bwWO.png]

You have now successfully “recreated” the pattern of the doubling sequence !

[Image: UuokBNQ.png]

But there still is more :

All digits are contained within the cross :

1 and 4 :

[Image: elsNQLG.png][Image: VLHjKPP.png]

3, 6 and 9 :

[Image: jRFyg9p.png][Image: Bvg7fKt.png][Image: w6jKmJ3.png]

2 and 5 :

[Image: Jugyzft.png][Image: xpGQnSg.png]

7 and 8 :

[Image: 6d2jNJU.png][Image: 0Unxap0.png]

[quote=’Back From The Future’ pid=’5165192′ dateline=’1360282149′]

All comes back to 9. Top is always sum of the base.

First let’s look at your drawing from a flat 2D perspective :

The top 9 is split into 5 and 4.
Sum of the base equals the top:

They form the top triangle :

[Image: JWnBqsr.png]

5 is split into 6 and 8.

4 is split into 3 and 1.

They form the two following triangles :

[Image: xBM7DVI.jpg]

Considering this becoming a 3D pyramid, and imagining an x, y and z coordinate, we see that the 8 and 1 actually coexist on the same perpendicular z line (so from this perspective they fall together on the same line).

The bigger triangle formed now still equals 9 :
The base of the bigger triangle is 6 and 3.

[Image: eNaYtjW.jpg]

But even by counting all numbers within it, we still get 9:


The sum of 8+1, still 9, is now also the TOP of the upside down triangle in the middle, with 5+4=9 as the bottom base :

[Image: us2L6dG.jpg]

6 splits further into 7+8=15=6
3 splits into 2+1=3

They form these triangles below :

[Image: nzLroGZ.png]

Now to get it right with all digits included :

[Image: jL3k2PP.png]

If we consider 9 as the projector, then the base of 4 and 5 defines the angle, or width, of projection.
The first triangle thus gets projected through this angle.

Below the first triangle the division complexifies along the sides, but at the same time the FIRST projection of the triangle is created again inside, but upside down and elongated.

Here you have your doplet upside down…I think…

So all triangles match up to 9.
Top triangle :

Base : 5+4=9
Sum : 4+5+9=9

Two triangles
5-> 6 + 8 = 5
3-> 1+2=3

Big triangle : 7+9+2=18=9, 7+6+5=18=9

These are the triangles formed :

[Image: 35bexIX.jpg]

The red small ones, the bigger blue ones, and the big green one.
All sides and bases add up to 9.

But this is a 2D representation of something projected into more then 2 dimensions, so that is why in this picture the bases and tops at the bottom seem to fall together.
There is actually an extra coordinate there, but we cannot distinuish it on this 2D pic.

Because of that, the relationships between the numbers may not be crystal clear in this manner.

So what about this in 3D then ? Well, then, it becomes ‘crystal’ clear !

Let’s try and do this with a 3D view, the only one we can truly understand :

We start with the same thing: a triangle.
But now we will go along a top-down view, so we can see 3 dimensions instead of 2 :

[Image: i4msdk.png]

The 9 is split into 5 and 4. The sum of all sides is 9.

But this is the 2D “side” view of a 3D object. What actually happens when the 9 splits, is it splits into 4 sides instead of 2. Why ? Simple, because otherwise there is no symmetry to hold the object together !

A side of 4 and one of 5 are assymetrical to each other, and without this symmetry, you simply cannot extrapolate one object into extra dimensions.

So nature comes up with this solution to provide symmetry :

[Image: Z1o2jAH.png][Image: lD23bCo.png][Image: DjOV36w.png]

Remember, this is the top view, and we are seeing it from the top. The extrapolation happens simultaneously.
We see a perfectly symmetrical pyramid, with each side symmetrical to it’s opposite. This is the only way to provide a continuus and orderly extrapolation of the same boundary.

ALL sides equal 9. Also the sum of the sides which form the entire base, equals 9. And the sum of both base and top also equal 9.

So the ENTIRE projection from source to here is still exactly the same as the initial source, only bigger and MORE detailed.

You can consider this to be a fractal in every sense or purpose: the pattern of 9 being projected according to a degree of magnification. The sum of the smaller parts is a BIGGER projection of the WHOLE, with more detailed complexity. This is God’s looking glass. It is how the creator looks upon his creation !

Still not convinced this is a fractal ? Still not convinced this is how matter “projects” it’s ‘centre’, it’s ‘source code’, into space ? Look at this animation for a moment :

This is our 9, the source, from which the projection expands outwards.
It is an infinitely small object in space. It is being projected downwards into a “bigger picture” of itself. Both are exactly the same, but only differ in scale, so as the projection grows bigger, more “details” of it’s boundaries become VISIBLE :

(appologies for the crappy animations…)

The pyramid is only a bigger projection of it’s absolute centre.

We extrapolate further :

The 5 splits further into 6 and 8 :

[Image: Catoj33.png]

We connect the sides again, and have now defined 4 more pyramids.
Notice they are ALL at a perfect 90 degree perpendicular angle to the previous pyramid at the centre… :

[Image: ZbZXSNf.png][Image: sA7NUSN.png]

If you look closely, you can see the swastika symbol here. Not referring to you know what, but the ancient meaning of the symbol. This is the true origin of the swastika. The meaning though, has been tainted.

The swastika is an equilateral cross with four arms bent at 90 degrees. The earliest archaeological evidence of swastika-shaped ornaments dates back to Ancient India, 3300 BC.
The word “swastika” comes from the Sanskrit svastika – “su” meaning “good”,” “asti” meaning “to be,” and “ka” as a suffix. The swastika literally means “to be good”, but a more accurate translation when knowing the ‘context’ of the meaning can be made: “swa” is “higher self”, “asti” meaning “being” or “existing”, and “ka” as a suffix, so the translation can be interpreted as “being/existing with higher self”.

So we have here a symbol formed from taking the most basic geometrical shape in existence, and extrapolating it with an added dimension at 90 degrees perpendicular, or in other words, by adding a higher complexity to the original boundary.
And 6000 years ago they knew that, because they knew this symbol AND it’s true meaning of “being/existing with HIGHER self”.

And also the infinity symbol is there, once again (the bow-ty in the middle).
We see this appearing in numerology as one of the basic iterations between digits.

To verify the unity of 9, we can see that the 4 newly formed pyramids are STILL equal to 9 :

[Image: 2sZHw8i.png]

If you add the bases with the tops you see that each one is still equal to the initial source of 9 :


Notice 18 and 27. They are multiples of 9.
They represent the degree of complexity, being 2 and 3 times the complexity of the initial source of 9…

And the entire thing is ALSO still equal to 9 :

[Image: G08WGsN.png]


Notice 63 here. VERY important, because 64 is the MAXIMUM possible iterations for ANY complexity we see in nature. After 64, you end up where you started, back at your initial source. In the next picture you can visualise this :

We still have to add the last two digits of 7 and 2 to complete our conduit.
We add the 7 and 2, again AT 90 DEGREES perpendicular to the previous projections :

[Image: wYni46W.png]

And what do we see ? We have again a bigger pyramid, but this one sits at the exact same angle as the starting point, and encompasses the entire whole this time :

[Image: 1ZrKzFt.png]

Remember the 63 just before…
We have now completed 64 iterations from the 4-5 pyramid to here, and the projection has completed one cycle.

Notice 9×7=63 -> 9 is the top, 7 the outer edge.

All it’s sides still equal 9, so does the sum of the entire thing. It still represents exactly the same as the initial source of 9, BUT much more detailed and magnified.

This bigger pyramid is not only a complete replicated projection of the source, but also sits at the exact same perpendicular angle, which means it sits back in the SAME DIMENSION as where it started ! Coincidentally we have now also completed a cycle of all 9 digits, and we are now back at the starting point regarding the numbers.

We can see in this last pic something else very peculiar when noticed, because it refers back to why we cannot see these other dimensions which we have partially plotted out here : All visible pyramids in our last picture sit noticably at the same perpendicular angle as the big one.

[Image: MTp9tt3.png]

So where are the other ones we plotted out ?? Suddenly they are gone…
No, but they are very obviously hidden from our view !

[Image: OYumh2D.png]

One last strange remark :

If you take the outer pyramid, and multiply the top with one of the base edges, you get exactly the number that is at the base in between :

[Image: l59KkJd.png]


…again referring back to the 64 iterations within ONE unity.

If we take a look at the ‘tree of life’, or what is known as the ‘Kathara grid’, it teaches us that matter is manifested in 4 different layers of existence, or densities (actually 5 if you count the state of the singularity itself), divided over a 15-dimensional time matrix, each density consisting of 3 spacial dimensions and one direction of time, and each density having it’s own amount of space- and time separation.

The lay-out is like this :

[Image: I1u4m8f.png]

If we consider the way matter expands and contracts in space and time, then the structure of this grid should contain the same principle of contraction and expansion into and from it’s source of origin.
This is actually already described as Partiki Phasing in the ancient Keylons. It is a single ‘Partiki Unit’, or unit of consciousness. It is a single unit of electro-tonal pulse emanating from the original source. It gets projected into a 15-dimensional structure, and when intercepted by each dimensional layer, it undergoes a process called fission, and seperates into two separate units, a particle and an anti-particle at the same time. One goes to our universe, and one goes to the parallel universe. Then they go back to the original Partiki unit through a process called fusion (reunion of particle and anti-particle), and create a backflow of energy that return to the original source. This “ON/OFF” process creates a pulsating rhythm that is very very fast. We see this rhythm everywhere in nature, also the stars and planets, but because of the scale we perceive the same thing as very very slow. The reality of the speed is however the same as the spinning atoms and such.

So can we see this “breath” when looking at the grid ?
If we consider the grid being a multi-dimensional pattern of a single unit, then yes indeed, we can conclude this movement from the image itself. It is a harmonica which replicates and fuses each unit upon itself :

[Image: ncB3sZq.png]

A closer look shows us the following process :
(Look at the first pic to compare where the densities separate and see how the units separate into the different densities !)

The 1 is replicated into the 3 and the 4.
3 in density 1 and 4 in density 2.
Both are opposites at a 90 degree angle perpendicular to the 1.
3 and 4 feed back unto each other and merge back into the 1.

[Image: Evt387B.png]

That’s the first replication and feedback of the singularity into density 1 and 2.

Second replication (from density 2 into density 3) :

The 3 and 4 both get replicated into the 2 and 5.
2 for density 1 and 5 for density 2 (see first pic).
They are the opposites of 3 and 4, and again at a 90 degree angular perpendicular to them and the one. All four are replications of the 1, and all feed back unto the 1.

[Image: 22xLI0J.png]

Now the 2, 3, 4 and 5 ALL get replicated again, making each 2 sides split into 4 sides.
For instance, the 5 gets replicated into 3, 4, 6 and 7.
(the three has now replicated into 4, from density 1 to density 2, and the 4 into 7, from density 2 into density 3).

[Image: T6UmqWe.png]

3, 4, 6 and 7 now also feed back unto the 5, and the 5, 2, 3 and 4 go back into the 1.

[Image: 1fsZ7mB.png]

The 3 gets replicated in the same manner, into 3, 4, 5 and 6, but doesn’t yet reach into density 3.

[Image: n2q3Qpy.png]

The 4 on the other side gets replicated into 3, 5, 6 and 7.

[Image: xtPaIOR.png]

(Also the 2 replicates like this on the backside…)

The entire picture, I think, is like this, but extrapolated ANOTHER 16 times, which is a bit too pecky to show in a 2D image. We would need a 3D rendering for this, and even that would be an incomplete view…

[Image: 3cFP7D3.png]

All of the above mentioned, ALL happens in one single breath, with all extrapolations of the one, feeding back unto each other throughout all densities of matter.

From the top down, it would look like this :

One point (black) repeating into 2 with 2 opposties each (blue), so 4 times in ONE density. Each replication then repeats further into the next density (red), and so on… :

[Image: PTrcQfk.png]

Right here and now, where the ONE point splits up into four, is when TIME becomes necessary. Why ? Because for the singularity to split into 4, a DIRECTION is needed, in other words, consiousness NEEDS to KNOW in which direction the one gets split. That direction is TIME.

[Image: jPmUl4y.png]

Envision this like a flat laserscan, one planck length thick, scanning a tetrahedron from the top one point down to the four points below, one planck length at a time, stacking all the layers on top of each other. Remember, ‘planck length’ is just a name for ‘one unit’, or in this case, one slice of the plane. Time is need to determine all the planck lengths at a time. A certain time dilation is needed to go from a to b to c.

Allthough a seems to move to b in four directions, the four arrows may be deceiving. The progression from a to b happens within a 3-dimensional space, but to “see” all 3 spacial directions at the same time (like we see our 3D), a direction of time is needed.

In other words, for matter to be able to replicate, we always need 3 spacial directions, and one of time.

All matter has 5 densities, each within a 3-dimensional space and all matter within that 3D space moving in one direction of time. All creating a 12-dimensional space within a 15-dimensional time matrix.

[Image: tbBcHyz.png]

Now a little bit more on the numbers themselves :

[Image: uCDVlQS.png]

When you compress the numbers like each unit is supposed to compress, we see interesting patterns. Compressing the numbers can be done by using number reduction. It reduces a number into one digit by adding a number’s digits each time untill only one digit remains.

Original layout:

[Image: oXF52n6.png]

When adding 9+6+3 (left), 10+7+4 (right), 2+1 (bottom), and 11+12 (top)…and reducing the numbers to it’s core digit…

Becomes :

[Image: ucJ6xaZ.png]

Further compressing them gives :

[Image: pN6NJGw.png]

The trinity of 3, 6 and 9, with 7 in the centre. Why is this special ?

1. The holy trinity of the Father, the Son and the Spirit

[Image: EIWgRKX.jpg]

It is also known in numerology as the trinity of 3, 6 and 9.
It is the 3 and the 6, the Father and the Son, governed by the 9, the Spirit :

[Image: ZuvwZWH.jpg]

And also as such hidden in the Yin Yang symbol :

[Image: FfSoOaE.png]

The number 7 is in the centre. the number 7 is special, and connected with sacred geometry : The rose pattern in sacred geometry is created by a series of concentric circles. The rose uses a geometry of SEVEN. 7 cannot be divided equally to create a lower number, nore multiplied equally to create a higher number under 10.
It is the Virgin number.

7 is what lies in the womb of the rose, and has always been connected with the womb of Mary Magdalene in Christianity. It’s meaning is fertility, and creation from the womb.

If we compress the numbers further this meaning for the number 7 is undeniably confirmed :

When we compress them further : 3+6+9+7 = 25 = 7 !!!
The virgin number, that what lies in the centre of the womb.

If we take the multiplication and division table of 8, we see the same rhythm, but counter clockwise :

[Image: 2IholTK.jpg]

1×8= 8 (8)
2×8=16 (7)
3×8=24 (6)
4×8=32 (5)
5×8=40 (4)
6×8=48 (3)
7×8=56 (2)
8×8=64 (1)
9×8=72 (9)

1:8=1 (8)
2:8=2 (7)
3:8=3 (6)
4:8=4 (5)
5:8=5 (4)
6:8=6 (3)
7:8=7 (2)
8:8=8 (1)
9:8=9 (9)

We say here that 8 is the receptacle of 8 when multiplying or dividing by it.
And again, this is also the case when adding or subtracting by 8.

So in this first rhythm, 1 and 8 are receptacles of themselves, which create these this pattern in opposite directions.

Another rhythm :

[Image: ob4HQMQ.jpg]

Here there are other receptacles for creating this rhythm in opposite directions.

Here we multiply by 2 and divide by 5 to create the clockwise rhythm.
2 is the receptacle of 5 and vice versa.

Clockwise :

1×2= 2 (2)
2×2= 4 (4)
3×2= 6 (6)
4×2= 8 (8)
5×2=10 (1)
6×2=12 (3)
7×2=14 (5)
8×2=16 (7)
9×2=18 (9)

1:5=0.2 (2)
2:5=0.4 (4)
3:5=0.6 (6)
4:5=0.8 (8)
5:5= 1 (1)
6:5=1.2 (3)
7:5=1.4 (5)
8:5=1.6 (7)
9:5=1.8 (9)

1+2= 3 (3)
2+2= 4 (4)
3+2= 5 (5)
4+2= 6 (6)
5+2= 7 (7)
6+2= 8 (8)
7+2= 9 (9)
8+2= 10 (1)
9+2= 11 (2)

We also multiply by 7 and divide by 4 to create the counter clockwise rhythm.
7 is the receptacle of 4 and vice versa.

Counter clockwise :

1:4=0.25 (7)
2:4=0.5 (5)
3:4=0.75 (3)
4:4=1 (1)
5:4=1.25 (8)
6:4=1.5 (6)
7:4=1.75 (4)
8:4=2 (2)
9:4=1.125 (9)

1×7= 7 (7)
2×7=14 (5)
3×7=21 (3)
4×7=28 (1)
5×7=35 (8)
6×7=42 (6)
7×7=49 (4)
8×7=56 (2)
9×7=63 (9)

We can again follow the pattern by adding or subtracting the receptacles, or 2 or 7 :

[Image: 7RrWe5U.jpg]

Going one further :

[Image: SP14Aow.jpg]

To create the clockwise pattern of this rhythm we multiply by 4 and divide by 7.

4 is the receptacle of 7, and vice versa.

Clockwise :

1×4= 4 (4)
2×4= 8 (8)
3×4=12 (3)
4×4=16 (7)
5×4=20 (2)
6×4=24 (6)
7×4=28 (1)
8×4=32 (5)
9×4=45 (9)

7:7=1 (1)

7 is special as it creates an infinite series in each outcome. The outcome is always 9, and you can add any number to 9, the outcome will always be the number without the 9. Same way in reverse you can multiply any number by 9, and the outcome will always be 9. More about this later one…

To create the counter clockwise rhythm, we now multiply by 5, and divide by 2.

5 is the receptacle of 2, and vice versa.

Counter clockwise :

1×5= 5 (5)
2×5=10 (1)
3×5=15 (6)
4×5=20 (2)
5×5=25 (7)
6×5=30 (3)
7×5=35 (8)
8×5=40 (4)
9×5=45 (9)

1:2=0.5 (5)
2:2=1 (1)
3:2=1.5 (6)
4:2=2 (2)
5:2=2.5 (7)
6:2=3 (3)
7:2=3.5 (8)
8:2=4 (4)
9:2=4.5 (9)

Again by adding or subtracting 4 or 5, we can follow the pattern in the figure above.

[Image: gPhfCQD.jpg]

NOTE: division by 7 is a special rhythm. It’s outcome is always an infinite series :


This division table shows another relationship :

[Image: NtyHEWi.jpg]

1:7 = 0.142857 142857 142857 142857 ….
2:7 = 0.285714 285714 285714 285714 ….

….each reiterating into infinity. Every series is once again defined within the circle. This can be backwards verified by reducing the repeating series (for instance 142857, or 285714). The sum is always the whole of the circle, being 9.

If you notice here, if you take what happens in between the numbers you get the 3,6 and 9.

[Image: SMPankS.jpg]

They form the archetype symbol of a sacred enclosure, the lateral triangle, since space cannot be bounded by fewer than three lines.
The triangle is thus the first closed figure to emerge from creation. In this aspect it is known as the root of all manifested nature, and is also known as the trinity of 3, 6 and 9.

The trinity : 3, 6 and 9

[Image: l37wVcf.jpg]

Something very special happens when applying this rhythm :

To create the clockwise rhythm, we multiply by 3, and divide by 6.
3 is the receptacle of 6.


1×3=3 (3)
2×3=6 (6)
3×3=9 (9)
4×3=12 (3)
5×3=15 (6)
6×3=18 (9)
7×3=21 (3)
8×3=24 (6)
9×3=27 (9)

1:6=0.16.. (3)
2:6=0.33.. (6)
3:6=0.49.. (9)
4:6=0.66.. (3)
5:6=0.83.. (6)
6:6=0.99.. (9)
7:6=1.16.. (3)
8:6=1.13.. (6)
9:6=1.49.. (9)

To create the counter clockwise rhythm, we multiply by 6 and divide by 3.
6 is the receptacle of 3.

Counter clockwise :

1×6= 6 (6)
2×6=12 (3)
3×6=18 (9)
4×6=24 (6)
5×6=30 (3)
6×6=36 (9)
7×6=42 (6)
8×6=48 (3)
9×6=54 (9)


The outcome is only 3,6 and 9. No other numbers appear.
With 9 being most special, because no matter whether you add, substract, divide or multiply by 9, the reduced outcome is always 9 when dividing or multiplying with it, and dissapears when adding or subtracting by it.
This makes 9 not only a receptacle of itself, but also a receptacle for all other digits, which explains the special behaviour of 9 at the top of the triangle (fig below), and as both beginning and end.

It is the divine number, and all subsequental patterns are governed by this number (as you can also see in all the previous mentioned relationships : they always begin and end with 9…and 9 becoming the beginning again).

Here you can see the three pattern groups once more, and the way they are formed :

[Image: DcHJ7Mb.png]

5 and 2 are each other’s receptacles, so are 7 and 4.
8 and 1 are receptacles of themselves, and so is 9, which is also a receptacle for all other digits at the top of all triangles.

The work of Marko Rodin shows something called “Vortex Based Mathematics”.

It is based on this source code alone :

[Image: W2c1mBN.jpg]

What we see here is a doubling sequence (again you can verify the numbers with the pattern created) :

1 (1)
2 (2)
4 (4)
8 (8)
16 (7)
32 (5)
64 (1)

Double 1, we get 2
Double 2, we get 4
Double 4, we get 8
Double 8, we get 16, which is 7
Double 16, we get 32, which is 5
Double 32, we get 64, which is 1 again

Also the other way around, as a halving sequence, we get the same thing in reversed order :

(1) 1
(5) 0.5
(7) 0.25
(8) 0.125
(4) 0.00625
(2) 0.003125
(1) 0.0015625

Both go on to infinity, and we can even ‘see’ the infinity symbol formed inside the circle.

Now a nice comparison to think about :

Computer language uses this exact doubling sequence (1-2-4-8-16-32-64-…). Computers are artificial, they are man made.

Nature uses cel division. It uses the exact OPPOSITE, the halving sequence, to divide cels into more cells. Nature is not artificial, not man made.

Ancient cultures always keep telling us to look inward for the truth, not outward. Inward we find the cell dividing halving sequence. The infinite divisions down towards the singularity. The creation of life.
Outward we find the expansion of space, the doubling sequence. The artificial computer language.
Science still looks outward for all answers, the radiating matter, the very destruction of life, and uses expansion and explosion tech in all of it’s ‘man made’ creations.

All these connections are no coincidence, and they show us a very simple truth which we blatently keep ignoring. Imo this is one of the strongest indications of our current wrong doings in science and technology. Implosion tech is the solution. It exists in forms like the energy from emitted sunlight, and other non poluting non explosive energy. Only reason why we don’t use it is because your govment wants the money and the power instead. By introducing implosive renewable energy they would loose everything they have in their control.

Going back to our picture, the dotted line is an iteration upon doubling from 3 :

[Image: W2c1mBN.jpg]

3 (3)
6 (6)
12 (3)
24 (6)
48 (3)
96 (6)
192 (3)

…and halving from 3 in reverse direction :

(6) 6
(3) 3
(6) 1.5
(3) 0.75
(6) 0.375
(3) 0.1875
(6) 0.09375

Again, both go on untill infinity, but they keep iterating from one to other through the 9.
Again, the 9 is very special, because it governs the iteration and also everything in between.
This iteration creates also an infinite rhythm: 396693

So whe have 3 rhythms here, going on at the same time : the doubling and halving between 1248751 forward and reverse, and the doubling and halving iteration between 396, with 9 governing the movement of all.

This figure shows the same rhythm, but here showing them in relation with their flow. Everything is governed by flow, angular momentum. This flow is a double torus vortex which is, as shown here, also apparent in the number rhythms themselves :

[Image: 6i2GE1Z.png]

These flows then, are actually all thin lines, or ‘threads’. They can be immensly long, and because of this “re-iterating” vortex flow they could go on forever (if necessary). Where do we see such threads which seem to go on forever ?

DNA. We know it forms in a spiral fashion, but the spiral flows according to patterns. These are the exact patterns that DNA builds upon, seemingly endless iterations upon iterations.
It is allmost inconceivable that a pattern this simple can get so complex when iterated again and again, but that is exactly what happens.

An example of a layout pattern for DNA structure :

+4 -2 +1 -5 +7 -8 +4 -2 +1
-3 +9 -6 +6 -9 +3 -3 +9 -6
+8 -7 +5 -1 +2 -4 +8 -7 +5
Halving (-) <——— +4 -2 +1 -5 +7 -8 +4 -2 +1
Special (0) <——— -3 +9 -6 +6 -9 +3 -3 +9 -6
Doubling (+) <———- +8 -7 +5 -1 +2 -4 +8 -7 +5
+4 -2 +1 -5 +7 -8 +4 -2 +1
-3 +9 -6 +6 -9 +3 -3 +9 -6
+8 -7 +5 -1 +2 -4 +8 -7 +5

Always grouped in a certain way. 4 and 7 always connect, so do 5 and 2, and the 1 with the 1, and the 8 with the 8 (remember the receptacles in the above rhythms !). They all have a positive (yin) value, or a negative (yang) value.

What is shown here is part of the actual skin of the apple.

If you look at each square, the cross-section follows another pattern, going on for as long as necessary to complete a full sequence of DNA.

[Image: SpH1tkT.png]

This represents the ‘life’ pulsing through the apple, and goes throughout the entire sequence :

[Image: 59vP42i.png]

This is about roughly the same thing we see when measuring our heart beat.

The middle, special 369 strand is not visible in our universe, it is the creating force in between that governs all yin and yang. Off course, energetically, it is not there (read: it is not being projected through energy in our dimension).

If you look closely, you can actually see where the third strand is supposed to run :

[Image: dneznAI.png]

Now, how much a lot may call BS, look at the way we know DNA is structured :

It has 4 different Basis : Guanine, Cytosine, Adenine or Thymine.

The 2 strands we see however form 3 times 4 combinations, or 4x4x4=64 combinations of those 4 basis between only 2 positions (respectively from position 1, and then two times from position 3 (????) ).
Off course, science has it’s ways of explaining the illogical, but the 4x4x4 coming from actual 3 positions seems (in this logically structured system !), a far more reasonable explanation.

64 is exactly the number we see in the doubling and halving rhythms:

64 upon each unit of 1.

The I-Ching for example, has 64 possible hexagrams:

[Image: AF2pu5Q.jpg]

A chess board is divided into 64 fields:

[Image: do0GfRe.jpg]

There are 64 combinations for DNA, and there are 20 amino acids formed from those 64 combinations :


We see here again the doubling sequence. The 20 amino acids are further doubled into molecules and such, untill 64 is reached again, which is another unity of 1, and doubles again from one untill 64, etc…

Hope this further solidifies the previous interpretations in this thread.

Everything is connected, from the smallest to the biggest, and all are connected through the simplest of numbers in an infinitely complex way…

CyberCyrus  Wrote: (03-04-2013 12:35 AM)

I only recently found out about the connection between 144, 432 and the speed of light.
Me and BFTF have been particularly busy finding what the connection actually is.

Various calculations kept pointing it out :

Speed of light : 299 792 458 m/s

3.33 / 11.11 = 0.2997 2997 2997 2997…


27 x 111 = 2997

9 x 333 = 2997

666 / 0.222… = 2997

9×9 = 81

81 – 14.4 = 66.6

9x9x9 = 729

729 x 4.111… = 2997

6x6x6 = 216

216 x 111 = 23976

This is the framerate standard for video.

216 + 144 = 360
2160 + 1440 = 3600

216 x 6.666… = 1440

81x81x81 = 531441

531441 / 369 = 1440.21951 21951

53144.1 / 123 = 432.065

1440 / 3.33 = 432.432 432 432…

4500 x 666 = 299 700

299.7 x (333)² = 33233433.3 -> 2 and 33+33+33 and 4+3 = 2 99 7

299.7 x (111)² = 3692603.7 -> 2 and 3+6+9 and 6+0+3 and 7 = 2 9 9 7

299.7 x 1.444 = 432.7668

299.7 x 432 = 693.75

299.7 x 33.3666… = 9999.989 999…

299.792458 (true speed of light) x 12 = 3597.509496 (=very close to a full circle and a full hour in seconds)

299.792458 x 12.008307427133473784720761721097 = 3600

We kept seeing 144, 432, 369, 360 and 299.7, but couldn’t understand the connection really…

I think I accidentally stumbled upon the connection :

A guy named Bruce Cathie figured it all out :…athie-grid

Quote:Light travels in a circular, three-dimensional wave, a wave that spirals to a certain height and a certain depth. You could graph this in two dimensions as a regular “sine wave,” with a horizontal line for its midsection.

[Image: xSbQNRc.png]

Quote: The wave spirals out to maximum height and “lowers” to the median again as it reaches the sphere’s equator, forming the first hemisphere. Then, the second hemisphere is formed the same way, as the wave “lowers” to its lowest point and again rises to the median. See the diagram for support in visualizing this.

The numbers at the bottom represent the harmonics that Cathie discovered as being associated with this movement.

-> 4116361
See one of my previous calc’s (729 x 4.111… = 2997 = speed of light)

It explains 411, and my continuus babbling about 3’s and 6’s. Seeing now for the first time this confirmation about the importance of those numbers is refreshing.

Now for the most interesting part of the article :

The HARMONIC speed of light

Quote: We have now determined that Cathie set up a basis for measuring time using a system of “grid seconds,” where the normal 86,400 seconds in a day based on a harmonic of 8 are expanded into 97,200 seconds, based on a harmonic of 9.

In so doing, one day of Earth’s rotation was split up into 27, or 9 x 3 “grid hours.” The number of “grid seconds” per day comes out to be the extremely harmonic number of 97,200. This is how Cathie achieved the first step towards putting the Speed of Light in grid terms; getting a time measurement based on grid seconds.

The Speed of Light as we now express it is measured in miles per second. We have already seen how Cathie converted the value of a second into its harmonic ideal, the Grid Second. We now also need to convert our regular system of miles into a grid-based measuring system.

As we remember from the discussion of the work of Aime Michel and the UFO tracklines that were symmetrically spaced apart from each other, Cathie used the system of “nautical miles” to determine where the “grid lines” were placed.

We also know that one nautical mile is equal to one minute of arc on the Earth’s surface, and that there is a “grid line” every 30 minutes. So, what we need to do is change the miles in the speed of light equation into nautical miles, or minutes of arc, as the two are interchangeable.

Therefore, the “grid speed” of Light would be expressed as (x) minutes of arc per grid second.

The incontrovertible truth of Cathie’s findings is that the “Grid Speed of Light” is EXACTLY 144,000 minutes of arc per grid second in free space.

Quote: As we look into this even further, we can see that the fundamental, harmonic [u]value of 144,000 for the speed of light is precisely the same as the fundamental harmonic values for many different things[/u], including:

– the Mayan Calendar’s baktun, at 144,000 Earth days;

– the Bible number of the 144,000 souls who will Ascend;

– the fundamental “building block” of all sound vibration frequencies, 144;

– the fundamental Gematrian “frequency number” for light, 144;

Meaning of 144 in gematria = LIGHT

144 really is light. I’ve babbled about 144 being ONE conciousness a lot. This is the connection: one conciousness, which is 144, is light.

Quote:There are 86,400 seconds in the Sun’s 360-degree arc, representing one day of time. So, to get the amount of relative movement between one second in the 360-degree clock face and one second in the Sun’s apparent 360-degree movement, we divide 86,400 by the number of seconds in one 360-degree circle, or one minute, which is 60 seconds.

The ratio that we are left with is 1440, which represents our current perception of time:

in other words, one second of our time is 1440 times faster in its movement through its arc than the movement of the Sun through the arc it traces in our sky.

This is the first time I truly understand WHY 144, 432 and the 360 cycle are connected…
369 pops up everywhere, and in numeric reduction, or paritising of numbers, the 9 is ALWAYS dicardable, or equal to 0. So 369 really is 360.

Quote:One of Cathie’s most impressive “harmonic” renderings of the Earth as a CU is the distance from the center of the earth to the average height of the atmosphere. This value is given as 4320 arc-minutes, which reduces down to 432, the number of “Consecration” and the fundamental vibration for the sixth node in the octave.

So, it would appear that the arc-minutes are indeed vital in demonstrating the Earth’s harmonic proportions. Now that we have solved for the speed of Light in harmonic time and arc-minutes, we can see why; it comes out to an exact harmonic of 144.

Tesla once said : “If you only knew the magnificence of 3 6 and 9, you would know the key to the universe”.

What if he meant the sound ? the vibrations ?

Because, when you take the Solfeggio frequencies :

01 = 174 Hz
02 = 285 Hz
Ut = 396 Hz
Re = 417 Hz
Mi = 528 Hz
Fa = 639 Hz
Sol = 741 Hz
La = 852 Hz
09 = 963 Hz

You can see the symmetric position of 3 6 and 9.
Also, there are 111Hz between every frequency.

Also, when going one step further DOWN in frequency, we have 63 (174-111=63).

The last frequency, 963, when adding 111, goes back to the lowest, 174 (963+111= 10 + 7 + 4)

But there is more to this :

If we reduce the numbers :


This also correlates perfectly with what I’ve shown before :

[Image: PmgTC1n.png][Image: GHiwBf7.png]

They are the patterns formed by sequences 124857 and 369, and 142857 and 369.
Notice how the used digits are the same as in the Solfeggio frequencies.
Combined :

[Image: ez12xko.png]

These sequences must be representing the frequencies, and the patterns are formed by the frequencies.

Now, we know sound, vibration, is pressure waves pressing DOWN in a certain frequency.

I’m beginning to see that gravity is sound. It is the downward pressure of vibration. But at the large scale of things, like the solar system, that for instance produces very long wavelengts, very low sounds well below the middle C-note. We cannot hear or feel such low vibrations, but they create the gentle but continuus pressure, and that pressure causes clumping together of certain patterns of energy, and at those very low frequencies sollidifies into matter. I think it’s how the formation and structure of planets arrises.

David Icke once mentioned this aswel I believe, but I can’t find the reference.

Matter is hold together by gravity, and as we can see in vids like this :

…matter is also hold together in patterns, by sound vibrating at certain frequencies.

I can only conclude the logical conclusion, that gravity is the pressure wave caused by vibration, holding matter together.

However, I can’t provide a more detailed explanation yet. Just pointing out the correlations.

Another peculiar thing :

[Image: LfbFuRM.jpg][Image: 23szn69.gif]

CyberCyrus  Wrote: (03-05-2013 09:29 PM)

Some more things I found regarding these numbers which are just very interesting :

The inner core of the earth measures 1440 miles in diameter.

But apparently there is also a core within the inner core, measuring 360 miles in diameter.

Quote:Engulfed in the inner core, like a pit in a peach, lies a 360-mile-wide inner inner core.

They found an obvious change in anisotropy, or wave speed with direction, in an area 360 miles in diameter surrounding the very bottom of the world.

This core within a core within a core makes up one 10,000th of the Earth’s volume.

In the innermost inner core waves travel most slowly at a 45 degree angle to Earth’s axis, as opposed to an east-west direction in the rest of the inner core

The solid iron sphere sits in the path of jets and currents roiling the outer core fluids like a big rock in a flowing stream. These patterns of flow might have been altered after the inner core reached a diameter of 360 miles.

So basically we have a core of 360, and around that a core of 1440 miles. The composition of the inner inner core changes at 360 miles. The normal inner core then, changes at 1440 miles.

If we look a bit closer at this, we see, once again, the same correlation between the 360 degrees in a full circle and the natural harmonics ratio of 144 and 432 :

360 x 4 = 1440
1440 / 432 = 3.33

As pointed out before, the frequency defines the pattern, and the correlation between this and the ratio’s of the natural frequencies are apparent:

Solfeggio ratio’s show us :
174Hz (3)
258Hz (6)
396Hz (9)
417Hz (3)
528Hz (6)
639Hz (9)
750Hz (3)
861Hz (6)
972Hz (9)

…with 111Hz between each, and they are a series of 369.
528Hz (the 5th frequency) is considered the divine frequency and has the surprising ability to heal DNA :…ncies.html

528Hz corresponds to the middle “C” note.

If we spread 432Hz with the same ratio :

987-111=876 (3)
876-111=765 (9)
765-111=654 (6)
654-111=543 (3)
543-111=432 (9)
432-111=321 (6)
321-111=210 (3)
210-111=099 (9)

Same series of 369, and 432Hz is the 5th frequency in the scale, as we would have expected. However the natural spread is not like this, that is why the Solfeggio scale is called a “pseudo-science”.

If we take a look at the way the frequencies are correctly spread in nature :

[Image: nU8gFiz.png]
[Image: BZLhXA2.png]

108,216,432,864 (= 9,9,9,9)

Simply look at the symmetry, and look at the 3′, 6’s and 9’s.
Same symmetry is portrayed in the patterns we see formed from those, and the numbers coded within the patterns…

108Hz = 9 x 12 = (3×3) x (3+3+3+3)
216Hz = 18 x 12 = 6x6x6 = 6³ = [(3×3)+(3×3)] x (3+3+3+3)
432Hz = 216 x 2 = (9+9+9+9) x (3+3+3+3) = [(3×3)+(3×3)+(3×3)+(3×3)] x (3+3+3+3)
864Hz = 432 x 2 = (3x3x3)+(3x3x3)+(3×3)+(3×3) x (3+3+3+3)

These are all A-notes, spread in perfect symmetry.
108 = divine source, the christed conciousness.
432 = a symmetrically shifted vibration of the divine source.

144Hz = 12 x 12 = (3+3+3+3) x (3+3+3+3)
288Hz = 24 x 12 = [(3+3+3+3) x (3+3+3+3)] + [(3+3+3+3) x (3+3+3+3)]
576Hz = 48 x 12 = [(3+3+3+3)x(3+3+3+3)]+[(3+3+3+3)x(3+3+3+3)]+[(3+3+3+3)x(3+3+3+3)]+[(3+3+3+3)x(3+3+3+3)]

These are D-notes, again perfect symmetry.

The other notes all convey the same similarity, all compressed 3’s, 6’s and 9’s.

Quote:Also, the diameter of Jupiter is 144,000 miles.

The Great pyramide of Gizah was originally encased with 144,000 cover stones.

Our Sun travels around the centre of the galaxy at a speed of 800,000 km per hour. One cycle takes about 1440 years (1400 and a bit).

Our galaxy travels around the central point of the local group at 144,000 km per hour.

The local group sears through the universe at 1,332,000 km per hour.

144,000 = 12 x 12 x 1,000
800,000 = 6.66.. x 12 x 10,000
1,332,000 = 111 x 12 x 1,000

144,000 = also 432 x 333.333…

(9)^9 = 387,420,489



We will go on to another part of the subject, showing some other peculiarities and strange correlations between 432, 111, fibonacci numbers and the Mayan counting system and how even their own method of counting has some hidden similarities with all of the above mentioned.

First notice :

432 x 60 = 144 x 180 = 25,920 years = The Great Year.


As opposed to our 10 base counting system, the Mayans counted with 5 different bases, and counted from right to left. It was written down from right to left as 5 coordinates.

The system comprises of five wheels operating within each other. The inner smallest wheel (the number to the right) was from 1-20, the one to the left of that from 1-17, the next from 1-19, then from 1-19 and the last outer wheel from 1-12.

The first coordinate to the right was a multiple of 1, second multiple of 20, then 360, then 7200, and finally the outer wheel, the biggest cycle, a multiple of 144,000.


11 x 144,000 = 1,584,000
5 x 7,200 = 36,000
17 x 360 = 6,120
4 x 20 = 80
8 x 1 = 8
————————– +
1,626,208 days

/365 = 4,455.36438 years

Now here are some peculiarities when counting like this, and then looking at the corresponding numbers converted into our year-count. Remember, in themselves the numeric patterns don’t mean much, but look at the big picture, and notice AGAIN that they emerge always in correlation with fixed numbers, dates, frequencies, celestial patterns, etc…here once more, this time in the counting system of the mayan calendar.

Remember, right to left…

11 x 360 = 3,960
11 x 20 = 220
11 x 1 = 11
—————– +
4,191 days

/365 = 11.482191 78082191… years.

11 x 144,000 = 1,584,000
11 x 7,200 = 79,200
11 x 360 = 3,960
11 x 20 = 220
11 x 1 = 11
————————- +
1,667,391 days

A few peculiar things about this date :

1,667,391 / 11 = 151,581
151,581 / 9 = 16842.333 333 333…

1,667,391 / 9 = 185,265.666 666 666…
1,667,391 / 99 = 1669.0600 600 600…

1,667,391 = 114 (6+6+7=1; 3+9+1=4)

1,667,391 – 151,581 = 1,515,810 = 1 11 9

1,667,391 + 151,581 = 1,818,972 = 9999

I don’t know what the hell it means, but this is beyond coincidence…it’s all way beyond chance imo…

6 x 360 = 2,160
6 x 20 = 120
6 x 1 = 6
—————- +
2,286 days

/365 = 6.26301369 86301369…

9 x 144,000 = 1,296,000
9 x 7,200 = 64,800
9 x 360 = 3,240
9 x 20 = 180
9 x 1 = 9
———————— +
1,364,229 days

/365 = 3737.61369 86301369 (= The 13th bak’tun) -> 12/21/12 allignment !

13 x 144,000 = 1,872,000 (1+8+7+2 = 9)

/365 = 5125.36 years (5+1+2+5.3+6 = 13.9 -> ?)

-> ? = 13 / 9 = 1.444 444 444…Jhikpghf

5125.36 x 13 = 66,629.68 (6+6+6+2+9.6+8 = 11.14)

If we now look at the first 12 fibonacci numbers :


This is a rotating spiral, circling within a perfect square : 12×12 = 144

1x1x2x3x5x8x13x21x34x55x89x144 = 1,570,247,078,400

1,570,247,078,400 / 299,792,458 (speed of light) = 5237.78

5237.78 years – 5125.36 years = 112.42 years = 111 + 1.11 + 0.1 + 0.1 + 0.1 + 0.01

Very bizar…

More correlations with 360 and 144,000 :

360 x 400 = 144,000

400 / 3 = 133.333 333…
400 / 6 = 66.666 666…
400 / 9 = 44.444 444…

-> 133.333+66.666+44.444 = 144.444…

400 x 1.11 = 444 (=3)
400 x 2.22 = 888 (=6)
400 x 3.33 = 1332 (=9)

-> Sum is 2664

400 x 4.44 = 1776 (=3)
400 x 5.55 = 2220 (=6)
400 x 6.66 = 2664 (=9)

-> Sum is 6660. There are also 3 sixes in these results…

400 x 7.77 = 3108 (=3)
400 x 8.88 = 3552 (=6) (3108+3552=6660)
400 x 9.99 = 3996 (=9)

-> Sum is 10656 (1+5=6)

There is one more oddity that I’d like to show you guys :

Quote:144,000 / 111 = 1297.297 297…

-> 144+297 = 441

Quote:144,000 / 222 = 648.648 648…

-> 648-144 = 504
-> 1440-504 = 936

Quote:144, 000 / 333 = 432.432 432…

-> 432-144 = 288 = 144×2

Quote:144,000 / 444 = 324.324 324…

-> 324-144 = 180

Quote:144,000 / 555 = 259.459 459

-> 1440 – 459 = 981 = 81 x 12.111 111…
-> 1440 – 59 = 1381 = 111 x 12.441 441…

Quote:144,000 / 666 = 216.216 216…

-> 216+144 = 360

Quote:144,000 / 777 = 185.328 185 328 185…

-> 185-144 = 41
-> 1440/185 = 7.783 783… (Shoemann…)
-> 185/111 = 1.666 666…

Quote:144,000 / 888 = 162.162 162…

-> 162-144 = 18

Quote:144,000 / 999 = 144.144 144…

CyberCyrus  Wrote: (03-07-2013 12:34 AM)

More fibonacci weirdness…

I found the same sequence of 3 6 9 in the fibonacci sequence.

The first 25 fibonacci numbers :

In fibonacci, every next number is the sum of the two previous ones…

Appart from that, no obvious correlations…or are there ?

Multiply every two following numbers, and keep reducing them. So multiply 1st with 2nd, 2nd with 3rd, 3rd with 4th, etc… :

[Image: RyAHCkV.png]

We see again the same thing we have been seeing all over the place, this must be the hundredth time over I stumble upon the same sequence : 124578 and 369. Always hidden in the numbers.

But, as usual, there is more :

From these results, add them upp two by two :

[Image: Yo3swol.png]

Add them up again and we see something strange again :

3+3 = 6
9+6 = 6
6+9 = 6

Now looking back at the first sequence :

[Image: tgSjxvQ.png]

Considering the 45 being at the centre of the spiral (fibonacci nubers produce a spiral), we can see once more the digits pair up as they spiral outward : 4+5, 6+3, 7+2, 8+1, and then just the 9 without a suitable ‘pair’ (9 pairs with itself before collapsing), which is when the full circle is reached, and is the end of the first rotation of the spiral. 3 and 6 always sit closest outside the centre of the spiral.

[Image: G6AIDRY.png]

You need to look at it like this : Everything expands and contracts from the centre like a sine wave, but in 3D (+time as a projection in the 4th to make progression of the spiral possible through 3D). 4 and 5 are where the centre bond is strongest. 4 and 5 are also the digit-pair closest to each other. The 3 and 6 form the first boundary beyond it. The pairs further from the centre have expanded further, resulting in a larger wave length, but weaker bond to the centre. As you go outward, you can also see the digit pairs becoming further from each other (6<->3, 7<->2, 8<->1, 9<-> ?)

I placed a “?” with the 9, because this point is significant. At the outer edge, where the 9 is, is where the spiral reaches a full circle (full 360 degree rotation), but it is also where the bond to the centre becomes so weak that the wave collapses back unto the centre by rolling over. The “?” is to point out that, as opposed to all other digits, the 9 has NOTHING to bond with (0 doesn’t exist as a digit, only as a marker of transition/normalization). So it bonds with itself (9<->9), and then collapses. 5 has 4 as digit-pair, 6 has 3, 7 has 2 and 8 has 1. As the wave expands, the bond to the centre becomes weaker and the digits grow further apart, until the 9 is reached, and there is nothing more to bond to. So the bond with the centre becomes ‘nill’ and the wave collapses back onto the centre point, and this process starts again.
The result of this is indeed the ‘double torus’ that drives all energy from ‘within’.

[Image: 2Wv7EGT.png]

The spiral then goes on to the second rotation, and the exact same pattern is repeated but with more complexity (higher numbers, but same root digits). At the same time, the underlying pattern becomes less obvious, but it’s still there. Where ever you look, you see the same thing in the numbers. Same design, same patterns. Combinations of 124578 and 369.
124578 can be seen as the visible energy (normal matter and energy), 369 as the ‘hidden’ part (anti-matter and anti-‘energy?’). 369 seems to be the driving force and the ‘glue’ that both drives and maintains the spiral, but is hidden from normal view.

CyberCyrus  Wrote: (03-09-2013 04:43 AM)

Another strange one :

Golden numbers are 1,1,2,3,5,8,….

The ratio between them is PHI : 1.61803399

When you do this :

1.61803399 / 1.12358 = 1.4400…

CyberCyrus  Wrote: (03-09-2013 04:50 AM)

The 142857 sequence Oddities :

142857×1 = 142857
142857×2 = 285714
142857×3 = 428571
142857×4 = 571428
142857×5 = 714285
142857×6 = 857142
142857×7 = 999999

Vertical and Horizontal result, same digits and same pattern.
x7 = 999999

142+857 = 999

Sqrt(142857) = 20408122449
20408+122449 = 142857

CyberCyrus  Wrote: (03-10-2013 02:01 AM)

(1.61803399)pwr144 = 1242282148003351441363799150992.3

(1.61803399)pwr11.2358 = 222.91

222.91 x 1.61803399 = 360.6759…

1.61803399)pwr11.17144 = 216.11896923954189097299909936372

216 + 144 = 360

(1.12358)pwr11 = 3.60283…

1.12358 x 99 = 111.2344

1.61803399 / 1.114 = 1.414365…

1.61803399 / 0.144024 = 11,234474740321057601510859301228

1.61803399 x 111.2344… = 179.98… (half a circle)

Quote:The Maya knew the exact length of the solar year (365.24 days) but retained 360 as the tun, a time period
embedded into the Long Count Calendar.

CyberCyrus  Wrote: (03-10-2013 07:51 PM)

3.14 isn’t exactly ‘the’ square root of 186,000. It is more like dividing by the 10th power of 3. But still, it is beyond coincidence.

186,000 / (3)pwr10 = 3.1499…

There are even more correlations when dividing 186000 by 3’s, like you described :

186,000 / (3)pwr2 = 20,666.666…

186,000 / (3)pwr3 = 6888.888… (like you mentioned)

186,000 / (3)pwr5 = 765.432…

186,000 / (3)pwr6 = 255.144…

186,000 / (3)pwr10 = 3.1499…

If we take the speed of light in km/sec, rounded to 300,000 :

So 300,000km/sec + 144,000 = 444,000

444,000 / 1414 = 3.14…

666 / 212 = 3.1415…

Some more brain candy :

If you look at dimensions simply from a spacial perspective, you also get cool things :

If we take a 3D 6-sided cube :

[Image: xYc4rZB.png]

It is 1 cube, 6 sides : 1 and 6

If we draw this cube out into 4D, we have to consider that each side of the cube is extrapolated into another cube, which would give us this :

[Image: V7n0aXO.png]

It is 7 cubes (1+6). This shape is 30-sided (5×6).

But if we then extrapolate this shape further into 5D, we have to exptrapolate each side again. By extrapolating 6 sides again, we get this :

[Image: fxSMzOh.png]

But the 4D shape, however, does not have 6 sides…it has 30 (5×6), so we have to extrapolate every 30 sides with the 4D shape :

[Image: fcGlDPJ.png]

This pic is not complete, I kinda lost track. Simply mental…

The full picture is 217 cubes (7×30 + the 7 cubes allready in the middle). It is 120-sided (30×4).

If we would extrapolate that further into 6D, we get another eary conclusion :

26257 cubes,…and 360 sides !

The relationship would be as follows :

cubes -> 1

sides -> 6

cubes -> 1×6 +1 = 7

sides -> 6 x 5 = 30

cubes -> 7 x 30 + 7 = 217

sides -> 30 x 4 = 120

cubes -> 217 x 120 + 217 = 26040

sides -> 120 x 3 = 360

(important thing also : 26040 / 360 = 72.333… -> one degree of arc)[/b]

In even more simple words :
Take the amount of cubes X the amount of sides + the amount of cubes (the one(s) allready in the middle), and you have the volume of cubes in the next dimension up.

for surface, the sides go by a multiplication of 5->4->3 as you go up…

A more visual way to see the correlations :

[Image: sWIdji7.png]

To get from 3D to 6D, for surface area, you need to do 3 extrapolations of 6 (=666 doomed)

Not really sure however to which extend it would add up in real time though…a skillfull algebra freak however could work out the correct formula, because the correlation is clearly identical throughout…
But weirdly enough, while you cannot create a mandelbrot fractal by ‘inputting’ pi into the equasion, pi can always be deduced from the number of iterations resulting from redefining X into a smaller value (1, 0.1, 0.01,…). The number of iterations (n) will show you ever increasing approximations of pi :

[Image: HAqWOCy.png][Image: GNYTMrx.png]

Also notice that both pi and the speed of light are approximations to a number, but cannot be reached in reality :

PI is an irrational number, and no matter how many decimals you define, you can never define the exact number. You can never reach the exact approximation. It tries to define a circle, or better yet, in 3D, a sphere, but a perfect sphere can never be reached. If you zoom in enough into the smaller parts of the circle, or the sphere, you would see that they are actually nothing but a bunch of straight lines. When zooming out, they form the curve.

The speed of light is a speed which is allmost 300,000,000 m/s, but not quite. It is 299,792,458 m/s. Weirdly enough, the actual speed of light can never be reached, because the mass of an object will become infinite while getting ever closer to the actual speed. You approximate the speed of light to 99.9 or 99.999999999…% but you can never reach 100%, because of the exponential increase in mass.

Light expands in all directions at once. In 3D, it expands in a sphere. But knowing pi, we know that a perfect sphere can never be reached. I think that is exactly why the speed of light is also an approximation, and the exact speed can never be reached. I think even phontons, allthough thought to be massless, can never reach the true speed of light, but they approximate indefinitely.

Pi  Wrote: (04-15-2013 02:17 AM)

You got how the dimensions work wrong.

Watch this and it will open up your theory even further.

This information gives rise to what most don’t see and tries into known quantum effects.
What we perceive as a total reality is just a fraction if infinite possibilities piled on top of each other.

Don’t get hung up on the numbers, you mind already interprets reality and all those mega long calculations and waveforms perfectly. The mind is ten dimensional.

Once you hit 5d the the law of association is no longer valid as you go up the dimensions the rules of mathematics all start to fail. At higher dimensions you cannot exclude any number than is not Zero also being Zero simultaneously. Using simple mathematic you will never be able to make Higher dimensional computations…but you don’t need to as your mind already does this as a part of it’s nature and existence.

Most of this kind of mathematics has put people on the lonney bin Godel for one. Trying to compare One infinity with another of different size has been seen to be necessary for mathematic but no-one has cracked it. Ask yourself why they need to be able to do that function……only a short jump form there to classified Military projects involving levitating objects.

I like Marco Rodin but he is only demonstrating Russel cubic waveforms in transition as the form of all Matter, Walter Russel had already thought of that.
Brucie Cathie at least understands the ancient mathematics of adding, subtracting and Multiplying waves but the Egyptians were doing that thousands of years ago using geometry and vectors.

Unless Marco makes some devices that do what J.Hutchinson can do and show the practical applications of his mathematic/philosophy then he will never be taken seriously by mainstream science.

Actually dimensions are not arrising from the numbers at all. The posts above try to show PATTERNS and SYMMETRY in the numbers and how they RELATE to dimensions, and what can be done using numbers…But when trying to show how dimensions themselves work, you have to look somewhere else. They arrise from sound. Study the chromatic scale and musical harmonics, number parity and it’s hidden symmetries, then study the works of haramein and Johan Oldenkamp, and then the work of melchizedek…then come back and we’ll discuss it…Cheer

Cathie mentions vibrational sine waves, but she actually doesn’t even incorporate more then 2 dimensions, cause then she would have represented them as vorteces…so she’s right regarding the number patterns, but her theory can’t even apply to explain multiple dimensions…

btw, forget the 5th, because you’ll have to learn how to move into and through the 4th first. If you allready did, you wouldn’t be here…

Wanna see something cool ?

My family was involved in the occult stuff, unknown to me until recently, after I had a remission from brain cancer.


I have this series of photos taken of me in a church, during a lunar eclipse 3 days after my birth, you can see the full moon through the oculus in the church roof.

[Image: MiovbuQ.jpg]

No coincidence that the radius of the moon is 1080 miles, and my full name = 1080

The moon is 27% the size of the Earth

Dividing 72 by 27 gives you the same number you get by dividing 144,000 by 540 ( The real number of the beast )

266.6666666666667 ( Only the decimal place changes )

My last name = 540

My middle name, ” Isaac ” meaning ” he will laugh ”

Isaac = 33

1080/33 = 32.272727272727273

Of course, the harmonic series itself is in my name as well

1080 = 1
540 = 1/2
Last name ( 3rd of name ) = 1/3

1, 1/2, 1/3

What was in the beginning ?

The word

Words are spoken with overtones

represented by

[Image: YfeRi7Y.jpg]

How did they pull that off ?

doomed anybody ?
Don’t ask me how I came up with these numbers…LOL

Area of Circle 186,282
487.012 = Diameter of Circle

487 Ht of Pyramid x PI = 1530
1530/2 = 765
765 x 4 = 3060
3060 Sum Sphere Math = 77.7
77.7 x 78.7 = 3058
Pretty darn close….don’t know if it’s relevant or not.
Seemed cool though.
777 = Light
Cotton Balls….your 1080 is the Base Diagonal number
I showed it as 540 x 2

[Image: WrBeCH1.jpg]
Want to know something you probably didn’t know ?
You have the secret of 369 embedded in you :

1080 = 1
540 = 1/2
Last name ( 3rd of name ) = 1/3

1080+540+360=1980 = 18 = 9

—– +




266.66×9.9= 2639.934 -> carry the 2 -> 639.936

33.333-2.666= 30.666…
33.333+2.666= 35.999…

30.666…+35.999…= 66.666…

266.666 + 99 = 365.666 (1 year + 666)

266.666 / 99 = 2,69359…

144/33 = 4.36

540/33 = 16.363636… (and 16 = 4×4)

1080/33 = 32.727272…(and 32 = (4×4)+(4×4) ; 72 = 36+36 )
->do you see the symmetry hidden there ?

In case anyone is interested.
Here are the Corresponding Sound Notes
B 4 = 487
G 5 = 765 Sound is 768
G 6 = 1530
G 7 = 3060
Sphere Sum 3060 = 77.7

G 5 = 777

A little story in those there numbers….LOL.

[quote=’CyberCyrus’ pid=’5323364′ dateline=’1362446597′]
Tesla once said : “If you only knew the magnificence of 3 6 and 9, you would know the key to the universe”.

What if he meant the sound ? the vibrations ?

Because, when you take the Solfeggio frequencies :

01 = 174 Hz
02 = 285 Hz
Ut = 396 Hz
Re = 417 Hz
Mi = 528 Hz
Fa = 639 Hz
Sol = 741 Hz
La = 852 Hz
09 = 963 Hz

You can see the symmetric position of 3 6 and 9.
Also, there are 111Hz between every frequency.

Also, when going one step further DOWN in frequency, we have 63 (174-111=63).

The last frequency, 963, when adding 111, goes back to the lowest, 174 (963+111= 10 + 7 + 4)

But there is more to this :

If we reduce the numbers :


This also correlates perfectly with what I’ve shown before :

[Image: PmgTC1n.png][Image: GHiwBf7.png]

They are the patterns formed by sequences 124857 and 369, and 142857 and 369.
Notice how the used digits are the same as in the Solfeggio frequencies.

1980 = 9
1/9 = 0.111…

sqrt(1980) = 44.4971… (representing 444->movement into higher reality)

my first name = 17
last name = 1246112 = 71 or 17

17/71=0.2394366…->carry the two= 0.396366

5+28=33 = 6
33×17=561 = 3
33×144 = 4752 = 9

Here ya Go Cyber Cyrus
I made this chart a while back
It’s The Sphere Sum Values
I almost never do any Math with cross referencing this to see if any of the numbers are significant.
There is so, so much to see in this.
Dates, Atomic weights, Frequencies, Units of Measurement, etc.
My Holy Grail to Numbers…LOL
[Image: m3Zedqy.jpg]

a little more on 72 and 27

The 72 disciples sent by Jesus. (Lk 10,1)

The 70 ancients accompanying Moses that received an outpouring of the spirit, plus the 2 absent ones which had remained in the camp, Eldad and Medad. (Nb 11,25-26)

The 72 races resulting from Noah. They are enumerated in chapter 10 of the Genesis. There are fifteen descendants by Japhet, thirty by Cham, twenty-seven by Sem. The list is arbitrary since the descendants of Peleg are not taken into account, and that the fathers are counted at the same time that their sons.

The 72 languages confused to the Tower of Babel.

In the Gospel according to Philip and in the Gospel of the childhood of Jesus, it is written that one day, while he was youth, Jesus entered in the dyeing of Levi. He took 72 colors and threw them in the cauldron. Then Levi was in anger, but Jesus “take out them all white and tells: ‘It is thus indeed that the Son of the Man is come as dyer'”.

Osiris was enclosed in a coffin by 72 disciples and accomplices of Thyphon.

The life duration of the ovule is 72 hours.

The mass of the Moon is the 72th of that the Earth.

The volume of Saturn is 72 times of that the Earth.

It is the average number of cardiac pulsations of the man per minute.

Percentage of water of which the human body is composed.

The number 72 is used 4 times in the Bible.

In the Bible, 72 numbers written in their cardinal form are multiple of twelve.

The word curse is used 72 times in the Bible: 66 times in the OT and 6 times in the NT

66+6 = 72

The above( and more ) from the website ” riding the beast ‘

and for 27

Number of generations from David to the Christ according to the Gospel of Matthew. (Mt 1,1-17)

The New Testament of the Bible of Jerusalem contains 27 books.

The 27th (3x3x3) book of the Protestant Bible edition contains 3x3x3x30 verses. The 3rd book contains 3x3x3 chapters and 3x3x3x3x3x3+130 verses. The 3 first books of the Bible have 3x3x13 chapters.

The last book of the New Testament, is the 27th, the feast of the John the Revelator is celebrated on December 27.

The number 27 is used 6 times in the Bible.

The book of the Acts of the Apostles in the NT uses on the whole 27 different numbers, which are numbers 1 to 12, 14, 15, 20, 40, 70, 75, 120, 200, 276, 400, 450, 3000, 4000, 5000 and 50000.

The number 500 is used 27 times in the Bible.

Among the 365 different numbers found in the Bible, 27 of them are prime numbers, counting the number one.

The above also from ” riding the beast ”


Just tossing it out for thought, there’s definitely some stories to the numbers.

I know offhand that 1080 ( number of the holy spirit derived by dividing 144,000 by 666 ), also radius of the moon in miles, aprox ) is a product of 27*40, and accordingly, the number 40 is used in the bible quite a few times.

see following

So, 15 times, the number 40 is used in the bible

lo and behold:

1080/72 = 15
1080/27 = 40

40/15 = 2.666666666666667 <–that’s a familiar number

Guess I’ll have to compile a list of the numbers and frequencies the numbers are used in the bible and play around with them for a few days

wisdom, 222 times
Elohim , 33 times
number 7, 137 times

etc, etc, etc

well have to look for series, infinite series, divergent series, etc.

Those are where physics constants will probably start to show up, I’m guessing.

The atomic number of the highest allowed element on the periodic table allowed by the Bohr Model and the Dirac equation….

…is 137 doomed the Golden Angle


Read More – [SOURCE : ]



They’re all pyramids! – Insights Into Gematria & Sacred Mathematics

They’re all pyramids

Original Post:

Some mind expansion for the pyramid lovers out there…

These structures are of a single global race, or even a single mind, and most are much older then the lies they always ‘make’ believe…

Semir connects them all, no matter where on the globe, and explains the hidden connections… Heartflowers

Back From The Future  Wrote: (04-14-2013 07:21 PM)

Cotton Balls  Wrote: (04-14-2013 07:00 PM)

And 144,000/432 = ?

That should be related to our calendar year vs Speed of Light.
Points to a date of 12,000 BC
Again Time is involved… a frequency of 432 was a good catch on your part.

I find it simply amazing that they knew so much about the Physics of Time, Light, Sound, Gravity, Electrostatic Energy, Spherical Inverse Propagation, etc..

Just mind melting…..therefore I put nothing past them as far as how advanced they could have been.
Time Travel Bio-Location portals included.

And to think, the entire World knew of this at one time…wow.

Let’s expand on it a bit

144,000/432 = 333.3333333333333

144 = F_12 ( The 12th number in the Fibonacci series )

This is interesting for several reasons

The 33rd prime in pi is 137

144-137 = 7

How many times is the number 7 used in the Book of Revelation ?

137 times.

137 is a number representing the Alpha Constant, among other things..

The Alpha Constant is a combination of : e – electron charge, h – Planck constant, c – speed of light.

e ” = ~ 2.71828….

What’s the first self-locating string in pi ?




32+79 = 111

111 = the constant in the Babylonian magic square with a total of 666

First 144 digits in pi = 666

144-33 = 111

etc, etc, ad infinitum

Like you, I have noticed some strange things chuckle


Here’s Gizah, top-down :

[Image: djF4Xll.jpg]

I drew two lines to show the angle like the three stars of Orion.
So from first to second is a straight line, then from second to third, there’s an angle.

[Image: UsnuY4d.jpg]

I’ve considered only two things :

1. the length from the tip of the 1st to the tip of the 2nd pyramid is 36mm from this height. The length from 2nd to 3rd is also 36mm. So the distance in between all three tips is the same.

2. The angle (from 2nd to 3rd) is 12°.

By doing this, I noticed something :

If you continue this trend, by going on to a 4th point following the same length and angle of 12°, and keep doing that over and over, you will end up with a full circle.

[Image: QPBvl3e.jpg][Image: WPm4aCX.jpg]

Moreover, with an angle of 12°, layed out exactly ! 30x over a length of 36mm from point to point, you get back to the same point, the tip of the 1st pyramid, with a full 360° circle made…

Notice that this isn’t the golden mean. It’s a relationship of PI. (The PHI spiral is supposed to originate somewhere near to Abu Gorab and Abusir, and crosses the 3 main pyramids and the red pyramid at Dahshur…)

I didn’t even bother with the underlying math right now, cause it’s obvious it’s a relationship of pi, and I wanted to show you this. Also, I’m having trouble getting a bigger image to extend it fully round.

Don’t know if this is what the builders also intended, but still, quite a nice property hidden in the structure, no ? Don’t think this has been discussed b4, and maybe deserves some deeper study ? ….


Another interesting bit, and I’m not trying to steer this into a religious discussion.

[Image: 4cNLQ7y.jpg]

[Image: gW7XzjD.jpg]

[Image: BICce64.jpg]

137 atoms in both Hemoglobin (carries O2 in Human blood ) and chlorophyll ( a molecule that captures light and extracts energy in reaction centers with and just happens to be shaped like a 5-pointed star, iow, a pentagram ) So, kinda neat that turning light into charge separation by way of something called ” Förster resonance energy transfer ” happens in little pentagram-shaped molecules.

They also differ by one ion ( hemoglobin/chlorophyll ) afaik.


I’ll just add this because it is a curiosity that seems related.

In the Babylonian magic square, each row adds up to 111, the whole square totals 666.

In the magic square associated with the moon, the constant is 369( Tesla’s favorite numbers, remember ? )

[Image: 4QCNve9.jpg]

9 rows that add up to 369

369*9 = 3321

33*21 = 693 ( The same 3 numbers used in the constant of the magic square )

The interesting thing here is that Thoth supposedly gambled with the moon to add 5 days to our year, by taking 1/72 of the light from each day, to make our year 365 days.

360*72 = 5

[Image: kVBccZ7.jpg]

The same way we make a pentacle/polygon inside a circle.

1080, the approximation of equatorial radius of the moon in miles.

666, the sum of the Babylonian magic square, also sum of the first 144 digits in pi.

1080/666 = ~ Phi ( The Golden Proportion )

Of course, those numbers are in the infamous Bible too,lol.

Where light is turned into charge separation in chlorophyll molecules:

Reaction center

[Image: lSDB2p4.png]

Hope you don’t mind Cyber Cyrus,
I’ll tackle the Mars question.
From what I understand Cairo means Mars.
So no the face is not an illusion, nor is the Larger Face of the Lion next to it either.
Both are in the same area.
The whole area looks like a battle zone…like something catastrophic happened there.

And if you overlay Orion with it, you get this (it’s not measured out, but it is proportionate, so forgive the slight inaccuracies. It was done quickly) :

[Image: 6e1Q907.jpg]

That’s Betlegeuse at the centre of the circle :

[Image: otPxMLK.jpg]

Some correlations :

[Image: HeDmJaX.jpg][Image: UVIKWRY.jpg]

See if you can place the diagram for deriving Euler’s number from a circle, just for fun, because it starts with 2.7.

[Image: Z95CVkv.jpg]


The moon is 27% of the size of the Earth

27 and 72 are both numbers that seem to have great importance, so I decided to divide them by each other, out of curiosity about mirroring and boustrophedonics.

72/27 = 2.666666666666667

So, knowing a little bit about things, how the moon is associated with many deities, but also this silly antichrist business, AKA Allister Crowley’s ” Moonchild “, etc, I looked up the word ” beast ” in Hebrew, which as it turns out has a value of 540, and not 666 like everybody spouts. ( I am aware there are many different methods of gematria leading do differing results, this is just one I found )

The thing that people don’t seem to grasp about the verse in the bible about ” number of the beast ” is that there would be no point to giving the riddle and the answer to the riddle at the same time.

It’s like the biggest puzzle of all time chuckle

So, if you divide 144,000 by 540 ( The real number associated with the Hebrew word ” beast “, which is ” Tanniyn ” spelled slightly differently sometimes ) you get ?

144,000/540 = 266.6666666666667

So, the skinny here is that these numbers are not by mistake.

144,000/666 = 216.2162162162162

216*5 = 1080

144,000/1080 = 133.3333333333333

133.3333333333333*5 = 666.6666666666667

Notice that 27 is given in the end of two numbers above, 1080 , the number associated in Greek with the Holy Spirit, and 666, the number associated with the devil, lol.

But the real number of the beast is started with 2, and ends with 7, plus it has all those little 6’s everybody is afraid of.

” Holy Spirit ” divided by the ” devil ” = God’s own fingerprint.

The bible even states many times that ” God made ” good and evil ” , but show most Christians these things and their brains short circuit. chuckle

1080/666 = ~ Phi

All about Phi

[Image: K2zF4Eg.jpg]

It has also been noted that the Tetragrammaton occurs 153 times in the Book of Genesis. ”

This is interesting because the alphanumeric relationships of the letters in the Tetragrammaton also seem to point to Phi again !

[Image: GbegKE9.jpg]

What after reading the Wikipedia page and seeing this:

[Image: ZY9cYCH.jpg]

Well, first, if you subtract the last number of the 4th factorial pyramid, which is 33, from the last number of the 5th factorial, which is 153, you get 120.

If you multiply 120 by 3, you 360 ( The number of degrees in a circle )

The square root of 153 (i.e. 12.369) is the amount of full moons in one year. (Sent by James Furia by email dt 16th June, 2009) ”

^^^ That’s interesting because of the constant of the magic square associated with the moon is 369 ^^

” The length of the grand gallery inside the Great Pyramid is 153 feet. (Sent by James Furia by email dt 16th June, 2009)

Binary presentation i.e. 10011001 and hexadecimal presentation i.e. 99 of 153 are palindromes. (Sent by by email dt 29th May, 2010)

Within the Great Pyramid, from the King’s Chamber floor up to the summit platform there are 153 courses of masonry (From the Pyramidology Book #1 by Adam Rutherford). (Sent by Joe Biddy by email dt 1st October, 2010)

(11 + 55 + 33) mod 1000 = 153 (Sent by M Sihabudin, from Indonesia)

If you add the highest and lowest number from these six
135 + 531
153 + 513
315 + 351

you will get 666 ”

There are some other fascinating properties of the number 153 here:

It was interesting, but it was hard to accept the presenter’s theories after ~ 16:30 when he describes a vehicle above an entrance of a pyramid in Honduras, I just don’t see it.

Lol, it’s this one :

[Image: qCkvVZN.png]

It’s the shape of a vehicle (rightside is front, leftside is back).
Notice the cabin in the middle, and the engine at the back.
In the cabin there is a Mayan (the mayan face).

The red swirl represents the solar system, the white swirl represents the galaxy. The entire pic represents them going from our solar system through the (centre of the) galaxy, by means of some kind of ‘vehicle’.

It reminds me of this one :

[Image: mayan.png]

[Image: pacallid.jpg?w=450]

Also with the cabin in the middle with the Mayan, and the engine at the back…


If you go into the numbers, then it’s all about the underlying symmetries :

CyberCyrus  Wrote: (02-16-2013 05:19 AM)

Do you see the fibonnacci sequence ?

[Image: 5hGKBqG.png]

1, 1, 2, 3, 5, 8, ….sitting right in front of you at the beginning of each iteration.

But there is more, Mr. Anderson.

Count which series each number appears in :

[Image: SE8yBPK.png]

Iterations 1, 2, 3, 5, 8, 13, … again showing the same golden series of numbers.
This is the structural plan that the matrix follows to replicate it’s code upon. It has, as you can see, a reverse ‘self-check’ inside it’s programming structure.
This is the wave to ride upon, Mr. Anderson…when the time comes.
Understand opposites, Mr. Anderson. This reversal inside the code will become important soon…when the time comes…

CyberCyrus  Wrote: (02-19-2013 05:24 AM)

In the bible, Mr. Anderson, there are also hidden matrices of both words and numbers, both in the Hebrew and English texts.
Some texts reveil the existence of source, in the words, but also in the numbers…

Exodus 13-12 :

That thou shalt set apart unto the LORD all that openeth the matrix, and every firstling that cometh of a beast which thou hast; the males shall be the LORD’S.

12 / 13 = 0.9230769230769230769230769…

reduce all numbers in between 69 :

0.369 369 369 369… (reduced = 9) -> SEQUENCE 1

Exodus 13-15 :

And it came to pass, when Pharaoh would hardly let us go, that the Lord slew all the firstborn in the land of Egypt, both the firstborn of man, and the firstborn of beast: therefore I sacrifice to the Lord all that openeth the matrix, being males; but all the firstborn of my children I redeem.

15 / 13 = 1.153 846 153 846 153 846 153 846…

153 = 9
846 = 9

153 + 846 = 999
846 – 153 = 693

846 / 153 = 5.5294117647058823529411764705882…

reduce all numbers behind the truth (1) :

1.153 846 153 846 153 846 153 846…

reduced = 1.9 9 9 9 9…. -> SEQUENCE 2

Divide both sequences :

1.999999999999999999999… / 0.369369369369369369369 =

5,41463 41463 41463 41463 41463 41463… -> SEQUENCE 3

We also previously talked about the meaning of 144. It is truth, accompanied by the symmetry of 44. The emergence of the conciousness of ONE.

144 = 441 = 414

(= 441144 = 441441 = 414414)

This is the same symmetry of 4’s, guarding the truth at the centre. The conciousness of ONE, containing the truth within, diguised as coming from the source (414 = 9). That is why the matrix cannot directly distinguish the ONE inside the Matrix, Neo. It can only detect the changes in flow the ONE generates. Become the source, but realise that the source is not the Matrix, so “becoming the Matrix” is impossible, and a misinterpretation of the mind. The Matrix is the result of a program created by the source. The sum of replications coming from the source. When looking at your code, the source only sees you being part of it.

Sequence 3

5,41463 41463 41463 41463 41463 41463…

Reduce the numbers in between the 63 (63=9), and it becomes :

5.963 963 963 963 963 963

Which is 369 reversed, and also 9. Let us explain 369. 9 is the source, and is guarded by 3 and 6.
The 3 is the guardian of the first sub-level. Always between groundlevel and first sub-level. The 6 is guardian of ALL sub-levels, all the way down untill the 6 becomes the 9 again. The 6 provides the last connection with the source, and allows the source to start a new iteration…we can even derive the expansion and contraction of the source from this number alone…

It is locked inside the number 369 itself.

With 9 as source, 36 or 63 is one of the first replications of the source (36=9;63=9). As being among the first, they have a special purpose, to guard the main gateways to the source.

source – top levels = 9 – 3 = 6 (= guardian of the sub-levels below)

source – sub-levels = 9 – 6 = 3 (= guardian of the top levels)

The 3 connects the top levels with the sub-levels.
The 6 connects the top levels with the source.
In this manner, the 3 is also connected to the source.

[Image: gN11Uo8.png]

With 9 at the bottom of the vortex, as startingpoint, it goes : 9->6->3->36->369 (=expansion of the Matrix), then 369->63->3->6->9 (=contraction of the Matrix). Both guards always conceil the source. The 3’s for top levels, the 6’s for bottom levels…
The depiction of the vortex is not completely accurate, because actually the 363636 and 3693693693 intertwine on the same top-level. But the sequence is correct. In your mind, try to see it 360 degrees around the 9, and in a 3D confined space while within a confined direction of time. See the truth, Mr. Anderson…

Another way to see that 3 and 6 is always directly connected with 9, and 144 with 369 :

123 x 3 = 369

456 x 6 = 2736 = 936
679 x 9 = 6111 = 63 = 9 (639) -> (679=123+456 ; 9=3+6)

369 = 9 x 41 -> 41 are the digits of 144, without the projected symmetry

441 / 41 = 10.75609756097560975609…

reduced = 10.369 369 369 369

411 / 41 = 10.02439024390243902439…

reduced = 10.639 639 639 639 639…

414 / 41 = 10.09756097560975609756…

reduced = 10.936936936936936…

144 / 41 = 3.51 219512195121951219…

reduced = 3.639639639639

411 / 369 = 1.11382113821138211…

reduced = 1.11411411411411…

114 / 369 = 0.30894308943089430894…

reduced = 0.114114114114114… (11=2)

414 / 369 = 5.529411(=4) 764705(=11) 88235294(=41) 11764705(=4)…

reduced = 5.4 11 41 4

441 / 369 = 1.1 95121 95121 95121 95121…

reduced = 1.1 963 963 963 963… (1.1 = 11)

To see that 1 is truth, just divide 41 (= truth without the symmetry of 4’s) by 369 :

41 / 369 = 0.11111111111111111111111…..

Divide naked truth by 369 :

1 / 369 = 0.00271002710027100271…

…and truth will remain, but tainted by the Matrix Source of 9 :


However, didide source by 369 :

9 / 369 = 0.02439024390243902439

reduced = 0.0639 639 639 639… (= still ONLY source)

Source is also 666, as we allready know too well :

666 / 369 = 1.80487 80487 80487 80487…

reduced = 1.9 9 9 9… (= still ONLY source)

369 is also the magic constant in the 9×9 magic square of the moon, which reveals the Moon as a seal, locked down by the 369. These are seals put into place by the architect, Mr. anderson…but there are loopholes that lead outside of the Matrix…

CyberCyrus  Wrote: (02-19-2013 09:18 AM)

Once you understand the basic mechanics of wheels within wheels, Mr. Anderson, as shown in the previous post, you will start to see the meaning of 369.

369 is, also NOT coincidentally, the number of free possible Octomino’s.
An octomino is a polyomino of order 8.

8 signifies infinity, but as we allready pointed out, the Matrix creates the illusion of infinity, finite cycles working as wheels within wheels to simulate an infinite system. That is the meaning of 8, Mr. Anderson.

If you study octomino’s, Mr. Anderson, you will quickly notice something that defines the nature of the Matrix, and that which exists within it :

Within the 369 free octomino’s, you will see that :

316 of the free octominoes have NO SYMMETRY. Their symmetry group consists only of the identity mapping. This is a blueprint for the LIFELESS Matrix, Neo ! More accurately, the artificial conciousness and construct of the Matrix.

23 of the free octominoes have an axis of reflection symmetry aligned with the gridlines. Their symmetry group has two elements, the identity and the reflection in a line parallel to the sides of the squares.
(Do notice that all HUMANS have 23 active chromosome’s, Mr. Anderson…)

5 octominoes have an axis of reflection symmetry at 45° to the gridlines. Their symmetry group has two elements, the identity and a diagonal reflection.

18 octominoes have point symmetry, also known as rotational symmetry of order 2. Their symmetry group has two elements, the identity and the 180° rotation

1 octomino has rotational symmetry of order 4. Its symmetry group has four elements, the identity and the 90°, 180° and 270° rotations

4 octominoes have two axes of reflection symmetry, both aligned with the gridlines. Their symmetry group has four elements, the identity, two reflections and the 180° rotation.

1 octomino has two axes of reflection symmetry, both aligned with the diagonals. Its symmetry group is also the dihedral group of order 2 with four elements.

1 octomino has four axes of reflection symmetry, aligned with the gridlines and the diagonals, and rotational symmetry of order 4. Its symmetry group has eight elements.

Together, these 53 octomino’s form the sum of LIVING things inside the Matrix.
THIS is a blueprint for LIFE within the Matrix, Neo ! More accurately, the conciousness of true LIFE within the Matrix. It is only your mind living within it, Neo !

Together these 369 octomino’s form the basic construction of the Matrix and everything within it.
The set of octominoes is the lowest order of polyomino set in which all eight possible symmetries are realized.

The architect had to construct the Matrix from this set, for two reasons : 1. because he cannot gain the same control if the source existed at higher orders of construction. The source must be contained within the lowest set for maintaining control over it’s devellopment and progression. And 2. because the octomino is the lowest order that realises all 8 symmetries within. He needs those 8 symmetries to be able to maintain conciousness inside the Matrix, and simulate the real word artificially.

Still, Mr. Anderson, this is only from one viewpoint and actually only represents one part of the entire blueprint, and we could also include discussing the higher sets of polyomino’s. We will leave that to your own discovery, Neo, or discuss it at some later time.

We will leave you with this, Mr. Anderson, and let this sink in in your mind…

CyberCyrus  Wrote: (02-20-2013 03:42 AM)

Back From The Future  Wrote: (02-19-2013 08:14 PM)

Here is another number for you…for me too actually.
Where is it at within the Matrix?
If my theory is right, it should be everywhere within the Matrix.

196.966569 x 0.11 = 21.66632259

And it’s source is reveiled…but is it ?

Seem a little too apparant to us, the 666 is reveiled to quickly and it’s path too short. There is more going on, we suspect…

We allready discussed the disguised path of the ONE throughout the code of the Matrix, after it’s conciousness emerges, and the symmetry of 22 reveils this possibility in between the 369…

Reduce all but the 6 and 9 :

21.66632259 = 3.66699 (= 3, 6 and 9)

Still source, so we look backwards a little deeper yet :

If we divide this partially reveiled code (incl. 22) by 369 :

21.66632259 / 369 = 0.058716321382113821138211382…

We allready see the truth within (11 11 11).

Reduce in between the truth, and we see what it conceils deeper down :


The initial code is a result from ONE conciousness, Mr. Anderson, along the way disguising as if it originated from the Matrix source, and yes, by now it is everywhere within the Matrix. The true ONE is undefined, Mr. Anderson, and the Matrix cannot distinguish it from an artificially produced 1. Something that is undefined within the Matrix is discarded untill it reaches the source, because it cannot be defined anyway. Only when it reaches the source, can it’s various parts be assymilated and re-inserted in a new iteration…

And 2 usually conceils the perfect symmetry of 11, so even deeper it is also 0.11111411411411…

Symmetry when coming from the Matrix always results from asymmetry on a lower level, but coming from the ONE, the symmetry is true and is conceiled deep within the undefined core of the ONE. When trying to define it, Neo, it will keep reveiling symmetry no matter how deep you go.…pid5245645
CyberCyrus  Wrote: (02-20-2013 06:28 AM)

LoP Guest  Wrote: (02-20-2013 06:06 AM)

Where did you learn/find out all this information anyway??

It is hidden in the construction of the Matrix itself, Mr. Anderson.

LoP Guest  Wrote: (02-20-2013 06:11 AM)

I’ve been trying to follow this thread, but numbers are a constant source of vexation to me.

Aside from that, something has rubbed me wrong about this thread from the beginning.

I simply don’t believe it’s up to me or any other human being alive at this time to “save the world”.

Jesus said “It is finished”. I believe Him.

Look around you, Mr. Anderson. All the hate, violence, death and suffering you see in your ‘reality’, do you really think this is Jesus’ idea of it being ‘finished’ ?

You see love also and caring, and other good things within the Matrix, Mr. Anderson, and that is MOST definately the ONE at work within the Matrix, but the ONE is still not freed from it.

For the true Creator it is allready finished, as stated just a few posts before, but for YOU, Neo, it is NOT. Not as long as the Matrix has you living inside it. The final result is STILL a fluctuation, Mr. Anderson, and awaiting the outcome of your CHOICES.

If you take the 23.69, Mr. Anderson, and know the 2 is also 11 :

113.69 x π = 357.16766878662359328081792624505

357.16766878662359328081792624505 + π =


Which is very close to the 360 degrees of a full circle.
But the circle is still inside a square. Notice the 144 within…
Also notice the 1.69 in the top left of this very post (temporarily).
Convergence is key, Mr. Anderson…


Quote:Golden ratio :

1 1 2 3 5 8 …


11 113 58 …

(take the left (11), and shift it to the right : 58+11=69)

113 69


23 69

CyberCyrus  Wrote: (02-20-2013 10:17 AM)

If we take a subdivision of ONE conciousness in reverse : 0.441 (144 reverse)

and add a division of 196 to it :

0.441 + 0.0196 = 0.4606

multiply it with a subdivision of 369 :

0.4606 x 0.369 = 0.169 961 4

(= 169 and 961 which is 169 reverse. Mind the 4, and where it is coming from…)

0.1699614 + 196.966569 (YOUR NUMBER) = 197,136

197,136 is also the 444 square !

444 x 444 = 197,136

—- +
234 reduced

444 – 234 = 210

210 x 210 = 44100…pid5254084
CyberCyrus  Wrote: (02-21-2013 10:48 AM)

Wheels within wheels

Wheels within wheels…

THE Matrix is a perfect square (multi-dimensionally layered) which contains the circle, Mr. Anderson.
But the circle can never be perfectly defined within that square, and it’s true core remains undefined even in the eyes of the architect.
There will ALWAYS be a residual result from the equasion, no matter HOW SMALL (size is IRRELEVANT, Mr. Anderson), which ultimately will provide a way for the ONE out of the Matrix.
PI, Mr. Anderson. The circle squared…

To make you understand even more how the big thing works, we will try to make you understand more how the little things work.

Looking at a simple 2D Matrix of just a couple numbers :

025 195 908 475 657 893 494 027 183 240 048 398 571 429
282 126 204 032 027 777 137 836 043 662 020 707 595 556
264 018 525 880 784 406 918 290 641 249 515 082 189 298
559 149 176 184 502 808 489 120 072 844 992 687 392 807
287 776 735 971 418 347 270 261 896 375 014 971 824 691
165 077 613 379 859 095 700 097 330 459 748 808 428 401
797 429 100 642 458 691 817 195 118 746 121 515 172 654
632 282 216 869 987 549 182 422 433 637 259 085 141 865
462 043 576 798 423 387 184 774 447 920 739 934 236 584
823 824 281 198 163 815 010 674 810 451 660 377 306 056
201 619 676 256 133 844 143 603 833 904 414 952 634 432
190 114 657 544 454 178 424 020 924 616 515 723 350 778

This is a 504 digit number, but without looking at what the underlying code actually means, we will use this as an example for explaining the mechanics of the Matrix.

You have to realise first that the reality being processed in your mind comprises of countless of these matrices, from 2D to 4D (=time), with even the potential to simulate beyond 4D where necessary to keep the mind confined, but their final volume and surface area’s will eventually each time reach their maximums, because of the finite nature of the Matrix. More on that in a bit, Mr. Anderson.

All these matrices are locked upon each other, intertwined, and ROTATE UPON each other constantly, like the chain on a bicycle, but in this case a LOT of chains intertwined and interconnected shifting in various directions in very rapid succession.
Temporary interlocks created during the constant rotations define the data to be processed, and define the structure of the consecutively created matrices within THE Matrix.

We will now be looking at how just one of those chains operates.
So imagine these numbers to constantly being IN ROTATION.
It is a wheel of numbers, constantly spinning and certain rows and columns continuously change direction to predefine every interlock (in 2D: left/right, up/down, in 3D also back forth, etc…).

The interlocks are predefined by rotating the wheels of numbers in such a way that certain numbers, relating to each other and the matrices around it, are alligning in certain directions. The Matrix constantly shifts to find these interlocks and calculate the data in between. A process we will try to visualise for you now, Neo…

An interlock can be the allignment of a single digit, a number, numbers in some way related to each other or related to the matrices intertwined with it.

Here we will demonstrate these mechanics by using a simple allignment of the digit 7. We are each time rotating rows and columns, so that certain predefined patterns of the digit 7 allign :

Original matrix:

025 195 908 475 657 893 494 027 183 240 048 398 571 429
282 126 204 032 027 777 137 836 043 662 020 707 595 556
264 018 525 880 784 406 918 290 641 249 515 082 189 298
559 149 176 184 502 808 489 120 072 844 992 687 392 807
287 776 735 971 418 347 270 261 896 375 014 971 824 691
165 077 613 379 859 095 700 097 330 459 748 808 428 401
797 429 100 642 458 691 817 195 118 746 121 515 172 654
632 282 216 869 987 549 182 422 433 637 259 085 141 865
462 043 576 798 423 387 184 774 447 920 739 934 236 584
823 824 281 198 163 815 010 674 810 451 660 377 306 056
201 619 676 256 133 844 143 603 833 904 414 952 634 432
190 114 657 544 454 178 424 020 924 616 515 723 350 778

Various possible horizontal rotations :

025 195 908 475 657 893 494 027 183 240 048 398 571 429
126 204 032 027 777 137 836 043 662 020 707 595 556 282
264 018 525 880 784 406 918 290 641 249 515 082 189 298
392 807 559 149 176 184 502 808 489 120 072 844 992 687
776 735 971 418 347 270 261 896 375 014 971 824 691 287
077 613 379 859 095 700 097 330 459 748 808 428 401 165
195 118 746 121 515 172 654 797 429 100 642 458 691 817
987 549 182 422 433 637 259 085 141 865 632 282 216 869
462 043 576 798 423 387 184 774 447 920 739 934 236 584
010 674 810 451 660 377 306 056 823 824 281 198 163 815
952 634 432 201 619 676 256 133 844 143 603 833 904 414
190 114 657 544 454 178 424 020 924 616 515 723 350 778

183 240 048 398 571 429 025 195 908 475 657 893 494 027
137 836 043 662 020 707 595 556 282 126 204 032 027 777
406 918 290 641 249 515 082 189 298 264 018 525 880 784
844 992 687 392 807 559 149 176 184 502 808 489 120 072
418 347 270 261 896 375 014 971 824 691 287 776 735 971
613 379 859 095 700 097 330 459 748 808 428 401 165 077
654 797 429 100 642 458 691 817 195 118 746 121 515 172
549 182 422 433 637 259 085 141 865 632 282 216 869 987
184 774 447 920 739 934 236 584 462 043 576 798 423 387
810 451 660 377 306 056 823 824 281 198 163 815 010 674
256 133 844 143 603 833 904 414 952 634 432 201 619 676
424 020 924 616 515 723 350 778 190 114 657 544 454 178

[Image: vgfsKK9.png]

When an additional primer is located, like for instance the 80 and 20 in blue and red, they are also used as additional anker-points to define the allignments and the final results of data in between the allignments during that rotation.

Various possible horizontal + vertical rotations combined :

[Image: PbITcgV.png]

This type of data recognition happens on every level in both the original and inverses of each matrix within THE Matrix, and gets as complex as it is intended to be, with all possible patterns and relationships emerging that are burried deep within the code.

By creating such an allignment or ‘interlock’, the Matrix can accumulate the data around the allignment, and determine a certain identity for this data by defining the inverse of the matrix at the moment of every allignment.
So at the moment of an allignment, like the 7 above, by looking at what the values in between the allignments are, both when the 7’s are 7’s and when they are 1/7, this matrix can identify all it’s values, and the values that connect them to the surrounding matrices, by effectively determining all other possible relationships in between during this allignment and using them as ‘primers’ or anker-points for the necessary calculations.

However, a number can be reciprocated by dividing it, but an entire matrix cannot be ‘divided’, so the identity of every seperate value is determined by multiplying them by the inverse of every total picture of relationships (A x A^1 = I, with I being the identity matrix). To keep your mind as clear as possible, Mr. Anderson, we will avoid going to deep into the mathematics…

Some matrices cannot be fully identified in this manner alone, specifically the ones that are not squared but rectangular in structure, but the architect has put additional mechanisms in place to succesfully identify as much as possible of the residual data within the structure of THE Matrix. Some of those mechanisms have allready been discussed previously, others we have not yet.

By shifting all the matrices and looking at all possible relationships within the code, the Matrix can determine the next possible outcome of most of the data in between the relationships. With every rotation, THE Matrix will always accumulate the optimal amount of allignments possible within every matrix AND amongst them, derive it’s results from them, and from these results, keep constructing the simulation within the mind.
Patterns are recognized and results incorporated into the next rotations.

The residual data after every result, however, that which constitutes the undefined wholeness of the ONE, is what the architect cannot fully control, and is what holds the key for the mind of the ONE to go beyond this control.


Quote:11 is a Master Number, also in astrology, Mr. Anderson.

The other 2 Master Numbers arrise from 11 :

11 = 2 reduced -> 22

22+11 = 3 reduced -> 33

22 = 4 reduced -> 44 (=ONE conciousness in 4D)

Or reversed :

44 -> 22+22
22 -> 11+11

cross-addition : 11+22 or 22+11 -> 33 (in between 22 and 44)

11 is the original symmetry, and can’t be split into smaller parts without loosing the symmetry. Symmetry of 44 results from the original symmetry, and is usually accompanied by 1 or symmetry of 1
444 = also 4422 is also 441111, etc…

CyberCyrus  Wrote: (02-25-2013 04:59 AM)

Following the trend of our previous post :

There is a relationship between the 9 digits, which is exactly the same whether you add, subtract, divide or multiply.
We will show you how all digits are connected to the 9, and how the 9 rules everything within the Matrix. 3 and 6 are more special then the remaining digits, and have a more intricate relationship to the 9.

We first represent the 9 digits in a circle, and we will explain how decimal parity works :

[Image: vM9eoas.png]

It’s just the circomference of a circle divided into 9.
This is your most important tool to visualise the relationships between the numbers and their parity :

First we will attempt to explain decimal parity.

When counting from 1 to 9, we progress simply clockwise starting at one, untill we reach 9 :

[Image: RET4Ip0.png]

After 9 comes 10, but we see in the picture that we are back at one.

10=1 reduced, so this adds up to what we see in the pic.





[Image: baZxCtJ.png]

1, 10 and 19 have the same parity they share parity 1). So do 2, 11 and 20 (they share parity 2), and so on…
You can go as high as you want, with or without decimals, it will ALWAYS add up.

When going from 9 back to 1, a normalisation must occur by adding a 0 to the start of the next cycle.
When going from 18 to 19, it is still the same parity of 9 going to 1 again by adding a 0 (an important notion to factor in!). 27 to 28 is still 9 going to 1 by adding a zero. The 0 is of upmost importance for a new cycle to start, but yet it’s role is played out allmost completely unnoticed…in fact without this normalisation the entire system of parities would collapse.

Now for the relationships between the parities. The same parities will keep arrising whether you add, subtract, divide or multiply any digit. It even works just the same if you use decimals, but for the sake of simplicity we will work with the integers alone.

We will however show this in the most elaborate way, by summing them all up, one by one, showing the sequences of numbers formed and how they are connected with each other. After that we will show them again, but also showing the PATTERNS that arrise from the parities, and how the SAME connections between the parities can be derived from the patterns themselves.

If you read on, having understood the above, you will be amazed at the manner which in which this connects it all, Mr. Anderson…

First we add, going through the entire cycle from 1 to 9 :

[Image: RET4Ip0.png]

We always start at the position of 9, because 9 is at the centre of the entire system :


9 +2=11=2
2 +2=4
4 +2=6
6 +2=8
8 +2=1
1 +2=3
3 +2=5
5 +2=7
7 +2=9

9+3 =12=3

9+4 =13=4

9+5 =14=5

9+6 =15=6

9+7 =16=7 ______72+7= 79= 16 = 7
16+7=23=5 ______79+7= 86= 14 = 5
23+7=30=3 ______86+7= 93= 12 = 3
30+7=37=1 ______93+7= 100= 1 = 1
37+7=44=8 ______100+7= 107= 8 = 8
44+7=51=6 ______107+7= 114= 6 = 6
51+7=58=4 ______114+7= 121= 4 = 4
58+7=65=2 ______121+7= 128= 11 = 2
65+7=72=9 ______128+7= 135= 9 = 9

9+8 =17=8

9+9 =18=9

Lots of things are allready revealed.
First of, every sequence starts and ends with 9 (9 as starting point, and last result is also always 9).
The addition of 3 only results in 369 throughout, and the addition of 6 only results in 936 throughout, showing the special relationship between these three numbers. 3 and 6 are the left and right hand of 9, and the guardians of the various levels, or loopholes, within the Matrix.

By looking at the final results above, we see these sequences from additions of 1 through 9 :


Look CLOSER, Mr. Anderson !
The entire grid is perfectly symmetrical, ALL ENCAPSULATED by the 9’s.
If you think it is not ‘fully’ encapsulated by the 9’s, you are forgetting one thing, Neo…
Add the INVERSE symmetries and stick them to the grid, and you get this :

[Image: zLaZYnc.png]

If you notice both the perfect symmetry and the encapsulation, Mr. Anderson, then you are paying attention…

The entire grid is in perfect symmetry, AND all occurs WITHIN the 9.
This entire grid, including the symmetry is reveiled from ONLY adding from 1 to 9, following the numeric reduced parity of the numbers.
The 3’s and 6’s are what binds and maintains the symmetry within.

If you look closely you can see how they do this :

[Image: 2pyaywh.png]

And they ROTATE around the central 9, all the way throughout and within the structure :

[Image: ml1t7b.png]

They form the initial rotating Matrix, around which all other patterns are binded, and they also form the MAIN anker-points which interconnect the various matrices in multiple dimensions, connecting all matrices wihin THE Matrix, all in symmetrically inversed polarity AND parity.

In the initial calculation tables above, in BLUE, we have pointed out some parts of the underlying sequences within the calculations (and one example with the +7 how the same parity is retained even in the higher numbers) from which you can derrive the same portrayed symmetry, but by simply laying them in a grid you can instantly visualise the complete symmetry without any further calculations…

Simplicity, Mr. Anderson. Even the most complicated things are constructed from the same SIMPLICITY OF 9. Within the 9, ALL patterns within the Matrix occur, even for instance the doubling sequence that constructs cel division, DNA sequences, bits and bytes, etc…
(->1 2 4 8 16 32 64, which comes from 1 2 4 8 7 5 1 parity).

64 represents one replicative UNIT. Upon each consecutive 64 (parity 1), the complexity of replication increases 1 level.
Notice also that within this process, 63 (=parity 9 on level 7) is the FINAL word within each replicative unit, again showing the additional and special role of 3 and 6.

Let’s look at that doubling pattern (1248751) within this grid :

[Image: 2a4odqv.png]

We can immediately notice, Neo, if you haven’t before, that it is simply the entire grid without the 3 and 6, still all revolving around the 9.
This is the doubling sequence of 1-2-4-8-16-32-64, but this little grid only shows 9 replications within a unit. To see the entire unit of 64, you’ll have to add another 54 replications outward with the same symmetry.

This pattern represents ALL life within the Matrix, held together by the forces of the 9, 3 and 6. The 1’s and 4’s you see in this grid form the conciousness of the ONE.
The constructing force within THE Matrix is not visible. The 3’s, 6’s and 9’s are also not visible within this pattern. If you are aware, however, you can derrive the force of 9 above 6 and 3 within the real thing, like it is portrayed here, the force which defines the entire construction of the Matrix and the life locked away in it.

Now for another way to see exactly what kinds of patterns are actually formed within this little matrix, we will work with the circle again :

Here are all additions from 1 through 9, showing well defined geometric patterns by simply drawing the sequence, always starting at the position of 9 :

Addition of 1 (= 123456789) :

[Image: eg8lm8.jpg]

Addition of 2 (= 246813579) :

[Image: 3583nkz.jpg]

Addition of 3 (= 369369369) :

[Image: otoj5z.jpg]

Addition of 4 (= 483726159) :

[Image: j62wbb.png]

Addition of 5 (= 516273849) :

[Image: j62wbb.png]

Addition of 6 (= 639639639) :

[Image: otoj5z.jpg]

Addition of 7 (= 753186429) :

[Image: 3583nkz.jpg]

Addition of 8 (= 876543219) :

[Image: j62wbb.jpg]

Addition of 9 (= 999999999) :

[Image: ify4k5.png]

This actually simply forms the entire circle in which all other patterns exist. AGAIN showing you that all occurs within the 9.

If you look closely at all patterns formed by the additions from 1 to 9, you will notice the following :

1 and 8 share the same pattern (1 is forward, 8 is reverse)

-> 1+8 = 9

2 and 7 share the same pattern (2 is forward, 7 is reverse)

-> 2+7 = 9

3 and 6 share the same pattern (3 is forward, 6 is reverse)

-> 3+6 = 9

4 and 5 share the same pattern (4 is forward, 5 is reverse)

-> 4+5 = 9

The parities which share the same pattern, always add up to 9 when combined, which MEANS that both polarities of the pattern sum up to the whole construction of the pattern within the Matrix.
9 rules all others, with the parities and polarities of 3 and 6 directly by it’s side, holding the entire construction together.

Polarity can be reversed, in other words 4 can be forward and 5 reverse or vice versa, as long as the symmetry is there…
Same thing as +4 and -4 in the old-fashion math for instance, but old-fashion math is WAY, and we mean WAAAAAAY to complicated for the mass conciousness of the ONE to actually understand anything explained with it. Number parities however can visualise it all to even the most dorment minds, and the most complicated calculations become as simplified as they can get, Neo…

Subtracting, multiplying and division ALL result in similar sequences and patterns, showing the exact same intricate level of symmetry, AND still with 3 and 6 holding it all together within the 9.
If needed or wanted, we will post those results aswell.




Saturn Worship – The Black Cube of Cronus


You might not know it, but the entire world has been worshiping Saturn for
thousands of years. The cult has never stopped and its rites are still present
to this day. Saturn, dubbed the “Lord of the Rings”, is the reason why we
exchange rings at weddings or put halos on the heads of godly people. This
article exposes the attributes of the god Saturn and the perpetuation of his
cult through in pop culture.
Since ancient times, sages gazed at the stars, admiring their heavenly glow
and attributing them godly powers, based on their effect on humans. Before the
Great Flood, Saturn was regarded by all mankind as the supreme god and ruler of
the kings. Occult researchers affirm that Saturn ruled the kingdom of Atlantis
and became the divine ancestor of all earthly patriarchs and kings. The cult has
been perpetuated through numerous gods during Antiquity:

“Chronos, or Saturn, Dionysos, Hyperion, Atlas, Hercules, were all
connected with ‘a great Saturnian continent;’ they were kings that ruled over
countries on the western shores of the Mediterranean, Africa and Spain. ”
Baldwin, Prehistoric Nations
In Egyptian mythology Isis is considered Saturn’s eldest daughter:

“I am Isis, Queen of this country. I was instructed by Mercury. No one
can destroy the laws which I have established. I am the eldest daughter of
Saturn, most ancient of the Gods”


United Nations headquarters
meditation/prayer room.





Dwave Quatum Computing Cube Symbolism for Gateway Portals
and Digital World creation for deception!
Cloning symbolism
Projection of Digital World they
try to create.
Illuminati and Freemasonic symbolism
of the Black and White etc…


Black Cube of Mecca..that they circle around it like Saturn rings!


The Borg Cube (which represents the Black Cube) passes by Saturn
Star Trek: The Next Generation  – 4×01 – The Best of Both Worlds (Part 2)


Saturn in Semitic Civilizations
Semitic civilizations referred to the god Saturn as “El”. The supreme deity
was represented by a black cube. We can find instances of the cube across the world.



Many esoteric researchers affirm that the name Is-Ra-El is the combination of the names of ancient pagan
Isis, Ra and El.


The Greeks and the Romans also worshiped Saturn as a cruel deity. Here’s a
brief summary of the mythology of Saturn in the western world:
With the deposing of his father, Saturn became the ruler of the Universe
for untold ages and he reigned with his sister, Ops, who also became his wife.It
was prophesied that one day Saturn would lose power when one of his children
would depose him. To prevent this from happening, each time Ops delivered a
child Saturn would immediately swallow it. When her sixth child, Jupiter (Zeus),
was born, Ops had him spirited away to the island of Crete. She then wrapped a
stone in his swaddling clothes. Her deception was complete when Saturn swallowed
it, thinking it was the child. When Jupiter was grown, he secured the job of
cup-bearer to his father. With the help of Gaia, his grandmother, Jupiter fed
his father a potion that caused him to vomit up Jupiter’s five siblings, Vesta
(Hestia), Ceres (Demeter), Juno (Hera), Pluto (Hades), and Neptune

-Wikipedia, Saturn (mythology)
Saturn always had a negative, if not evil significance. In ancient times, it
has been called “The Greater Malefic” which was opposed to Jupiter, “The Greater
Benefic”. Saturn is esoterically associated with man’s limitations,
restrictions, death and decay. His Greek name was “Kronos”, the ruler of time,
time being the main factore inevitably leading to the death of
mortals.Traditional representations of the “grim reaper” originate from the
attributes of the god Saturn, who held the sickle with which he slain his father.



Saturn has also been associated with Satan and this, for numerous reasons.
First, many authors argue that the word Satan is derived from the word Saturn.
Second, Saturn is associated with the color black as well as Satan. Third, Ancients considered Saturn to be the farthest planet from the sun , the latter
being associated with the principle of Good. (Note that Pluto never was considered a planet). Saturn is consequently the celestial body that is the less
exposed to the sun’s divine light and thus associated with the coldness of the
principle of Evil. Finally, the “great god Pan”, the horned deity, represented
Saturn in ancient paganism. This half-man half-goat creature is considered the
ancestor of our modern depictions of Satan.

“Pan was a composite creature, the upper part–with the exception of
his horns–being human, and the lower part in the form of a goat. (…)The pipes of
Pan signify the natural harmony of the spheres, and the god himself is a symbol
of Saturn because this planet is enthroned in Capricorn, whose emblem is a goat”
– Manly P. Hall, Secret Teachings of All Ages
So Pan was depicted with horns due to the fact it represented Saturn, the
ruler of the house of Capricorn which symbol is a goat.
Pan was the controlling spirit of the lower worlds. He was portrayed roaming
through the forests, penis erect, drunk and lascivious, frolicking with nymphs
and piping his way through the wild. We might say he ruled the lower nature of
man, its animal side, not unlike Satan.

Despite acknowledging its association with Evil, secret societies find the
veneration of Saturn necessary to obtain illumination. It is the necessary
counterpart of the principle of Good. Masonic authors clearly associate Saturn
with Satan:

“Saturn is the opposite to Jupiter; his symbol is the cross above the
sign of Luna. He is the Satan, the Tempter, or rather the Tester. His function
is to chastise and tame the unruly passions in the primitive man.”

– J.S. Ward, Freemasonry and the Ancient Gods
Probably the most extreme example of a secret society worshiping Saturn’s
Evil principle is the “Fraternitas Saturni”. This occult organization is based
in Germany and openly embodies the hidden side of Saturn worship.

“The Fraternitas Saturni (FS), the Brotherhood of Saturn, has become
known to English readers through fragmentary descriptions which emphasize the
sensational, sex-magical aspects of this lodge’s work or else its darker, more
Satanic, side.This is understandable in light of the fact that the FS is (or
was) the most unabashedly Luciferian organization in the modern Western occult
revival, and its practice of sexual occultism perhaps the most elaborately
detailed of any such lodge. The FS represents a unique blend of astrological
cosmology, neo-Gnostic daemonology, sexual occultism, and Freemasonic
organizational principles. This grand synthesis was originally the vision of one
man, the long-time Grand Master of the FS, Gregor A. Gregorius.”
– Stephen E. Flowers, Fire & Ice: The History, Structure, and Rituals of
Germany’s Most Influential Modern Magical Order: The Brotherhood of Saturn




The great amount of symbols associated with this obscure deity only emphasize
its importance in human history. The advent of the monotheistic religions of
Christianity, Judaism and Islam confined the worship of Saturn to occult
circles. As we saw here, the Lord of the Rings is still omnipresent in popular
culture but only recognized by those who have eyes to see and ears to hear.


Loki arrives on Earth standing upon a
black hexagon. The hexagon is a subliminal 2D representation of a 3D

The Avengers (2012)
In geometry, a hexagon (from Greek ἕξ hex, “six”)
is a polygon with six edges and six vertices. A regular hexagon has Schläfli symbol . The total of the internal angles of any hexagon is 720°.


Loki represents SET (Saturn/Satan), the
Ancient Egyptian God of Evil, Darkness, Chaos, War & Conflict.
He is seen holding a staff, which represents the
War Scepter.

The Avengers (2012)


The Black Cube represents the ‘All-Spark’ (cube)
Transformers (2007)



In the Ausarian drama we find that Ausar (Greek: Osiris) is chopped into 13 pieces by Set. Auset (Isis) collects all of his pieces save his phallus. Horus, son of Ausar and Auset sets out to avenge the death and dismemberment of his father by confronting Set. Horus is victorious over Set and Ausar, being brought back from the dead becomes lord of the underworld. It is this drama that gives

us the cosmic conflict between good and evil, evil being embodied by Set. This is not to say that Set was always seen as
an evil character in Ancient Egyptian
theology. There are many times in
Ancient Egyptian history where conflicts
between different “houses” lead to the depreciation of one god relative to another.

As in most polytheistic faiths, the characters involved differentiate
themselves from the Western tradition of a devil in that all the gods are
closely related. In this case, numerous
historic texts suggest that Set is the
Uncle or Brother of Horus and
in the “defeat” of Set, we see another separation
from the norm in the devouring/assimilation
of Set into Horus with the result of
Horus having depictions of both the falcon
head and the (unknown animal) head of
Set. This (like Buddhism) represents a dissolution of dichotomy.



Do U C What EYE C? The XCUBE


XBOX ONE with Kinect or X(CUBE) One Hive Mind to CONNECT
Click Pic to Enlarge

– See more at:

Satanism & Saturnism Pt.2 [ Above: Brotherhood of Saturn fraternity ring ] Fraternitas Saturni (lat.: “Brotherhood of Saturn”) is a German magical order, founded on Easter 1928 by Eugen Grosche aka Gregor A. Gregorius and four others. It is one of...

Satanism & Saturnism Pt.2

 [ Above: Brotherhood of Saturn fraternity ring ]

Fraternitas Saturni (lat.: “Brotherhood of Saturn”) is a Germanmagical order, founded on Easter 1928 by Eugen Grosche aka Gregor A. Gregorius and four others. It is one of the oldest continuously running magical groups in Germany.[1] The lodge is, as Gregorius states, “concerned with the study of esotericism, mysticism, and magic in the cosmic sense”.[2] Today its purpose is in working on the spiritual evolution of humanity by means of development and advancement of the individual being. This is to be attained by mental and ethical schooling of the personality and complete mastery of esotericism and occultism. The FS adopts a system of 33 degrees to reach this goal. The lodge claims further no political or economical objectives. It propagates ideals of freedom, tolerance and fraternity.[3]

Symbol of the Fraternitas Saturni


The background of Saturn worship goes back to 600 BC with Greek poet Hesiod’s ‘Works and Days’ where he discusses the various ages of man. One of the ages was referred to as the Golden Age. The Golden Age was referenced in several prominent ancient cultures, similar to how the cultures would adopt each other’s gods and rename them. The ancient Romans worshipped the god Saturnus, who was the god of agriculture and time, and his reign was known as the time of Golden Age of peace and harmony. The Greek god that was the same as Saturnus was Cronus, the youngest of the Titans. The Carthaginian god Ba’al (or Moloch) was the same god, and devoured children (similar to Cronus who ate children).

For the rest of the beginner’s guide to Saturn Worship, please pickup my book: A Grand Unified Conspiracy Theory: The Illuminati, Ancient Aliens and Pop Culture. I cover all of the images you see below and detail the full extent of Saturn Worship that includes black cubes, twin towers, Golden Ages, and other symbolism. I also have the full review of the banned documentary about the murder of Princess Diana Unlawful Killing.

Salt, from Godlike Productions forums presents this theory:

The solar system looks as though it was constructed as a “time trap.” since the entities are so interested in governing this portal, i would be willing to postulate that this is the device that brings back Christ (The Kryst frequencies). they do not, of course, want this to happen.

Christ uses this portal to return. the device is destroyed. liner time is no longer imprisoning us.

we are locked into linear time, but it is only temporary. this is why the illuminati want control of the Linear Time Device.

Kubrick revealed many of these important facts. the elite know. Kubrick was murdered for trying to tell.

Then i think its important to go back and watch the whole series from start to finish. It clearly profiles the Saturnian cults which are Satanic and how the illuminati are involved.

Afterward, there are a couple of additional videos regarding the Kubrick leaks in Odysee, AI, Eyes Wide Shut that lend data to this subject.

Not all of this is “new” info, but it is “now” info, and important none-the-less.

Watch the documentary here: [ ]

Get inside the brotherhood’s own doctrine and discover their revealing secrets and practices, – FIRE & ICE: MAGICAL TEACHINGS OF GERMANY’S GREATEST SECRET OCCULT ORDER Read here [ ]

There is an ancient Saturn cult in power today. It is composed of a Who’s Who of elites and celebrities. And they practice an ancient occult science the Bible warns us about in Ephesians 6:12. This Pre-Flood cult harneses the power of planets and hinders mankind with dark forces using blood sacrifice. It is most likely the home of Fallen Angels.

This video is an introduction to this reality with more to come. [ ]

Saturn – Cosmic Keeper of Time…ts/saturn.html

If Jupiter is the King of the Planets, then Saturn is the Queen of the Planets. Saturn, in ancient days, was known as Chronos, the keeper of Time. Chronos, was the son of Uranus and his wife, Rhea (the firmament). Chronos’ wife was Gaia (the Earth). Saturn is the mother and giver of all forms, both mother and father, and posessing qualities of both sexes.

The rings around Saturn were easily seen by the ancients, and limit the planet within them, as time limits our existence here on Earth. Saturn is the last planet the ancients could see with their primitive telescopes, and so we have 7 days in the week, each day named after a corresponding planet. This is most evident from the French (or Spanish) names for the days of the week, as follows:

  • Sunday – SUNday – pretty obvious, eh?
  • Monday – MOONday – Lundi (Luna’s Day)
  • Tuesday – MARSday – Mardi (Mars’ Day) (eg Mardi Gras)
  • Wednesday – WODEN’sday – Mercredi (Mercury’s Day)
  • Thursday – THOR’sday – Jeudi – (Jupiter’s Day)
  • Friday – VENUSday – Vendredi – (Venus’ Day)
  • Saturday – SATURNday – Samedi – (Saturn’s Day)

In fact, the word MONTH comes from the length of time the moon takes to complete one revolution around the Earth (a MOONTH) or 28 days. There are 13 lunar months and 12 solar months in each year of our Earth.

You can also go to The Birth of Islam, a fascinating essay in progress which discusses the theory that the Ancient Egyptians used just such a 10-day week, and it was subsequently reduced to 7 days for various reasons. The author declares Egypt held on to her “ancient celestial tradition of reality” until it was replaced with the “7 days of creation, the 7 spirits of God, and the 7 wandering bodies in the heavens” for which our days of the week are so aptly and obviously named.

Days of week names are related to occult powers inside the man (alchemy):

7. Sun-day – Gold – Crown chakra – URANIC gate – Point of soul

6. Moon-day – Silver – Third eye

5. Tues-day (in italian marte-dì or Mars day) – ETHER – Iron/Sulphur – Throat chakra

4. Wednes-day (in Italian mercole-di or Mercury day) – AIR – Mercury – Heart chakra – Point of spirit

3. Thurs-day (in Italian giove-di or Jupiter day) – FIRE – Tin – Solar plexus chakra

2. Fri-day (in Italian vener-di or Venus day) – WATER – Copper – Sacral plexus chakra

1. Satur-day (Saturn day) – EARTH – Lead/Steel/Salt/Ammoniac – Root chakra – TELLURIC gate

The same for the months that have an alchemy meaning:

1. Aries, FIRE, Calcination
2. Taurus, EARTH, Congelation
3. Gemini, AIR, Fixation
4. Cancer, WATER, Dissolution
5. Leo, FIRE, Digestion
6. Virgo, EARTH, Distillation
7. Libra, AIR, Sublimation
8. Scorpio, WATER, Separation
9. Sagittarius, FIRE, Incineration
10. Capricorn, EARTH, Fermentation
11. Aquarius, AIR, Multiplication
12. Pisces, WATER, Projection


Hotel Saturnia logo with its Dragon looks very fishy like Dagon known as Saturn (EL)

Hotel Saturnia & International
S. Marco 2398 – Via XXII Marzo Venice – Italy


Hotel Saturnia is located in the heart of Venice, only 250 metres from St. Mark’s Square


“SATURN wandered to Italy, where he ruled as king in the Golden Age and gave the name SATURNIA to the country.”(Encyclopedia Britannica, “Saturn,” p. 231)

Pope Benedict XVI wears a “saturno hat”, inspired by the ringed planet Saturn, to shield himself from the sun as he waves to the crowd of faithful prior to his weekly general audience in St. Peter’s Square at the Vatican Wednesday.

The Pope’s Mitre is simply taken from once again Saturnknown as Dagon
Catholic means UNIVERSAL and it is the sum of Christianity , mitraism, cult of Saturn and other pagan rites and cults. This in order to create a super-religion with the purpose to dominate and enslave people under the Roman empire.

Another target of catholic religion was to bind temporal power with spiritual power.

Vatican is a monument to occult powers:

URANUS AND THE MYTH The implications of Uranus in the chart seem to be reversed in comparison to the mythical meaning of Ouranus. Uranus is the sun of the earth goddess Gaea. And at the same time her husband. The children born out of this relationship were imprisoned but one of them, Cronus (later called Saturn) was able to castrate his father (encouraged by his mother). The genitals fell into the see and so Aphrodite was produced (Venus).


Saturn is the mythical son of Uranus. Saturn is the rebel, but Uranus is prominent in the charts of disasters, revolutions and rebellious people. It is Uranus who locks in his children and yet Uranus is the symbol of liberation. I must add to this that afflictions with Uranus are seen at the time of arrest and loosing freedom or being robbed of freedom. Like in the case of Jeanne d’Arc and Ringeard (one of the trappist monks murdered in Algeria). Sometimes Uranus makes free, but the person concerned is dead. Saturn is the law, but Uranus is the shocking arrest. In short: the myths of Saturn and Uranus seem to be twisted and turned. Or we might consider the fact that the relationship Uranus had with his mother was abnormal and extraordinairy and Saturn (Cronus) ended the incest.

URANUS IN THE SIGNS Uranus is now in the astrological ‘sign’ of Pisces. Pisces is the period for church and religion, especially the Christian belief and then specifically the roman catholic church. Uranus is the planet of renewal and weak in the sign of Pisces.

This section is from an occult book by franz bardon on the intellegences/elemental beings from saturn, written in the 50s i think:

10. The Saturn Sphere

The Jupiter sphere does not bring us to the end of the descriptions of the
planetary system of our cosmos. The next sphere to mention is the Saturn
sphere. Like the Mars sphere, this sphere is very hard to contact, and only a
well trained sphere magician should dare to embark upon it after having gone
through different initiating systems with a few original intelligences and after
having gathered much experience, during the course of many years, in mental
wanderings to the individual spheres and thus feeling almost at home in them.
Not every human being is strong enough to stand up against the oscillations
of the Saturn sphere, since they have the depressing quality of a nightmare.
The Saturn sphere is, in fact, the socalled Sphere of Karma. Its intelligences
may be regarded from man’s rational intellectual point of view, the Judges of
all beings, planets and spheres. From the magical quabbalistic point of view,
direct contact with any of these judges has no practical value. If, however, the
magician considers himself mature enough and well acquainted with the
spheres, he might as well try to get into contact also with the intelligences of
the Saturn sphere. I desist, however, from giving any description of the
individual intelligences of the Saturn sphere, even from mentioning their
names and seals, for it could so happen that some presumptuous human
being, without thinking of the consequences, would dare to call up a Saturn
being by evocation. If the person is, in such a case, not strong enough ro
resist the vibration of that Saturn intelligence, not only his physical, but also
his astral death becomes unavoidable. Therefore a general description of this
sphere will suffice for the mature and wise, and such will, in spite of such a
short description, be able to get a clear picture of the effectiveness of the
Saturn sphere.
The few Saturn intelligences that have been mentioned in known books
written by authors such as Agrippa, Khunrath, and others, are not the highest
intelligences of this sphere and have, in general, only a subordinated range of
competence when compared with the genuine original intelligences of the
Saturn sphere, forty-nine in number. The already known intelligences named
Agiel, Arathron, Cassiel, Machatan, Uriel, etc., have, therefore, not much
importance in the Saturn sphere and are by no means original intelligences.
However, they show a certain affection for the zone girdling the earth, are
friendlier with the magician and therefore also easier to get into contact with.
What these intelligences can offer the magician in respect of magic and
quabbalah, the latter is sure to get to know much more from the intelligences
of any other planet’s sphere. I am talking in this respect from the point of
view of personal experience, and every magician is able to find out the truth
of these words himself. What, for instance, Arathron can offer the magician,
each of the 360 heads of the zone girdling the earth can also do, without the
magician having to travel to the Saturn sphere. The same is true of Agiel and
the other so-called intelligences of the Saturn sphere mentioned in the
common grimoires. During wanderings, in my mental body, through the
Saturn sphere a long time ago, I personally came across Agiel and Arathron
and conversed with them, so I am recording here personal experience.
As far as the 49 original intelligences of the Saturn sphere are concerned, it
should be mentioned that they are responsible for the original Karmic principle
of all spheres, especially for the doings and effectiveness of all the negetive
beings of each sphere, beginning with our physical world. In accordance with
Divine Providence, they allow for the bad effects of negative beings. They are
in charge of the powers and effects of the principle of destruction in the whole
cosmic hierarchy. They see that justice is done and – depending on the
approval of Divine Providence – let negative effects become reality by their
subordinate beings. The Saturn intelligences allow wars not only on our
planet, but wherever love and hate exist; they let the negative principle work
up to a certain point and they are the ones that have to judge rigorously upon
human beings and beings of all spheres in accordance with divine orderliness
and legality. Therefore the Saturn intelligences are regarded as the so-called
Judges and Executers of Fate in the word’s highest sense. Moreover, they
decide upon how long magicians who have concluded a pact with beings
negative or positive – have to remain under the power of the relevant beings.
Each original intelligence of the Saturn sphere has a certain range of power:
they have each a certain planet and a certain sphere under their command. If
the sphere magician is interested in learning about the range of effectiveness
of anyone original initiator of the Saturn sphere, about his influence and
subordinated planet, he can get exact information from a subordinated
intelligence like Agiel or Arathron. From what has been said here, the
magician will gather that he need not actually avoid the Saturn sphere, but he
will less care to contact its 49 original intelligences. It is not a pleasure to see
the doings of negative beings or to watch mentally how they are controlled
and punished. One needs strong nerves and a strong mental steadfastness to
do that. So much about the Saturn sphere. The seals of Agiel, Arathron and the other inferior intelligences of the Saturn sphere are generally known.
Every magician will take heed not to reveal the names and the seals of the 49 original intelligences of this sphere to any immature person and will fully
understand why I desist from giving details.

The SATURN’s place is the Latium, Lazio in italia, where is founded ROME.

This black cube is a remnant of the ancient worship of El.


“The Black Stone is a Muslim object of reverence, which according to Islamic tradition dates back to the time of Adam and Eve. Many consider it to be a Tektite. It is the eastern cornerstone of the Kaaba, the ancient sacred stone building towards which Muslims pray, in the center of the Grand Mosque in Mecca, Saudi Arabia.”

Twin towers:

Twin towers represent Saturn, the Freemasons believed that the entrance of sacred and mysterious places should be guarded with two pillars. The towers are seen throughout various cultures and are frequently referenced as Hercules pillars. Solomon’s Temple featured the two towers Boaz and Jachin and this tradition was followed through the secret societies to display these twin towers/pillars as a show of who is in charge.

Arguably, the attack on the World Trade Center “Twin Towers” is an outright demonstration of an internal war between factions of this Illuminati agenda.

The twin towers are seen on the world’s first currency, from the Spanish ‘piece of eight’ coin that was internationally used to trade goods with silver back in the 1700s. The dollar sign is actually just the scroll and two pillars found on this first coin, so we can all see that the currency trading is more Saturn worship (as discussed earlier in this article with the emphasis on materialism).

piece of eight

More twin towers featured in The Hitchhiker’s Guide to the Galaxy:


And a “coincidental” shot of Saturn in the background of same film:

A Hitchhiker's Guide To The Galaxy

And we also have the twin towers concept in films such as Lord of the Rings which has multiple images in it. It has the twin towers, an all seeing eye, crescent, and the towers are in the shape of bull horns; all pointing to Saturn worship. Sauron worked with the dark forces of the Dark Lord, Morgoth as a Satanic force.

Not to mention the story revolves around the ring (hence the name Lord of the Rings) which is yet another reference to the rings of Saturn. The ring was an evil artifact created by Sauron and helped create illusions (you can read into this as the virtual reality Matrix world we live in).

“One Ring to rule them all, One Ring to find them, One Ring to bring them all and in the darkness to bind them”

All Seeing Eye:

This is one of the most common symbols that occur throughout several entertainment outlets and also in wealthy elite families. The tie-in with Saturn is that the All Seeing Eye is seen on the southern pole of Saturn as an unexplainable hurricane storm photographed by NASA’s Cassini spacecraft:

Fire, light and the symbol of the Phoenix bird:


David Icke The Saturn Matrix & Saturn Symbolism

Metatronics In Our Crop! – “Alien Geometry”

This page has been created to provide graphics and information about the radio show that took place September 10, 2009. The show as an interview of myself, Joseph E. Mason, by Rick Osmon, the host of Oopa Loopa Cafe Radio. Click on this link to listen to the show —


The audio file can also be found here (a slow loading page) —

Find the listing, and click on “Play.” You may have to reopen this page in another browser. Alternately, you can click on “Download” and play the audio from your own computer.

The primary topic was about the Code of Carl Munck. The Code is about the exact positioning of ancient sites around the world. A key part of the Code involves a system of numbers which also appear in myths, religions and metrological systems from the ancient past. The same numbers sometimes appear in crop circle formations and dreams.

Carl’s website is at: Pyramid

The following information, taken from or Code page will serve as an introduction to Carl Munck’s Code —

Excerpted from:
Hard Evidence of a Grand Design to Creation

By Joseph E. Mason

     The great mysteries of life are quite elusive.  We do not have the “hard facts” needed to feel sure that our theories about the mysteries are true.  Sometimes we feel sure, but convincing others is not so easy.  Alas, they want “facts,” and we cannot produce them.  Well, times are changing.

This is the start of a series of articles that will present many “facts” concerning some major mysteries of our world.  These “facts” will show evidence that –

  The ancient sites around the world are very precisely positioned on a global coordinate system in relation to the position of the Great Pyramid at Giza.

   The positions of the sites are given in the geometry of their construction.

  A very ancient system of numbers was used in the system, which we will call “Gematria.”

  “Gematrian” numbers are found in ancient myths and religions, including the Bible.

   Gematrian numbers were used in systems of weights and measures by ancient peoples, including the Greeks, the Egyptians, the Persians, the Babylonians and the Romans.

  The ancient Mayans used Gematrian numbers in their very accurate timekeeping.

  The Code system uses mathematical constants, such as pi and the radian.

  The system also uses conventions that are still in use, such as the 360 degree circle, 60 minute degree, 60 second minute, the base-ten numbering system, the 12-inch foot, and the 5280-foot mile.

  The Nazca Line ground markings “locate themselves” on The Code Matrix system.

  Crop circle formations suggest the same ancient numbers by way of their positions and measurements.

  The very ancient “Monuments on Mars,” including “The Face on Mars,” were positioned in exact locations, just as the ancient sites on Earth.


Explanation of The Code System

   The Code system is quite like the cartographic system we still use today . . . which was probably handed down to us from very ancient times.  In both the old and new reckoning systems, the earth is divided into 360 degrees around the equator for longitude coordinates, and latitude coordinates are reckoned at 90 degrees, from the equator to either Pole. Each degree is further divided into 60 “minutes,” and each minute is divided into 60 “seconds.”  Thus, by giving the degrees, minutes, and seconds of East or West longitude and same for the North or South latitude, we can “locate” any point on the earth, similar to the way we give two street addresses to locate a place in our cities and towns.  The big difference between the two systems is that today we use Greenwich, England as the starting point (zero degrees), or “Prime Meridian,” for the longitude coordinates, whereas the ancients used the Great Pyramid of Giza. The difference in longitude between the two Prime Meridians is 31 degrees, 08 minutes, 0.8 seconds, so this must be taken into account when calculating “The Code.”


Introduction to The Code

Stonehenge – Circular Data Base

by Michael Lawrence Morton

   It was Carl P. Munck’s article on Stonehenge, in a newsletter put out by Richard C. Hoagland called “Martian Horizons” in the early 1990s, that really got me interested in Munck’s work. Munck calls himself an archeocryptographer . . . and he is the pioneer in this new field, having re-discovered an amazingly-advanced “geomath matrix” from very deep antiquity, encoded in the precise latitude/longitude positions of ancient pyramids, mounds, effigies, monuments, and stone circles.

Munck has been able to confirm the reality of this incredible discovery (or, re-discovery) by simply pointing-out what is *there* for all to observe, by way of modern satellite-accurate maps, simple math, and a hand-held calculator. Indeed; aerial photography, satellite imaging, and calculators (computers) have proven essential for the birth of archeocryptography.

In his ‘decoding’ of Stonehenge, Munck first determined that the original Sarsen Circle was constructed of 60 stones . . . 30 uprights and 30 cross-pieces.  The Sarsen Circle, like any circle, has 360 degrees of arc on its circumference if we assume “our” circle/sphere math conventions. Here was a major key in this re-discovery process:  the hypothesis that 360 degrees on a circumference was ‘always’ an integral part of this advanced ‘matrix’!

Munck took the 60 original Sarsen Circle stones and multiplied them by 360 . . . 60 x 360 = 21600 . . . which “happens to be” the number of arc-minutes on any circumference, according to “our” math conventions.  And, 21600 also “happens to be” the number of Nautical Miles on the polar circumference of Earth.  Isn’t it interesting that one Nautical Mile equals exactly one ‘minute’ of Earth latitude?  Of course, we also “happen” to use the number 60 for “time circles” . . . minutes in an hour and seconds in a minute . . . as on the circumference of a clock face.  We are finding out (re-discovering) that the numbers 60 and 360 are not *really* arbitrary, in terms of what we know as time and space.

I think the number 60 is very “geometric” because it is devisable by many whole numbers into many *other* whole numbers, and this is part of the inherent “nature” of our number system.

(I now think that the distance, on a baseball field, from the pitcher’s mound to home plate . . . 60 feet, 6 inches . . . is not really *arbitrary*, either.  60 x 6 = 360.  But that’s a subject for another article.)


Latitude of Stonehenge

  Using the most accurate maps available, Carl P. Munck looked to see if he could find some meaningful relationship between the precise location of Stonehenge, on Earth in terms of latitude and/or longitude, and the number 21600. He noted its latitude of approximately 51 deg 10 min North. Suppose he would, for instance, divide the number 21600 by 51, and then divide that result by 10 ? Yes, this is what he did :

21600 / 51 = 423.5294118

Then, 423.5294118 / 10 = 42.35294118

Amazingly, Stonehenge centers itself precisely AT this latitude :

51 deg 10 min 42.3529 sec

Munck calls the product of a site’s (centered) degrees x minutes x seconds . . . the ‘Grid Latitude’ (or ‘Grid Longitude’ for the site’s centered longitude).

So; the Grid Latitude of Stonehenge is :

51 deg x 10 min x 42.35294118 sec North = 21600 North


Original Longitude of Stonehenge

  One of Munck’s major discoveries is his re-discovery of “our” (?) original prime meridian for longitude measurement.  He determined that the prime meridian for this ‘geomath matrix’ passes directly through the center of The Great Pyramid at Giza in Egypt.  So; we adjust our longitude (east or west, according to the site we are working with) by 31 deg 08 min 0.8 sec . . . the exact longitude distance between the current Greenwich, England prime meridian and the center of The Great Pyramid.  In our current system, the longitude for Stonehenge is –

01 deg 49 min 28.0173748 sec W.Greenwich (West of Greenwich)

In the ancient “Code” system, the longitude for Stonehenge was –

32 deg x 57 min x 28.8173748 sec W.Giza = 52562.89164 W.Giza

To explain – using the best maps available, we know that Stonehenge is centered at W.Greenwich longitude 01 deg 49 min 28 sec.  So; because Stonehenge is located not that far to the west of the Greenwich, England prime meridian, we *add* the (31 deg 08 min 0.8 sec) variance-distance onto the W.Greenwich longitude:

         01 deg 49 min 28 sec W.Greenwich
+ 31 deg 08 min   0.8 sec (variance)

32 deg 57 min 28.8 sec W.Giza

Now, if we multiply . . . 32 deg x 57 min x 28.8 sec . . . using the “numbers only” . . . we will be multiplying 32 x 57 x 28.8 . . . for a product of 52531.2.  At this point, we look through the matrix to see if there is a figure “close to” 52531.2 . . . and we find such a figure in the number 52562.89164 . . . which turns out to encode the ‘product’ of certain math constants and a certain astronomical/geometric number, the multiplied product of . . .

RAD (deg) x Pi x 2Pi x Square Root of 2160 = 52562.89164

57.29577951 x 3.141592654 x 6.283185307 x 46.47580015 = 52562.89164

Now, to “check” this figure . . . we start with 52562.89164 . . . and divide, first by the number of degrees, and then divide that result by the number of minutes, like this . . .

52562.89164 / 32 / 57 = 28.8173748 sec

We can see, here, that this “very precise” number of longitude seconds is only 0.0173748 (28.8173748 – 28.8) longitude seconds away from our *approximation* of 28.8 longitude seconds.  In terms of actual FEET, this would be a difference of approximately a Foot and a half. Yes, we now have figured out the W.Giza longitude of Stonehenge (the way Carl P. Munck did it) :

32 deg 57 min 28.8173748 sec W.Giza

In dealing with circles and spheres, we run into the math constants of Pi and RADIAN measure, and these constants are integral to this ‘geomath matrix’, along with the number 360.  Pi is the ratio of circumference to diameter of any given circle or sphere.  Radian (deg) is the arc-distance on the circumference that is equal to the radius of any given circle or sphere.  In degrees of arc, the Radian is equal to 57.29577951 (deg) . . . to eight decimal places.  It is an irrational number, like the Pi constant 3.141592654 . . . to nine decimal places.  

[Note from Joe:  The Radian can be figured by dividing 180 by Pi.]

The relationship between Pi, the Radian (deg), and 360 (deg) can be shown with this equation : RAD x 2Pi = 360

Now, back to the Grid Longitude of Stonehenge . . .

52562.89164 = RAD x Pi x 2Pi x Square Root of 2160 (46.47580015)

Here we have 4 terms, or quantities, multiplying to a number that encodes the precise original (Giza-based) longitude of Stonehenge.  And, each of these 4 terms are important “entities” that are integral to both the design and the essence of this re-discovered ‘matrix’.

Notice that the number 2160 is a “base-ten harmonic” of the number 21600, and vice-versa . . . the decimal point is simply moved one place, ‘horizontally’.

Note also that 2160 refers to:  diameter of The Moon in statute miles (regular miles), years in a Zodiac Age, and the total number of corner-angle degrees on the surface of a Cube.


Grid Point Value of Stonehenge

  The intersection point of latitude/longitude is represented in this ‘matrix’, for any given site, by the ratio of the Grid Latitude to the Grid Longitude, always greater-than-one. This resulting number is the Grid Point Value:

52562.89164 / 21600 = 2.433467206

[Joe’s note:  The intersection point-Grid Point Value is also called the “Coordinate Intersect,” or C. I.]

Munck has determined that the precise (matrix-valid) radius in Feet, of the Sarsen Circle at Stonehenge, is 48.66934411 . . . to eight decimal places.  If we divide that radius in Feet by Stonehenge’s Grid Point Value, we get . . .

48.66934411 / 2.433467206 = 20 . . . a base-10 harmonic of the ‘binary’ number 2.

Suppose we divide the Sarsen Circle radius in Feet into the RAD (deg) constant?

57.29577951 / 48.66934411 = 1.177245771

Munck found that this number is the TANGENT of the precise azimuth-of-orientation of the ‘Avenue’ at Stonehenge . . . 49.65408598 degrees.

He found further that 49.65408598 is equal to:  (e / Pi) RAD . . . where ‘e’ is the base of the so-called “natural logarithms,” observed in the ‘growth patterns’ of natural things such as conch shells . . . approximately the value 2.72 . . .

(2.72258992 / Pi) x RAD (deg) = 49.65408598

Stonehenge, of course, is a very important site in this re-discovered matrix.  Next to only The Great Pyramid at Giza, it is apparently the most important site on Earth in the Geomath Matrix.

Michael Lawrence Morton graduated from Franklin and Marshall College
(Lancaster, Pennsylvania) in 1973 with a B.A. degree in English Literature.
He is an independent researcher into lost and suppressed human history
and culture. He is an archeocryptographer and an alpha-numerologist.

To contact Michael Lawrence Morton, please e-mail him at, or phone him at 412-921-9116 in Pittsburgh, PA.


Gematria by HannaH

 The 5th Century B.C. trading empire of the Eastern Mediterranean Phoenicians saw the appearance of a writing mode in which alphabetical letters served as numbers.  Even at this early date, however, its roots were lost in the mists of time.  From this base evolved the Hebraic and later Greek systems of Gematria.  Both had reached a high degree of development by the 3rd Century B.C.

These alpha-numeric alphabets exhibited qualities and inter-relationships for which there is no logical intention.  Yet an entire symbolic teaching evolved around them which incorporated the principles of number, form, sound and astronomy.  Only number combinations and figures could be utilized to express this knowledge.  Today, we view numbers as merely an expression of quantity.  To the ancients, every number had its own character and identity; a place in an arithmetic chain that leads from one dimension of understanding to another.

This extraordinary system of arithmetic, or concealed geometry, form the link between the languages of literature and mathematics.  With this knowledge, ancient literature, metrology and Sacred Geometry can be viewed with new eyes.  With numbers, alphabetical cryptography becomes the law.  Biblical numbers and structure dimensions become alphabetical statements. The WORD (number) becomes FLESH (dimensional) for numbers are words.

(Example:  3168 = Lord Jesus Christ – – Kupios Inoors Xpioros)

HannaH – 1992


Carl Munck Finds Gematrian Numbers Related to The Code

   Among the material HannaH sent to Carl was some of the papers of the late Louis K. Bell, one of the foremost ancient metrologists of modern times.  Carl found that some of the numbers were the same as the ones he had found in the Pyramid Codex.  Carl gave examples in his newsletter –

 In ancient Babylonia, a long unit of measure called the “Kasbu” was well known.  It was 129600 “Susi” in length.  129600 is the square of 360, and in the global matrix, the same figure which was used to encode the West Giza Longitude of the Shark Mound on North Bimini Island.

 Also in Babylonian metrology was the “Maneh,” a unit for measuring volume.  It was equivalent to 7776 cubic inches by modern reckoning, but to them, 21600 “Um.”  21600 is the grid latitude of Stonehenge!  Is this only coincidence?  After all, at the time Babylonia was great, Stonehenge hadn’t yet been built – at least where our dating of the site is concerned, a date which could be WAY off the mark.

   A long unit of measure used by the ancient Egyptians was the “Schoenus,” a unit of 216000 modern inches.  The same figure finds the longitude of the Octagon at Newark, Ohio. Did they know that?

 The Roman “Load” was 3000 Libra; 2160 pounds today.  2160, the grid latitude of Newark’s Observatory Circle.  More coincidence?

 The earliest recorded bushel was equal to 2160 cubic inches.

 Over time, the ancient Egyptians employed several “cubits” in their body of metrology.  Among them was the so-called “Royal cubit” – 20.67 modern English inches.  20.67; the actual longitude of the Mycerinus Pyramid to the West of the Great Pyramid.

 In ancient Persia, a “talent” of gold was equal to 388800 grains.  388800 is what happens – exactly what happens – when we multiply MY-2 (7.396853329) by 52,562.89164, the grid longitude of Stonehenge.  Who told them about that?

[Joe’s note – 7.396853329 is a master Giza longitude. MY = Megalithic Yard]

Carl suspected that formal ancient metrology was rooted in the even more ancient pyramid codex. He went on to read into the subject, including the works of Charles Warren, and A. E. Berriman. Most of the authorities agreed that no one knew where ancient metrology came from – it was already in use when men first began writing.  “Obviously,” Carl said, “it is incredibly ancient.”


Carl’s Breakthrough in Gematria

 Carl listed some of the Gematrian numbers with their “Alpha” or “Word” meanings in the newsletter –

144    = Light

288   = Double light, the Kingdom of Heaven.

432   = Consecration (also the square root of the classical speed of light, 186624 miles per second).  Several Biblical references are also tied to it; Luke 8:15, Revelation 2:17, etc.

396    = Classical earth radius (3960 miles).

576    = Prophecy and Gospel.

864    = Time (2) the source of light and life, (3) Most Holy.

1152  = Witness (576 x 2).  Biblical references include Luke 14:26, Revelation 3:12, 12:11 and 19:9.

1296  = Circle of space (360 x 60 x 60).  1296 was also Plato’s favorite number.

1548  = Priest of God.

1728  = A-flat in music.

2304  = False Christs and False prophets (1 Cor. 14:22, Mark 13:12).

3168  = Lord Jesus Christ.

3888  = New Jerusalem (Rev. 21:2, 1 Cor. 12:27, Luke 8:21, etc.).

5184  = Victory over the beast (Rev. 15:2).

Carl explained that although this is quite confusing to the layman, even when the Biblical references are consulted, “the shamen of these sacred numbers are convinced that certain passages in Holy Scripture actually represent a codex in their own right, wherein certain communications from ancient men of wisdom were very carefully positioned in the Bible in order to secretly transmit vital information across time itself – not unlike what we are seeing in the pyramid codex.”

Carl listed some units of weights used by the ancient Romans, marking the Gematrian numbers with an asterisk (*):

*432 grains   = 1 Uncia

3024 grains  = 7 Septunx

648 grains     = 1.5 Sescuncia

3456 grains  = 8 Bessis

*864 grains     = 2 Sextans

*3888 grains = 9 Dodrans

*1296 grains = 3 Quadrans

4320 grains   = 10 Dextans

*1728 grains = 4 Triens

4752 grains   = 11 Deunx

2160 grains   = 5 Quintux

*5184 grains = 12 Libra

2592 grains   = 6 Semis


Another Roman system of weights was also listed:

36 grains     = 12 Semisextula 216 grains    = 72 Semuncia
72 grains     = 24 Sextula *432 grains   = 144 Unica*
108 grains   = 36 Sicilicus *5184 grains = 1728 Libra*
*144 grains = 48 Duella _

Surprisingly, many of the Roman numbers are the same as those used in the Gematrian system. Since metrology came before written records, and was likely handed down to the Romans, the number system came LONG before the Bible.

Even more amazing is the fact that the same system of numbers was used by the ancient Mayans in the West in their very precise time-keeping!  The Mayans used a 20-day month in their calendar. Carl showed the arrangement in the newsletter, again marking the Gematrian numbers with an asterisk (*):

20 days     = 18 kin *288   days = 20 bactun
36 days     = 20 uinals *576 days   = 20 pictun
72 days     = 20 tuns *1152 days = 20 calabtun
*144 days = 20 katun *2304 days = 20 kinchilton

(Joe’s note:  See “corrections” below this section)

The Mayans also broke down their hours into specific groups of minutes:

24 hours      = 144 minutes* 6912 hours  = 41472 minutes
48 hours      = 288 minutes* 13824 hours = 82944 minutes
*864 hours  = 5184 minutes* 27648 hours = 165888 minutes
*1728 hours = 10368 minutes 55296 hours = 331776 minutes


Continuing with Carl’s Breakthrough in Gematria

Since these number systems were in place long before the arrival of Columbus in the West, the mystery thickens.  Carl suggests that the ancient people held the numbers to be of vital importance, and thus placed them in their metrology and calendars in order to preserve them in the best way they could.  The numbers were there, before the beginning of writing.  The people who recorded the numbers via their special systems, probably did not know what the numbers really meant.

Carl checked the tangents of the numbers, and realized there were just four, and only two if the plus/minus signs are ignored.  He organized the numbers by their Tangents, and noted which number systems used them:  

  Common Tangent of + 0.726542528       Common Tangent of – 0.726542528




 Roman __













































































Common Tangent of + 3.077683537     Common Tangent of – 3.077683537




Roman _






















































































A Frequency of Light

 Carl was shocked when he multiplied the two Gematrian tangents:

3.077683537 x 0.726542528 = 2.236067977

He knew that 2.236067977 is THE SQUARE ROOT OF FIVE!!!

That’s the pyramid codex talking!”, Carl says.

He asks, “Why does the square root of five answer the sine waves of the Sacred Numbers?  What was the reasoning behind it?”

“Because the square root of five is ITSELF a Tangent; the Tangent of 186234.09485.”

Which is the SPEED OF LIGHT IN AIR!!!  

Carl points out that the speed of light in a vacuum is 186282.5894 miles per second, but when light travels through air, it is slowed down to 186234.09485 miles per second.

Carl concludes –

“And there we have it, the reasoning behind the Sacred Numbers of Gematria, the same ones preserved in eastern metrology and western calendrical computing; square roots and tangents – all keyed to the terrestrial speed of light – AND DELIVERED THROUGH THE PYRAMID CODEX IN NEARLY THE EXACT METHODOLOGY THEY USED IN KEYING THE EARTH’S EQUATORIAL CIRCUMFERENCE TO THE CUBE ROOT OF DOUBLE-PI when they built the Great Pyramid at Giza.”

“No communications across ancient oceans?  No prehistoric writing that makes any sense? Ignorant stone age progenitors?  I’m afraid I’m not buying anymore, not when I can so easily find this kind of mathematical evidence to the contrary.”

“Someone back there had it all; maps of enviable accuracy, a complete knowledge of every inch of our planet, a thorough understanding of mathematics and, yes, even calculators and computers we take for granted today – because without such tools, they could never have put it all together.  Why do I say that?  Because the U.S. Geological Survey advises me that they have the only computer in the United States which is programmed to calculate accurate distances between widely separated points anywhere on the planet – which means – that before the ancients could have marked out the pyramid grid system, they required a computer of the same caliber!!”


Joseph Mason’s Gematria System

 Reading Carl’s work was staggering to me – it felt like my head was reeling!  I’m sure this would have been the case even if I had not experienced all the “coincidences” about such numbers . . . but read on, to grasp how all this fit in with my own findings.

I’ll give a few examples.  In September 1991, I read John Michell’s article in The Cerealogist, #4, about the great triangular crop formation that appeared near Barbury Castle.  A diagram with dimensions was illustrated.  John pointed out that the sum of all the four circular areas in the formation was 31680 square feet.  He went on –

“The significance of this number, in arithmetic, cosmology, ancient theology and temple architecture was first explored in City of Revelation (1972) and is summed up in a section of The Dimensions of Paradise (Thames & Hudson, 1988).  In traditional cosmology, 31680 miles was taken to be the measure around the sub-lunary world, and the early Christian scholars calculated the number 3168 as emblematic of Lord Jesus Christ.  The same number was previously applied to the name of a leading principle in the pagan religion.”

I tried some calculations in an attempt to figure out “31680.”  I tried assigning the number 8 to the North sun symbol, and 9 to the moon symbol at the southwest corner of the triangle, and multiplied to get 72, which are the number of Divine Names used as codes in Creation according to Dr. J. J. Hurtak, author of The Book of Knowledge, The Keys of Enoch.  To arrive at the number 31680, I needed to assign the number 440 to the ratchet (Mercury) spiral glyph on the southeast corner of the crop formation (8 x 9 = 72 x 440 = 31680).  It struck me that 440 yards is a quarter mile, so I tried dividing 31680 by 5280, feet in a mile, to find it was exactly 6 miles.  At the time, I wondered how ancient people could use one of our “modern” measurement numbers. Little did I know!  Interestingly, a relative informed me later that 440 is the cycles per second of the musical note of “A.”

Back around 1992, a strange thing happened.  One night at work the numbers 72 and 360 kept coming into my mind over and over.  I knew about the 72 Divine Names, and I had read that 360 was called a “Prophetic Year,” by certain proponents of the Bible.  It is part of an interpretation concerning the dream of Nebuchadnezzar in the Book of Daniel.  He dreamed that a great tree was cut and banded, which caused a period of insanity for seven years.  This is calculated as Prophetic Years, giving 7 x 360 = 2520 years.  From the fall of the Temple at Jerusalem, this is said to give the year 1914 as the beginning of the Apocalypse (The year 1914 seems to be off a bit).  I finally stopped and multiplied the numbers coming into my head.  72 x 360 = 25920.  I was startled, because I knew this was the number of years of the precession, caused by the “wobble” of the earth’s axis, giving us our 12 Zodiac Ages of 2160 years each.

I had read about the precession number in Joseph Campbell’s, The Inner Reaches of Outer Space back in 1990.  It was mentioned that when the precession number is divided by the ancient number 60, called “Soss,” the result is 432, which is a cycle of time number(Consecration in Gematrian). Apparently the ancients knew about the precession long ago.

In 1992 and 1993, I had some strange dream-coincidences which eventually became centered on Revelation 11:11.  The verse includes the words, “three and a half days.”  At one point, I re-read some dreams I had received, and two of them made a connection.  In one of them a voice said, “The children were born in the sign of 42.”  In the other dream, I saw “Trinity 11:2.”  I looked up Revelation 11:2, and found that it speaks of the holy city being trampled over for 42 months.  I then realized 42 months is is 3 1/2 years, perhaps connecting with the 3 1/2 days in Rev. 11:11.  I then read the next verse, Rev. 11:3, which speaks of 1260 days.  This was not quite 3 1/2 years, but dividing 1260 by 3.5 gives 360.  It’s like 3 1/2 times around a circle, again matching the 3 1/2 in the other verses.  At the time, I did not know that the Hebrew calendar had 30-day months, but I now see that 1260 days is another way of indicating 3 1/2 years.

In Joseph Campbell’s book, he gave the number of years from Adam’s creation to the time Noah’s Ark landed on the mountain, as 1656.  The number of weeks in that period of years is 86400, it is figured.  A human heart, beating once a second, gives the same number, 86400, in one day (60 x 60 x 24).  Dividing the number in half gives 43200, strongly suggesting the ancient cycle of time number.  The number 108 is the number of names of the Mother Goddess in India, and figures in the time cycle number as 108 x 4 = 432.

I had written about these subjects and others in my letter to Madelon, which she passed on to Carl. As you can see, many of the numbers are the same or similar to those in Carl’s work.  I noticed that Carl had the number 1656 listed in his “sine wave” type illustration (I stopped short of it in my rendition above).  But it was apparently a “fill in the blank” type number, as it had no asterisk indicating that it was used by the ancients.  The number 1260 was not listed anywhere, yet it seemed to me that it should fit somehow.


Joe’s Dream of the Gematrian Wheel

 Some months after learning of Carl’s work, I had a dream of a circle divided into parts, and I knew it was about the Gematrian system. It came out to a 360 degree circle, or “Wheel,” divided into 10 parts of 36 degrees each, giving the sequence – 36, 72, 108, 144, etc. Full revolutions produce the same numbers with factors of ten – 360, 720, 1080, 1440, etc. The pattern keeps repeating on a base-ten system, so, for example, 144,000 is 400 times around the “Wheel.” Each section is divided into 6 parts, for a total of 60 marks. The top and bottom points of the “Wheel” have a zero tangent. The other eight points have the same four tangents listed by Carl, two if you do not consider plus and minus signs.

The Gematrian Wheel

The Bythorn Mandala crop formation of 1993 had a ten petal lotus with a five-pointed star inside. It may hint at the Gematrian system by the ten petals, and the star, which has 36 degrees in each point, and 72 degrees between points. The design is very similar to a yantra to the Goddess, Kali (one of 108 aspects of Sakti) of the eastern religions. Two of the points of the star were facing toward the North. In esoteric traditions, such a star with two points (or horns) up, signify the Kali-Yuga time cycle, called the Age of Iron, which we are now in. This is said by some to be 432,000 years.

Interestingly, Daniel’s interpretation of Nebuchadnezzar’s dream of the frightening image, was that it represented the Ages, symbolized by the metals, gold, silver, bronze, and iron, followed by the iron and clay mix in the feet of the image. The Hindu chronology has the same four metals in the same order.

Twenty-Part (“666” Tangent) Wheel

   Some other significant numbers are located at “in-between” points on the “Gematrian Wheel.” It could be considered a 20-part Wheel.  Each of these points are 18 degrees between the Gematrian numbers, such as 18, 54, 90, 126, 162, 198, and 234. Notice that 54, 126, and 234 all have the same tangent (again, ignoring plus/minus). Check this against the number 666, to see it has the same tangent. 666 is one of the ‘”in-between” points, being between 648 and 684 on the “Gematrian Wheel.”  Notice too, that some of these numbers rearranged, and with various zeros, form regular Gematrian numbers.  For example, add a zero to 126 to get 1260, or insert a zero into 234 for 2304.  Notice also that the “in-between” numbers also add to nine or a multiple of nine, and are devisable by nine.  The numbers often show a repositioning, such as 432 and the reverse, 234 (an in-between point), and 324.  Such is the odd nature of Gematrian and Gematrian-related numbers.

Six-Part Wheel

   Other related numbers can be put on a six-part wheel, of 60 degrees per segment, giving the sequence 60, 120, 180, 240, 300, etc. Various designs, such as the Star of David, fit with this “Wheel.” Remember that Joseph Campbell pointed out that 60 was an important number called, “Soss,” by the ancients, who used it in various calculations, as we do today with our time-keeping and coordinate system.

Remember too, that 31680 divided by 6 results in 5280, feet in a mile. Carl points out that these numbers were also used by the ancients, and the tangents are the square root of three (again, excluding the top and bottom marks). The number 88, which sometimes appears in dreams, may be something of a “connecting” number between the two “Wheels,” as 88 x 60 = 5280 and 88 x 360 = 31680.

For my part of this article, I will speak of the various numbers in terms of the “Wheels,” explained above.  If a number fits on the ten-part “Gematrian Wheel,” meaning it is evenly devisable by 36,  I will term it a Gematrian number. But, keep in mind that this is just my personal convention. Others may not consider certain numbers, such as 1260, as being Gematrian.  If a number, such as 666, fits on the 20-Part Wheel, but not on the 10-Part Gematrian Wheel, I consider it Gematria-related, as being an “in-between point” on the Gematrian Wheel.   If an established convention existed, I would use it instead of my personal system, but such a convention is not available at this point.

Also see: Dream of the Gematrian Wheel and Carl Munck’s Response


The Special Number 153
By Joseph E. Mason

Several years ago, I read a book about Greek Gematria called Jesus Christ, Sun of God, by David Fideler.  He explains where the Biblical story about the 153 fish in the net (John 21) came from.  As a source, he refers to John Michell’s City of Revelation.   The story was taken from prior Greek works, which demonstrated names and numbers which were crafted to reflect geometrical diagrams with cosmological significance.  The Greek words for “FISHES” and “THE NET” both equate in Greek Gematria to the number 1224, and 153 is 1/8 of this amount.  In the Biblical story, then, Simon and his other six fishermen correspond to a circle with six interlocking rings with a central circle inside, known as the Seed of Life.  This also forms an six-petal flower-like shape inside the central circle, like “The Flower of Life.”  As the story continues, more geometric shapes are added, one of which is a grid of diamond shapes forming a larger diamond.  This is the “NET” in the story. A vertical measurement is 153 and the horizontal is 265.  This demonstrates a number very close to the square root of three by 265 / 153.

It was quite a synchronicity when I received a letter from Jimi with this information:


Music, Stonehenge and The Great Pyramid
by James Furia

 D# = 152.89924 cycles per second, the augmented 4th from its root “A.” This interval was outlawed a few hundred years ago. Divide by pi = the radius of the inner circle of Stonehenge. Multiplied by pi = height of the Great Pyramid.

Also, this note is extremely close to the number 153, an ancient Pythagorean story problem that we of “The Code” have solved. Found in The Bible, John Chap 21, Jesus returns from the dead and mentions this highly significant number to some of the apostles. What we discovered recently is that the entrance to the Great Pyramid is at the 17th course (level)

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17 = 153

17 X 9 (total pyramids at the Giza complex) = 153

204 (total courses of stone on the Great Pyramid) / 1.3333333(a 4th in music intervals) = 153

360 feet up the Great Pyramid is the 153rd course

The length of the grand gallery inside the Great Pyramid is 153 feet

153 + 513 = 666           6 x 6 x 6 = 216(new standard)

315 + 351 = 666            2160 miles is the diameter of the moon

135 + 531 = 666            (not the devil but astronomy)

1 and 5 and 3 are the degrees in a scale used to make a chord


The Crop Circle Connection
By Joseph E. Mason

 In 1997 an article appeared in a crop circle journal, written by two German researchers. By measuring and analyzing the various distances of the crop circle formations, they discovered that ancient numbers were revealed. They did not use the term “Gematrian,” but the numbers are basically the same.

Other crop circle researchers have noted the significance of the number nine in the crop formations.  Nine and multiples of nine show up in dimensions, angles and distances between crop formations and various sites.

Carl Munck has written a few articles about the crop circles and possible Code connections.

I have found a number of connections, other than the ones noted in the above article.  A notable connection was the Double-Helix/DNA Formation of 1996, which was 648 feet in length.

For a number of years the Mayan Daykeeper, Hunbatz Men, has been speaking about great earth changes coming.  He said the prophecies indicate that the changes involve a “DNA repair.”  He has been involved in “activating” the ancient sites, as part of this process.

While searching the internet for information about various the subjects in these articles, I found a page that speaks of  Crop Circles and Mayan Time.

In 1997 a “Grid” crop formation appeared, which may be related to the Mayan system. An article was written about it called, The Strange Attractor Crop Formation and the End of Time.

Also see: The Crop Circle Connection (to the Code)


The Great Pyramid and 432 –
Confirmation from The Message of the Sphinx

I recently found a confirmation of “The Code,” in The Message of the Sphinx, by Graham Hancock and Robert Bauval (pages 37, 38):

“Also ‘almost impossible’, since the mathematical value of pi (3.14) is not supposed to have been calculated by any civilization until the Greeks stumbled upon it in the third century BC, is the fact the designed height of the Great Pyramid – 481.3949 feet – bears the same relationship to its base perimeter (3023.16 feet) as does the circumference of any circle to its radius.

Equally ‘impossible’ – at any rate for a people like the ancient Egyptians who are supposed to have known nothing about the true shape and size of our planet – is the relationship, in a scale of 1 : 43,200, that exists between the dimensions of the Pyramid and the dimensions of the earth.  Setting aside for the moment the question of whether we are dealing with coincidence here, it is a simple fact, verifiable on any pocket calculator, that if you take the monument’s original height (481.3949 feet) and multiply it by 43,200 you get a quotient of 3938.685 miles. This is an underestimate by just 11 miles of the true figure for the polar radius of the earth (3949 miles) worked out by the best modern methods.  Likewise, if you take the monument’s perimeter at the base (3023.16 feet) and multiply this figure by 43,200 then you get 24,734.94 miles – a result that is within 170 miles of the true equatorial circumference of the earth (24,902 miles).  Moreover, although 170 miles sounds quite a lot, it amounts, in relation to the earth’s total circumference, to a minus-error of only three quarters of a single per cent.”

(This is the end of the excerpts from our Code page.)

Also see: The Cycle of Time Number 432

Yucatan Coincidence
Cellular Communication Via DNA

A strange series of coincidences over a period of some twenty years brought a very big message — that the psychic abilities of the human race will be greatly enhanced in the future through our DNA, as it functions like a radio tuning coil. Part of the story relates to the Code of Carl Munck. It began with this —

Yucatan, Mexico

I am standing on top of the steps of the Temple of the Warriors at Chichen Itza, looking across the grass at the Pyramid of Kukulkan (El Castillo), with its double stone images of the great Feathered Serpent at the bottom of the stairway. I felt a stirring feeling, a special moment in time.

View from the Temple of the Warriors,
looking at the Kukulkan Pyramid

Kukulkan Pyramid on the equinox, showing the “Serpent”
on the stairway formed by light

Temple of the Warriors
viewed from the Kukulkan Pyramid

I experienced two other special moments nearby, — at the Ball Court and at the Sacred Cenote Well.

Ballcourt at Chichen Itza

Cenote Well at Chichen Itza

Map of Chichen Itza
Ball Court on the left
Temple of the Warriors on the right
Kukulkan Pyramid  (El Castillo) in the center
path to Sacred Cenote Well at top center

I could not have recognized back then, that I was standing atop and within a revelation set in stone. The symbolism, the ancient numbers, and some of the meaning would find their way to me in the decades to come. I would learn that the apparent “end of time” itself was some thirty years hence, in 2012, after the DNA repair.


In 1990 I began to experience many dreams, that led to “coincidences” that seemed meaningful. Early that year, I had a dream in which a voice spoke, saying, “Human global link to Mexico found, like headline.” Some months later I heard a news report about a perfect ring of circles showing up on a satellite photograph of the Yucatan.

The ring of circles are the Sacred Cenote holes, or natural wells. One of the Cenote holes is the one I saw at Chichen Itza back in 1982. The wells are now thought to mark the spot where the great meteorite struck 65 million years ago that caused the extinction of the dinosaurs and other large species. Core samples revealed crystallized quartz 1,100 meters below ground.

In early 1991, I saw this map of the Yucatan in a book —

The Sacred Grid

The book was The Book of Knowledge: The Keys of Enoch, by scientist, James J. Hurtak. Dr. Hurtak claims to have had a spiritual visitation in 1973. The book tells of a great evolutionary leap for mankind. The Yucatan  map is called “The Sacred Grid”.

Dr. Hurtak was told that this area had triangular grids of crystal and is a communication point with the heavens. It will be involved in a grid shift and alignment ,effecting the changes here.

The book contains new information about DNA.

When I first read the material, it seemed quite fantastic and farfetched. However, subsequent events and findings clearly confirmed that there are indeed messages coming about DNA. Some of the ideas could be symbolic rather than literal. In any case, it appears to be quite important.

On July 17, 1991, the Barbury Castle pictogram crop circle appeared —

I noticed that the triangular form was similar to the Sacred Grid at the Yucatan. The crop formation indicated various ancient numbers —

Excerpts from: The Pleiades and the Seventh Ray on the Seventh Day

In John Michell’s article about the formation in The Cerealogist, No. 4, he pointed out that the total square footage of the circles in the Barbury Castle formation added to 31680. He continued:

“In traditional cosmology, 31680 miles was taken to be the measure around the sub-lunary world, and early Christian scholars calculated the number 3168 as emblematic of Lord Jesus Christ. The same number was previously applied to the name of a leading principle in the pagan religion.”  


The ratchet, or Mercury spiral in the Barbury Castle formation may also indicate a cycle of time of six steps, followed by a seventh. The angle from the center of the triangle to the corner touching the ratchet was at 120 degrees, a tetrahedral point. From that point to the center of the ratchet, the angle was 108 degrees. 108 is a Gematrian number, and is associated with time cycles of 108 x 4 = 432, or 1080 years. It is the number of names for the goddess in India. 108 x 120 = 12960, the number of years in half the precession of the equinoxes through the Zodiac signs. Divided by the six arcs, gives 2160, the length of one Age of the Zodiac. This may suggest the period of time between Leo through Pisces. The Sphinx may also indicate this by the head of a man and the body of a Lion. It was probably built in the Age of Leo, over 12,000 years ago, and it faces east, corresponding to the equinox points at that time. Directly behind, at 180 degrees, would be Aquarius.

The most significant number, above, relating to this article is 12960. Gematrian numbers are often investigated in a form where the zeros are ignored. In this case, the number 1296 is key, which is six to the fourth power (6 x 6 x 6 x6).

The Barbury Castle triangle may also symbolize the “consciousness unit,” the smallest particle of consciousness and matter.


Decoding the Temple of the Warriors

Around 1994 I began to learn about the Code of Carl Munck. In 1996, I read Carl’s decoding of the Temple of the Warriors at Chichen Itza.

There are 36 steps in front (which I climbed back in 1982). From a overhead view, the width and length of the steps are the same, indicating a square, giving the calculation —

36 x 36 = 1296

At the top of the steps are 20 columns, indicating the calculation —

1296 x 20 = 25920 (the precession number)

This indicates the longitude of 119 degrees 42′ 05.18607443″ West Giza

119 x 42 x 05.18607443 = 25920

1296 indicates the latitude of 20 degrees 41′ 01.580487802″ North

20 x 41 x 01.580487802 = 1296 (rounded up)

The Coordinate Intersect (CI) is 25920 / 1296 = 20

It seemed like a meaningful coincidence that the number 12960 was encoded in the Barbury Castle Pictogram, and one tenth of that value (1296) was encoded at the Temple of the Warriors, the spot where I had the stirring moment in 1982. The coincidence seemed magnified by the triangular “Sacred Grid” from the “Enoch” book having a shape similar to the Barbury Castle Pictogram.


Decoding the Kukulkan Pyramid

Carl’s decoding of the longitude of the Kukulkan Pyramid is based on the numbers 9, 365, 4, and 4.

There are 9 terraces, 4 sides, and 4 stairways. The number 365 is derived from the 91 steps on each of the four stairways, plus the platform at the top. Then —

9 x 365 x 4 x 4 = 52560

After adjusting for the Prime Meridian offset, this figures as —

119 degrees, 42 minutes, 10.51620648 seconds
119 x 42 x 10.51620648 = 52559.99999


Early DNA Connections

In the early 1990s, I read a number of articles in crop circle journals about DNA theories (see Extra Data below). One theory is that DNA is shaped like a radio tuning coil, and therefore is sensitive to dowsable earth energies. This may be the basis of “cellular communication. According to Mayan Daykeeper, Hunbatz Men, there is going to be a “DNA repair,” which requires “activating” ancient sites.

Dowsable “ley lines,” form grids across the landscape of the Earth. Ancient sites and crop circles appear at crossing points of the gird lines. Crop circles often appear next to or aligned with the ancient sites.

The articles explained that the ley lines are related to naturally sited underground quarts. The claim was made that the dowsable energy was growing stronger over the years.

Quartz crystals, of course, are used as oscillators in radios. I began to wonder if the quarts within the Earth functioned like radio oscillators, effecting the energy grid. I wondered if our DNA tuning coils functioned like signal receivers of the Earth’s energy, including coherent messages from it.

I also wondered about the upcoming “grid shift and alignment” regarding the “Sacred Grid” at the Yucatan, as a communication point with greater grids in the heavens. The image of a great seven mile wide underground crystal oscillator below the Yucatan came to mind.

The picture that seemed to be emerging was that a change will happen that will greatly increase our “cellular” communication, that is, our psychic or Gnostic  abilities, often associated with the feminine aspect. I still have doubts about the “reality” of these “coincidental” messages, but I do think it has a symbolic truth of some kind.

Over the years, I noted that telephones are a common dream symbol. In recent years, I noted that people often dream of “cell phones.” It is possible that dreams of these “phones” are attempting to deliver the same message.


Jeff’s DNA Repair Dream

In late 1995, a work colleague, Jeff, dreamed of being on a spiral staircase with maintenance mechanics on every rung, each having a tool box. Jeff took a clip type hand gun out his toolbox and showed to it to one of the mechanics. It was a clip type pistol. He then showed the man another gun from his toolbox, a six-shooter type of revolver.

I was amazed by the dream and informed Jeff that the dream seemed to be about the “DNA repair.” Jeff had never heard anything about the “DNA repair.”  I therefore I took the dream as a strong confirmation that there was some truth to the idea, even if only symbolically.

In January 1996, I wrote a letter to the Editor of the “Sussex Circular” magazine, telling of Jeff’s DNA dream. I included information about Munck’s Code and the ancient Gematrian numbering system.


The 1996 DNA Crop Circle Formation

Around 17 June 1996, a crop circle formation appeared at Alton Barnes, Wiltshire

Image credit: Lucy Pringle

It was widely reported that the formation represents DNA, with its double helix. The formation was 648 feet in length, which is half of 1296, and another ancient Gematrian number. The base-ten harmonic, 6480, is one fourth of the precession in years.

In my January 1996 letter to the “Sussex Circular” magazine, I had mentioned the number 648. The number 666 is equally between the numbers 648 and 684. The primary Gematrian numbers are evenly devisable by 36, while the “in between” types, such as 666, are evenly devisable by 18.

The various “coincidences” involved here certainly seemed quite meaningful. The experience was actually common by 1996, in the sense of a related crop circle formation appearing after having experienced dreams and coincidences about a certain number and/or symbol.


The 2002 Mitochondrial DNA Crop Circle Formation

Around August  28,2002, tube torus type crop circle formation appeared at Crooked Soley , near Hungerford, Wiltshire —

Image credit: Lucy Pringle

I realized that the formation had that DNA look. The pattern of little diamonds reminded me of the skin of a snake.

Near the end of 2005, I learned that a book had been published about the 2002 Crooked Soley formation , called Crooked Solely – A Crop Circle Revelation, by Allan Brown and John Michell —

Crooked Soley (book cover)

I bought a copy of the book and was absolutely astounded by the information inside. The formation is said to represent mitochondrial DNA. There were a total of 1296 little diamonds making up the snake-like pattern! My Chichen Itza experiences immediately came to mind. I also recalled reading that an image of a coiled serpent was found in the water of the Cenote Well at Chichen Itza. It was thought to be based on a type of rattlesnake found in that area, which has diamond patterns —

Suddenly, I recall the serpent pattern on the hoops of the ballcourt at Chichen Itza —

Ballcourt Hoop at Chichen Itza

It is quite like the Crooked Soley crop formation.

Later, I recalled Jeff’s “DNA repair” dream. This part now seemed especially significant —

“Jeff took a clip type hand gun out his toolbox and showed to it to one of the mechanics. It was a clip type pistol. He then showed the man another gun from his toolbox, a six-shooter type of revolver.”

The “clip type hand gun” compares to the 1996 DNA crop formation, while the “six-shooter type of revolver” compares to the 2002 Crooked Soley mitochondrial DNA crop formation —

revolver cylinder

I was reminded once again how amazing dreams can be. Again, the crop formations seem to follow the dreams of the people. Paying attention to numbers and coincidences helps to put the puzzle-pieces together.

Now I am wondering if there are other puzzle-pieces within ancient sites that will lead to amazing discoveries about the greatest mysteries of creation.

Not long after the Crooked Soley book was published, I found an article on-line, titled, The Soul in Crooked Soley, which reviewed the information in the book, and provided some additional information. Here are a few excerpts from the article –.

Excerpts From The Soul in Crooked Soley

There is now a great deal of research material that indicates a divine or creative intelligence in the DNA. There are the findings of the Russian molecular biologists, Dr Pjotr P. Garjajev and Dr. Vladimir Popinin, that the DNA has a mysterious resonance that continues to manifest even after the DNA sample has been physically removed. This has been termed the DNA Phantom Effect.(2) These same researchers have found that the DNA reacts to voice activated laser light provided the correct frequency is found.(2) Using these methods it is possible to actually communicate with the DNA, as well as change the information patterns in the DNA. The Russian researchers have concluded that the DNA acts as a solitonic/holographic computer, and that it acts as a superconductor at body temperature. In addition it is known that the DNA is emitting light photons, (3) and it has been concluded that this resonance and these emissions of the DNA are capable of interacting with conventional electromagnetic forces, the natural magnetic resonance of the Earth, as well as the brain waves of living creatures.

Grazyna Fosar and Franz Bludorf in their book Vernetzte Intelligenz (2) describe the findings of the Russian molecular biologists, as well as the theories of Matti Pitkänen, and they conclude that at the level of the DNA there is hypercommunication amongst all sentient beings, a hypercommunication that effectively sets up a networked intelligence that underpins all life in the Universe.

As John Martineau subsequently pointed out to me, the Crooked Soley formation seems to be a depiction of mitochondrial DNA, which is the form of DNA that is passed down purely through the matriarchal line. It is distinct from the regular DNA molecule in that the open ends of the chain are linked together forming a complete loop. The mitochondrial DNA is an unbroken chain that binds us to the primordial Eve, the Goddess of All.�

The Crooked Soley crop circle is about 300 ft across, and the pattern is made up of 1296 �curved squares�. In 504 of those squares the crop has been left standing, and they depict the double helix DNA spiral. The other 792 curved squares are in fact flattened crop that enables the DNA pattern to stand out in relief. John Michell tells us that these are the numbers of sacred geometry. If you multiply 504 by 10 you get 5040 which is the number much favoured by Plato for the planning of his ideal city. The recommended number of citizens is 5040, and all the institutions in the city are based on that number, as is the physical radius of the city as well. Plato took this number to be the key for a divinely ordered creation.

5040 is a most significant and auspicious number in numerology and arithmetic. It is factorial 7 (7!), that is to say the result of 1x2x3x4x5x6x7. It is also the result of 7x8x9x10, and it therefore occupies a pivotal position in systems based on real numbers that impact on every facet of life. �The number Seven has unique qualities that make it the natural symbol of the universal soul. Philosophers call it the Virgin and the eternal feminine in nature. On the lower plain, where numbers multiply and grow elaborate, the archetypal Seven is represented by its factorial, 5040.”(1) St John, as well, in his vision of the Heavenly City, describes its radius as 5040, this same number that Plato adopted as the key to a divinely ordered Creation, the �heavenly pattern.�

Both Plato and St John referred to a �squared circle� with the radius of 5040, which means that the circumference of their city would be determined by the ? relationship. The circumference of a circle is 22/7 times its radius, so the circumference of the ideal or heavenly city is therefore 31680. �The square has the same measure round its four sides, so the length of one side is a fourth part of 31680, which is 7920. That brings in the second number in the Crooked Soley circle.”(1) We have seen that there were 792 flattened curved squares in the formation. John Michell goes on to explain that these same numbers or multiplications or divisions of them, figure in the mystical system of the early Christian Gnostics, as well as being the length of the circumference of the ring of lintel stones at Stonehenge.

The same numbers also reappear in the dimensions of the Earth and the moon. The Earth�s mean diameter is 7920 miles, and the sum of the two radii of the Earth and the moon is 5040 miles. �Thus, unnoticed by modern astronomers, the earth and the moon together demonstrate the squared circle – and in the same canonical numbers that appeared in the crop circle.

Many of the numbers within the article, such as 1296, 504, 792, 5040, 7920, and 31680, are the Gematrian types that we have had on our pages since 1997. Others, including Carl Munck and John Michell, have been writing about the ancient number systems for decades.

John Michell wrote extensively about the New Jerusalem plan, which incorporates the numbers 7920, 5040, and 31680 (see additional information about the New Jerusalem pattern below).


The Seed of Life and 153

The Crooked Soley mitochondrial DNA crop formation appears to be a six-fold design, similar to the geometry of the Seed of Life

It is part of the Flower of Life series, which includes Metatron’s Cube and the Tree of Life. Variations of the Seed of Life are one of the most common types of crop formations. It fits with the “Six-Part Wheel,” mentioned above. The Star of David also fits with this geometry. Each segment of the Six-Part Wheel is 60 degrees, giving the sequence: 60, 120, 180, 240, 300, 360, 420, etc. One of the numbers that locates on this wheel is 5280 (88 x 60), feet in a mile. Six miles in feet equate to 31680 (528 x 60), the sub-lunary measure around the New Jerusalem. These numbers tend to have a tangent that is equal to the square root of three.

The Seed of Life is part of the geometrical story of the 153 Fish in the Net, found in John 21. An interesting “coincidental” connection to the Kukulkan pyramid is in the form of English Alphanumerics (A=1, B=2, etc.) —

Quetzalcoatl = 17 + 21 + 5 + 20 + 26 + 1 + 12 + 3 + 15 + 1 + 20 + 12 = 153

The Aztec word for Kukulkan, the Feathered Serpent, was Quetzalcoatl.

The distance across the New Jerusalem is figured by adding the radius of two of the small “Moon” circles, and the diameter of the big circle that represents the Earth —

1080 + 7920 + 1080 = 12240
Moon + Earth + Moon = 12240

The number has a 153 connection —

12240 = 80 x 153


The Cosmic Serpent and DNA Communication

In 2007, I talked on the telephone with Jeffrey Wilson, the crop circle researcher. During our talk, I mentioned some of the DNA ideas expressed on this page. Jeffrey asked me if I knew of the book, The Cosmic Serpent, by Jeremy Narby. I did not know of it, but later discovered that we owned a copy.

The Cosmic Serpent
(book cover)

Jeffrey informed me that Narby, an Anthropologist, studied the shamen of the Amazon. He was amazed that the shamen had the ability to solve problems, such as illness, by going into trance. Somehow, they brought back technical knowledge that was previously unknown to their people.

Narby asked the shamen how they learned the information. He was told that light beings within twisted vines gave the information. He asked a shaman to draw what he saw. Later, Narby showed the drawing to a biologist, asking if he recognized the image. The biologist responded, “What you are looking at is mitochondrial DNA.”

I informed Jeffrey that Narby’s findings were exactly in line with my own findings via dream-coincidence and crop circle formations.


Garden of Eden Connections

My partner, Dee, and I have found that many dreams seem to support certain ideas of Gnosticism. In 1990 ,I wrote some ideas in my notebook about the Garden of Eden story. Based on some dreams and related symbols, I speculated that Adam and Eve represent one person, with a large rational aspect and a small, rib-sized, intuitive/dreaming aspect.

Within weeks, a “coincidence” happened. While looking at some books at the library, I had the feeling to turn around and look at the shelves behind me. It was in a section about religion. I quickly selected, The Gnostic Gospels, by Elaine Pagels, which is about the Nag Hammadi library manuscripts found buried in Egypt in 1945. I soon came to a part telling of the vision of an early Gnostic Christian, telling how Adam and Eve represent one person.

My notebook speculations continued with the idea that the Tree of the Knowledge of Good and Evil in the Garden represents infinite idea potential in the dream world. Eve, the dreaming side of the self, eats the fruit first, and then gives it to Adam. This corresponds to when we awake and remember the symbols/fruit in the dream. The Adam self then interprets the dream symbols. That is symbolized by naming the animals.

I learned later that certain Gnostics claimed that we were supposed to eat from the Tree, and the “god” who tried to prevent it was the demiurge, the false god. I noted my feeling that the demiurge symbolized the consciousness gestalt of mankind.

I also learned that the Gnostics associated the serpent in the Tree to the Divine Sophia, wisdom, the feminine aspect of the Creator.

The great mythologist, Joseph Campbell, claimed that the serpent represents the ability to change by the shedding of the old skin. The Garden story may symbolize how humans and humanity change through time through dreams.

Years later, after learning of the DNA connection to the Serpent, I realized that the Garden of Eden story had the same basic ideas.

Pi In the Fields

On 1 June 2008, a crop circle appeared in England at Barbury Castle, Wiltshire —

Image credit: John Montgomery

Astrophysicist Mike Reed deciphered the puzzling formation, showing that it is a pictorial representation of the first ten digits of Pi, one of the most fundamental symbols in mathematics. This diagram illustrates the idea by color code —

The circle is divided into ten sections, based on the placement of the ratchets. The inner light blue area covers three sections, indicating the first number of Pi. The next section is green, has a black dot, and covers one section, for the next number after the decimal point (3.1). The next section is orange and covers four sections, indicating 3.14. And so on up to the tenth digit.

Easy as Pi: Astrophysicist Solves Riddle of Britain’s Most complex crop Circle

It seems significant that ten sections were used to illustrate the Pi number. The Gematrian Wheel (see above) has ten sections. Indications are that the system is based on two five-pointed stars inside a circle —


Decagon DNA Geometry

Interestingly, a cross-sectional view from the top of the DNA double helix forms a decagon, a ten-sided figure, like two pentagons, with one rotated by 36 degrees from the other. Each spiral of the double helix traces out the shape of a pentagon. The shape, as with the five-pointed star (pentagram), features the Phi ratio or Golden Section. Here are three examples indicating the geometry —

See —

The Golden Decagon

The Beauty Code

The DNA spiral is a Golden Section

I am wondering if the Pi crop circle formation and the Gematrian Wheel are related. Other crop circles follow similar shapes —

The 1993 “Bythorn Mandala” is on the left. Some say it represents the third chakra, which has ten petals. The formation in the center appeared at Beckhampton, Wiltshire, around August 8, 1998. The image on the right is a representation of the Universe, indicated by recent data as having the shape of a dodecahedron. The dodecahedron shape is similar to a soccer ball (called a football in Europe), which has twelve pentagons on the surface.  See —

Universe could be football-shaped


The New Jerusalem Decagon

Professor D.G. Leahy discovered a “hidden circle” (the green circle) within the New Jerusalem pattern —

It is effectively the value of the diameter (= 11) of the decagon formed by the double helix structure of the DNA molecule, which decagon is visible in the top-down view of the molecule. See —


The New Jerusalem plan is based on Revelation 21, and indicates the order of the heavens made apparent on earth.

Numbers that relate to the diagram include 7920 (Earth diameter), and 5040 (radius of the Earth plus the radius of the moon 3960 + 1080). Remember, the base ten harmonics of the first two numbers (792 and 504) were revealed in the Crooked Soley DNA crop circle formation (792 + 504 = 1296).

The sub-lunar distance around the New Jerusalem is figured (using Pyramid Pi 22/7) —

(2 x 22/7) x 5040 = 31680

This is represented by the circle just inside the green circle above, which passes through the center of the twelve “Moon” circles.

Another interesting calculation is the distance across the New Jerusalem, figured as —

Moon diameter + Earth diameter + Moon diameter
2160            +       7920           +        2160             = 12240

The number 12240 is part of the 153 Fish in the Net story —

153 x 80 = 12240


The Big Pi Coincidence

I awoke early on the morning of 8 September 2009, at 2:57 AM. I had most of this page finished by that time, including the Pi crop circle portion. I sent some e-mail to announce the upcoming radio show. I then decided to post it on the Crop Circle Connector Forum. I chose a thread about the Pi formation, that was started by RAJIMMO. I had read the first page of the thread in August. RAJIMMO had mentioned DNA and a number code.

I decided to read the rest of the thread, which had now come to seven pages. On the second page, RAJIMMO gave this interpretation of the  first ten digits of Pi —

3 x 1 x 4 x 1 x 5 x 9 x 2 x 6 x 5 x 4 = 129600

To me, this was an incredible coincidence. I responded with a post on the seventh page of the thread

Post subject: Big Pi Coincidence
Posted: Tue Sep 08, 2009 2:29 pm

RAJIMMO wrote:


Seriously, I believe this to be the most important crop circle ever to show up!

I also believe that this formation is directly connected to MAY FIRST.

Is there anyone on this forum that is an expert on this crop circle formation as to why the 666 number is in association with it? I would also like to know if anyone can connect it to the bible, the Illuminati, DNA, and the modern day latin alphabet of 26 letters, from the A to the Z. And, or do you consider this formation to be made from certain intelligent life here, on this planet.

Later, RAJIMMO wrote:


Here we are at PI 3.141592654, tenth decimal place from Barbury Castle Crop Circle. This is a “SIMPLE” equation.

3*1*4*1*5*9*2*6*5*4= 129600.

Thank you so much for this RAJIMMO. This is one of the biggest “coincidences” out of almost 20 years of such “coincidences.”

I have been working on a web page for about five days. It includes information about the 2008 “Pi” crop circle formation.

The number 1296 is a major theme, from a visit to Chichen Itza in 1982 to the “Mitochondrial DNA” formation in 2002.

The number of little diamonds in the 2002 mitochondrial DNA formation was 1296.

This will be part of a radio interview on September 10th.

After reading your post about 129600 this morning, I made these notes —


3*1*4* = 12

3*1*4*1*5 = 60 (the ancient “Soss” of the Sumerians)

3*1*4*1*5*9 = 540 (harmonically related to the Code position of the Sphinx)

3*1*4*1*5*9*2 = 1080 (The radius of the Moon, the Mother Goddess number, associated with dowsing energy by mystics (3 x 360)

3*1*4*1*5*9*2*6 = 6480 (One-fourth of the Precession. Length of the 1996 “DNA” formation)

3*1*4*1*5*9*2*6*5 = 32400 (related to the coordinate system 90 x 360, as 90 degrees from the equator to the poles, and 360 degrees around the equator)

3*1*4*1*5*9*2*6*5*4 = 129600 (6 to the fourth power times 100. Ten times half the precession, encoded in the 1991 Barbury Castle pictogram as 120 x 108, the angles to the ratchet spiral).

The number 540 is the first regular (old system) Gematrian number on the list (15 x 36). This means that all the remaining multiplications of the remaining numbers of Pi will also be Gematrian.

The number 54 is the first one with the 666 tangent, but positive rather than negative. The first negative 666 tangent is 126, which is 180 degrees from 306 (2 x 153).

I included this information in my post about the 2008 Barbury Castle formation, which was before the “Pi” encoding was figured out —


The ratchet, or Mercury spiral of the 1991 Barbury Castle formation was said to be 333 feet in length. There were hints that it may have represented six ages, from Leo through Pisces, totaling 12960 years. See –

The Pleiades and the Seventh Ray on the Seventh Day

RAJIMMO also wrote:


In Gematria, May = 234 & First = 432, mirror image of each other.

I have had 234 + 432 = 666 listed in a table of numbers since 2004 on this page —

The ideas came from the two “Quintuplet Pyramid” type formations of 1999 —

The “female” had 288 circles (a major Gematrian number) —

The “male” had 156 circles —

288 + 156 = 444

BTW, the “Moon” glyph of the 1991 Barbury Castle formation was at an angle of 234 degrees, instead of where it “should have been” at 240 degrees.

At one point, I realized that 234 has the positive tangent of 666. I figured this as “in between” points by multiplying 18 by 13. I looked up the “666” verse in the Bible, and saw the “coincidence” — Revelation 13:18!

The number 54 is the first “666 tangent” number on the “Gematrian Wheel” It is a positive number. The first negative “666 tangent” number” is 126. The harmonic 1260 shows up as days in Revelation 11 and 12. On the other side of the Wheel, 180-degrees away is 306, which has the same tangent. Interestingly, 306 is twice 153, the number of fish in the net in John 21. One full circle from 306 is 666 (306 + 360).

The year 1776 is also the year of independence of the USA.

1776 = 2 x 888
1776 = 8 x 222

It is said that the winter solstice sun was aligned in the center of the Milky Way in 1998.

1998 = 3 x 666
1998 = 999 x 2

Interesting . . . the 999 day is tomorrow.

As for mirror imaging, check out this page —

The Great Serpent Mound

Serpent Mound is a prehistoric effigy mound located in Adams County, Ohio —

Like certain sites in the Yucatan, the area was formed by a meteorite impact millions of years ago.

In a portion of his book, The Mystery of the Serpent Mound: In Search of the Alphabet of the Gods, Ross Hamilton pointed out that the geometry of the effigy — incredibly — demonstrates the Pythagorean Theorem. The ancient theorem states that the square of the length of the hypotenuse (long side) of a right triangle is equal to the sum of the squares of those of the other two other sides. The formula can be written —

a^2 + b^2 = c^2

Interestingly, Pythagoras was named after the great Python serpent at Delphi by the Oracle.

The Oracle at Delphi
(note the Python serpent)

Ross did not mention it, but it is also interesting that the 153 Fish in the Net story, in pre-Christian times, was associated with Apollo’s Oracle at Delphi. This is part of the related Greek Gematria —

Delphi 619 + Omphalos 911 = 1530

According to Ross, the triangle indicated in Serpent Mound is based on the 6-8-10 triangle —

6^2 + 8^2 = 10^2
36   + 64  = 100

The numbers are associated with Roman figures, and their Magic Squares. The numbers 6 and 36 (6 x 6) are related to the Sun. The numbers 8 and 64 (8 x 8) are related to Mercury. The numbers 10 and 100 (10 x 10) are related to the Earth.

The actual measurements of Serpent Mound are 34 times the numbers in the basic formula —

204^2 + 272^2 = 340^2

The same numbers added give — 204 + 272 + 340 = 816. The number 816, divided by 34 is 136, which is related to the Magic Square of Jupiter, a 4 x 4 gird, where the 16 numbers add to 136. Each row, column and diagonal adding to 34. The numbers are also associated with the Tree of Life —

The Sun on the above list is related to Helios. I believe it could also be related to Apollo, who was considered a sun god, or the Sun behind the sun.

The number 34 is, of course, twice 17, and, remember,  the numbers 1 through 17 add to 153.

The number 272 is a harmonic of the Megalithic Yard of 2.72 feet. This numbers is thought by some to be related to the mathematical constant ‘e’ — the base of the natural system of logarithms, 2.718282.

The same type of numbers appeared in the Milk Hill Mega Glyph crop circle formation of 2001 —

It appeared around August 13, 2001, a few weeks prior to the terrorist attacks of September 11, 2001. The formation was composed of 409 circles. Significantly, it is patterned after the Seed of Life, in a form related to ancient sun symbols. Each of the six segments had 13 major circles and 55 smaller circles. The total circles in each segment are multiples of 17 –

Mega Glyph Numbers





by 17































Add the central 72 foot circle to
408 to arrive at the total of 409.

Note that the numbers from the Serpent Mound triangle appear in the table — 204, 272, and 340. The total of all the circles except the center circle amount to 408, which is half 816.

Norma Smith decoded the 409 circles of the Milk Hill Mega Glyph as relating to the English alphanumerics of the seven colors of the spectrum as —

















Chakra 1

Chakra 2

Chakra 3

Chakra 4

Chakra 5

Chakra 6

Chakra 7


4 petals

6 petals

10 petals

12 petals

16 petals

2 petals


50 + 972

These are also the colors associated with the seven chakras, in the order of chakra one through chakra seven, from left to right. “Green = 49” is the fourth-Heart chakra. This is figured as A=1, B=2, etc. The * is placed beside the 972 to note that the number is not accepted by everyone. Perhaps the most common number given for the seventh chakra is 1000 petals. The 972 figure is given here, based on the information in our 1997 article:

Crop Circle Formations As Chakras

In 2004, the chakra message seemed to be confirmed when the “Chakra System “Crop Circle Formation appeared —

The message seems to be that humanity will make the leap to the heart chakra level of consciousness evolution.


The Snake Crop Circle Formation

Around June 12, 1999, the “Snake” formation appeared at East Field, Alton Barnes, Wiltshire —

I, and others, felt that it might be related in symbolism to Serpent Mound. Jonah Ohayv created an interesting article about the formation —

I wrote an e-mail to Jonah about the article. He included it on the page —

Joe Mason, whose several articles on the relations between various chakras and crop-circles are found on his website, contributes this excerpt from Moira Timms’ book, “Beyond Prophecies and Predictions” (p. 256):

“The name Quetzalcoatl is derived from the quetzal bird of Guatemala and Mexico. The quetzal had golden-green and scarlet plumage, and was considered the most beautiful of all birds. “Quetzal” also means precious. ‘Coatl’ is serpent. In the Maya language, ‘Kukulcan’ means approximately the same thing. According to Hunbatz Men, ‘Ku’ is sacred, God. ‘Kul’ is coccyx, the base of the spine, where latent spiritual energy resides. ‘Can’ means serpent.

‘Kukulcan’ therefore is synonymous with ‘kundalini’ — which is what the Kukulcan/Quetzalcoatl archetype is all about, of course. To be iconographically correct, however, the god Quetzalcoatl is not himself the feathered serpent, but the one who emerges from the serpent, just as the spirit emerges from the body through the top of the head, and the Morning Star emerges from the horizon.”

The Kundalini is the female energy, symbolized by a serpent, that lies coiled at the base of the yogic body. Through combined techniques, the Kundalini is �awakened� and made to rise through the charkas to the cranial vault.

In 2003, a crop formation appeared in a soybean field across from the entrance to the Serpent Mound on State Route 73 near Locust Grove —


Romain’s 1053 Foot Measure

William F. Romain also wrote about Serpent Mound, in his book, Mysteries Of The Hopewell. He tells about the 1053 foot measure of the ancient Hopewell people, who left markings all over Ohio. In the appendix of the book, he uses Serpent Mound as an example of the 1053 foot measure. I believe that number is also related to 153 (900 + 153 = 1053).

I found a posting on-line with this information —

Romain further reduces this measure to a “Hopewell” yard of 2.106 feet. That’s about 7.2 inches less than Thom’s Megalithic yard.

The number 2.106 relates to Gematria 216 when ignoring the zeros and decimal points. It is apparently figured as —

1053 / 500 = 2.106

Links, by Carl P. Munck

Primary Perception — Cellular Communication
12 Videos – Cleve Backster

Chichén Itzá: El Castillo

Roundhill Press –
Crooked Solely – A Crop Circle Revelation

The Soul In Crooked Soley

Revelation 2012: DNA is the Word of God
“Open the Gateway to God within our DNA
and behold the vision I see in 2012—and beyond.”
From John Jay Harper

Russian DNA Research

New Discovery of DNA Variability
Holographic Blueprints and the Symphony of Life

DNA, Apocalypse, & the End of the Mystery
(The New Jerusalem Diagram)

David Wilcock on Coast To Coast Radio
(includes information on DNA & our rapidly increasing ability to use intuitition)

BioActive “Fractal” or Phase Conjugate
Electric Fields which Cause LIFE! Applied

(includes DNA, the Golden Ratio & five-fold geometry)

Temporal Epoch Calculations
by James Q. Jacobs
(tools employed in archaeogeodesy & archaeocosmology)

Pyramids of Precession

Seed of Life

Introduction to Sacred Geometry
by Charles Gilchrist
(Includes the Seed of Life and the Flower of Life)

Charles Gilchrist YouTube Videos

Solfeggio Frequencies Links

The Use of Tonal Frequencies to Enhance, Heal, & Rejuvenate

Forgotten In Time: The Ancient Solfeggio Frequencies

Crop Circle Music Wheel


Hephaestus (Vulcan) – DNA Engineer

Dream and Nostradamus Connections To The Anomalous
Object Near The Hale-Bopp Comet – Part 2

(DNA Connections)

Birthing the DNA of Light

Revelation 2012: DNA is the Word of God
“Open the Gateway to God within our DNA
and behold the vision I see in 2012—and beyond.”

The Pleiades and the Seventh Ray on the Seventh Day

The Trinity Crop Circle Theme of 2001

Dreams About the Triple Male Trinity

Dreams of the Grid Shift

The Global Consciousness Project
(The study of the subtle reach of human consciousness in the physical world)

Culture-Centered Music Therapy

Visionary Music
DNA Activation

The Antikythera Mechanism
Converting To Ancient Gematria Numbers
By Jerry Iuliano

The Works of Jerry Iuliano
Ancient Numbers Revealed in Scientific Formulas

Serpent Mound Crop Circle Lights Synchronicity

Venus – Morning Star, Evening Star

Fractality in Time: Defining Co-Incidence
(Venus, the Star Mother, & the dodecahedron of DNA)

The Spiritual Genome

Latest Finding – Crop Circles and DNA

Garjajev Vladimir Poponin “Phantom-DNA Effect”

Crop Circle Photographers
We thank the crop circle photographers and urge support for them.

 Lucy Pringle  

 Busty Taylor  

 Stuart Dike  

Freddy Silva

Ron Russell
Crop Circle Anomalies

Steve Alexander
and Karen Douglas

 Peter Sorenson  

Werner Anderhub

Frank Laumen

.Janet Ossebaard

Andrea Feliziani

Julian Gibsone

 Eva-Marie Brekkesto  

Bert Janssen

Jan Schwochow

Olivier Morel

Graham Tucker

Nick Nicholson

Andreas Müller

Jim Miller

Colin Andrews

Rob Speight

Patricia Murray

Seiichi Nakazato

David Russell

Richard Wintle
Calyx Photo Services

Andrew King

Richard Harvey

Russell Stannard

Doe Kelly and
Andrew Wheeler

Summer Garland

A.J. Samuels

 Clemens Richter  

If you have any questions, or comments, or would like to add a link to this page, please e-mail

This page was originally uploaded September 3, 2009

This page was last updated November 18, 2009

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Extra Data

Russian DNA Research

Russian biophysicist and molecular biologist Pjotr Garjajev and his colleagues have been carrying out cutting-edge research the more esoteric nature of DNA. They simply did not believe that 90% of our DNA is �Junk DNA�. From the German book Vernetzte Intelligenz by Grazyna Fosar and Franz Bludorf (summarised and translated by Baerbel):

The latest research explains phenomena such as clairvoyance, intuition, spontaneous and remote acts of healing, self healing, affirmation techniques, unusual light-auras around people (namely spiritual masters), mind’s influence on weather-patterns and much more. The Russian scientists also found out that our DNA can cause disturbing patterns in the vacuum, thus producing magnetized wormholes! Wormholes are the microscopic equivalents of the so-called Einstein-Rosen bridges in the vicinity of black holes (left by burned-out stars). These are tunnel connections between entirely different areas in the universe through which information can be transmitted outside of space and time. The DNA attracts these bits of information and passes them on to our consciousness.

What we are seeing here is �Hyper-communication�, where information is passed inter dimensionally. It is as though the DNA acts as a �Stargate� between this dimension and others. In the book there are several stories of how this information is downloaded via DNA.

The Italian composer Giuseppe Tartini for instance dreamt one night that a devil sat at his bedside playing the violin. The next morning Tartini was able to note down the piece exactly from memory, he called it the Devil�s Trill Sonata. For years, a 42-year old male nurse dreamt of a situation in which he was hooked up to a kind of knowledge CD-ROM. Verifiable knowledge from all imaginable fields was then transmitted to him that he was able to recall in the morning. There was such a flood of information that it seemed a whole encyclopaedia was transmitted at night. The majority of facts were outside his personal knowledge base and reached technical details about which he knew absolutely nothing.

It was also noted how this information can be passed between individuals who�s DNA is �turned on�. This helps explain how many of the Psychic Children can exchange complex concepts to each other through an invisible web. It is the DNA communicating over vast distances:

We now know that just as on the Internet, our DNA can feed its proper data into the network, can call up data from the network and can establish contact with other participants in the network. Remote healing, telepathy or remote sensing about the state of relatives etc. can thus be explained. Some animals know also from afar when their owners plan to return home. That can be freshly interpreted and explained via the concepts of group consciousness and hyper communication.

Russian researcher Dr.Vladimir Poponin put DNA in a tube and beamed a laser through it. When the DNA was removed, the laser light continued spiralling on its own, like it would through a crystal! This effect is called �Phantom DNA Effect�.

It is surmised that energy from outside of space and time still flows through the activated wormholes after the DNA was removed. The side effect encountered most often in hyper communication and also in human beings are inexplicable electromagnetic fields in the vicinity of the persons concerned. Electronic devices like CD players and the like can be irritated and cease to function for hours. When the electromagnetic field slowly dissipates, the devices function normally again. Many healers and psychics know this effect from their work.

More and more children are being born with these amazing abilities and is becoming very clear it has to do with the DNA change. This has never occurred before in quite this way and many researchers believe our DNA will become fully functional by late 2012. It is no coincidence that 2012 is the end of the Mayan calendar and the proposed time of �Galactic alignment� and the move from the age of Piscies into the Age of Aquarius. New research shows there is an intimate link between DNA, the Sun and what is going on in our Galaxy.

The Spiritual Genome – Crop Circles Explained
Bradley York Bartholomew

The findings of the molecular biologists Dr Pjotr P. Garjajev and Dr. Vladimir Poponin of the Russian Academy of Science concerning the �Phantom-DNA Effect� have a radical connection with the formation of crop circles in the United Kingdom and throughout the world in recent times. According to these scientists the DNA is emitting electromagnetic waves that continue to manifest even after the DNA sample has been removed from the experiment. Hence the name �Phantom-DNA Effect�. The genetic procedures being adopted by these scientists have been commented on and explained by Grazyna Fosar and Franz Bludorf in their book Vernetzte Intelligenz (1), who have put forward the theory that self-radiating balls of light often seen in the sky and mistaken for extra-terrestrial visitors are in fact a group consciousness phenomenon brought about by hypercommunication within the DNA. This theory by Fosar and Bludorf can also explain the formation of crop circles which are also commonly attributed to extra-terrestrial visitors. In addition it will be shown that the precise technology being adopted by the aforesaid scientists in Moscow represents a new energy source, previously unknown to mankind, that is capable also of creating crop circles.

The sensational discovery of the Phantom-DNA Effect by Drs. Grajajev and Poponin, as described by Fosar and Bludorf, occurred when they were attempting to measure the actual vibration pattern of a DNA sample. They illuminated this specimen DNA with a laser light that produced a typical wave pattern on a screen. However when they removed the sample the wave pattern did not completely disappear. There remained on the screen a regular wave pattern as if there was still a material sample of DNA being illuminated. A control experiment demonstrated that this secondary wave pattern must still be coming from the original DNA sample that was removed. The control experiment had no DNA sample placed in the radiation beam and only a random pattern was produced on the screen. This phantom DNA effect is always repeatable when a DNA sample is used.

Fosar and Bludorf also describe other findings of this Moscow Group particularly concerning the 90 percent of human DNA that does not code for protein synthesis, and is therefore considered to be biologically inert. They point out that these days we refer to the DNA quite naturally as a �genetic code�, and we look upon it as a systematic encoding of information. Yet at present main-stream geneticists remain committed to examining the DNA exclusively trough chemical processes instead of bringing in speech and linguistic analysts which would normally happen when you are attempting to decipher a code.

Not so in Moscow, however. Here the genetic code is being examined precisely as an exercise in linguistics. This is the science of the structure and construction of speech. It can be used to explore not only natural speech that has evolved in individual countries and cultures, but it can equally be applied to artificial speech, for example computer programming languages. By examining speech one ascertains the basic rules of syntax (the creation of words from letters or characters), of semantics (a study of the meaning content of words) and these together make up the foundation for a grammar. By applying this scientific form of linguistic examination to the genetic code the Moscow group have found that the DNA follows similar grammatical rules as human speech.

Albeit not the rules of a particular language ( in this case for example the Russian language), but at a more fundamental level the DNA does follow the rules that contain the common features for all languages. What they have found is that there is an essential relationship between the structure of the genetic code and all the languages of mankind. For centuries scientists have been speculating on a human protolanguage, and it may well be that Pjotr Garjajev and his colleagues in the Moscow group have actually found it.

Fosar and Bludorf tell us that we must think of the normal relationship in reverse. The structure of DNA does not correspond to human speech structures, but all human language rather follow the pattern of the genetic code. After all DNA and the genetic code existed long before the first human uttered the first word. So the human languages that have evolved since the advent of humans must have followed the grand pattern that was already laid out in the structure of the genetic code.

Fosar and Bludorf warn us that this is not a question of an orthodox material worldview, according to which the facility of speech is merely a secondary effect of being bodies constructed of proteins that are coded for in some genes. The arrangement of the elementary bases in the DNA itself follows a fixed grammar, an ethereal plan, to which our human language is analogous. That this is not a question of a bodily event is already demonstrated by the following finding of the Moscow group, namely that the analogy between the structure of the DNA and human language is particularly pronounced in the particles of the larger molecular structure that actually serve no purpose for protein synthesis.

Herein lies a revolutionary discovery for the entire field of genetics. Those who are only interested in examining the known genes, and derogatively dismissing the rest of the genome as �junk DNA�, are possibly missing what is really fundamental. It is truly a paradox says Fosar and Bludorf, for it is precisely the �dumb DNA� that is actually speaking.

According to Pjotr Garjajev: �The majority seek to understand the principles of DNA-Biocomputers in which they refer exclusively to the DNA-Watson-Crick-Rules: A-T, G-C. That is correct, but it is not enough. The DNA-Chromosomal continuum in living systems has wave attributes, that have remained elusive to us, and that are like a computer program for the structure of organisms. The known genetic code is a code for protein synthesis, and nothing more. Living chromosomes however function just like solitonic/holographic computers using the endogenous DNA laser radiation.�

Fosar and Bludorf list some of the extraordinary consequences of this new approach to genetics which has been pioneered by the Moscow group. They were able to modulate certain frequency patterns into a laser beam in such a way as to influence the DNA frequency, that is to say they could influence the genetic information itself. It was not necessary to painstakingly decode the sequences of base pairs in the DNA, and thereby artificially formulate genetic information. Quite simply these Russian researchers were able to use the words and sentences of human language to change the information in the DNA once they had ascertained the basic structures were synonymous.

The Moscow group were able to prove this astounding procedure experimentally. DNA substance in vivo (i.e. living tissue, not in vitro) reacts to the speech modulated laser light, as well as radio waves, provided the correct frequency is found. They were able to direct the information pattern from one DNA sample onto a different sample, and thus able to effect a transmission of the genetic information. This function can be demonstrated in natural cells in various ways. Garjajev and his colleagues have already succeeded in this manner to reprogram cells with information taken from a different genome. Specifically they have managed to convert frog embryos into salamander embryos simply by exchanging the information patterns in the respective DNA. They have therefore demonstrated a radical new way of interacting and even communicating with the DNA through voice modulated laser beams. This has to be seen as a totally new form of energy which has been discovered and harnessed, that opens up virtually unlimited possibilities for the evolution of life not only on earth but in the Universe.

Fosar and Bludorf also relate the findings of the Russian physicists Alexej Dimitrijev and Vjatcheslav Djatlov. These two were commissioned by the Russian military to investigate the many sightings of self-radiating balls of light that appear regularly in Siberia on the border with China. They came to the conclusion that these UFOs were actually caused by vacuum domains where gravitational forces can change into electricity, and vice versa. This theory introduces a sensational new element into the New Physics because it opens up the possibility of hypercommunication through stable wormholes into other parts of the Universe.

The theory however has radical implications for the functioning of DNA as well. It is now known that DNA functions as a superconductor at body temperature and is able to store light and information. Fosar and Bludorf have come up with the theory that the DNA itself acts as an intelligence network which enables hypercommunication via these wormholes. Effectively then these sightings of mysterious balls of light in the Russian sky can be explained as a phenomenon based in group consciousness brought about by hypercommunication through the wormholes in the DNA. In this way they are able to explain the often reported experience of people who have seen them, that the balls of light are in various subtle ways interacting at a psychic level.

In order to demonstrate the connection between wormholes in space and wormholes in the DNA, Fosar and Bludorf refer to the theory of the Finnish physicist, Matti Pitkänen, who some years ago formulated a new theory about the construction of the universe, based on an eight-dimensional space geometry. The theory is called TGD (Topological Geometrical Dynamics). In this complex theory magnetic wormholes play a very significant biological role. In fact the innovative thrust of his theory is to establish a scientific link between Physics and Biology. His theory leads to a cosmology of sentient beings. Contained in the DNA is much more than simply the instructions for synthesizing proteins for the construction of living cells. These powerful genetic biomolecules also contain the data for the operation of magnetic wormholes as biological communication channels.

Pitkänen has come up with a genuinely new approach of incorporating the mental concepts of consciousness and perception into the New Physics. According to Pitkänen, Wormhole-Magnetic-Fields, which present as Space-Time-Layers, are contained in the normal biological material, and are excellent candidates for a physical explanation of perception. Magnetized wormholes can really be seen as the quintessential living system. Fosar and Bludorf explain that Pitkänen�s TGD theory demonstrates the long suspected connection between Gravitation and Consciousness – namely, that Gravitation and Consciousness represent antipoles. It even suggests that Gravitation is a fiction, evidenced by the fact that gravitational force can be converted into electricity (i.e. electromagnetic vibrations synonymous with brain waves) in vacuum domains. Here is the explanation how self-radiating balls of light can enter into telepathic communication with observers.

There is a lot of material on the internet concerning the ability of DNA to react to various vibrations and electromagnetic waves. Much of this material seems to be based on the findings of Popp (2) that DNA emits quantum coherent photons. The Institute of Heart Math at Boulder Creek, Colorado presents published articles concerning the modulation of DNA by heart frequencies (4). There are theories about DNA resonance actually emitting information as well as acting as antennae. In a particular experiment conducted by Vladimir Poponin it was found that DNA will cause randomly dispersed light photons in a vacuum to line up in an orderly fashion in alignment with the DNA. In other words the DNA was having an effect on the light particles that are in its external environment. Other experiments describe how DNA removed by as much as fifty miles from the biological donor will show identical and simultaneous responses to the changes in the emotional state of the donor. There is no lag time whatsoever. In other words, as argued by Fosar and Bludorf, there is a simultaneous hypercommunication within the DNA. It may be reasonably predicted that samples of DNA taken from astronauts traveling in outer space would likewise display this hypercommunication ability.

In his book, Secrets in the Fields, Freddy Silva (5) argues that the energy behind crop circles is natural, and �that an intelligent source is able to control it to a very high degree. How else can we explain a �natural phenomena� that selectively avoids houses, towns, gardens, and parks? That produces hundreds of geometrical and philosophically significant shapes of great complexity? That interacts with, even reads, the minds of its human observers.�

According to Fosar and Bludorf therefore this natural energy is brought about by hypercommunication via magnetic wormholes in the DNA. The crop circle is a group consciousness phenomenon. Dr Poponin (3) himself states: �Perhaps the most important finding of these experiments is that they provide an opportunity to study vacuum substructure on strictly scientific and quantitative grounds. This is possible due to the phantom field�s intrinsic ability to couple with conventional electromagnetic fields.� This surely has to mean that the waves emanating from the DNA are resonating with external electromagnetic fields, which implies as a matter of logic that these waves from the DNA are capable of changing and directing the external electromagnetic fields. Again to quote Dr Poponin: �This model is suggested as the basis for a more general nonlinear quantum theory which may explain many of the observed subtle energy phenomena and eventually could provide a physical theory of consciousness.�

The geometrical and philosophically significant shapes of the crop circles can be explained, as pointed out by Fosar and Bludorf, in terms of Jungian archetypes in the collective unconscious. This also of course explains a very essential element of crop circle phenomena, namely that they seem to interact with the psyche of the human observers. Hypercommunication through magnetic wormholes in the DNA could not fail to impact on the psyche of persons observing the formation of these crop circles in a group consciousness experience.

Another essential characteristic of crop circles is that they appear to have been formed by some form of electromagnetic energy. According to Professor Charles Thomas (5) who visited crop circles in Wiltshire and Cornwall in 1991/92, �The process of crop circle formation in these cases appears to have produced a local magnetic anomaly detectable with a reliable instrument. One could add the comment that the anomaly appears to be linked to the direction in which the stalks are flattened and that the strength of the anomaly appears to vary with the distance from ground level. There may be a suspicion that the magnetic field is created at the time of the formation and decreases through time.� Freddy Silva documents many incidents where all sorts of electrical and mechanical equipment has malfunctioned precisely when taken into a crop circle, and then resumes normal functions as soon as it is removed from the immediate vicinity of the crop circle. The engines of aircraft flying over crop circles have even been known to malfunction. According to the theory of Fosar and Bludorf these crop circles appear precisely as a result of hypercommunication through magnetized wormholes in the DNA, and this would explain the magnetized anomalies aspect of this phenomenon.

The stem of the plants within a crop circle are bent in a manner which cannot be explained by conventional science. Crop circles have appeared in wheat, canola, barley, rye and linseed as well as many other cultivated crops. With a number of these crops any attempt to bend the stalk will result in it snapping. However all plants in a crop circle have the stem permanently bent, and yet apart from that they remain alive and well. As regards the walls of crop circles (5), �this force is capable of incising pictograms containing over a thousand elements with surgical precision, covering areas of up to 150,000 square feet, and with such unerring accuracy that �curtains� of wheat one stalk wide are sometimes all that separate one circle from another. The perimeter walls resemble the seamless curve of a drum, and where inward-curving walls meet inside a design, the central point can be defined down to a single stalk.� From this description it is a abundantly clear that the force that creates these crop circles has to include precision laser beam technology. The same technology that is being used by the Moscow group in their experiments with DNA vibrations.

The floor of crop circles consists of plants that have been flattened, but are otherwise undamaged and unharmed. The flattened plants can be woven into complex spirals and swirls, and there can also be several layers of densely interwoven stalks resembling interrelated wave patterns. Generally any attempt to pry the interwoven plants apart will destroy them. The flattening process can also exhibit extraordinary selectivity. Different species of plant can be left standing amongst an otherwise flattened crop. The selectivity can even extend to plants of the same type and age which are left standing amidst flattened crop. This again recalls an aspect of these experiments on DNA by the Moscow group, where it is found that the DNA will only respond to vibrations of exactly the right frequency. It is only technology of this sophistication that can explain how some plants can be deliberately spared the flattening process on the floor of a crop circle.

Laboratory analysis (5) has revealed the crystalline structure of the flattened plants has actually been changed by some force. Even more significant is the fact that the DNA is considerably different from the plants that have not been flattened. In other words this force that has flattened the crop had the exact vibrational frequency necessary to modify the information patterns in the DNA. The laboratory analysis also found that the seeds and the germinating process of the affected plants had been changed. Although the plant itself was unharmed, this force had made substantial changes to the plants natural regenerative processes. It is suggested that this kind of change can only be brought about by tampering with the information patterns in the DNA of the plant. As regards the flattening process itself, the laboratory analysis undertaken by Dr Levengood concluded that an energy source �originating in the microwave region had boiled the water inside the plants� nodes, effectively transforming it into steam.� Again indicating that electromagnetic waves of a certain frequency are involved, and from the statement by Dr Poponin above we know that Phantom DNA has the ability to couple with conventional electromagnetic fields. In this way the force can modify biologically inert matter such as soil and rock as well as boiling water.

Freddy Silva reviews the evidence of eye witnesses to the formation of crop circles and the most consistent observation seems to be that there appeared a �tube of light�. Silva himself concludes that it is something like a laser beam, and he quotes observations of the Russian metaphysician P.D. Ouspensky that the ray of light can be transformed �into a spiral, into a hollow cylinder� where the photons lie close to one another lengthwise �with two kinds of thread�. Silva concludes, �Regardless of what we call the energy inside those tubes, it seems to send a �code� which tells plants what to do and when.� This light energy is clearly analogous to the voice modulated laser beam that the Moscow group is using to modify the information patterns in DNA. Putting aside for one moment the actual source of the energy, it is almost certain the energy that is creating crop circles and the energy that the Moscow group is using to modify DNA is one and the same.

There has also been many reports of a very distinctive sound that is heard when crop circles are being formed. Freddy Silva refers to the findings that music can actually cause plants to move towards or away from the source of the sound. It has also been found scientifically (3) that spiritual musical chants resonate with the DNA. Silva refers to references in ancient religious scripts that the Sanskrit language is sacred because it is �the language of light�, and its characters were considered to be �the sounds of light�. The geometrical vibrations in language were not only believed capable of harnessing the power of light, but also were capable of actually creating matter. Here again we find exactly the same principles being applied by the Moscow group using voice modulated laser beams to modify the information patterns in DNA. Sanskrit may be the source language for Indo-European languages, but obviously all language has this ability to resonate with the DNA.

Effectively the researchers in Moscow are talking to the DNA through these laser beams, and the DNA is responding. There is communication. With these crop circles the DNA is demonstrating to us how sound vibrations contained in beams of laser light can create intricate and intelligent patterns in organic external matter simply by modifying the information patterns in the genome of the plants. It may even come to pass that once the significance of crop circles is known, they will begin to contain even more sophisticated patterns to better enable us to decode the DNA.

At the conclusion of his book, Freddy Silva refers to the published channelings of a clairvoyant, Isabelle Kingston. In 1989 she had contact with a Universal Consciousness, called the Watchers. This was before much of the recent upsurge in crop circle activity. Amongst other things, she was told by the Watchers that �the energy has been put through crop circles through thought processes�. She was also informed that �this new source of energy is now being created and certain beings are being prepared to understand the messages being projected at this time. Power is being created through the intellect of the scientist, knowledge is being awakened; some scientists are very close to the answer – an energy machine. This energy is only partially linked to magnetism. It is linked to the illusion of time. Rather like thought-transference, man will be able to change the molecular structure of things, including himself. Within the energy-pattern of the circles we give you this information.�

Not long after this channeling experience by Isabelle Kingston, the crop circle activity started to appear in earnest, and around about the same time the Moscow group of scientists came together to commence their experiments with the DNA using voice modulated laser beams produced by a �MALVERN� LCPS (Laser Photon Correlation Spectrometer). This laser technology – the energy machine – was literally a new form of energy which has the capacity to change the molecular structure of all things. While they were developing this energy, the divine intelligence in the DNA was creating these crop circles using exactly the same source of energy, as a means of demonstrating to us how the Universe was created in the first place, and how it may now be modified and colonized.


1. Grazyna Fosar and Franz Bludorf. Vernetzte Intelligenz [Networked Intelligence]. Aachen: Omega, 2003.

2. Rattemeyer M., F.A. Popp. Naturwissen 68 (1981): 572.

3. Glen Rein. Biological Effects of Scalar Acoustic Energy: Modulation of DNA. Columbus, Ohio: Proc. US Psychotronics Assoc., 1998.

4. Glen Rein. Modulation of DNA by Coherent Heart Frequencies. Institute of Heart Math.

4. Dr. Vladimir Poponin. The DNA Phantom Effect: Direct Measurement of A New Field in the Vacuum Substructure.

5. Freddy Silva. Secrets in the Fields. Charlottesville, VA: Hampton Roads, 2002.

Venus Conjunctions Form A Five-Pointed Star

The conjunctions of Venus trace a five-pointed star patterns in the heavens. Refer to this web page —

Gematrian numbers appear in the process. Multiples of 36 days are one key element.

1) a superior conjunction occurs very near to 648 degrees (one complete circuit around the zodiac plus 288 degrees or four points of a five-pointed star) from the inferior conjunction which opened its cycle;

2) successive inferior conjunctions occur about 936 degrees zodiacal degrees apart — that’s two circuits around the zodiac, plus 216 degrees or three points of a five-pointed star;

superior conjunction occurs 216 days after maximum elongation

4) a complete pentagram is formed after five complete cycles, totaling two days, eight hours short of eight years;

Why Study Metrology?
[Excerpt from:]

One of the central ideas of ancient metrology is explained by the much read and little understood Fifth Book of Aristotle’s Ethics, in which the idea of justice is explained by referring to money and to the price structure.

This book explains why money is called by the same name that applies to civil law and to natural law (nomos) and why this term is synonymous with arithmos; metrology first developed as an attempt to assure justice in the contract of sale by mathematizing the relation.

The origins of the art of legislation and of legal science are to be found in lists that state how many measures of a given commodity would correspond to a measure of another commodity.

Once one takes this practical outlook, one can see how, in the Bible, the idea of Divine Providence is linked with the methods used in the rationing of food, of which Greek inscriptions provide the most abundant evidence.

Once one keeps in mind the metrological aspects of the idea of Providence, one can see the meaning of the word epiousios in the Lord’s Prayer, a word on the interpretation of which an entire library has been written.

One must keep in mind the ethical aspects of metrology to see in the Gospels the metrological reasons for the two miracles of the multiplication of the bread, the Feeding of the Four Thousand and the Feeding of the Five Thousand.

In metrology, one must steadily shift from metaphysical and ethical presuppositions to practical aspects. This has been the concern of Greaves and Bernard, who came to metrology from the study of cosmogony but at the same time travelled extensively in the Orient and saw the ancient system of metrology still used by the Arabs.

Early DNA Notes

Crop Circle Reports

The message of a DNA change or “repair” has been coming from various sources for quite a few years. I began to learn about it in 1991. I read some information about DNA theories in various crop circle journals, primarily The Cereologist and The Circular.

One theory is that DNA is shaped like a radio tuning coil, and therefore is sensitive to vibrations. The vibrations include subtle ones, such as dowsable earth energies. This may be the basis of “cellular communication,” telepathy, automatic writing, channeling and such phenomena as dowsing, use of pendulums, and Ouija boards.

Quite a lot of scientific research has been done in the area of cellular, or cell-to-cell, communication. Even single cell animals and scrapings of human skin, seem to be telepathic. The cells are apparently aware of human thoughts and to the experiences of the cells of other living creatures. Scientific experimentation of this phenomena apparently began with Cleve Backster, many years ago. See:

Primary Perception
Biocommunication with Plants, Living Foods, and Human Cells

There were a number of articles in the crop circle journals about dowsing and the related subtle energy, especially that found in “ley lines,” which are said to form grids of lines across the landscape of the Earth. Another term for the ley lines is “Dragon Paths.” The Chinese called this energy “chi.” It was known as the Holy Spirit to early Christians. Mystical scholars associated the energy with the number 1080. The number 1080 is said to be a Mother Goddess and time cycle number.

There is a major energy line, called the Michael/Mary Ley Line or Serpent Line that stretches across southern England, where most of the crop circle formations appear. The two lines are actually made up of a male and female pair of lines that twist across the landscapelike electrical wires. The line is aligned with the rising sun at Beltane in May and Lugnassad in August.

Some say that various ancient sites are the chakras of Earth. Perhaps the Michael/Mary Serpent Line corresponds to ida and pingala, the two “spine snakes” of the chakra system. There may be a double helix DNA suggestion as well. Many crop circles seem to represent chakras.

Various patterns, such as star shapes and Teutonic Crosses, were found by dowsing within crop circle formations. In one case, the basic layout of the New Jerusalem Plan was found by dowsing inside a crop circle. The same dowsing layout was also found within ancient sites, such as Avebury and Stonehenge.

Ancient sites are said to be positioned at crossing points of the grid lines. The crop circle formations also tend to locate themselves on the crossing points. Quite often, the crop formations are located in close proximity to ancient sites, and/or aligned toward them.

The articles explained that the ley lines were related to naturally sited underground quarts. Some said the energy was effected by underground water and by the cycles of the moon. The claim was made that the dowsable energy was growing stronger over the years.

Quartz crystals, of course, are used as oscillators in radios. I began to wonder if the quarts within the Earth functioned like radio oscillators, effecting the energy grid. I wondered if our DNA tuning coils functioned like signal receivers of the Earth’s energy, including coherent messages from it.

John Haddington

Crop circle investigator, Sir John Haddington, wrote several articles in which he mentioned DNA.

He pointed out that the snail type crop formations may suggest DNA by the helix shapes on the two sides of the shell, suggestive of a double helix.

Fossilized snails were found within ancient sites. In ancient England, the word for snail was “Dodman.” The word had an alternate meaning — “surveyor of the landscape.” The surveyors of old apparently used dowsing techniques. Another word for such a person is “Geomancer.” The reason for the association is thought to be the two antennas of snails, as symbolically related to dowsing or divining rods or the like.

It was pointed out that snails leave tracks that look like ladders, and that ladders have appeared as parts of crop formations. A twisted ladder, of course, is geometrically similar to DNA. Some called those types of crop formations “Laddergrams.” Others called them “Insectograms,” because the formations looked like a type of insect, perhaps a beetle, including the two antenna.

Formation near
Stonehenge 1991

The “Laddergrams” of the early 1990’s, such as the one above, appeared in pairs. In one case, the pair appeared on different days in the field across the highway from Stonehenge. All of the ladders had either seven or fifteen rungs. Someone pointed out that the numbers seven and fifteen, in binary, are 111, and 1111. Such numbers have been reported often in coincidences.

Very ancient Dodman/Geomancers apparently used dowsing in locating and designing ancient sites.

Sir John Haddington wrote an article detailing apparent symbolic associations between the snail and the Roman god, Mercury. The Greeks called him Hermes. To the Egyptians he was Thoth.


Hunbatz Men

One of the articles in the crop circle journals reported on Native American symbolism. Some Native American symbols are similar to various crop circle formations. Part of the article was about the Mayan Daykeeper/Shaman, Hunbatz Men. He taught that something went wrong in the creation of man. A very great change is coming, he claimed. This will involved a “DNA repair.” In order to help bring this about, he was organizing people to have ceremonies at the ancient sites, to activate them.


Barbury Castle

In September 1991, I received The Cereologist.. There was a photograph, diagram, and article by John Michell about a triangular crop circle formation that had appeared at Barbury Castle on 7 July 1991.

image: Barbury Castle

He also mentioned the double-helix of the shells, and how they leave ladder-like tracks, indicating DNA. He connects this to Mercury. The Romans depicted him sometimes with three penises. The Mercury spiral of the Barbury formation coiled counter-clockwise from a small circle, with the wheatstalks also laid down in the counterclockwise direction. There were straight-lined offsets in the spiral, making it like a ratchet shape. There were six sections. The angle from the center of the triangle to the southeast corner was at 120 degrees, a tetrahedral point. From that point to the center of the spiral the angle was 108 degrees, a mythical and Gematrian number. 120 x 108 = 12,960 – six to the fourth power times ten, and half of the precession number. Divided by the six sections gives 2,160 – the length of each zodiac age. The formation appeared on July 17, 1991. In Genesis 8:4 the Ark lands on the mountains of Ararat on the 17th day of the 7th month. Blavatsky shows how the patriarchs represent zodiac signs, and Noah is Pisces. It seems to be an additional clue that our age is coming to an end. It may be that the Sphinx also represents Leo through the beginning of Aquarius. Several weeks ago, a co-worker told me he dreamed of being driven in an airliner on a highway near here by a water treatment plant operator named Andy. They took a detour to the right because of construction work. Then the dreamer was with his boss, an engineer, and a woman. They were planning to put a new transformer under a grate at the water treatment plant. The woman whispered something into the engineer’s ear. This same man has had other dreams where there are three males, counting himself, and in one of them there was a woman broadcasting from her car, and then she changed stations. I asked my friend what highway he was on in the airliner dream. It is some 20 miles from his house, on the highway from Oakdale, California toward Yosemite. It was on the section were highway 120 and 108 run together! I know this is a very strange story, but it is quite typical of my dream-coincidence experiences over the past six and a half years. The idea of a change in DNA is coming from a lot of sources, including dreams. In one, it was a huge sphere orbiting earth that communicated through our amino acids. So it could well indicate a Hale-Bopp Companion connection. A number of clues suggest that there will be a change in the Trinity itself, which will effect every particle in Creation. A common thread in the various messages, from Mars, Giza, the moon landings, the crop formations, and perhaps Nostradamus and Hale-Bopp, is the Trinity. I ask, why is it that there is so little discussion about it?


The New Jerusalem Plan was developed by John Michell, based on Saint John’s description in Revelation 21. The basic pattern has been found by dowsing in ancient sites, such as Stonehenge and Avebury. The basic pattern was also dowsed within a crop circle formation prior to 1990. John is the author of many books:

Books by John Michell

The total square footage of the circles in the 1991 Barbury Castle crop circle formation was 31680. This is associated with the sub-lunar distance, in miles, around The New Jerusalem, corresponding to the length of the circle drawn above through the twelve small “moon” circles. The box drawn around the “Earth” circle (above) is also 31680 miles (4 x 7920). The base ten harmonic, 3168, is Greek Gematria for “Lord Jesus Christ.”

On the 28th of September, 1991, I was writing a letter and decided to quote Seth. (channeled by Jane Roberts). When I picked up “Seth Speaks”, I was startled at the cover picture. It is quite similar to The Barbury Castle pictogram.

Yesterday, I finally obtained a copy of the article about the meteorite that possibly struck the Yucatan 65 million years ago.

The city of Merida is almost in the center of the ring of Cenote holes. I flew to that city on a visit in 1982.

When I read that a giant circle of quartz was suspected to lay below the area, bells started to go off in my head so-to-speak. I recently read abut the crystal skull that was found near the area. It seems to have magic powers. I am wondering if it was formed by, or even is a piece of, the meteorite. I remembered stories abut crystal being the power source of UFOs, and people who think crystal has magic powers.

I remembered the crystal radio, and use of crystal in electronics as oscillators. It started to sink in. My dream interpretation material led me to believe that a divine message came, or would come, at the Yucatan.

About the same time, I saw the map of the Yucatan in the ‘Keys of Enoch” and realized that it was quite similar (pictured above) As I understand it, energy is coming to earth at the Yucatan. And now I am seeing that a giant crystal sphere is located there, like a grand radio receiver.

I remembered reading that quartz was associated with dowsed energy. I found the article in the Number 3 ‘Cerealogist’. This statement is on page 22:

“Whatever the method, (To run lines of energy across the landscape) there appears to be some extraordinary knowledge behind it, because the main source of the energy appears to be naturally sited quartz.”

This extensive article on dowsing tells of vast circuits of energy across the earth, and its association with water. I am starting to see a vast communication network across the planet Earth through water and crystal, with the big one at the Yucatan. The energy probably comes in from space. The ancient people were aware of this energy, and built the megalithic structures at energy points.

It remains a mystery to me why the crop circle phenomena is centered near Stonehenge, rather than the Yucatan, or even Giza. The only guess I have thought of, is the idea of colonization, like the legends of MU, perhaps a spiritualization process will spread from the island.

There are approximately 3,000 Cenote holes with 1400 inspected and registered.

On page 21 of the Cerealogist:

“The (dowsing) project was prompted by my discovery of a henge site where many lines of energy appear to have been tapped in a numerical sequence which relates to fifty-six pits on the perimeter of the sites – similar to Stonehenge.”

Perhaps the pits are like a ring of Cenote holes on a smaller scale.

I have quite a story to tell about how my dream material has told me a symbolic story of evolution. At this point, it is dispersed throughout my notes. At a certain point, I realized that it was similar to the movie, “2001: Space Odyssey.” This sounds off-the-wall, but the theory is that such things come from dreams and inspirations, and may contain some truth, if one can interpret the symbolism. There are many examples, such as Jules Verne, but the most startling I can think of, is the book, “Futility”, which predicted the sinking of the Titanic.

As I understand it, the movie shows that an unknown, intelligent power, represented by the obelisk, controlled evolution by showing the ape how to use a bone for a weapon.

The action shifts to the year 2001, when a mysterious obelisk is found buried on the moon. The obelisk seems to be communicating to another planet. A spacecraft is sent to find the source of the communication. Only one man reaches the destination. Reality become like a dream. The man, Dave, ages rapidly and then becomes a baby in a bubble that returns to the earth. A great cycle of evolution has been completed. The next great cycle begins.

Part f my symbolic evolution story involves the moon landing. The statement, “One small step for a man, one giant leap for mankind.”, has a deep and profound meaning. A symbolic, manifest event occurred shortly before the moon landing, with a large portion of humanity watching on their television sets. It was the ‘giant leap’ of Bob Beamon in the 1968 Olympics. I felt that it was a psychic event, and the feeling was strengthened when I saw Mr. Beamon interviewed last year. (1990) . I speculated then about the symbolic connection to the moon landing. Some time later, while reviewing my notes, I saw my dream voice message: “Human global link in connection to mexico seen.” It looked like a headline in a newspaper.

I realized that the giant leap had occurred in Mexico City and that my dream voice predicted that I would make the connection to the moon landing and the profound symbolic significance. I remember thinking later that the dream voice could have been more specific if it had said, “Mexico City, instead of just ‘Mexico’. But I understand now that I have found another human global link at the Yucatan.

As I was looking at the map in the Science News article, it struck me that the circle marking the Cenote holes is somewhat like he Yin-yang symbol. The ocean is a dream symbol of the spirit world, (the souls) and the land, or earth is a symbol of the physical world. So the substance of this big Yin-yang symbol is quite appropriate. The importance of the duality balance in the great change seems to be communicated often, and in a variety of ways. So the giant Yin-yang is probably not an accident.

I read, or re-read some of ‘The Keys of Enoch’ today. There are many references to crystal energy and evolution. As I understand it, Mr. Hurtak is speaking of an evolution in consciousness, rather than the physical evolution of animals. Key 1-0-5 on page 43, tells of the ‘three and one’ alignment of consciousness forces in the great pyramid.

On page 50, verse 64, Mr. Hurtak predicted: “For behold, a great sign will be given unto you which will be the coming of the pyramidal capstone of the Christ Light in the skies, which will land upon the pyramidal foundations of the righteous to quicken the ‘living dust’ of gravitationally trapped light to become a New Earth.”

It seems to me that such a sign has been given near Barbury Castle. Perhaps another sign was planted 65 million years ago, and is awaiting discovery.

Mr. Hurtak claims that pyramidal grids were established on planets, such as Mars. On page 35 is a Mariner 9 photo of the surface of Mars. The pyramid structures are strikingly like the Barbury Castle pictogram.

Verse 2 on page 33 sounded familiar; “Therefore, each pyramid of light is energized with YHWH’s (God’s) Eye in the center of the pyramid….”

As I understand it, this light pyramid concept effects everything from sub-atomic particles, on up to universal scales.

This sounds absolutely mind-boggling, but a dream told me pretty much the same thing.

I had the dream months before hearing about the idea. Confirming information has come to me from two other sources. Jon Klimo, author of ‘Channeling’, told me that we must understand the sub-atomic nature of the change. An article in ‘Reality Change,’ from the Seth group, stated that the duality was inherent in each unit of consciousness. Seth teaches that all that exists, is All-That-Is, or God, manifesting himself, the smallest division is the ‘consciousness-unit.”

Mr. Hurtak says in verse 14, on page 84, that master grids were established in units of eighteen, nine ‘A-line’ and nine ‘B-line’ controls, with, “A non-planetary pyramid-five formation, which is the central model for information processing.”

In “he Cerealogist” article on dowsing, Hamish Miller reported that the energy defining a shape were in multiples of five. The measurements of one of the pictograms at Pepperbox Hill was also in units of five. I am wondering if this is suggestive of the ‘pyramid-five formation.’

Dream of Woman Communicating Through Our Amino Acids

In 1992, a dream reported in the Dream Network Journal. The dreamer was awestruck by a huge sphere with many facets in the sky. It had once been a woman in the very distant past, but had turned into this thing. It still had maternal feelings.

Sometimes it came close to the earth, like near mountains inhabited by humans, and felt connections. The sphere then exploded, filling the sky with stars. Then, the dreamer was by a tree, and the message was communicated to her that the object/woman communicated to us through our amino acids.

Since amino acids are molecules that make up DNA, this seemed to be the very same message as the other sources.


Excerpts from:

The discovery of DNA variability, holographic blueprints and the symphony of life
by Mike Adams

Announced with great fanfare in late November, 2006, scientists have discovered that human DNA is far more variable than previously thought. Contrary to previous beliefs, as much as 10 percent of human genes vary wildly from one person to the next. The mainstream press is hailing the discovery and some sort of breakthrough that will shed light on so-called “incurable” diseases and give researchers the ability to create more targeted medicines. (There’s always a pro-Pharma slant in the mainstream media isn’t there?) In reality, this new DNA discovery explains why most pharmaceuticals don’t work for most people.


If you look around in nature, where else do you notice copies of the same information? In harmonics, of course. A complex sound such as a single note on a violin is not made up of a simple square wave tone, it’s made up of highly complex harmonics which give the violin its own tone and timbre, a sort of auditory personality. On an oscilloscope, these often appear as copies of the same underlying waveforms.

They’re also called “overtones,” and they’re present throughout the human experience.

Simple saying the word, “we,” for example, involves shaping the mouth and tongue into an arrangement that creates complex, high-frequency overtones. The “ee” sound is the highest multi-frequency overtone sound created in human speech, but every vowel sound has its own unique pattern of repeating information. From low to high, it’s “uuu”

“ooo” “aaah” “eh” “eee.”

Physically, a human being is more like musical expression than a set of construction blueprints. The human body has near-perfect symmetry and economies of expression through fractal geometry that are quite evident in the structure of the circulatory system, for example, or the nervous system. Just look at a drawing of veins and arteries and you’ll notice the fractal patterns of geometry — the same patterns you’ll see drawn in the underside of a leaf, by the way.


Throughout the human body, from the lining of the cells of the stomach to the structure of the eye, you find patterns that go way beyond mere construction blueprints. The human body is a symphony, a grand musical masterpiece played out in billions of variations across the planet.

And the DNA, in my view, is a holographic reflection of the whole being. The repeating patterns of genes and the symmetry of the double helix are all expressions of music.

The human genome is a symphony, and it is through this symphony that we play the music of life. Combined with environmental factors and energetic factors (such as parental love), the symphony of human DNA creates a physical being. But it doesn’t stop there. It also helps create the framework for an emotional being, an energetic being and a spiritual being.


And “self” does not exist in isolation. We are, in every way imaginable, intertwined. We are all made of the same stuff, wrought from the same patterns of nature, and in fact, formulated from the same musical notes played out in five billion unique but compatible tunes. With this discovery, Western science has concluded we are all more different from each other than previously thought, but I believe it is evidence that we are all just unique verses of the same universal poem.

[End of excerpts]



English Vowels A(1) E(5) I(9) O(15) U(21) = 51 =153 / 3

Sometimes “Y”: 51 + 25(Y) = 76

codon 3 15 4 15 14 = 51 [AEIOU (vowels)]

The Mandelbrot Set might be considered the fractal of all fractals. The Mandelbrot Set crop circle formation is also a music metaphor.

The Mandelbrot Set Crop Circle Formation

(explain Hawkins work)

More Information about The Book of Knowledge: The Keys of Enoch

In early 1991, a relative handed me, The Book of Knowledge: The Keys of Enoch, by scientist, James J. Hurtak. He wrote the book after an amazing spiritual experience in 1973. The Light Being, Enoch, led him in spiritual flight, where he learned many things about the creation and changes to come in the next few decades.

The book is difficult to comprehend, as it is complex and uses specialized information. I will attempt to summarize briefly, the relevant parts here, that cover the DNA material, in terms of how it seems to relate to the other parts of the article. This summery is by no means a comprehensive accurate account of Dr. Hurtak’s writings on the subject.

Dr. Hurtak learned that there are connections between DNA and the Divine Name of God (YHVH or YHWH).

While at the University of California, Dr. Hurtak developed ideas about a connection between a series of linguistic and genetic associations in the spelling of God�s name in the biblical Hebrew (YHVH).

The four letters of the Divine Name, often called the Tetragrammation, were used as a code in the creation of man. The four bases of DNA and the four chambers of the heart, are examples. Through this, “The Word becomes flesh.”

The four letters of the Divine Name are also related to the Four Living Creatures of Ezekiel and Revelation. The Four Living Creatures are related to the Merkabah, which appears in a multiplicity of forms. It is called a “vehicle of vehicles.” It can guide a person into other experiences of creation, including a hookup or overlap between dimensions of light. It has the ability “to speak” through electromagnetic sinks (Key 3-0-1).

Dr. Hurtack wrote about the subatomic parts of creation. For example, he said that the Eye of YHWH is within each pyramid of light (Key 1-0-4). He also wrote that one can be connected to a parent mind through proton precession at the same frequency (Key 2-0-2). This seems to indicate a mental communication on a subatomic level.

On pages 35 and 36 are photographs of three-sided pyramids on Mars, taken by the Mariner 9 spacecraft in 1972.

The Brotherhood of Light established pyramids on certain planets in our solar system in relationship to Saturn. These pyramids are built in a grid formation. They are used to measure vibratory levels of consciousness (Key 1-0-4).

Pyramidal grids of information were established on Mars for gathering information deciphered from the magnetic lines of force attuned with thinking servomechanisms or computers existing in our solar system.

Master grids were established in units of 18. Nine are A-line controls and nine are B-line controls connected with a non-planetary pyramid-five formation, a central model for information processing. The pyramids are both three-sided and four-sided.

The grids collect information. For example, the grids measure energy as order and disorder transmitted through crystal structure and sunlight, and calculate all astronomic forces passing through the inner planetary crystalline network.

The greater pyramids on Mars cover ten times the area used by the Co-Creators in establishing the major pyramidal grid at Gaza, and five times the area of the major pyramidal grid established in China during previous evolutionary cycles.

There is a map titled, “The Return of the Dove,” on page 49 (Key 105). It is shown as a stylized bird superimposed over North and Central America.

A map of the Yucatan is shown on page 311, called “The Sacred Grid.” A triangle is drawn between ancient sites, one of which is Chichen Itza. This is the area of the “Return of the Dove.” It will be the key earthly location of the grid shift and alignment of Magnetic grids in space and life meridians in greater universe. This will involve a trinitized unfoldment, and will prepare man for the shift in his life cycle (Key 215).

Within the Head of the Dove, which includes the general area of the Yucatan, are girds of crystal  which mark sacred energy complexes. The cycle of Atlantis also involved key points in the Americas  (Key 215, #30-39).

When I first read the above material, it seemed quite fantastic and farfetched. However, subsequent events and findings clearly confirmed that there are indeed messages coming about DNA. Some of the ideas could be symbolic rather than literal. In any case, it appears to be quite important.

[ ]

Sacred Geometry – The Biblical Perspective

This is something I did a while back to explain sacred geometry to some devoutly Christian people and so I used the Bible’s story of creation to give it a framework. In creating this I also looked at the Quran, the Tao te Ching, and a variety of creation myths and stories from various other cultures. I was going to revise these images with the texts of other creation stories but never got around to it. However, every creation story follows the same format: From one comes 2, from 2 comes 3, from 3 comes 4, and from 4 the whole of physical creation. It is not, repeat not, the exclusive domain of the Christian story of creation. Take these images and do some of your own reading on other cultures creation myths and you will see what I mean. The last image–A Practical Application–shows how it is present in things we don’t even necessarily think about in being present in and addresses the 3D vs 2D. The whole thing also addresses the question of what the FOL is and why it has been important in so many cultures.

Day 1 & 2:


Day 3 & 4:


Day 5 & 6:


Day 7:



Practical Application:



“Article 64” – Deeper Insights Into Metatronic Finite Death Sciences


Article 64 title


Stephen M. Phillips

Flat 4, “Oakwood House,” 117-119 West Hill Road. Bournemouth. BH2 5PH. England.



Previous articles have revealed in sacred geometries analogous patterns of division of shared parameters. This article will analyse those divisions that have particular relevance to the account given by Annie Besant and C.W. Leadbeater of their remote viewing of what they took to be the basic constituents of atoms. The divisions:

48 = 24 + 24,

336 = 168 + 168


168 = 84 + 84

in these shared numbers will be examined for the following examples of holistic systems/sacred geometries:

1. the inner form of the Tree of Life;

2. the dodecagon;

3. the Sri Yantra;

4. the 64 hexagrams known to students of the I Ching;

5. the five Platonic solids;

6. the disdyakis triacontahedron;

7. the {3,7} tessellation of the 3-torus;

8. the seven diatonic musical scales.

The exact correspondences in their properties is too extensive to be attributed, plausibly, to chance. Instead, these holistic systems should be recognised as triangular, polygonal, polyhedral, topological or musical manifestations of a universal, mathematical pattern that governs such systems and which is realised in the subatomic world in the E8×E8 heterotic superstring that was paranormally described over a century ago by Besant and Leadbeater. 


Table 1. Gematria number values of the ten Sephiroth in the four Worlds.












(I am)




(Angel of the Presence)


Chaioth ha Qadesh

(Holy Living Creatures)


Rashith ha Gilgalim

First Swirlings.

(Primum Mobile)








(The Lord)




(Herald of the Deity)







(The Sphere of

the Zodiac)








(God in multiplicity)




(Contemplation of God)
























(Benevolence of God)




(Shining Ones)












(The Almighty)




(Severity of God)




(Fiery Serpents)



Vehement Strength.









(God the Creator)




(Like unto God)








The Solar Light.









(Lord of Hosts)




(Grace of God)



Tarshishim or




Glittering Splendour.









(God of Hosts)




(Divine Physician)



Beni Elohim

(Sons of God)



The Stellar Light.









(Almighty Living God)

          49, 363



(Strong Man of God)




(The Strong)



The Lunar Flame.









(The Lord and King)




(Manifest Messiah)




(Souls of Fire)


Cholem Yesodeth

The Breaker of the Foundations.

The Elements.



(All numbers in this table that the article refers to are written in boldface).

The Sephiroth exist in the four Worlds of Atziluth, Beriah, Yetzirah and Assiyah. Corresponding to them are the Godnames, Archangels, Orders of Angels and Mundane Chakras (their physical manifestation). This table gives their number values obtained by the ancient practice of gematria, wherein a number is assigned to each letter of the alphabet, thereby giving a number value to a word that is the sum of the numbers of its letters. Numbers from the table are written in boldface in the article.


1. Introduction

Previous articles have established that sacred geometries embody in their mathematical properties a common set of patterns relating a shared set of structural parameters. Some of these numbers — like 26, 248 and 496 — have become established in the research literature of theoretical physics in the form of superstring physics, although whether they apply to the real world remains experimentally uncertain, despite the beautiful, mathematical ideas that surround them. Other parameters have not (yet) appeared, giving sceptics scope to dismiss as the product of chance all evidence of correlations between these geometries and recent discoveries in theoretical physics. This article will analyse and compare those mathematical correspondences that have particular relevance to the remote-viewing investigations of subatomic particles by Annie Besant and C.W. Leadbeater. The number relationships in question are:

336 = 168 + 168,

168 = 84 + 84 = 24 + 144.

The upward continuations of these divisions:

672 = 336 + 336


1344 = 672 + 672,

also appear in sacred geometries. As they have been analysed in detail and given scientific interpretation at the author’s website [1], they need not be discussed here. The purpose of this article is more than just to map out the correspondences. It is to convince the reader that they are too detailed and

(7+7) enfolded polygons

Figure 1. The inner form of the Tree of Life.

 shared geometrical elements in outer and inner Trees of Life

Figure 2. Each set of 7 enfolded polygons in the inner Tree of Life shares with its outer form three corners & two sides of its triangles (coloured green).

too pervasive to be due to chance. The fact that this demonstration provides highly convincing support for the objective character of the paranormal observations of Besant & Leadbeater is incidental, although highly pertinent.

2. The Inner Tree of Life
Implicate in the geometry of the outer form of the Tree of Life (Etz Hayim, עץ חיים) known to traditional Kabbalah is its inner form. It consists of two sets of seven enfolded, regular polygons:

triangle, square, pentagon, hexagon, octagon, decagon, dodecagon.

(24+24) corners of 7 separate polygons

Figure 3. The 7 separate polygons with 48 corners is divided into two sets, each with 24 corners.
S1 & S2 in 7 enfolded polygons Two S1 and two S2

Figure 4. The two sets of enfolded polygons: S1 & S2.

Figure 5. The two sets of enfolded polygons: S1 & S2 and their mirror images S1′ & S2′.


The polygons in one set are the mirror images of their counterparts in the other set (Fig. 1) and share the so-called “root edge” separating the two sets. The 14 polygons lie in the plane formed by the two side pillars of the outer Tree of Life, namely, the right-hand Pillar of Mercy and the left-hand Pillar of Judgement (Fig. 2). The top, bottom and centre of each hexagon coincides with corners of triangles belonging to the outer Tree of Life, and the two internal, vertical sides of their sectors are sides of these triangles. Hence, 10 of the geometrical elements making up the inner Tree of Life are shared with its outer form.

It has been pointed out in previous articles that these seven separate, regular polygons with 48 corners comprise two sets of polygons with 24 corners: the first set (let us call it “S1”) consists of the triangle, square, pentagon & dodecagon; the second set (call it “S2”) consists of the hexagon, octagon & decagon (Fig. 3). (remember that in situ (Fig. 4), S2 has the sector of its hexagon missing that is occupied by the violet triangle in S1 because all the polygons lie in the same plane). Similarly, Figure 5 indicates that each red polygon in S1 has its mirror-image in S1 and that each blue polygon in S2 has its mirror image in S2′. As we shall discover later, two other sets of polygons with 24 corners exist, but — unlike S1 & S2 — they do not exactly divide in half the collective properties of the seven polygons — whether the latter are separated or enfolded.

This 24:24 division of the parameter 48 is characteristic of all holistic systems. It manifests in the 4‑dimensional projection of the 421 polytope as the 120 vertices of each of the two 600-cells whose compound is the 4-dimensional projection of this polytope in the Coexter plane [1]. This is because the 120 hexagonal yods in the four separate polygons of S1 constructed from tetractyses symbolise the 120 vertices in one 600-cell and the 120 hexagonal yods in the three polygons of S2 symbolise the 120 vertices in the other 600-cell. If the inner form of the Tree of Life is thought of as the “DNA” encoding how its outer form replicates, then S1 and S2 are the “strands” of this DNA and have their microscopic realisation in the outer and inner halves of the 10 helical whorls of the UPA/E8×E8 heterotic superstring, the two halves being generated by the 240 vertices of the two 600-cells (or, rather, the 240 E8 gauge charges that these vertices represent). It is worthwhile, therefore, to examine the geometrical and yod compositions of S1 and S2. Later, it will be shown that these combinations are unique in the sense that no other grouping of the seven polygons into two sets with equal numbers of yods and equal numbers of geometrical elements leads to equal numbers when they become enfolded in one another as the inner form of the Tree of Life.

Geometrical composition of S1 & S2

Listed in Table 2 are the numbers of corners, sides & triangles in the seven separate, regular polygons of the inner Tree of Life when they are divided into their sectors:

Table 2. Geometrical composition of the seven separate Type A polygons.













































When they are separate, S1 and S2 have — by definition — the same number of corners (24), the same number of sides (48) and the same number of triangles (24). When they are enfolded (Fig. 6), the right-hand corner of the triangle coincides with the centre of the hexagon, its two sloping sides coincide with sides of sectors of the hexagon and the right-hand corner of the pentagon coincides with the centre of the decagon. Associating the root

176 corners, sides & triangles in 7 enfolded polygons S1 & S1
Figure 6. The 7 enfolded polygons have 47 sectors with 41 corners & 88 sides.

Figure 7. S1 (red polygons) & S2 (blue polygons).

edge with S1, the polygons in both S1 and S2 have 18 corners and 21 sides. In terms of just their boundaries, S1 and S2 are the two halves of the right-hand half of the inner Tree of Life. The same is true for their respective mirror images S1′ and S2′ in its left-hand half. But what happens when their sectors are taken into account? Table 3 lists the geometrical compositions of the root edge and what is outside it in S1 and in S2 when their enfolded polygons are divided into their sectors (Fig. 7):


Table 3. Geometrical composition of S1 & S2 outside the root edge.

Root edge
























S1 and S2 cannot have the same number of corners of their sectors because the total number (41) is an odd integer, not an even one, and is, therefore, not exactly divisible by 2. However, if we associate the root edge with S2, the latter has the same number of sides (44), as well as the same number of corners & triangles (44) and the same number of corners, sides & triangles (88), as S1. Whether as combinations of just polygons or as combinations of polygons divided into their sectors, S1 and S2 can be regarded as the two halves of the set of seven enfolded polygons provided the root edge is assigned to S2.

Intrinsic geometrical elements

The right-hand corner of the triangle coincides with Chesed in the Tree of Life, whilst the two internal vertical sides of sectors of the hexagon form its side pillars. This means, referring to Table 2, that, outside the root edge, S1 has 87 geometrical elements unshared with the Tree of Life and that S2 has 81 unshared geometrical elements, so that S1 & S2 have (87+81=168) geometrical elements outside the root edge that are intrinsic to them. The number 87 is the number of Levanah, the Mundane Chakra of Yesod, which is the penultimate Sephirah. The number 168 is the number of Cholem Yesodeth, the Mundane Chakra of the last Sephirah. Amazingly, it is embodied in the inner Tree of Life in two different ways because the topmost corner of the hexagon coincides with the lowest corner of the hexagon enfolded in the next higher Tree, so that (176−1−7=168) elements intrinsic to each set of seven polygonssurround their centres.

Yod populations of S1 & S2

Let us now consider the yod compositions of S1 and S2. Listed in Table 4 are the numbers of yods in the seven separate, regular polygons whose sectors are constructed from tetractyses:

Table 4. Yod populations of the seven separate, Type A polygons.


















Hexagonal yods


















Table 5 lists the yod populations of the root edge and what is outside it in S1 and in S2:

Table 5. Yod compositions of S1 & S2 outside the root edge.

Root edge









Hexagonal yods










If we associate the root edge and its four yods with S2, the latter has the same number of yods (132) as S1. In other words, the yod population of the seven enfolded polygons then becomes evenly divided between S1 and S2, just as we saw earlier that their number of geometrical elements is. The split of the seven separate polygons into two sets with the same numbers of corners, sides & triangles surrounding their centres and the same numbers of yods surrounding their centres persists when they are enfolded in the form of S2 having the same number of yods as S1 has outside the root edge.

Proof of uniqueness of S1 & S2 as the two halves of the seven polygons

In terms of the numbers of corners of the seven regular polygons making up the inner Tree of Life:

3, 4, 5, 6, 8, 10, 12

four combinations of numbers add up to 24:

1.                        3 + 4 + 5 + 12

2.                        6 + 8 + 10

3.                        3 + 5 + 6 + 10

4.                        4 + 8 + 12


This allows two possible sets of polygons with 24 corners: either (1) & (2) or (3) & (4). The sets (1) & (2) are, respectively, S1 and S2. Let us call the sets (3) & (4), respectively, S3 & S4. The geometrical compositions of the root edge and what is outside it in S3 and in S4 are shown in Table 6:

Table 6. Geometrical compositions of S3 & S4 outside the root edge.

Root edge
























We see that the geometrical compositions of S3 and S4 (either for each type of geometrical element or in total) cannot be made equal by associating the three geometrical elements in the root edge with either S3 and S4. Listed in Table 7 are their yod populations:

Table 7. Yod populations of S3 & S4 outside the root edge.

Root edge









Hexagonal yods










We see that their various yod populations cannot be made equal by associating the four yods in the root edge with either S3 or S4. Only the 24:24 division of the seven separate polygons into S1 and S2 creates equal total numbers of geometrical elements and equal yod populations when the two combinations with 24 polygonal corners become enfolded. This remarkable fact indicates that only S1 and S2 can be regarded as true halves of the set of seven polygons and vindicates the use of only these two combinations in various analyses in previous articles of the inner Tree of Life basis of holistic parameters, such as the superstring structural parameters 1680, 336 & 168. As this has shown, they are in fact the only two sets of polygons that have equal populations of geometrical elements and yods.
524 yods in inner Tree of Life Figure 8. The root edge with 4 yods separates the two sets of 7 enfolded polygons containing 260 yods.

Further evidence of the unique status of S1 and S2 vis-à-vis the inner Tree of Life is provided by the (S1+S1′) and the (S2+S2′) making up the (7+7) enfolded polygons. According to Table 5, (S1+S1′) have (2×132=264) yods outside the root edge and (S2+S2′) have (2×128=256=44) yods outside the root edge, i.e., 260 yods when the latter is included. Compare this with the fact that the seven enfolded polygons have 264 yods, of which 260 yods lie outside the root edge (Fig. 8). (S1+S1′) without the root edge have the yod population of the seven enfolded polygons, i.e., one half of the inner Tree of Life, and (S2+S2′) with the root edge have the yod population of the other set of seven enfolded polygons outside their root edge. Table 8 lists the numbers of yods lining the tetractyses in S1 and S2:

Table 8. Numbers of boundary yods in S1 & S2.



Root edge



Yod population






Number of hexagonal yods at centres of tetractyses





Number of boundary yods







216 intrinsic boundary yods in 7 enfolded polygons 216 boundary yods in two S1
Figure 9. 216 yods intrinsic to a set of 7 enfolded polygons line their 47 tetractyses.

Figure 10. 216 yods outside the root edge line the 48 tetractyses in S1 & S1′.

We see that S1 and S1′ have 216 boundary yods outside the root edge. The seven enfolded polygons have 264 yods, of which 47 are hexagonal yods at centres of tetractyses. This leaves 217 boundary yods, of which one is the top of the hexagon and coincides with the lowest corner of the hexagon enfolded in the inner form of the next higher Tree of Life. This means that 216 yods lining the sides of tetractyses are intrinsic to the inner form of each overlapping Tree (Fig. 9). This is the number of boundary yods in S1 & S1′ (Fig. 10).

According to Table 8, S2 & S2′ have 214 boundary yods when the root edge is included. This is the number of yods in the outer Tree of Life with Type A triangles (Fig. 11). S2 has 109 boundary yods when the root edge is included. As it contains the hexagon, the topmost corner of which coincides with the lowest corner of the hexagon enfolded in the next higher Tree of Life, 108 such yods are intrinsic to S2. This is also the number of boundary yods in S1outside the root edge.

214 yods in Tree of Life with Type A triangles

The Tree of Life contains 214 yods when its 19 triangles are Type A.

214 boundary yods in two S2

214 yods line the 46 tetractyses in S2 & S2′.

Figure 11. (S2+S2′) are lined by as many yods as the Tree of Life contains yods when its triangles are Type A.

Not only are the yod populations of S1 and S2 equal, but so, too, are the numbers of yods on the boundaries of their tetractyses when the root edge is associated with S2. The 216 boundary yods intrinsic to the seven enfolded polygons are divided equally by S1 and S2, whilst (S1+S1′) and (S2+S2′) embody the same holistic parameter. It is further evidence that S1 and S2 uniquely embody properties that are quantified by the same numbers that quantify properties of the complete form of the inner Tree of Life. The implication of this is that these two halves of the inner Tree should be regarded as holistic structures in themselves. It should, therefore, come as no surprise that S1 and S2 can be regarded as representing the two 600-cells that are the two halves of the Petrie projection onto the Coexter plane of the 421 polytope which in turn generate the outer and inner halves of the UPA, the subquark state of the E8×E8 heterotic superstring (see the discussion under Fig. 4 here). They can further be associated with the 120 vertices & edges of the 24-cell making up each 600-cell and with its 120 faces & octahedral cells, that is, with its 0- & 1-polytopes and with its 2- & 3-polytopes, for the polytope composition of the 24-cell conforms to the archetypal pattern of the seven regular polygons in the inner Tree of Life (see beginning of #4 here). This 120:120 division exists in S1 and S2 not only when their polygons are regarded as enfolded but also when they are separate. The number of hexagonal yods in an n-gon is 5n, so that each combination of separate polygons has 5×24 = 120 yods. Assigning a different colour to each of the five hexagonal yods per sector of an n-gon, every colour appears 24 times in S1 and 24 times in S2. For the 600-cell, each hexagonal yod denotes a vertex of a 24-cell, the five


colours signifying the five such cells whose compound is the 600-cell (Fig. 12).

Five sets of (24+24) hexagonal yods in 7 separate polygons Figure 12. The five sets of 24 hexagonal yods in S1 denote the five sets of 24 vertices in the compound of five 24-cells that is the 600-cell. Similarly, for S2. (S1+S2) represents the 240 vertices of the compound of two 600-cells that is the Coexter plane projection of the 421 polytope whose 240 vertices map the 240 roots of E8. Similarly, (S1′+S2′) represents the 240 roots of E8′. Therefore, the complete inner form of the Tree of Life represents E8×E8′.

The number of corners, sides & triangles surrounding the centre of a Type B n-gon is 10n. The 10 geometrical elements per sector comprise five sides and five corners & triangles. The 240 geometrical elements in either S1 or S2 that surround centres of polygons comprise 120 sides and 120 corners & triangles (Fig. 13). So they display the 120:120 division characteristic of holistic systems in both their sides and their corners & triangles.

240 geometrical elements in S1 & S2
Figure 13. Containing Type B polygons, S1 and S2 each has 240 geometrical elements comprising five sets of 24 sides and five sets of 24 corners & triangles. This is the geometrical analogue of the (240+240) roots of E8×E8′. The five types of sides, repeated 24 times, correspond to the five 24-cells, each with 24 vertices, making up a 600-cell. The five types of vertices or triangles, repeated 24 times, correspond to the five 24-cells making up a second 600-cell. S1 is geometrically analogous to the compound of two 600-cells whose 240 vertices are the projections of the 240 vertices of the 421 polytope representing the 240 roots of E8. Similarly, S2 is analogous to E8′. (S1+S2) is analogous to E8×E8′. The division of the seven enfolded polygons into S1 & S2 generates, therefore, a pattern of geometrical elements that is analogous to the root composition of E8×E8′. This is the symmetry group of one of the two types of heterotic superstrings that has been shown to be free of quantum anomalies.

Whether we are speaking of hexagonal yods in Type A polygons or geometrical elements in Type B polygons, the number 240 is present. In the case of the latter, because the 10 geometrical elements per sector divide into two sets of five, S1 and S2, the two halves of the seven separate polygons, whose centres are surrounded by 480 geometrical elements, each comprise 240 such elements. As the parameter 240 always refers in sacred geometries to the 240 roots of E8, we see that the two halves signify the two identical E8 Lie groups that appear in the direct product E8×E8, one of the two symmetry groups that were discovered in 1984 to describe the interactions of superstrings that are free of quantum anomalies. We saw earlier that, even though they are, separately, only half of the whole set of polygons making up the inner Tree of Life, S1 and S2 possess properties quantified by numbers that refer to this whole set. Here, once again, is evidence that S1 and S2 can be regarded as wholes in themselves. They remind one of the division of the Tao into the polar opposites of Yin and Yang — complementary components of the Whole, yet complete in themselves.

Superstring structural parameters 84, 168 & 336 embodied in S1 & S2

According to Table 3, S1 has 88 geometrical elements outside the root edge, i.e., 84 elements surround the centres of its four polygons. S2 has 85 geometrical elements outside the root edge. Of these, one is the centre of the octagon, the centres of the hexagon and decagon being counted as belonging to S1 because the right-hand corner of the triangle coincides with the centre of the former and the right-hand corner of the pentagon coincides with the centre of the latter. Therefore, 84 geometrical elements surround the centres of its three polygons. Surrounding the centres of S1 & S2 in Figure 7 are (84+84=168geometrical elements outside the root edge. Similarly, (84+84=168) geometrical elements outside the root edge surround the centres of their mirror images S1‘  & S2′. (S1+S2) and (S1′+S2‘)  consist of (168+168=336)


geometrical elements outside the root edge that surround the (5+5) centres that are not also corners of polygons. They comprise four sets of 84 geometrical elements, so that 168 geometrical elements surround the centres of not only S1 and its mirror image S1′ but also S2 and its mirror image S2′ (Figs. 14 & 15).

Figure 14 (84+84) intrinsic geometrical elements in two S2
Figure 14. (84+84=168) geometrical elements surround the centres of the eight polygons in S1& S1′. Figure 15. (84+84=168) geometrical elements surround the centres of the six polygons in S2 & S2′.

According to Table 3, the seven enfolded polygons have 176 geometrical elements, including the root edge. Therefore, (176−7=169) geometrical elements surround their centres. One of them is the topmost corner of the hexagon in S2, which coincides with the lowest corner of the hexagon enfolded in the next higher Tree. The number of geometrical elements surrounding the centres of the 7n polygons enfolded in the n-tree = 168n + 1. 168 such elements are intrinsic to each set of polygons. S2 has 85 geometrical elements outside the root edge, so that 83 elements intrinsic to it surround its centres. Including the root edge, S1 has 91 geometrical elements, so that (91–4–2=85) elements are not centres. The 168 intrinsic elements that are not centres comprise 85 elements in S1 and 83 in S2. The 84:84 division of the holistic parameter 168 exists for the generic set of seven polygons enfolded in a single Tree. It does not exist in the inner forms of successive Trees of Life. The S1:S2 division does not lead to an 840:840 division in 10 Trees of Life. But this should not be a surprise, because we know that holist systems embody the number 336, which divides into two halves, and this is not possible in this context because the number 168 includes the root edge, so that it cannot have a mirror-image set of 168 elements. The correct embodiment in the inner Tree of Life that permits generalisation to multiple Trees is the pattern of 168 geometrical elements outside the root edge in each set that are unshared with the outer Tree of Life. S1 has 88 geometrical elements outside the root edge, of which one (corner of triangle) is shared with the Tree of Life. The 168 elements intrinsic to the inner form of each Tree comprise 87 elements in S1 and 81 elements in S2. 87 is the number value of Levanah, the Mundane Chakra of Yesod, which is the Sephirah preceding Malkuth, whose Mundane Chakra has the number value 168! Here is a remarkable example of how the gematria number values of the Sephiroth, their Godnames, etc. quantify properties of whatever is a holistic system (in this case, that part of the inner Tree of Life that is intrinsic to it).

Both the 84:84 division of the holistic parameter 168 and the 168:168 division of the holistic parameter 336 have been discussed in many earlier articles as characteristic of sacred geometries. Later sections of this article will review their embodiment in the Sri Yantra, disdyakis triacontahedron, the four Platonic solids, the table of 64 hexagrams used in I Ching, the seven diatonic, musical scales and the 3-torus. The 8:6 division of the 14 regular polygons making up the inner Tree of Life splits in half the 336 intrinsic geometrical elements surrounding their centres. As discussed in Section 10, we find a similar division in the 14 types of notes that make up the seven diatonic scales [2] and whose tone ratios are:

1    256/243     9/8    32/27    81/64    4/3    1024/729 │ 729/512    3/2    128/81     27/16    16/9    243/128    2

The vertical line divides the first seven notes from their inversions.[1] Eight notes with their tone ratios written in black) constitute the Pythagorean scale and six notes written in red are non-Pythagorean notes. It occurs also in the outermost group of 14 triangles of the Sri Yantra. Six of these triangles touch the circular ring of eight lotus petals that surrounds the 43 triangles and eight triangles do not touch it (see Fig. 34).

The inner Tree of Life has 336 intrinsic geometrical elements outside the root edge surrounding the centres of its 14 polygons. It is divided into two halves (S & S′), with S′ the mirror image of S. Each half has 168 such geometrical elements and is further split into two halves: S1 & S2. Each “quarter” of the inner Tree of Life has 84 geometrical elements surrounding centres of polygons. Compare this with the following structural properties of the UPA: each helical whorl with 1680 turns twists five times around the axis of spin. It makes five half-revolutions, each of 168 helical turns, in the larger spiral of its outer half and five half-revolutions, each of 168 turns, in the narrower spiral of its inner half. Each turn is a circularly polarised oscillation consisting of two perpendicular plane waves vibrating 90° out of phase, so that a half-revolution

[1] The inversion of a musical note with tone ratio m is a note with tone ratio 2/m.


comprises 336 plane wave oscillations grouped into 168 pairs. A factor of 2 manifests in a half-revolution of a whorl, firstly, as its two quarter-halves and, secondly, as the two perpendicular oscillations generating each turn. Two schemes of correspondence between the inner Tree of Life and a half-revolution of a whorl are possible:

Case A

Case B

168 oscillations

168 geometrical elements in S

168 geometrical elements in S1 & S1

168 oscillations with 90° phase difference

168 geometrical elements in S′

168 geometrical elements in S2 & S2

84 oscillations in first ¼-revolution

84 geometrical elements in S1

84 geometrical elements in S1

84 oscillations in first ¼-revolution with 90° phase difference

84 geometrical elements in S1

84 geometrical elements in S2

84 oscillations in second ¼-revolution

84 geometrical elements in S2 84 geometrical elements in S1

84 oscillations in second ¼-revolution with 90° phase difference

84 geometrical elements in S2 84 geometrical elements in S2

Intuitively speaking, case A seems the correct correspondence, with S1 and S2 denoting the two quarter-revolutions and the two halves of the inner Tree corresponding to the two plane wave oscillations that are 90° out of phase. This is because each half of the inner form of the Tree of Life constitutes a whole in itself and is a more fitting representation of each set of 168 orthogonal plane waves that makes up the half-revolution of a whorl. This is consistent with the Tree of Life nature of a whorl because the latter makes 10 half-revolutions around the spin axis of the UPA, each being analogous to one of the 10 Sephiroth, so that a whorl is represented by 10 Trees of Life, each corresponding to a Sephirah, and its 10 half-revolutions are also represented by 10 overlapping Trees. Figure 16 summarises the analogy between the geometries of the inner Tree of Life and the UPA. Figure 17 shows

168 turns in whorl as the inner Tree of Life

Figure 16. The (7+7) enfolded polygons of the inner Tree of Life represent a half-revolution of the 10 whorls of the UPA/subquark state of the E8×E8 heterotic superstring.

the inner form of 10 overlapping Trees of Life divided into the sets of polygons S1, S2, S1′ & S2′. Each of the 3360 intrinsic geometrical elements in the (79+70=140) polygons that make up this inner form corresponds to a plane wave component of the 1680 circularly polarised oscillations present in a half-revolution of the 10 whorls of the UPA. That there are four components of the inner Tree of Life and that each half of it results from pairing of these components only in one way:

S1 → S2 and S1′ → S2


  (1680+1680) unshared geometrical elements in inner form of 10-tree



S1 → S2′ or S2 → S1

reminds us of the four types of nitrogen bases in the DNA molecule: A, T, G & C, and how base A always pairs with base T through two hydrogen bonds and base C with base G through three hydrogen bonds when they form a rung of base pairs in the helical DNA ladder. It is as though the complementary pairs of bases (A, T) and (C, G) are analogous, respectively, to (S1, S2) and (S1′, S2′), so that the two helical halves of the DNA molecule are analogous to the two sets of sinusoidal waves in each helical whorl of the E8×E8 heterotic superstring that generate its 1680 circularly polarised waves because the waves in one set are 90° out of phase with those in the other set. A turn in a whorl would then correspond to a rung of base pairs, whilst the complementary nitrogen bases at each end of a rung would correspond to the two sinusoidal oscillations of the same amplitude but 90° out of phase that constitute a turn. The pairing of complementary bases in the molecule of life is an expression of the Taoist principle that the yang aspect of nature is always balanced by its yin aspect. The supposition of two orthogonal, sinusoidal oscillations in every turn of a whorl is another manifestation of this cosmic balance. In the inner form of the Tree of Life, it is expressed by its two halves, one associated with the right-hand Pillar of Mercy, which embodies the male principle (Siva, or Yang), and the other associated with the left-hand Pillar of Judgement, which embodies the female principle (Shakti, or Yin). These principles, of course, are entirely metaphysical.

S2 & S2′ embody the dimension 248 of E8

According to Table 4, S1 has 132 yods outside the root edge, where 132 = 4×(1!+2!+3!+4!). S2 has 128 yods outside the root edge. This is the sum of the Godnames of the first four Sephiroth:

21 + 26 + 50 + 31 = 128.

S2 & S2′ have 256 yods outside the root edge, where 256 = 44. These properties demonstrate the role of the Tetrad in determining the yod population of the inner Tree of Life. Of the 128 yods in S2, six yods lie on the two vertical sides of tetractyses inside the hexagon that are shared with triangles in the outer Tree of Life because they form its Pillar of Mercy and Pillar of Judgement. (128−6=122) yods outside the root edge are intrinsic to S2. Including the

S1:S2 division defines middle of 49-tree
Figure 18. The 295 yods in the seven polygons denote the 295 SLs up to Chesed of the 49th Tree. The S1:S2division corresponds to the middle of the 49-tree and is marked by the 148th SL. This is Netzach of the 25th Tree. It is the SL most characteristic of this Sephirah, whose gematria number value is 148.

root edge, the number of yods intrinsic to S2+S2′ in the inner form of the Tree of Life = 4 + 2×122 = 248This is the dimension of E8, the Lie group associated with the E8×E8 heterotic superstring. Of the 132 yods in S1, one yod (right-hand corner of the triangle) is shared with the outer Tree because it is located at the Sephirah Chesed; this leaves 131 intrinsic yods. 131 is the number value of Samael, the Archangel of Geburah, whose number 216 was found earlier to be the number of yods lining the 48 tetractyses in the two S148 being the number of Kokab, the Mundane Chakra of Hod.

The significance of the S1:S2 division for CTOL

According to Table 4, the seven separate Type A polygons have 295 yods. 288 yods surround their centres, where


288 = 1!×2!×3!×4!.

There are 295 SLs up to Chesed of the 49th Tree (Fig. 18). In order of emanation in the Tree of Life, Chesed is the first of the seven Sephiroth of Construction. The 49th Tree is the first of the 49 Trees mapping the 49 subplanes of the seven planes of consciousness. As each Tree expresses the essence of one of these Sephiroth of Construction, the 49th Tree expresses Chesed. So the 295th SL expresses par excellence the quality of this Sephirah. Each yod in a polygon denotes one of the 295 SLs up to the starting point for the emanation of the 49-tree representing the cosmic physical plane. According to Table 3, the four separate polygons in S1 contain 148 yods and S2 has 147 yods. The S1:S2 division therefore splits in half the yod population of the seven separate polygons of the inner Tree of Life. The number 148 is the gematria number value of Netzach. The 148th SL is Netzach of the 25th Tree, which is the middle of the lowest 49 Trees. The 25th Tree maps the fourth subplane of the fourth plane of consciousness, both the subplane and the plane corresponding to Netzach because it is the fourth Sephirah of Construction. So the number 148 — the halfway point in the emanation of the 295 SLs —locates the very SL in the 49-tree that most expresses this Sephirah, just as the number 295 locates the SL most expressive of the Sephirah Chesed! This remarkable property cannot be a mere coincidence. Instead, because of the correspondence between yods and SLs, the 24:24 division of the corners of the seven polygons, which splits the 168 intrinsic geometrical elements surrounding their centres into two sets of 84 elements, also divides in half the SLs that their yods symbolise and which belong to the 49 Trees mapping the cosmic physical plane. The following correspondences between yods and SLs exist:

  • 4 centres of S1 → 4 SLs from bottom of 1-tree to Netzach of 1-tree;
  • 144 yods surrounding centres of S1 → 144 SLs up to Netzach of 25th Tree;
  • 144 yods surrounding centres of S2 → 144 SLs above Netzach of 25th Tree to Netzach of 49th Tree;
  • 3 centres of S2 →3 SLs above Netzach of 49th Tree to Chesed of 49th Tree.

Here is remarkable confirmation of this conclusion: the numbers of corners, sides, triangles & tetrahedra making up the n-tree are shown below:

Number of corners = 6n + 5;
Number of sides = 16n + 9;
Number of triangles = 12n + 7;
Number of tetrahedra = n +1.

Total number of points, lines, triangles & tetrahedra in the n-tree = 35n + 22.

Every 48 overlapping Trees of Life contain (48×35=1680) geometrical elements and every 24 Trees contain 840 elements. Dividing any section of 48 Trees into two sets of 24 Trees generates two sets of 840 geometrical elements. Apart from the Pythagorean factor of 10, here is the 84:84 division

42-42 division in the Cosmic Tetractys  84 yods surround centre of 2nd-order tetractys
Figure 19. The 42 blue “yods” in the Cosmic Tetractys symbolise the 42 subplanes above the cosmic physical plane; the 42 red yods denote the 42 subplanes above the physical plane, whose 7 subplanes are symbolised by the 7 grey yods in the central tetractys. Figure 20. 84 yods in the 2nd-order tetractys surround the central black yod denoting Malkuth, or the physical universe.


of geometrical elements found earlier for the division of the seven polygons with 48 corners into S1 and S2, each with 24 corners. In fact, in the encoding of CTOL in the 12 separate polygons other than one square and one triangle, their corners mark out Trees of Life, so that S1 with 24 corners is associated with 24 Trees and S2 with 24 corners is associated with the next higher 24 Trees. The same 840:840 division exists in the inner form of 48 Trees. This is because the number of corners of the 7n polygons enfolded in the n-tree = 35n + 1, so that the 336 polygons enfolded in 48 Trees have (48×35=1680) corners and the 168 polygons enfolded in 24 Trees have 840 such corners. Their counterparts in the UPA are the 840 turns in either an outer or an inner half of a single whorl or in a quarter-revolution of all 10 whorls. This mathematical analogy between the subquark superstring and the cosmic physical plane is a powerful and beautiful illustration of the hermetic principle: “As above, so below.” The 70 enfolded polygons making up the inner form of 10 Trees of Life consist of 10 S1, with 840 intrinsic geometrical elements surrounding the centres of 40 polygons, and 10 S2, with 840 intrinsic geometrical elements surrounding the centres of 30 polygons.

Square representations of 84  336 = 336 yods in the cross pattee
Figure 21. The Tetrad expresses the holistic parameter 84.

Figure 22. The Tetrad expresses the 4-fold pattern within the holistic parameter 336.

Returning to CTOL, the number of SLs on the central Pillar of Equilibrium of the n-tree = 2n + 3. For n overlapping Trees, the number = 2n + 2. Seventeen SLs span the central pillar of the 7-tree mapping the physical plane and 184 SLs span the 91 Trees of CTOL. 167 SLs span the 84 Trees above the 7-tree, that is, the apex of the 7-tree is the 168th SL on the central pillar, counting from the top of CTOL. The apex of the 49‑tree mapping the cosmic physical plane is the 101st SL on the central pillar, that is, the 84th SL, counting from the top of CTOL. Fittingly, the number value 168 of Cholem Yesodeth, the Mundane Chakra of Malkuth, locates the Malkuth level of CTOL. The 84:84 division created by the geometrical composition of S1 and S2 in the inner Tree of Life appears in CTOL as the 84 SLs on the central pillar down to the top of the 49-tree and the next 84 SLs down to the top of the 7-tree. Each set of 84 SLs belongs to 42 Trees (Fig. 19).

As the next higher order tetractys above the well-known tetractys, or 1st-order tetractys, the 2nd-order tetractys (Fig. 20) is a representation of holistic systems. Its 10 tetractyses contain 85 yods, where

85 = 40 + 41 + 42 + 43.

84 yods surround its central yod, where

84 = 12 + 32 + 52 + 72.

(Fig. 21). The pattern of four groups of 84 structural units will always be found in a holistic system. It is represented by a cross pattée whose four arms are 2nd-order tetractyses (Fig. 22) with 84 yods outside their shared apex. The diagram aptly illustrates how the Tetrad expresses parameters characterising holistic systems and their four-fold division.

Compare this with the result obtained earlier that the centres of the four polygons in S1 are surround by 84 geometrical elements, as are the centres of the three polygons in S2. The two halves of the set of seven enfolded polygons are themselves holistic because they require 84 bits of information in the form of points, lines & triangles to create them, starting in each case from a mathematical point. This is what the 2nd-order tetractys signifies: 84 bits of information (whatever their meaning) symbolised by the 84 yods surrounding its centre are required to generate a holistic system, the outer, material form of which is symbolised by this central yod, signifying Malkuth. In the case of CTOL, they are the 84 Trees/subplanes whose final manifestation at the level of Malkuth is the 7-tree that maps the physical plane, or physical universe. In the case of the UPA, they are the 84 turns in an outer or inner half-revolution of each whorl. The factor of 4 results from each turn being a circularly polarised oscillation with two plane wave components and two half-revolutions forming a complete, 360° revolution of a single whorl: 4 = 2×2.


3. The 24:24 division in the 1st (6+6) polygons
Article 4 analysed how the gematria number values of the Godnames of the 10 Sephiroth prescribe the properties not only of the (7+7) enfolded polygons making up the inner Tree of Life but the first six polygons and their mirror image counterparts on the other side of the root edge. The first six separate polygons have 36 sectors with 42 corners, so that the first (6+6) separate polygons have 72 sectors with 84 corners. Whether they are separate or enfolded, let us call them “H.” Their embodiment of the holistic parameter 84 expressed by the 2nd-order tetractys in Fig. 20 indicates that this subset of the 14 polygons constitutes a holistic system in itself. The 42:42 division of its corners is analogous to the same division of Trees in CTOL above the 7-tree shown in Fig. 19 that is created by the six cosmic superphysical planes with 42 subplanes and by the six superphysical planes with 42 subplanes. Their holistic character is confirmed by their enfoldment to produce a geometrical structure with 50 corners, where 50 is the number value of ELOHIM, the Godname of Binah. YAHWEH, the Godname of Chokmah on the other side of the Tree of Life with number value 26, prescribes the first six enfolded polygons because they have 26 corners. Each set has 24 corners outside the root edge, so that both sets have (24+24=48) external corners (Fig. 23). The 24:24 division that splits in half the seven separate polygons with 48 corners re-appears by dividing H in half. As the topmost corner of each hexagon coincides with the lowest corner of its counterpart enfolded in the next higher Tree of Life, the H enfolded in each Tree has 48 unshared corners (24 associated with each set of six). Unlike that displayed in Fig. 23, this 24:24 division gets repeated in every Tree, which means that, as the correct way of dividing the 48 corners, the two endpoints of the root edge must be included, one with each set of 24 corners.

The 168:168 division in the 1st (6+6) polygons
When its (35+35=70) sectors are turned into tetractyses, H has 386 yods [3]. The topmost corners of the two hexagons coincide with the lowest corners of the two hexagons enfolded in the next higher Tree, leaving 384 yods intrinsic to the H in each Tree. This is another indication of its holistic nature, for previous articles have revealed how this number appears as a global parameter of well-known sacred geometries, as well as objects for which considerable evidence has been accumulated in the author’s articles and website to indicate that they possess a similar status. Surrounding the hexagonal yods at the centres of the 70 tetractyses are (384–70=314) yods intrinsic to H. Outside the four yods in the root edge are 310 (=31×10) intrinsic yods lining these tetractyses. This shows how EL, the Godname of Chesed with number value 31, prescribes H. 155 yods outside the root edge lie on the boundaries of the 35 tetractyses in each set of six polygons. This shows how ADONAI MELEKH, the complete Godname of Malkuth with number value 155, prescribes the form of H.

(48+168+168) yods in 1st (6+6) polygons (24+24+168+168) yods of 1st (6+6) polygons

Figure 24. 24 intrinsic corners & 168 yods are associated with the first 6 polygons enfolded in each Tree.

The 384 yods intrinsic to H comprise 48 corners of its 12 polygons and 336 other yods, where

336 = 4×84 = 22 + 62 + 102 + 142.

Associated with each half of H are 24 corners and 168 other yods (Fig. 24). The division:

48 = 24 + 24


in the polygonal corners intrinsic to H automatically generates the division:

336 = 168 + 168

in its yod population. Each set of 168 yods consist of 78 yods in the triangle, square & octagon and 90 yods in the square, hexagon & decagon (Fig. 25).

(78+90) yods in first 6 enfolded polygons Figure 25. The yod populations of subsets of polygons are the gematria number values ofCholem & Yesodeth appearing in the Kabbalistic name of the Mundane Chakra of Malkuth

These numbers are the gematria number values of, respectively, Cholem and Yesodeth, which are the two words making up the Kabbalistic name of the Mundane Chakra of Malkuth.

The 84:84 division in the 1st (6+6) enfolded polygons

Just as the 24:24 division of the corners of the seven separate polygons generates an 84:84 division of the yods in S1 & S2, so, too, the 24:24 division of the corners of H corresponds to a 84:84 division in the yods lining the sides of its polygons, as now shown. The first six separate polygons have 36 sides. Enfolded, they have 31 sides, showing how ELOHA, the Godname of Geburah with number value 36 and EL, the Godname of Chesed opposite it with number value 31, prescribe this holistic set of polygons. Two hexagonal yods lie on each side, totalling 62, where 62 is the number value of Tzadkiel, the Archangel of Chesed.

 168 yods on boundary of 1st (6+6) enfolded polygons

Figure 26. (84+84=168) yods outside the root edge line the sides of the 1st (6+6) enfolded polygons. They include (24+24) corners.

Notice that, as H contains 384 intrinsic yods, 192 yods are associated with each half of it, so that the first six enfolded polygons contain (192+2=194) yods that are intrinsic to them, where 194 is the number value of Tzadekh, the Mundane Chakra of Chesed. Both sets of six separate polygons have 72 corners, where 72 is the number value of Chesed. Here is a remarkable conjunction of four gematria numbers referring to the same Sephirah! The 12 polygons in H have 61 sides lined by (61×2=122) hexagonal yods and 50 corners, i.e., 172 yods. Hence, 168 yods outside the root edge lie on the sides of these polygons (Fig. 26). Each set of six polygons has 84 such yods (coloured red or blue in the diagram). (172–2=170)

Examples of the number 70 as a holistic parameter

 Figure 27. Examples of the number 70 as a holistic parameter.


boundary yods are intrinsic to H, and 87 such yods line the sides of each set of six enfolded polygons. 87 is the number value of Levanah, the Mundane Chakra of Yesod.

The 84 yods lining the sides of each set of six enfolded polygons divide into 42 yods on the sides of the triangle, pentagon & decagon and 42 yods lining the square, hexagon & octagon. These are the only possible combinations of polygons showing this division. The sequence of divisions:


Is always displayed by holistic systems. The way other sacred geometries exhibit it will be discussed in the remaining sections. Their higher-order transformations reveal that the sequence proceeds in the opposite direction as well. The most remarkable example of this is the Gosset polytope, whose 672 edges divide into the 336 edges in each half and which has (2×672=1344) hexagonal yods lining its edges when its faces are turned into tetractyses. Its Tree of Life basis is analysed in Article 62 (see ref. 1).

4. The dodecagon
As the tenth type of regular polygon and the last of the seven polygons making up the inner Tree of Life, the dodecagon is unique in that it is the single, polygonal representation of holistic systems. One of the parameters that define such systems is the number 70. It is embodied in the outer Tree as its 70 yods when its 16 triangles are tetractyses and as the 70 sides of the sectors of these triangles when they are Type A (Fig. 27). It is embodied in the inner Tree of Life as the 70 corners of its polygons, in the first (6+6) enfolded polygons as their 70 sectors and in the dodecagon as the 70 yods associated with each of the two joined dodecagons that surround its centre. The number 48 of Kokab, the Mundane Chakra of Hod, is embodied in these sacred geometries because 1. the outer Tree of Life is composed of 48 geometrical elements (10 corners of 16 triangles with 22 sides), 2. its 16 triangles have 48 sectors, 3. the seven separate polygons have 48 corners, 4. the first (6+6) enfolded polygons have 48 corners that are intrinsic to them, and 5. 48

 48 hexagonal yods in dodecagon surround centres of tetractyses

Figure 28. 24 red hexagonal yods & 24 blue hexagonal yods surround the black centres of the 12 tetractys sectors of the dodecagon.

geometrical elements surround the centre of a Type B dodecagon. It is also embodied in the Type A dodecagon, as it contains 73 yods, of which one is its centre, 12 are corners and 60 are hexagonal yods, 48 of which surround those at the centres of its 12 tetractyses (Fig. 28). The dodecagon conforms to the division:

48 = 24 + 24

that is characteristic of holistic systems because 24 hexagon yods line its sides, inside of which are 24 hexagonal yods surrounding centres of tetractyses. This 24:24 division was shown in Section 2 to divide equally the 264 yods of the seven enfolded polygons into S1, whose four polygons have 24 corners when they are separate and 132 yods when they are enfolded, and S2, whose three separate polygons have 24 corners and 132 yods when enfolded. This same division appears in the two joined Type B dodecagons, as now explained. Each dodecagon has 181 yods, so that the two joined dodecagons have 358 yods. Of these, 22 are their corners and 72 are hexagonal yods at the centres of their tetractyses. This means that (358–22–72=264) yods line the sides of these tetractyses, 132 boundary yods being associated with each dodecagon (Fig. 29). The two joined dodecagons display the 24:24 division characteristic of holistic

Correspondence between boundary yods in 2 dodecagons and yods in S1 & S2
Figure 29. The (132+132=264) yods other than corners lining sides of tetractyses in two joined Type B dodecagons correspond to the (132+132=264) yods in S1 & S2.


systems because their 24 sectors have 24 corners and their tetractyses have 24 more corners. There are 131 yods outside the root edge in each dodecagon. This is the number value of Samael, the Archangel of Geburah, whose Godname ELOHA has the number value 36, which is the number of yods lining the sides of the dodecagon. 130 yods outside the root edge surround the centre of each dodecagon. This is the 65 th even integer and the 129th integer after 1, showing how ADONAI, the Godname of Malkuth with number value 65, and YAHWEH SABAOTH, the Godname of Netzach with the

168 yods other than corners in Type B dodecagon  336 yods other than corners in two Type B dodecagons

Figure 30. 168 yods are needed to transform the 12 sectors of a dodecagon into Type A triangles.

Figure 31. The two joined Type B dodecagons have (168+168=336) yods other than their 22 corners.

number value 129, prescribes the Type B dodecagon. These are examples of how the Godnames mathematically prescribe the properties of holistic systems.

The 168:168 division

A Type B dodecagon with 181 yods requires 168 more yods to transform its 12 sectors into Type A triangles (Fig. 30). Joined together, two such dodecagons contain 358 yods — 336 yods in addition to its 22 corners (Fig. 31). 168 such yods are associated with each dodecagon. Their 24 sectors have 24 corners and their 72 tetractyses have another 24 corners. This is how the 24:24 division generates the 168:168 division in the outermost polygons of the inner Tree of Life. There are (358–48=310=31×10) hexagonal yods, showing how EL with number value 31 prescribes the pair of dodecagons. 155 hexagonal yods are associated with each dodecagon, where 155 is the number value of ADONAI MELEKH, the complete Godname of Malkuth. 154 such yods are outside each dodecagon, where 154 is the 153rd integer after 1. The number 153 is the number value of ELOHIM SABAOTH, the Godname of Hod.

The 84:84 division
There are 15 yods per sector of the Type B dodecagon (14 other than a corner of the polygons). Seven blue yods line internal sides of the three tetractyses in each sector and seven red yods are either hexagonal yods at their centres or yods lining the sector (Fig. 32). The 168 yods that are not corners of sectors comprise (12×7=84) red yods and 84 blue yods. When two dodecagons become joined, one of their 168 yods becomes associated with the other dodecagon.

Figure 32 Four sets of 84 geometrical elements in Type C dodecagon

Figure 32. The two sets of 84 yods in each Type B dodecagon.

Figure 33. The 84 geometrical elements in each quadrant of a Type C dodecagon correspond to the 84 intrinsic geometrical elements surrounding the centres of S1, S2, S1′ & S2′ — the quarters of the (7+7) enfolded polygons of the inner Tree of Life. The quadrant corresponding to S1′ is diametrically opposite that for S1; similarly, for S2′ and S2.

To compensate for this, the centre of the dodecagon must be included to maintain the set of 168 yods in each dodecagon. Each set is a pair of 84 yods. They correspond to the two sets of geometrical elements that surround the centres of the polygons


in S1 & S2 and in S1′ & S2′ (see Figs. 14 & 15). Which set corresponds to S1 and which corresponds to S2 is an issue that need not be resolved here. It is sufficient to have demonstrated that the pair of dodecagons constitute a holistic system, embodying the parameter 336 as four sets of 84 yods. However, the 84 red yods include one on the root edge, so that they “need” the root edge to make up the set, just as, according to Table 5, S2 needs it to complete the 132 yods in half of the seven enfolded polygons. This provides a reason for arguing that S1 in the right-hand dodecagon corresponds to the 84 blue yods and S2 corresponds to the 84 red yods and that S1′ corresponds to the 84 light blue yods in the left-hand dodecagon and S2′ corresponds to the 84 light red yods.

The 168:168 & 84:84 divisions manifest in the geometrical composition of a single dodecagon, namely, the Type C dodecagon. The number of corners, sides & triangles in a Type C n-gon = 28 +1. Hence, (12×28=336) geometrical elements surround the centre of a Type C dodecagon (Fig. 33). 168 elements exist in each half of the polygon and 84 elements exist in each quarter. Here is further, striking evidence for the dodecagon being the polygonal version of the inner Tree of Life, for the geometrical composition of each half is the same as that outside the root edge and surrounding the centres of the seven enfolded polygons. Each quarter corresponds to S1, S2, S1′ & S2′.

5. The Sri Yantra
The Sri Yantra (Fig. 34) is revered by Hindus as the most powerful and sacred of the yantras (images used for meditation). Five downward pointing triangles symbolizing the feminine, creative energy, or Shakti, intersect four upward pointing triangles symbolizing the masculine, creative energy, or Siva. This generates 42 triangles arranged in four layers of eight, 10, 10 and 14 triangles. They surround a down-ward-pointing triangle whose corners

The Sri Yantra Four Sets of 84 yods on sides of Sri Yantra
Figure 34. The Sri Yantra, Figure 35. 336 yods line the sides of the 42 triangles of the 3-d Sri Yantra when they are tetractyses. They form four sets of 84 yods. For clarity, hexagonal yods at the centres of tetractyses are omitted.

denote the triple Godhead of Siva, Brahma and Vishnu. At its centre is a point, or bindu, representing the Absolute. It is the source of all levels of existence. As such, it ‘exists’ outside them, although this is hardly the right word to express such an exalted level.

Let us consider the 3-dimensional Sri Yantra, in which the parallel sheets of triangles are stacked on top of one another so that none of their outward points touch triangles in a different layer. Let us regard the 42 triangles as tetractyses. There are nine yods intrinsic to each tetractys because it shares two corners with adjacent tetractyses in the same layer. Eight of these line its sides. Therefore, (42×8=336) yods line the (42×3=126) sides of the 42 triangles. 168boundary yods lie in the 21 tetractyses in the upper half of the Sri Yantra and 168 yods line the 21 tetractyses in its lower half (Fig. 35).[1]

Although it does not amount to exact mirror symmetry in the horizontal plane, there is an isomorphism in

[1] As long as its central triangle is excluded, the 3-d Sri Yantra can be divided in an upper half and a lower half with the same number of triangles, although — unlike the inner Tree of Life — they are not exact mirror images of each other.


 (168+168) yods on sides of Sri Yantra

Figure 36. (168+168=336) yods line the sides of the 42 triangles in the 3-d Sri Yantra. Those in one set of 168 yods are the inverted images of their counterparts in the other set. (The hexagonal yod at the centre of each tetractys is omitted for the sake of clarity).

 4 sets of 84 yods in Sri Yantra

Figure 37. The 336 boundary yods in the Sri Yantra comprise 4 sets of 84 yods. The 4 pairs per triangle comprise a pair of corners and 3 pairs of hexagonal yods. The 16 circles denote corners of triangles directly above corners of triangles in the next layer below them. (The hexagonal yod at the centre of each tetractys is omitted for the sake of clarity).


the distribution of yods in the 42 triangles to the extent that for every yod in one half of the Sri Yantra there exists a counterpart in its other half that is its inverted image, reflected not through a horizontal or vertical mirror but through its centre. There are 168 pairs of such yods (Fig. 36). Noting that two black corners are associated with each tetractys, which has three pairs of hexagonal yods on its sides (two red, two green & two blue), four pairs of yods per tetractys lie on its boundary. Each set of 21 tetractyses contains (4×21=84) pairs of yods. The 336 boundary yods consist of 168 pairs in two ways.

Comparing this property with the 168 intrinsic geometrical elements surrounding centres of polygons in S1 & S2, the following correspondences naturally emerge:

3-d Sri Yantra

 Inner Tree of Life

336 yods line (21+21) tetractyses;


336 geometrical elements surround centres of (S1+S2) and (S1′+S2′);
168 yods line 21 tetractyses in each half;


168 geometrical elements surround polygonal centres in each half;
168 yods in each half comprise 84 pairs, or two sets of 84 yods;


84 geometrical elements surround centres in S1 (S1′); 84 geometrical elements surround centres in S2 (S2′);

The distinction between pairs of hexagonal yods or corners is what corresponds to the difference between S1 and S2 as the two halves of the set of seven enfolded polygons of the inner Tree of Life. It cannot arise from the 21 triangles themselves in each half of the Sri Yantra because, being an odd integer, the number 21 cannot be divided into two integer halves. The possibility of dividing the four pairs of yods per tetractys into two sets of two pairs is less natural because there does not seem to be any reason why one pair should join any other pair to generate a group of 84 yods. The fact that the eight yods are already forming four pairs (one pair of corners, three pairs of hexagonal yods) argues against this alternative. Fig. 37 shows the 84 pairs of yods (now coloured red & blue) in the upper half of the Sri Yantra and the 84 pairs of yods (light red & light blue) in its lower half. They correspond to, respectively, the 84 geometrical elements surrounding centres of polygons in S1 and in S2 and their mirror images in S1′ and in S2′. Each pair of yods in one half of the Sri Yantra corresponds to a geometrical element in S1 and a geometrical element in S2. Each pair of yods in the other half corresponds to a geometrical element in S1′ and a geometrical element in S2′. Unlike in the case of the inner Tree of Life, where each element has a chiral counterpart in the other set of seven enfolded polygons generated by reflection in the mirror plane containing the root edge that is perpendicular to the plane containing all the polygons, the 336 yods consist of 168 yods and their 168 point reflections, although some are not true inversions, as the 2-dimensional Sri Yantra is not centrally symmetric. Despite the lack of exact mirror symmetry in this yantra, it is symmetric enough for the counterparts of its yods and geometrical elements to be identifiable in an unambiguous way.

Geometrical composition of the Sri Yantra

Table 9 shows the numbers of corners, sides & triangles in the 3-dimensional Sri Yantra:

Table 9. Geometrical composition of the Sri Yantra.

Table 9

(The bindu is a point, like the corners of the triangles, and may be included in the count of corners because what is really being counted here are points, lines & triangles). The 42 triangles in the four levels have 84 corners and 126 sides. The Godname EHYEH with number value 21 (see Table 1) prescribes the number of triangles because 42 is the 21st even integer. It prescribes the number of sides because 126 is the sum of the values of all the possible combinations of the three letters A, H & I in AHIH:

A = 1, H = 5, I = 10


 1. A + H + I =


 2. AH + HI + AI + HH =


 3. AHI + HIH + AHH =


 4. AHIH =





The number of geometrical elements is 252, which is the 126th even integer. The first three levels have 84 sides, 56 corners and 28 triangles, that is, 84 corners & triangles, totalling 168 geometrical elements. This 84:84 division of the number 168 was encountered in Section 2 (p. 9) as the 84 geometrical elements surrounding the centres of S1 and of S2. The fourth layer has 84 geometrical elements, whilst all four levels have 84 corners and 168 sides & triangles (84 in each half of the Sri Yantra). We do not yet see in its geometry the appearance of the holistic parameter 336 as four sets of 84 (that must await the division of the triangles into their sectors — to be discussed next). That there are, according to Table 9, 260 geometrical elements in all 43 triangles when the bindu is included is a clue to the more appropriate comparison, namely, with the yod composition of S1 & S2 outside the root edge. We see from Table 5 that S1 has 132 yods and that S2 has 128 yods outside the root edge. The centre of the triangle in S1 coincides with a hexagonal yod on the line joining Chesed and Geburah in the outer Tree of Life, whilst seven yods (four hexagonal yods & three corners) on the internal vertical sides of tetractyses in the hexagon in S2 are shared with it. Therefore, 252 yods are intrinsic to S1 & S2 and (1+7=8) yods are shared. Compare this with the 252 geometrical elements in the 42 triangles of the Sri Yantra and the eight geometrical elements (one triangle, four points & three lines) that make up the central triangle & bindu (see Table 9). All these correspondences cannot be accidental. It is clear that the geometry of the Sri Yantra manifests in a one-to-one way information abstractly symbolised by the yods in the inner Tree of Life because it is a different representation of the same archetypal blueprint.

Table 10 shows the geometrical composition of the 3-d Sri Yantra when its triangles are Type A:

Table 10. Geometrical composition of the 3-d Sri Yantra with Type A triangles.

  Table 10

Whereas before, the first three layers had 168 geometrical elements, they now have 336 elements, whilst the fourth now has 168 geometrical elements instead of 84. The 336 elements comprise 168 sides, 84 corners and 84 triangles, i.e., 168 corners & triangles, reproducing the holistic division: 336 = 168 + 168, whilst the 168 elements in the fourth layer comprise 84 sides and 84 corners & triangles, reproducing the holistic division: 168 = 84 + 84. The division 48 = 24 + 24, which appeared in the separate polygons of S1 and S2 as their 24 corners, re-appears in the first layer of triangles as the 24 sides of the four triangles in each half, or, alternatively, as the 24 corners & triangles in each half of the Sri Yantra.

According to Table 10, the 3-d Sri is composed of 518 geometrical elements. It has 131 corners, where 131 is the number value of Samael, the Archangel of Geburah. The 43 triangles have 130 corners, 258 sides and 129 sectors, where 130 is the 129th integer after 1, 258 is the 129th even integer and 129 is the number value of YAHWEH SABAOTH, the Godname of Netzach. This number appears in the 43 triangles because 129 = 3×43. The (7+7) enfolded polygons of the inner Tree of Life contain 524 yods, of which four make up the root edge and two are the topmost corners of the two hexagons that coincide with the lowest corners of the hexagons enfolded in the next higher Tree. Hence, (524–4–2=518) yods outside the root edge belong exclusively to the set of 14 polygons enfolded in each Tree (Fig. 38). Each of these yods corresponds to a geometrical element making up the Sri Yantra with Type A triangles. Surrounding the centres of the 14 polygons are (518–14=504) such yods. They symbolise the 504 geometrical


3-d Sri Yantra with Type A triangles
Fig 38a


Fig 38b


Figure 38. The 518 geometrical elements composing the 3-d Sri Yantra correspond to the 518 yods in the (7+7) enfolded polygons outside their root edge that are unshared with polygons enfolded in the next higher Tree. The 504 geometrical elements in the four layers of triangles correspond to either (a) the 504 intrinsic yods that surround the centres of the 14 polygons, or (b) the 504 intrinsic yods unshared with the outer Tree of Life.

elements in the four layers of triangles. Six yods in S1, which has 132 yods outside the root edge, are centres of polygons and one yod in S2, which has 128 yods, is a centre. Hence, 126 yods in S1 are not centres and 127 yods in S2 are not centres. One of the latter yods is the topmost corner of the hexagon that is shared with the hexagon enfolded in the next higher Tree. Therefore, S2 has 126 intrinsic yods that are not centres. Compare this with the 126 corners, 126 triangles & 252 triangles in the 3-dimensional Sri Yantra, that is, with the 126 corners & triangles and the 126 sides in each half of it. Just as four sets of 126 yods in S1, S2, S1′ & S2′ surround the (7+7) centres in the polygons of the inner Tree of Life, so, too, four sets of 126 geometrical elements make up each half of the Sri Yantra. The 14 centres correspond to the 14 geometrical elements making up the central triangle and the bindu. An alternative possibility needs to be considered. The 518 yods include six yods in each hexagon that are shared with the outer Tree because they lie on its side pillars and the centre of each triangle that coincides with a hexagonal yod belonging to the outer Tree because it lies on the side of the triangle connecting Chesed to Geburah. Hence, 14 yods in the set of 518 yods are shared with the outer Tree, leaving 504 yods outside the root edge that are unshared. Each set of seven enfolded polygons contains 252 such yods. S1, then, has two shared yods (centre & corner of triangle), so that it has (132–2=130) unshared yods, whilst S2 has six shared yods, so that it has (128–6=122) unshared yods. Comparing these two numbers with the 126 corners & triangles and 126 sides in each half of the Sri Yantra, we conclude that, although the total number of yods is the same as the number of geometrical elements, S1 and S2 do not have the same


numbers of unshared yods. The alternative view in which the 14 yods contributed by the bindu and central triangle correspond to the 14 shared yods is, therefore, incorrect. These 14 yods correspond only to the centres of the 14 polygons making up the inner Tree of Life.

Comparison with the Type C dodecagon
The number of yods in a Type C n-gon = 42n + 1, where “1” denotes its centre. A Type C dodecagon (n=12) has (12×42=504) yods surrounding its centre. It was pointed out in Section 4 that this regular polygon is the single, polygonal representation of the Tree of Life (see Fig. 27). The Type A version has 60 hexagonal yods, which is the number of hexagonal yods in the outer of Life, 264 yods line the 72 tetractyses in two joined Type B dodecagons and this is the number of yods in the seven enfolded polygons, whilst the 504 yods surrounding the centre of the Type C dodecagon is the number of yods

Figure 39

intrinsic to the (7+7) enfolded polygons that are outside the root edge. As 168 = 12×14 and 42 = 3×14, these 504 yods consist of three sets of 168 yods, the 42 yods per sector consisting of three sets of 14 yods. One set comprises 14 red yods that are either corners & centres of tetractyses (Fig. 39). The 168 such yods in the Type C dodecagon correspond to the 168 geometrical elements in the fourth layer of 14 red triangles in the 3-dimensional Sri Yantra. The 28 yods remaining in each sector comprise 10 green, hexagonal yods, 10 blue, hexagonal yods and 8 violet, hexagonal yods — the same numbers as thenumber of triangles in the first three layers. The 120 green yods, the 120 blue yods and the 96 violet yods in the dodecagon symbolise the geometrical elements in respectively, the third, second and first layers of the Sri Yantra with Type A triangles. In other words, the Type C dodecagon is an exact representation of the geometrical composition of the Sri Yantra. This is because they are both equivalent representations of the divine paradigm.

 64 hexagrams

Figure 40. The 64 hexagrams.

This isomorphism between two sacred geometries and its embodiment of the holistic parameters 84, 168 & 336 are unmistakable, strong indications of the objective nature of the century-old, micro-psi observations of the UPA by Annie Besant and C.W. Leadbeater. Had they been otherwise, these numbers would not manifest so frequently in the geometrical and yod compositions of these and other sacred geometries to be discussed later in this article. Nor, indeed, would the gematria number values of the 10 Sephiroth and their Godnames, etc. This is not — as a sceptic might suggest — because their appearance has been contrived by some kind of cherry-picking of properties. The parameters with a paranormal provenance have entirely


natural meanings in the context of these sacred geometries that cannot result from random chance or deliberate selection. To suggest the latter is to beg the question that it is always possible to reproduce all the levels of correlation between two geometries as soon as some global choice of yods or geometrical properties has been made. It clearly is not possible do this deliberately. The fact that these levels exist at all can only be sensibly understood as due neither to chance, which is highly implausible, nor to cherry-picking, because the correspondence runs too deep to make that possible. Instead, it can be due only to an inherent, mathematical design that is revealing a transcendental intelligence within it.

6. I Ching table of hexagrams
Used in China for thousands of years as a form of fortune telling, the system of 64 hexagrams (Fig. 40), upon which the commentaries in the famous I Ching (“Book of Changes”) are based, consists of an 8×8 square array of the (82=64) possible pairings of eight trigrams. Each trigram (Fig. 41) is a

   Figure 41. The eight trigrams.

combination of three lines. A line can be either ‘yin,’ the female power, or gentleness: − − , or ‘yang,’ the male power, or strength: —. Fig. 41 shows the eight combinations (2×2×2=8) of yin and yang in the three lines of a trigram. They will be called ‘lines’ if they denote yang and ‘broken lines’ if they denote yin. Each pairing of trigrams is called a ‘hexagram.’ More details can be found in Article 18 [4].

That there are (26=64) hexagrams is a direct consequence of the Taoist belief in a fundamental duality in Nature, where active (yang) and reactive, or passive (yin) forces create a balance, or harmony. This cosmic polarity is represented in the Pillar of Mercy and the Pillar of Judgement of the Tree of Life, the middle Pillar of Equilibrium representing the homeostasis resulting from the dynamic interplay of these two complementary, cosmic principles. The number 64 is the gematria number value of Nogah, the Mundane Chakra of Netzach. The number value 148 of this Sephirah is the number of yods in the four separate polygons in S1 (see Fig. 18), so that it determines the division in half of the seven types of polygons with 48 corners that make up the inner form of the Tree of Life, this number being the number value of Kokab, the Mundane Chakra of Hod, which follows Netzach in the Tree of Life.

 Fig 42

Figure 42. The 14 enfolded polygons of the inner Tree of Life with 70 corners share six corners (black yods) with the outer Tree, which has 70 yods. 64 yods or corners are intrinsic to the outer and inner Trees. They correspond to the 64yods outside the root edge on the boundaries of the two dodecagons whose sectors are tetractyses.

The holistic parameter 64 is revealed by superimposing the outer form of the Tree onto the plane of its inner form (Fig. 42). When the 16 triangles in the former are tetractyses, three of their corners located at the positions of Sephiroth (the black yods in Fig. 42) lie on each side pillar and are shared with each hexagon as corners of its sectors. Of the 70 yods in the outer Tree of Life, (70−6=64) yods are not corners of triangles in the inner Tree. Similarly, 64 of the 70 corners in the inner Tree are intrinsic to it. None of the four yods in the root edge are shared because they lie in the plane formed by the two side pillars and this does not contain any yods belonging to triangles in the outer Tree of Life. The 94 sectors of the (7+7) enfolded polygons have 80 corners, (80−6=74) of which are unshared with the outer Tree, so that the (94+16=110) triangles in the combined Trees of Life have (10+74=84) corners. This embodiment of the holistic parameter 84 demonstrates par excellence their holistic character. Their counterpart in the Sri Yantra are the 84 corners of the 42 triangles surrounding the central one. The pair of dodecagons also display the holistic parameter 64 because 32 yods outside the root edge line each one, so that 64yods line both.

According to Table 10, the 42 Type A triangles in the 3-dimensional Sri Yantra have 126 corners & 252 sides. The corners of the central triangle symbolise the Hindu trinity, or trimȗrti, of Siva, Vishnu & Brahma. If we regard it as an ordinary triangle without sectors, so that it has three corners and three sides, 129 corners and 255 sides surround the centre of the Sri Yantra, that is, 384 corners & sides. This is the


counterpart of the polygonal geometry of the inner Tree of Life because 384 corners, sides & triangles surround the centres of the 14 polygons, each half of the Sri Yantra having 192 corners & sides and each of the inner Tree of Life having 192 corners, sides & triangles. The 384 corners & sides include the 24 corners & 24 sides of the eight triangles in the first layer. This corresponds to the 24 corners, sides & triangles surrounding the centre of each

Figs 43 & 44

hexagon. Surrounding the centres of the six other polygons in each half of the inner Tree of Life are 168 geometrical elements. Similarly, the Sri Yantra has 336 geometrical elements (168 elements in each half) other than the 48 corners & external sides of the eight Type A triangles. The counterparts of these in the table of hexagrams are the 48 lines & broken lines in the eight diagonal hexagrams and the 168 lines & broken lines in the 28 off-diagonal hexagrams in the upper and lower halves of the 8×8 square array of 64 hexagrams (Fig. 43). It is no coincidence that the first layer in the Sri Yantra has eight triangles. They correspond to the eight diagonal hexagrams, each trigram corresponding to either three corners (two external, one internal) of each Type A triangle or its three external sides.

 Fig 45

Figure 45. 168 is the sum of the 12 odd integers after 1 forming the edges of a square. It is the number of lines and broken lines in the 28 hexagrams on the four sides of the 8×8 square array.


The 84:84 division
The 168 lines & broken line in the 28 hexagrams on either side of the diagonal of the 8× 8 array consist of 84 lines and 84 broken lines. The yang lines are coloured dark or light red and the yin lines are dark or light blue. This colour scheme is applied in order to correspond to that used earlier to distinguish the two halves of the inner Tree and the two halves of each half (Fig. 44). As both yang and yin lines exist in each diagonal half of the square array, the two

 Square representation of 840

Figure 46. The sum of the first 28 odd integers arranged eight to a side of a square is 840. This is the number of circularly polarised oscillations in the inner or outer half of a whorl of the UPA. It is also the number of such oscillations in a half-revolution of all 10 whorls. The Tetrad symbolised by the square determines holistic parameters like this structural parameter of the E8×E8 heterotic superstring.

halves of the inner Tree should not be seen as the manifestation of the cosmic polarisation or duality of yang and yin. Rather, as each half is a whole in itself, it has a yang sector and a yin sector that correspond to, respectively, S1 & S2 (and to S1′ & S2′). What is remarkable that each sector should

Holistic parameter 84 embodied in square Figure 47. Two sets of 84 yods surround the centre of a Type C square. The (4×84=336) yods in two separate Type C squares are the counterpart of the 336 geometrical elements in the pair of two sets of polygons [(S1, S2) & (S1′, S2′)] that make up the inner Tree of Life.

embody the same parameter 84 as both the Sri Yantra and the square array of 64 hexagrams — extraordinary, certainly, but not surprising, in view of the fact that they are all isomorphic representations of the same archetypal pattern.

The boundary of the 8×8 array of hexagrams contains 28 hexagrams with 168 lines & broken lines made up of 84 lines and 84 broken lines (Fig. 45). Arithmetically, this can be expressed as the sum of the first 12 odd integers after 1 lining the sides of a square, four to each side, because:

132 – 1 = 3 + 5 + 7 + 9 + 11 + 13 + 15 = 168.


292 – 1 = 3 + 5 + 7 +… + 57 = 840,

the number 840 is the sum of the first 28 odd integers after 1 that can be assigned to the sides of a square, eight to each side (Fig. 46). That the square, either four units long or eight units wide, where 8 is the fourth, even integer, should determine both the superstring parameters 168 and 840 is a remarkable illustration of the Tetrad Principle at work [5]. The square even embodies the number 168 as the number of yods surrounding the centre of a Type C square (Fig. 47).

The archetypal divisions:

384 = 192 + 192,

84 = 48 + 336,

48 = 24 + 24,

336 = 168 + 168,


displayed by holistic systems are hidden within them when they are sacred geometries. They are most


explicit in the 8×8 array of hexagrams because they can be recognised by simple counting. Moreover, the yin/yang nature of its lines and broken lines is explicit. But this duality does not correspond to the chiral nature of the geometrical elements in the two mirror-symmetric halves of sacred geometries (or almost so, in the case of the Sri Yantra). The 192 lines & broken lines in each diagonal half of the square array of hexagrams consist of 96 lines and 96 broken lines that form eight copies of the basic set of eight trigrams. The 168 lines & broken lines in each set of 28 off-diagonal hexagrams are seven copies of the 12 lines & 12 broken lines making up the basic set of eight trigrams. The two sets of 28 hexagrams are not mere mirror images of each other, reflected across the diagonal. Nor is the “reflection” of each hexagram the result of replacing each line by a broken line and vice versa. Rather, its reflection inverts the order of its pair of trigrams. This is like what happens in the intervals between the eight notes in a musical scale. The rising interval between two notes with tone ratios m & n (m>n) is m/n. The falling interval between them is n/m. It is as though the array of 56 off-diagonal hexagrams is representing the 28 rising intervals between the eight notes in an octave (represented by the eight trigrams) and their 28 falling intervals, whilst the eight diagonal hexagrams represent the unit interval between a note and itself. In fact, it is doing so, as the eight-note diatonic scale is a holistic system, the 36 possible intervals being symbolised by the 36 corners of the seven enfolded polygons of the inner Tree of Life. But a more fundamental level of interpretation exists for the trigrams, lines & broken lines: the 64 hexagrams also express the intervallic composition of the seven types of diatonic scales [6]. As explained in Article 39 [7], the 192 lines & broken lines in the upper diagonal half of the square array denote the 192 rising intervals between the notes in the seven types of diatonic musical scales, whilst the 192 lines & broken lines in the lower half denote their falling counterparts with reciprocal tone ratios. How the rising and falling intervals and the types of intervals correspond to the 84 geometrical elements in S1 and the 84 geometrical elements in S2 will be discussed in Section 10. The following correspondences exist between the 64 hexagrams and inner form of the Tree of Life:

28 upper, off-diagonal hexagrams

84 yang lines → 84 geometrical elements surrounding centres of polygons in S1.

84 yin lines → 84 geometrical elements surrounding centres of polygons in S2.

eight diagonal hexagrams → root edge.

28 lower, off-diagonal hexagrams

84 yang lines → 84 geometrical elements surrounding centres of polygons in S1′.

84 yin lines → 84 geometrical elements surrounding centres of polygons in S2′.

The connection to the UPA
Each whorl of the UPA makes 168 circularly polarised oscillations in every half-revolution around its axis. The five inner half-revolutions and the five outer half-revolutions of each whorl correspond in the Tree of Life to, respectively, the five Sephiroth belonging to its Upper Face and the five Sephiroth spanning

 Holistic character of half-revolution of a whorl

Figure 48. Each half-revolution of a whorl of the UPA/superstring comprises 168 circularly polarised oscillations. Each oscillation has a positive phase (yang) and a negative phase (yin). The 168 positive phases correspond to a yang line in the 56 off-diagonal hexagrams. The 168 negative phases correspond to a yin line. They are split into 84 oscillations belonging to an outer ¼ revolution and 84 oscillations belonging to an inner ¼-revolution. The two sets of 28 off-diagonal hexagrams, each with 84 yang lines & 84 yin lines, represent these two sets of 84 oscillations, each having a positive and a negative phase.


its Lower Face. This ten-fold nature of a whorl is, simply, the manifestation of its Tree of Life nature, each one corresponding to a Sephirah because the UPA with 10 whorls is a microscopic manifestation of the Tree of Life blueprint. As a Tree of Life structure in its own right, a half-revolution may be divided into an “Upper Face,” namely, a quarter-revolution comprising 84 oscillations that belong to the inner half of the UPA, and a “Lower Face”, a quarter-revolution with 84 oscillations that belongs to its outer half. Being a whole, it is represented by a 2nd-order tetractys, the 84 yods surrounding its centre symbolising these oscillations.

A sinusoidal oscillation has a positive phase and a negative phase. The upper diagonal half of the 8×8 array with 28 off-diagonal hexagrams composed of 84 yang lines and 84 yin lines represents the 84 positive and 84 negative phases of 84 oscillations making up the outer half of the UPA (Fig. 48); the lower diagonal half with 28 off-diagonal composed of 84 yang lines and 84 yin lines represents the 84 positive and 84 negative phases of 84 oscillations making up its inner half.

Notice that in all cases of sacred geometries considered so far (including the 64 hexagrams), a one-to-one correspondence exists between certain subsets and their elements in each one. There is not necessarily the same number of elements in all cases, only the same numbers of corresponding elements in certain subsets of structural elements. The differences between these cases arises from the different forms taken by source. It may be a mathematical point, as in the case of the dodecagon, the root edge in the case of the inner Tree of Life, the central triangle and bindu in the case of the Sri Yantra and the generic set of eight trigrams whose pairing with themselves forms the eight hexagrams in the diagonal of the square array of 64

 5 Platonic solids

Figure 49. The five Platonic solids with Type A  polygons as their faces.

hexagrams. They all display a symmetry (point reflection symmetry in the inner Tree of Life, imperfect mirror symmetry of the Sri Yantra, inversion symmetry for the dodecagon and symmetry between yang and yin lines in the table of hexagrams). This symmetry exists in them because they are different, but equivalent, representations of the Whole, which, by definition, is mathematically complete.

7. The five Platonic solids
Let us consider the construction of the five regular polyhedra from the tetractys. The simplest case is when their regular faces are Type A polygons (Fig. 49). To be consistent, the internal triangles generated by joining their centres to their vertices must be Type A as well. The yod populations of individual Platonic solids need not be discussed here. Details may be found in Article 3 [8]. For the present purpose, only the classes of yods and their numbers needed to construct the mathematically complete set of five Platonic solids need be considered here. Table 11 lists the numbers of yods & hexagonal yods in the faces and interior of each polyhedron.

Table 11. Yod populations of the five Platonic solids.

(V = number of vertices; E = number of edges; F = number of faces; m = number of sectors of a face).










of yods

Number of hexagonal

of yods

Number of hexagonal

Number of yods

Number of hexagonal yods









68 + 1


124 + 1










132 + 1


242 + 1










136 + 1


246 + 1










324 + 1


596 + 1










340 + 1


612 + 1








1000 + 5


1820 + 5


(“1” denotes the centre of the polyhedron).

1820 yods surround the centres of the five regular polyhedra. Of these, 50 yods are centres of faces and 90 yods are centres of internal triangles. Hence, (1820−50−90=1680) yods surround these (90+50=140) centres. 140 is the number value of Malachim, the Order of Angels assigned to Tiphareth. As we shall see, these centres, which are the starting points for the construction of faces and internal triangles, play


the same role as the centres of the (7+7=14) regular polygons of the inner Tree of Life, surrounding which are (168+168=336) yods that are intrinsic to them. In a remarkable, analogous way, (1680/5=336) yods on average surround the centres of faces and internal triangles in the five Platonic solids, 168 yods in each half. These famous polyhedra are the 3-dimensional representation of the 1680 turns of each helical whorl of the UPA. It is unequivocal evidence for C.W. Leadbeater’s paranormally derived number 1680 being embodied in the five Platonic solids constructed from tetractyses. The average yod population 336 is the number of turns in one revolution of a whorl. The 840 yods in each half of all five Platonic solids correspond to the 840 turns in each half of a whorl. There are, of course, not 168 yods in the half of every Platonic solid. That number represents only an average, made possible by the fact that the number of Platonic solids is the same as the number of revolutions of each whorl, so that the 10 halves of the former correspond to the 10 half-revolutions of the latter.

Let us now examine the classes of yods making up the tetractyses in the faces and interiors of the Platonic solids, as well as the numbers of each type. There are seven types, excluding the centres of faces and internal triangles:


1.    vertices (V);

2.    hexagonal yods on edges (2E);

3.    hexagonal yods on sides of sectors (2mF);

4.    hexagonal yods at centres of sectors (mF);


5.    hexagonal yods on sides joining centre of polyhedron to vertex (2V);

6.    hexagonal yods on sides of sectors of internal triangles (6E);

7.    hexagonal yods at centres of sectors of internal triangles (3E).

Total number of yods = 3V + 11E + 3mF = 6 + 14E + 3(m−1)F,

where Euler’s polyhedral formula for a convex polyhedron:

V – E + F = 2

has been used. The number “6” measure the number of yods on the two semi-axes passing through two opposite vertices and the centre of a polyhedron. Excluding their centres, 30 yods line the 10 semi-axes of the five Platonic solids, so we see from Table 11 that 1790 yods surround these axes. On average, a Platonic solid has 384 yods (192 in each half), of which six yods line its two semi-axes and 378 yods surround them (189 in each half). These divisions define all sacred geometries. For example, the 3-dimensional Sri Yantra has six hexagonal yods on the sides of its central triangle/tetractys and 336 yods line the 126 sides of its surrounding 42 tetractyses (Fig. 36), at the centres of which are 42 hexagonal yods, so that it has 384 yods. On average, it takes as many yods to build a Platonic solid as it does to construct the 3-dimensional Sri Yantra from tetractyses. This, of course, is not a coincidence, for they are both expressions of a universal, archetypal pattern. The number that shapes the 42 triangles is 336, and this is the average number of yods in a Platonic solid that surround the centres of its faces and interior triangles. The question to be answered now is whether the 168 yods in an average half of a Platonic solid divide evenly into two sets of 84 yods, just as we have seen for the 168 yods or geometrical elements in other sacred geometries.

Table 12 displays the yod populations of half a Platonic solid for the seven classes of yods other than centres of faces and internal triangles:

Table 12. Yod populations in half a Platonic solid for the seven classes of yods.





Hexagonal yods on edges

Hexagonal yods on sides

Hexagonal yods at centres

Hexagonal yods on sides

Hexagonal yods on sides of sectors

Hexagonal yods at centres























































En passant, it is worth noting that each half of the tetrahedron — the building block of solid geometry —


has 26 yods in its faces of each half and 31 yods in its interior, showing how YAHWEH, the Godname of Chokmah with number value 26, and EL, the Godname of Chesed below it with number value 31, prescribe this Platonic solid. Also, the 12 faces of the complete dodecahedron contain 260 (=26×10) yods, showing how it is prescribed by YAHWEH. Of its 285 yods in each half, three yods lie on the semi-axis, leaving 282 yods, where 282 is the number value of Aralim, the Order of Angels assigned to Binah.

The following analysis applies to either half of a Platonic solid: according to Table 12, there are (30+45=75) hexagonal yods at the centres of the 75 tetractyses in the dodecahedron, leaving (285−75=210) yods lining their sides. The corresponding numbers for the first four Platonic solids are tabulated below:

Table 13. Boundary & central hexagonal yods in the first four half-Platonic solids.

Platonic solid

Central hexagon yods

Boundary yods


6 + 9 = 15

57 –  15 = 42


12 + 18 = 30

111 –  30 = 81


12 + 18 = 30

114 –  30 = 84


30 + 45 = 75

273 –  75 = 198




The number of yods in the tetrahedron and on the sides of tetractyses in the octahedron, cube & icosahedron = 405 + 15 = 420. This leaves (150−15=135) central hexagonal yods in these three solids. The octahedron, cube, icosahedron & dodecahedron have (135+75=210) central hexagonal yods. The number of yods either at centres of tetractyses in these four solids or lining the sides of tetractyses in the dodecahedron = 210 + 210 = 420.

We find that the 840 yods in each half of the five Platonic solids comprise two sets of 420 yods. On average, the 168 yods in half a Platonic solid consist of two sets of (420/5=84) yods. On average, there are 336 yods in a complete Platonic solid that comprise four sets of 84 yods surrounding the centres of their faces or internal triangles. This is the polyhedral counterpart of the 84:84:84:84 division of the holistic parameter 336 found in previous sections for the inner Tree of Life, the dodecagon and the Sri Yantra.

According to Table 12, the number of yods in the faces of the five half-solids is 385. This the sum of the squares of the first 10 integers:

Tetractys representation of 385

It is a beautiful illustration of how the Decad expresses properties of holistic systems. The dodecahedron has 285 yods in each half surrounding centres of faces and internal triangles, so the first four Platonic solids have (840−285=555) such yods in each half, i.e., 1110 altogether, where

1110 = 101 + 102 + 103.

If we imagine them as concentric and orientated so that none of their yods coincide, the total number of yods, including their shared centre = 1111, where

1111 = 100 + 101 + 102 + 103.

This is the sum of the first four powers of the fourth triangular number. It demonstrates in a remarkable way how the Tetrad expresses the properties of holistic systems.

Table 14. Yod and geometrical composition of the five complete, Platonic solids.




Hexagonal yods on sides

Central hexagonal yods

Total number of yods



Total number of geometrical elements


















































It is instructive and revealing to calculate the average yod and geometrical composition of a Platonic solid. Table 14 shows how many yods & geometrical elements surround the centres of faces and internal triangles of each whole Platonic solid (the centres of the solids are excluded for the moment).

1. (1180+50=1230) yods line the 450 tetractyses. Including the 140 corners that are centres of faces or internal triangles, 1370 yods lines their sides. This property is stunning, for it is the number of yods in the inner form of the Tree of Life with Type B polygons (Fig. 50)! It means that the number of yods that shape all the tetractyses needed to construct the five Platonic solids is precisely the number of yods in the inner Tree of Life. Moreover, it means that, on

1370 yods in (7+7) enfolded Type B polygons
Figure 50. The (7+7) enfolded Type B polygons of the inner Tree of Life contain 1370 yods. This is the number of yods that line the 450 tetractyses needed to build the five Platonic solids.

average, 137 yods line the 45 tetractyses in a half-Platonic solid, showing how the Platonic solids embody the mysterious number 137 at the heart of atomic and particle physics whose reciprocal is the approximate value of the fine-structure number 137.

2. The number of vertices & sides is 640. This is the number value of Shemesh, the Mundane Chakra of Tiphareth, whose Order of Angels is Malachim, with number value 140! If the 140 centres of faces and internal triangles are included, it is also the number of corners & central hexagonal yods.

3. The 25 vertices of the five half-Platonic solids are joined by 25 sides of 225 tetractyses, where 225 = 152 and 15 is the number value of YAH, the shorter form of the Godname assigned to Chokmah. Each side has two hexagonal yods, and therefore the number of yods (including centres of solids) that line these sides in the five half-solids = 2×25 + 25 + 5 = 80. This is the number value of Yesod. The number of yods lining the sides joining centres to the 50 vertices of the Platonic solids = 2×50 + 50 + 5 = 155. This is the number value of ADONAI MELEKH, the complete Godname of Malkuth.

4. According to Table 12, the number of hexagonal yods lining tetractyses in the faces of the five half-Platonic solids = 90 + 180 = 270. Their number of sides = 135. The 50 faces of the five Platonic solids have 270 sides of 180 triangles with 50 vertices and 50 more corners that are the centres of faces. The total number of geometrical elements in the faces = 550, that is, 50 vertices and (50×10) more geometrical elements. This demonstrates how ELOHIM, the Godname of Binah with number value 50, prescribes the shapes of the Platonic solids. It is determined by the Decad because 550 = 10×55 and 55 is the tenth triangular number:

55 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10.

5. Including the 140 centres of faces & internal triangles, the total number of geometrical elements = 1090 + 140 = 1230. This is also the number of boundary yods (excluding the 140 corners) in the 450 tetractyses. The average number is 246. This is the number value of Gabriel, the Archangel of Yesod. There are, on average, 123 geometrical elements per half-Platonic solid. 123 is the tenth Lucas number in the Lucas series:

2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, …


named after French mathematician, François Édouard Anatole Lucas (1842-1891), who gave the name of “Fibonacci numbers” to the closely related type of number. The number of yods in a Type D n-gon = 123n + 1. Therefore, the Type D decagon has 1230 yods surrounding its centre (Fig. 51).

 1230 yods surround centre of Type D decagon

Figure 51. 1230 yods surround the centre of the Type D decagon. This is the number of geometrical elements in the 5 Platonic solids whose faces & internal triangles are Type A. The 123 yods per sector denote the 123 geometrical elements on average in each half-Platonic solid.

Once again, the Decad determines the geometrical composition of the five Platonic solids. It is a remarkable example of the Tetrad Principle at work in determining holistic parameters, for the decagon has 10 corners, where 10 is the fourth triangular number, and the Type D decagon is the fourth in the series of types of division of the decagon:

Type A decagon → Type B decagon → Type C decagon → Type D decagon.

6. The five Platonic solids have 90 edges and 500 (=50×10) more sides of 450 triangles.

The average Platonic solid has:
1. (50/5=10) vertices, (90/5=18) edges, (1180/5=236) hexagonal yods lining the (590/5=118) sides of (450/5=90) tetractyses. There are (450/5=90) hexagonal yods at their centres. The average number of boundary yods excluding vertices (236) is the same as the number of yods that line the sides of the (7+7) enfolded polygons of the inner Tree of Life (Fig. 52).

 236 boundary yods in (7+7) enfolded polygons

Figure 52. 236 yods line the sides of the (7+7) enfolded polygons of the inner Tree of Life.

2. 55 geometrical elements in its faces, where 55 is the tenth triangular number.

3. (10+236+90=336) yods and (1090/5=218) geometrical elements surrounding centres of faces and internal triangles. Including, on average, the 28 centres of faces & internal triangles per solid, (336+28=364) yods and (218+28=246) geometrical elements surround the centre of the solid, whilst (236+28=264) yods other than vertices line the 90 tetractyses. This is the number of yods in the seven enfolded polygons of the inner Tree of Life (Fig. 8). Including vertices, (10+264=274) yods on average line the 90 tetractyses, 137 in each half of a Platonic solid, which also contains 168 yods other than the 14 centres of faces & internal triangles. As a check, according to Table 11, the five Platonic solids have 1820 yods, so that the average number of yods per half-solid = 182 = 137 + 45, where 45 is the average number of hexagonal yods at the centres of the 45 tetractyses in half a Platonic solid, all five complete Platonic solids having 450 tetractyses.


8. Disdyakis triacontahedron
There are only five Platonic solids, each having regular polygons, that can exist in 3-dimensional space.If a polyhedron has two or more faces that are different polygons, then 13 so-called “Archimedean solids” exist (15, including two chiral varieties). Their duals are called the Catalan solids (Fig. 53). The Catalan solid with the most faces is the disdyakis triacontahedron. It has 62 vertices (31 in each half), where 62 is the number value of Tzadkiel, the

Figures 53 & 54

Figure 53. The disdyakis triacontahedron has the most faces of all the Catalan solids.

Figure 54. 360 (=36×10) geometrical elements surround the axis of the disdyakis triacontahedron.

Archangel of Chesed, and 31 is the number value of EL, the Godname of this Sephirah. It has 180 edges and 120 faces that are scalene triangles. The disdyakis triacontahedron is formed by sticking rhombic pyramids on the 30 faces of the rhombic triacontahedron (another Catalan solid that is the compound of the icosahedron and the dodecahedron). Figure 54 shows the three types of vertices: 30 A vertices (peaks of the pyramids), 12 B vertices (vertices of the icosahedron) and 20 C vertices (vertices of the dodecahedron). There is the same number (60) of the three types of edges.

Many previous articles by the author have accumulated evidence that the disdyakis triacontahedron is the single, polyhedral form of the inner Tree of Life (or, more generally, the universal blueprint governing holistic systems). The five Platonic solids, too, are its polyhedral form, but only collectively, not in any individual sense. The disdyakis triacontahedron should be seen as their apotheosis, containing all those types of information that exist separately in individual members of the mathematically complete set of regular polyhedra. In confirmation of this conclusion about its status as sacred geometry, further evidence will now be presented proving that the holistic divisions:

336 = 168 + 168


168 = 84 + 84

found in earlier sections to be present in the inner Tree of Life, the dodecagon, the Sri Yantra & the 64 hexagrams are embodied as well in the disdyakis triacontahedron.

Let us, firstly, consider the case where all faces and internal triangles formed by joining vertices to the centre of the polyhedron are simple triangles; later, we shall consider them divided into their sectors. Table 15 shows the geometrical composition of the faces and interior of the disdyakis triacontahedron.

Table 15. Geometrical composition of the disdyakis triacontahedron.






2 + 60



2 + 360



2 + 60


3 + 240


3 + 60

2 + 240


5 + 600


 600 geometrical elements surround the axis, which comprises five elements (three vertices, two sides).


Including the centre, there are 363 corners & triangles, where 363 is the number value of SHADDAI EL CHAI, the complete Godname of Yesod. There are 150 (=15×10) corners & sides surrounding the semi-axis in each half of the polyhedron, where 15 is the number value of YAH. Including this semi-axis, each half has (150+3=153) corners & sides, where 153 is the number value of ELOHIM SABAOTH, the Godname of Hod. Including both semi-axes, there are (150+5=155) corners & sides in the axis and faces of half the polyhedron. This is the number value of ADONAI MELEKH, the complete Godname of Malkuth. They comprise one centre, (2+30=32) vertices, 90 edges and 32 internal sides, i.e., 90 edges and 65 corners & sides. 90 is the number value of MELEKH and 65 is the number value of ADONAI.

Surrounding the axis are 24 vertices, 84 edges & 60 triangular faces either above or below the central 12-gon. They comprise (24+60=84) corners & triangles and 84 sides. These 168 geometrical elements consist of two sets of 84 elements, so that the 336 geometrical elements surrounding the axis in both halves of the polyhedron comprise four sets of 84 elements. This is the polyhedral counterpart of the four sets of 84 structural elements found in previous sections for the inner Tree of Life, the dodecagon, the 64 hexagrams and the Platonic solids. This pattern is part of the larger holistic pattern:

384 = 48 + 336 = (24 + 168) + (24 + 168),

which is revealed particularly clearly in the 64 hexagrams as the 48 lines & broken lines in the eight diagonal hexagrams and as the 336 lines & broken lines in the 56 off-diagonal hexagrams (168 in each half). The counterpart in the disdyakis triacontahedron of the central set of 48 lines & broken lines (24 lines, 24 broken lines) are the 24 corners & triangular sectors of the central 12-gon and their 24 sides.

Next, consider each face and internal triangle as a Type A triangle. Table 16 lists the geometrical composition of the disdyakis triacontahedron:

Table 16. Geometrical composition of the disdyakis triacontahedron with Type A triangles.






Faces 2 + 60 + 120 = 2 + 180

180 + 3×120 = 540

3×120 = 360

2 + 1080


1 + 180

2 + 60 + 3×180 = 2 + 600

3×180 = 540

3 + 1320


2 + 360

2 + 1140


5 + 2400


2400 geometrical elements surround the five geometrical elements making up the axis. The 900 (=90×10) triangles comprise 360 (=36×10) triangles in the faces and 540 (=54×10) internal triangles. This simple 36:54 division of the holistic parameter is characteristic of holistic systems, being embodied in Plato’s Lambda Tetractys [9] as the difference between the sum (36) of the integers at its corners and the sum (54) of the seven remaining integers at the centre and corners of a hexagon (Fig. 55). Comparing Tables 14 & 15, the intermediate stage of transformation of the disdyakis triacontahedron in which only internal triangles are Type A adds 1320 internal geometrical elements (180 corners, 600 sides, 540 triangles) to the 360 elements (60 corners, 180 sides, 120 triangles) that surround the axis The 1680 geometrical elements surrounding the axis comprise 840 in each half. This should be compared with the 1680 turns

Figures 55 & 56


in each whorl of the UPA described paranormally by C.W. Leadbeater, its outer or inner half having 840 turns. It is additional evidence for the disdyakis triacontahedron being the polyhedral version of the universal blueprint that governs the form of the basic constituent of matter that he claimed to remote-view. Notice that the upper or lower half of the polyhedron is now composed of (600+180=780=78×10) sides and (180+540+60+120=900=90×10) corners & triangles. As well as embodying the number value 168 of Cholem Yesodeth, its geometry also embodies the gematria number value 78 of Cholem and the number 90 of Yesodeth! Evidence that this particle really was (and is) a superstring is the fact that 720 geometrical elements are added by dividing the 120 faces of the disdyakis triacontahedron into their 360 sectors, so that:

2400 = 720 + 1680.

Compare this with the mathematical fact that the rank-8 exceptional Lie group E8 in E8×E8 heterotic superstring theory has 240 roots, whilst E6, its rank-6 exceptional subgroup, has 72 roots, leaving 168 other roots. We see that there is a correlation between the geometrical composition of the disdyakis triacontahedron and the root composition of E8 and its subgroups (it is analysed in detail on the author’s website (10)). This would not exist unless:

1. the UPA is a state of the E8×E8 heterotic superstring, making its “observed” structural parameter 168 assume group-theoretical significance;

2. the disdyakis triacontahedron is the polyhedral representation of holistic systems in which the group E8 plays a fundamental role.

The central plane of the disdyakis triacontahedron is a 12-gon whose corners are three A vertices, three B vertices & three C vertices. As the number of geometrical elements surrounding the centre of a Type A n-gon = 10n, the centre of the 12-gon is surrounded by 120 geometrical elements. (2400−120=2280=228×10) geometrical elements above and below the central plane surround the axis. 228 is the 227th integer after 1, where 227 is the 49th prime number. This shows how EL CHAI, the Godname of Yesod with number value 49, prescribes the disdyakis triacontahedron.

Figure 56 depicts the types of yods in a face and an internal triangle when both are either tetractyses or Type A triangles. In the former case, in each half of the disdyakis triacontahedron (24+60+84=168) corners or centres of tetractyses, (2×84=168) hexagonal yods on edges and (2×24=48) hexagonal yods on internal sides surround the axis. In other words, the holistic parameter 384 manifests in each half of the disdyakis triacontahedron. It embodies the characteristic pattern:

384 = 48 + 336 = 48 + 168 + 168

that we find in the 64 hexagrams and sacred geometries [11]. As the 24 vertices consist of 12 A vertices, four B vertices & eight C vertices, i.e., all even numbers, and all the other sets of yods are exactly divisible by 2, the 384 yods divide naturally into two sets of 192 yods that display the characteristic pattern:

192 = 24 + 168.

The number of yods surrounding the axis above or below the 12-gon that line faces = 24 + 2×84 = 192. The same pattern therefore appears in just the yods that line the 120 tetractyses in the disdyakis triacontahedron. The division:

384 = 192 + 192

divides the polyhedron into two equal halves above or below the central 12-gon, each half being composed of 60 tetractyses bounded by 192 yods.

Let us now regard as a tetractys every sector of the 300 triangles making up the disdyakis triacontahedron. For simplicity, the yods on the axis will be excluded from the calculation. Table 17 shows the number of yods in the faces and interior that surround an axis perpendicular to the 12-gon passing through two diametrically opposite A vertices. Figure 56 depicts the different types of yods.

Table 17. Yod composition of the disdyakis triacontahedron with Type A triangles.






Hexagonal yods


Hexagonal yods






24 + 60 = 84

2×84 + 2×3×60 = 528

3×60 = 180


2×24 + 2×3×84 = 552

3×84 = 252




2×12 = 24


2×4×12 = 96

3×12 = 36



24 + 60 = 84

2×84 + 2×3×60 = 528

3×60 = 180


2×24 + 2×3×84 + 552

3×84 = 252











Above or below the central plane are 1680 yods surrounding the axis that include 24 vertices. The 24:24 division of the 48 vertices surrounding the axis above and below the central plane defines the division:

3360 = 1680 + 1680,

which (apart from the tetractys/Tree of Life factor of 10) was proved in earlier sections to exist in certain sacred geometries. The question is whether each yod population 1680 has the natural division:

1680 = 840 + 840

which (apart, again, from the factor of 10) was found for these sacred geometries. Figure 56 shows that 10 yods are inside an internal Type A triangle having an edge of the polyhedron as its base. But there are 84 such edges above the central plane containing the 12-gon and 84 edges below it. Hence, the 1680 yods in each half contain (10×84=840) yods inside 84 internal triangles, leaving 840 yods either in the faces or on sides of internal triangles. The 3360 yods outside the 12-gon that surround the axis divide into four sets of 840 yods. This conforms to the pattern:

336 = 4×84

found for sacred geometries discussed in previous sections.

By exchanging the 84 blue yods at the centres of internal Type A triangles with 24 black vertices, one set of 840 yods decreases by 60, becoming 780 (=78×10) yods, and the other set increases by 60, becoming 900 (=90×10) yods (see Fig. 56). With its yods regrouped this way, the disdyakis triacontahedron is seen to embody in a natural way the gematria number values 78 and 90 of, respectively, the words Cholem and Yesodeth making up the Kabbalistic name of the Mundane Chakra of Malkuth.

Including the central 12-gon, 3540 yods surround the axis of the disdyakis triacontahedron, of which 360 yods are yods at the centres of tetractyses in faces and 540 yods are at centres of tetractyses in the interior. The number of yods lining the 900 tetractyses = 3540 – 360 – 540 = 2640 = 264×10. The number of yods in the seven enfolded polygons of the inner Tree of Life is 264 (Fig. 8). Assigning the Decad to all their yods generates the number of yods on the sides of the tetractyses in the disdyakis triacontahedron. Including just its centre, the polyhedron has 3541 yods. Amazingly, this is the 496th prime number, where 496 is the number of Malkuth and the dimension of the two symmetry groups SO(32) and E8×E8 providing superstring interactions that are free of quantum anomalies! [12]. Alternatively, including the seven yods spaced evenly along its axis, the disdyakis triacontahedron constructed from Type A triangles contains 3547 yods in total, where 3547 is the 496th prime number after 2. There must be a profound connection between the prime numbers and the structural parameters of holistic systems, for it is too improbable for these two properties to be due to chance.

9. 3-torus
The German mathematician Felix Klein (1849-1925) is well-known to mathematicians for his work in group theory, complex analysis, non-Euclidean geometry and on the connections between geometry and group theory. In 1878 he discovered that the quartic equation

u3v + v3w + w3u = 0

(henceforth called the “Klein quartic” [13]) relating three complex variables u, v, w that are the homogenous coordinates of a point on its Riemann surface has the 336 symmetries of the group SL(2,7). Klein showed that it is mapped onto itself by 168 analytic transformations, or orientation-preserving “automorphisms.” The remaining 168 antiautomorphisms” reverse orientation, causing reflection. Hurwitz [14] showed that a compact Riemann surface of genus g≥2 has at most 84(g−1) automorphisms and the same number of antiautomorphisms. A Riemann surface with the maximum number of automorphisms for a given g is called a “Hurwitz curve” of genus g (g≥3). A Hurwitz curve of genus 3 has 168 automorphisms, so that the Klein curve is the Hurwitz curve with the smallest genus g = 3. In plain English: it has the most symmetries of any surface that is topologically equivalent to a sphere


Figure 57. The 3-torus.

with three holes, and there is no sphere with fewer holes that has the most symmetries for that number of holes. Macbeath [15] showed that there is an infinite number of Hurwitz curves. But none other than the Klein curve with g = 3 and one with genus 7 have equations currently known to mathematicians [16]. Because the Klein Quartic is a Riemann surface of genus 3, it can be realised as a regular map in an orientated 2-manifold of genus 3, i.e., the 3-torus (Fig. 57).

SL(2,7) is the double cover of the Klein quartic symmetry group PSL(2,7). Its order 336 is the number of



{7,3} & {3,7} tiling of 3-torus
 Figure 58. The {7,3} & {3,7} tiling on the Poincaré disk of the 168 symmetries of the Klein quartic.

automorphisms and antiautomorphisms of the Klein quartic. The 168 elements of PSL(2,7) are represented either by the {7,3} tiling [17] of the Poincaré disc with 24 heptagons having 168 vertices, three heptagons meeting at each of the 56 vertices, or by its {3,7} tiling with 56 triangles having 168 vertices, seven triangles meeting at each of the 24 vertices (Fig. 58). The Riemann surface of the Klein quartic is a 168-sheeted covering of the sphere, branched over the following three points of the sphere:

  • Above one of these points, the 168 sheets join in groups of seven to give 24 points of the surface. These are the points of inflection of the curve described by the Klein quartic. They are also the Weirstrass points. The 24 orbits of subgroups of order 7 correspond to these points.
  • Above another branch point, there are 84 points of the surface, where the sheets join in twos. These are the sextactic points through which pass a conic section that has six-fold contact with the curve. The 84 orbits of subgroups of order 2 correspond to them.
  • Above the third branch point, the sheets join in threes to give 56 points of the surface. These 56 points are the points of contact of the Klein quartic with the 28 bitangents, or lines that are tangent to the curve at two points. The 56 orbits of subgroups of order 3 correspond to them.

The author’s website and articles has provided illustrations of not only how the numbers 336 & 168 are characteristic parameters of sacred geometries but also how they naturally display the factorisations:

336 = 2×168

168 = 84×2 = 56×3 = 24×7.

If we dismiss as implausible that these properties appear merely by coincidence, it implies that the geometry underlying the Klein quartic conforms to the archetypal patterns of sacred geometries. This was explored in earlier articles ([18], [19]). To avoid repetition, we shall focus here on showing how the {3,7} tessellation of the 3-torus by triangles that are either tetractyses or Type A triangles displays the 168:168

3-torus Triangular prisms & square antiprisms

Figure 59. The 3-torus constructed from 4 triangular prisms and 6 square antiprisms.

Figure 60. The triangular prism and the square antiprism constructed from tetractyses.


division of 336 and the 84:84 division of 168, thereby providing more evidence that the geometry underlying the Klein quartic conforms to the patterns characteristic of sacred geometries.

Figure 59 shows the {3,7} tessellation onto the 3-torus of the 56 orbits of order 3 that correspond to the 56 bitangents of the Klein quartic. The 3-torus is topologically equivalent to six square antiprisms (Fig. 60) with their 12 square faces stuck to the 12 square faces of four triangular prisms in a tetrahedral formation, each antiprism being given a twist. This leaves 56 triangular faces. Each triangular prism has six vertices, nine edges & two triangular faces; each square antiprism has eight vertices, 16 edges, of which eight edges coincide with edges of the former when they are stuck together, and eight triangular faces. This leaves 24 vertices and (4×9 + 6×8 = 84) edges. Compare this with the 24 vertices and 84 edges of 60 triangles that surround the axis of the disdyakis triacontahedron in its upper or lower halves (Fig. 61). In fact, just as it has 144 edges & faces, so the six square antiprisms have 144 edges & triangular faces. Of itself, this does not prove some kind of isomorphism exists between the polyhedron and the 3-torus constructed from prisms and antiprisms, because it is illegitimate to compare an intact system with the separate components of another — whether holistic or not! However, the division:

168 = 24 + 144

is characteristic of such systems because it is part of the tetractys representation of the holistic parameter 240:

Tetractys representation of 240

For example, the 168 yods needed to transform the sectors of a dodecagon into Type A triangles comprise 24 hexagonal yods on its sides and 144 yods inside it (Fig. 62), whilst the 168 corners & sides in two separate Type B dodecagons consist of their 24 corners and 144 sides & other corners

24:144 division of 168 yods in Type B dodecagon

24:168 division of 240 corners & sides in twoType B dodecagons

 Figure 62. The 168 yods needed to turn the sectors of a dodecagon into Type A triangles consist of 24 red hexagonal yods lining its sides and 144 black yods.

Figure 63. 240 geometrical elements surround the centres of the two Type B dodecagons. They comprise 72 blue triangles and their 168 corners & sides. The latter comprise 24 red corners of the dodecagons and 144 black corners & sides.

(Fig. 63). This division reflects the fundamental Kabbalistic distinction between Malkuth and the six Sephiroth of Construction preceding it:

7 = 1 + 6

168 = 24×7 = 24×1 + 24×6 = 24 + 144.


The 24 vertices surrounding the axis above or below the equator of the disdyakis triacontahedron minimally mark out the skeletal shape of each half of the polyhedron, as expressed by its 144 edges & faces (see Fig. 61); similarly, the 24 vertices of the four triangular prisms minimally define the prismatic construction of the 3-torus, the 48 vertices of the six square antiprisms not adding to its shape because they coincide with these vertices when the 12 square faces of the triangular prisms are stuck to the 12 square faces of the square antiprisms.

To investigate other analogous properties, we will analyse the geometrical and yod composition of the prisms and antiprisms when separate and when assembled. Table 18 shows the populations of geometrical elements and yods in the separate polyhedra when their faces are simple triangles/tetractyses and when they are Type A triangles.

Table 18. Geometrical/yod composition of the four triangular prisms & the six square antiprisms.


Type A triangle











Number of vertices

4×6 = 24

6×8 = 48


24 + 4×2 = 32

48 + 48×1 = 96


Number of edges

4×9 = 36

6×16 = 96


36 + 8×3 = 60

96 + 48×3 = 240


Number of triangles

4×2 = 8

6×8 = 48


8×3 = 24

48×3 = 144


Number of geometrical elements







Number of hexagonal yods on sides of tetractyses

36 = 72

2×96 = 192


2×60 = 120

2×240 = 480


Number of hexagonal yods

8 + 72 = 80

48 + 192 = 240


24 + 120 = 144

144 + 480 = 624


Number of yods on sides of

24 + 72 = 96

48 + 192 = 240


32 + 120 = 152

96 + 480 = 576


Number of yods

8 + 96 = 104

48 + 240 = 288


24 + 152 = 176

144 + 576 = 720



1. The 10 separate prisms & antiprisms have 72 vertices. This is the 36th even integer, showing how ELOHA, the Godname of Geburah with number value 36, prescribes the geometry of the 3-torus in a minimal way. They have 132 edges, where 132 is the 65th even integer after 2. This shows how ADONAI, the Godname of Malkuth with number value 65, prescribes the form of the 10 prisms & antiprisms through their edges. The two types of structural units have 14 vertices, 25 edges & 10 triangular faces, i.e., 49 geometrical elements, showing how they are prescribed by EL CHAI, the Godname of Yesod with number value 49.

2. There are 260 (=26×10) geometrical elements in the 10 separate prisms & antiprisms. This is strong evidence for the holistic nature of the 3-torus prescribed by the Godname YAHWEH with number value 26 because there are 260 yods outside the root edge of the seven enfolded polygons, whilst 260 geometrical elements make up the 3-dimensional Sri Yantra (Fig. 64).

 Inner Tree of Life and Sri Yantra embody the number 260  260 geometrical elements in prisms and antiprisms
Figure 64. The Godname YAHWEH with number value 26 prescribes the yod population of the inner Tree of Life and the number of geometrical elements in both the 3-d Sri Yantra & the 10 separate prisms & antiprisms that form the 3-torus.

3. 264 hexagonal yods line the 132 edges of the 10 prisms & antiprisms. This is the number of yods in the seven enfolded polygons of the inner Tree of Life when their 47 sectors are tetractyses. The 132 hexagonal yods in half the complete set of prisms & antiprisms have their counterparts in the 132 yods


making up S1 and the 132 yods in S2 — the two halves of the set of seven polygons. This correlation indicates that the 3-torus is the counterpart of one set of seven enfolded polygons. The counterpart of the set in the mirror-image half of the inner Tree of Life will be discussed shortly.

4. 336 yods line the 132 sides of the 56 tetractyses (Fig. 65). The number 336 is the order of SL(2,7), the group describing the 336 automorphisms and antiautomorphisms of the Klein quartic whose Riemann surface is topologically equivalent to a 3-torus. It is remarkable that this parameter of holistic

336 yods line edges of prisms and antiprisms

Figure 65. 336 yods line the edges of the 10 separate prisms and antiprisms

systems should be embodied in the separate building blocks needed for the {3,7} tessellation of the 3-torus. Not that it is unique, for 336 yods are needed to turn the separate polygons in either S1 or S2 with 24 sectors into Type B polygons, whilst the seven separate Type B polygons have 336 corners & sides of 144 triangles [20]. Furthermore, compare this property with the fact that 336 yods line the sides of the 42 triangles in the Sri Yantra (see Fig. 35), whilst 336 yods other than corners surround the centres of two joined, Type B dodecagons (see Fig. 31). This number appears in the building blocks of the {3,7} tessellation of the 3-torus not by accident but because the geometry underlying the Klein quartic conforms to the universal patterns of sacred geometry.

5. The 168 sectors of the 56 Type A triangles contain 896 yods, of which 56 are their centres, leaving 840 yods that surround these centres. When the triangles are tetractyses, there are 336 yods surrounding these same centres. Here is the meaning of these two numbers in the context of the structure of the UPA: one revolution of each helical whorl with 1680 turns contain 336 turns and the 2½ revolutions constituting an outer or inner half of a whorl contain 840 turns. It is remarkable that the ten prisms & antiprisms embody three structural parameters (168, 336 & 840) of the basic unit of matter paranormally described over a century ago by Annie Besant & C.W. Leadbeater. Far from being coincidental, it points towards the Klein quartic and its connection to the octonions playing a leading role in the still-sought unification of superstrings and supergravity by M-theory.

Let us now consider the prisms and antiprisms joined together at their square faces to form the {3,7} tessellation of the 3-torus. Table 19 lists their geometrical and yod composition.

Table 19. Geometrical/yod composition of the 3-torus constructed from tetractyses & Type A triangles.


Type A triangle











Number of vertices

4×6 = 24


24 + 4×2 = 32

48×1 = 48


Number of edges

4×9 = 36

6×8 = 48


36 + 8×3 = 60

48 + 48×3 = 192


Number of triangles

4×2 = 8

6×8 = 48


8×3 = 24

48×3 = 144


Number of geometrical elements







Number of hexagonal yods on sides of tetractyses

36 = 72

48 = 96


2×60 = 120

2×192 = 384


Number of hexagonal yods

8 + 72 = 80

48 + 96 = 144


24 + 120 = 144

144 + 384 = 528


Number of yods on sides of

24 + 72 = 96



32 + 120 = 152

48 + 384 = 432


Number of yods

8 + 96 = 104

48 + 96 = 144


24 + 152 = 176

144 + 432 = 576



1. When each face is a tetractys, the 56 tetractyses contain 248 yods. Given the connection to UPAs as superstrings indicated by the presence of three of their structural parameters, it is very remarkable that the dimension 248 of the very Lie group E8 that describes the unified force of one of the two types of heterotic superstrings should manifest as the number of yods needed to construct the prisms and antiprisms from tetractyses. Once again, it is highly implausible to be due to chance. Rather, the presence of the holistic parameter 248 is yet again an indication of the sacred geometrical nature of the {3,7} tessellation of the 3-torus whose 56 triangles represent the 168 automorphisms of the Klein quartic. But it is more than this, for, if each yod corresponds to one of the roots of E8, then we should expect to see the geometry of the prisms and antiprisms dividing this group up into certain subgroups. Indeed, we do. The 248 yods comprise eight yods at the centres of the faces of the four triangular prisms, leaving 240 yods that are made up of their 24 vertices, 48 hexagonal yods at the centres of the faces of the six


antiprisms, i.e., 72 yods, and 168 hexagonal yods on the 84 sides of the 56 tetractyses. The division:

248 = 8 + 240

corresponds to the eight simple roots of E8 and its 240 roots. The division:

240 = 72 + 168

corresponds to the 72 roots of E6, an exceptional subgroup of E8, and to the 168 remaining roots of E8. We see that the tetractys construction of the tessellated 3-torus reveals some of the root structure of E8 (this will not be explored further here).

The division:

168 = 2×84

that was shown in previous sections to appear in sacred geometries manifests trivially in the pair of hexagonal yods lying on each of the 84 sides of the tetractyses in the six square antiprisms. It denotes the 84 sextactic points where the 168 sheets of the Riemann surface of the Klein quartic join in 84 pairs. It corresponds in the 64 hexagrams as the 84 solid lines (yang) and the 84 broken lines (yin) that make up the 56 trigrams in the upper or lower set of 28 off-diagonal hexagrams. The division:

336 = 2×168

that previous sections showed resulted from the mirror symmetry of the sacred geometry (or near mirror symmetry, in the case of the Sri Yantra) expresses the fact that the number of antiautomorphisms of the Klein quartic is equal to the number of its automorphisms. The former can be represented by a version of the 3-torus which is turned inside out, reversing the orientations of all triangles (Fig. 66). Their counterparts in the inner Tree

248 yods in 56 tetractyses of 3-torus

Figure 66. The 496 yods in the (56+56) tetractyses tiling the 3‑torus and its turned-out version symbolise the 496roots of E8×E8.

of Life are the 168 geometrical elements outside the root edge that are intrinsic to one set of seven enfolded polygons and their 168 chiral counterparts in the other set of seven enfolded polygons. The pair of 3-tori contains 336 hexagonal yods on sides of the two sets of 56 Type A triangles, there being (248+248=496) yods altogether. The number 496 is the crucial dimension of any gauge symmetry group that describes superstring forces free of

Correspondence between 1st (6+6) polygons and {3,7} tessellation on 3-torus

Figure 67. Correspondence between the 1st (6+6) enfolded polygons of the inner Tree of Life and the {3,7} tessellation of the 3-torus & its version turned inside out.

quantum anomalies [12]. The conjunction of structural parameters of a particle claimed to have been remote-viewed over a century ago and this theoretical requirement for a certain type of superstring is undeniable. These numbers have not been concocted by cherry-picking. Instead, they quantify natural, mathematical features of the tessellated 3-torus. It is evidence that UPAs are E8×E8 heterotic superstrings.

2. The number of yods on the 84 sides of the 56 tetractyses is the sum of the 24 vertices of the four triangular prisms and the 168 (=84×2) hexagonal yods on these sides:


24 + 168 = 192.

This is a characteristic division of holistic systems. For example, Figure 67 shows that, associated with each set of the first six enfolded polygons of the inner Tree of Life, are 24 corners and 168 other yods. The pair of chiral 3-tori exhibit the complete division displayed by holistic systems:

384 = 192 + 192 = 48 + 336,


48 = 24 + 24

is the number of vertices of their eight triangular prisms and

336 = 168 + 168.

is the number of hexagonal yods on the sides of their 112 tetractyses. The number 48 is the number value of Kokab, the Mundane Chakra of Hod, and112 is the number value of Beni Elohim, the Order of Angels assigned to this Sephirah. Figure 31 in Article 43 compares how the holistic parameter 384 is embodied in various sacred geometries, including the {3,7} tessellation of the 3-torus.

3. The 10 prisms & antiprisms constructed from Type A triangles form a 3-torus with 500 (=50×10) geometrical elements. This shows how ELOHIM, the Godname of Binah with number value 50, prescribes the form-determining geometrical composition of the 3-torus constructed from Type A triangles. It is a clear demonstration of the archetypal power of Godnames in their prescription of holistic systems. It is the counterpart of the 500 geometrical elements needed, starting from their 50 vertices, to shape the faces of the five Platonic solids (see comment 4, p. 33).

672 hexagonal yods in 56 triangles of 3-torus Figure 68. The 672 hexagonal yods in the 168 tetractyses of the 56 Type A triangles of the 3-torus comprise two sets of 336 yods (336 red or blue yods; 336 green yods).

4. The 168 triangles making up the 3-torus when the triangular faces of the prisms &antiprisms are Type A consist of the 24 triangles in the former and the 144 triangles in the latter. This is another example of the pattern displayed by holistic systems that was discussed on p. 39. The 56 sets of three triangles and their counterparts in the 3-torus turned inside out are the geometrical analogue of the 56 trigrams in the 28 off-diagonal hexagrams that make up the upper and lower diagonal halves of the 8×8 square array of hexagrams.

5. The 168 tetractyses in the 3-torus tessellated with 56 Type A triangles contain 168 hexagonal yods on the 84 edges of the prisms & antiprisms,168 hexagonal yods at the centres of these tetractyses and 168 pairs of hexagonal yods on sides inside the Type A triangles (Fig. 68). The 672 hexagonal yods comprise two sets of 336 yods. This division conforms to the patterns of sacred geometry. For example, the first four Platonic solids contain 672 yods (336 yods in each half) when they are constructed from tetractyses [22], whilst each set of seven separate Type B polygons in the inner form of the Tree of Life has 336 corners & sides surrounding their centres [23]. The 3-torus and its version turned inside out have (672+672=1344) hexagonal yods. This is the number of yods surrounding the centres of the 14 enfolded Type B polygons of the inner Tree of Life that are unshared with the outer Tree of Life [24]. This demonstrates that the 3-torus with Type A triangles is the counterpart of one half of the inner Tree of Life and that its turned inside-out version is the counterpart of its other half. The turning inside out of the 3-torus, which reverses the orientation of all triangles, is analogous to the reflection of all geometrical elements/yods in the seven enfolded polygons across the root edge that joins them to their chiral images.

For further analysis of the remarkable correspondences between the 3-torus and sacred geometries, see reference 19.

10. The seven diatonic musical scales
Two divisions characteristic of holistic systems:

336 = 168 + 168


168 = 84 + 84

are embodied not only in sacred geometries but also in the seven ancient, diatonic musical scales that


were known to the ancient Greeks as “harmoniae” and which entered the plainsong of the Roman Catholic Church. That these patterns exist in music will be demonstrated in this section in two ways.

The Pythagorean musical scale consists of five tone intervals of 9/8 (T) and two leimmas of 256/243 (L):

Tone ratios of Pythagorean scale

By starting with successive notes to generate scales of eight notes and then normalising the tone ratios so that the tonic in each scale has a tone ratio of 1, the pattern of intervals is repeated at the eighth sequence, thereby generating seven distinct, octave species:

8. T L T T T L T Hypomixolydian (Mode 8, D’ scale)
7. T T L T T T L Hypolydian (Mode 6, C scale)
6. L T T L T T T Hypophrygian (Mode 4, B scale)
5. T L T T L T T Hypodorian (Mode 2, A scale)
4. T T L T T L T Mixolydian (Mode 7, G scale)
3. T T T L T T L Lydian (Mode 5, F scale)
2. L T T T L T T Phrygian (Mode 3, E scale)
1.  T L T T T L T Dorian (Mode 1, D scale)

These are the musical modes used for hundreds of years in the plainsong of the Roman Catholic Church. Mode 8 (Hypomixolydian) is the D scale with different ‘dominant’ and ‘finalis’ notes. Table 20 displays the values of the tone ratios of their notes with Pythagorean tuning.

Table 20. Tone ratios of the seven diatonic scales.

Musical scale

Tone ratio

B scale









A scale









G scale









F scale









E scale









D scale









C scale









Tone ratios of notes belonging to the Pythagorean scale are written in black and non-Pythagorean tone ratios are written in red. The 42 notes between the tonic and the octave comprise 26 notes with Pythagorean tone ratios belonging to the Hypolydian mode (C scale) and 16 with non-Pythagorean values. Table 1 indicates that 26 is the gematria number value of YAHWEH, the Godname of Chokmah. As 42 is the 21st even integer, EHYEH, the Godname of Kether with number value 21, prescribes the seven musical scales. We shall see shortly that it does so in a more direct way.

The seven diatonic scales comprise 14 different notes. In order of increasing tone ratios, they are:

1       256/243      9/8      32/27       81/64      4/3     1024/729   729/512   3/2     128/81      27/16     16/9      243/128      2

There are six Pythagorean notes and six notes that belong to the six other diatonic scales. Let us define the inversion of a note with tone ratio n as a note with tone ratio m, where nm = 2. The inversion of a note has a tone ratio that is equal to the interval between that and the octave. It does not necessarily belong to the same scale as the note. But, if not, it will be a note of another diatonic scale, as can be seen from a comparison of Table 20 with the 14 notes arranged as seven pairs of notes and their inversions:





= 2





= 2





= 2





= 2





= 2





= 2





= 2

The rising interval between two notes with tone ratios n and m (m>n) is the ratio m/n. The falling interval is n/m. Just as eight objects can be paired in 28 ways, so there are 28 rising intervals between the eight notes forming one octave of a diatonic scale. One of these is the octave itself, so that in each diatonic scale, there are 27 intervals below this last note. They comprise six notes above the starting note, or tonic, and 21 intervals, including 15 intervals between these six notes. The Godnames EHYEH with number value 21 and YAH, the shorter Godname of Chokmah with number value 15, prescribe these intervals.



84 Pythagorean repetitions of basic notes in 7 diatonic scales

Figure 69. The intervals between the notes in the seven diatonic scales/Church modes.


There are (7×27=189) intervals below the octave between the notes on the seven diatonic scales. They comprise 21 notes up to the note with tone ratio 1024/729 and 168 more intervals made up of the remaining 21 notes that are the inversions of the first set of 21 notes and 147 intervals. Figure 69 displays their values. They are all instances of the basic set of 13 types of notes above the tonic that make up the seven diatonic scales. All cases where these intervals first appear are given dark blue cells. Cells enclosing Pythagorean repetitions of the basic set are coloured dark red, whilst yellow cells refer to repetitions of non-Pythagorean intervals. The corresponding cells for falling intervals are coloured light blue, light red and light yellow. Counting the numbers of Pythagorean repetitions in each Church mode (i.e., dark red cells), we find that the 168 intervals, including inversions with tone ratios larger than 1024/729, contain 84 repetitions that have the intervals of notes belonging to the Pythagorean scale (Hypolydian mode). These are actually among the 147 non-note intervals because they are repetitions of notes. In terms of Pythagorean notes, five different intervals make up the composition of the 84 Pythagorean intervals:

 D  E  F  G  A
 28  11  23  17  5

The interval 243/128 for note B is absent because it is the only note amongst the first seven notes that never appears more than once in a church mode (Phrygian, Lydian, Hypophrygian & Hypolydian) and so it has no repetitions.

We discover that the divisions:

336 = 168 + 168

168 = 84 + 84

found in previous sections to be characteristic of holistic systems manifest in the seven diatonic scales as:

1. the 168 rising intervals (and their 168 falling counterparts) other than the ‘core’ set of 21 notes up to that with tone ratio 1024/729;

2. the 84 repetitions (red cells) of the six Pythagorean notes among the basic set of 12 notes and the 84 intervals that are either members of this set (blue cells) or repetitions of their non-Pythagorean members (yellow cells).

 36-48 division of yods in 2nd-order tetractys  
Figure 70. 36 yods line the sides of the 2nd-order tetractys, leaving 48 yods that surround its centre.

Figure 71. The patterns of division amongst the 384 rising and falling intervals between the notes of the 7 diatonic scales.

Notice that the four Authentic Modes (Dorian, Phrygian, Lydian & Mixolydian) have 48 repetitions among the 84 that are Pythagorean, whilst the three Plagal Modes (Hypolydian, Hypophrygian & Hypodorian) have 36 such repetitions. This 36:48 division of the holistic parameter 84 corresponds in the 2nd-order tetractys (Fig. 70) to the 36 red yods that line its boundary and to the 48 blue yods inside it that surround its central, black yod. In the case of the 3-torus, it corresponds to the 36 edges of the four triangular prisms and to the 48 unshared edges of the six square antiprisms (see Fig. 60).

These holistic divisions are a part of the more-inclusive division found in sacred geometries:


 384 = 192 + 192,


192 = 24 + 168


24 = 3 + 21,

so that

192 = 3 + 189 = 3 + 21 + 168.

The three extra intervals are the tonic (1), the octave (2) as a note and the interval of 2 between corresponding notes in successive octaves. The 168 falling intervals are the counterparts of:

1.   the 168 anti-automorphisms of the Klein quartic mapped by the {3,7} tessellation onto the inside-out version of the 3-torus;

2.   the 168 solid lines & broken lines of the 28 off-diagonal hexagrams in the lower diagonal half of the 8×8 array;

3.   the 168 intrinsic geometrical elements making up the reflected half of the inner Tree of Life;

4.   the 168 yods other than corners associated with the second dodecagon that is the mirror image of the first one;

5.   the 168 yods lining the 21 triangles in the second half of the 3-dimensional Sri Yantra.

We will now consider the second way in which the number 168 appears in the intervallic composition of the seven diatonic scales. Each of the seven scales has 27 intervals below the octave. The (7×27=189) intervals include the 42 notes between the tonic and octave. Inspection of Fig. 71 shows that there are 21 notes that pair with their 21 inversions. The Godname EHYEH with number value 21 prescribes each set because its letter values denote subsets of notes and their inversions:

AHIH = 21

A = 1 → 1×(1024/729)


H = 5 → 5×(9/8)


I = 10 → 4×(32/27) + 6×(4/3)

4×(27/16) + 6×(3/2)

H = 5 → 2×(256/243) + 3×(81/64)

2×(243/128) + 3×(128/81)

Just as a note is at least mathematically paired with its inversion (even though it may not appear in the same diatonic scale), so any interval can be paired with its inversion. However, unlike notes, there is not the same number of intervals and their inversions. Figure 72 below:
Composition of intervals in the 7 diatonic scales

Figure 72. The 168 notes & intervals in the 7 diatonic scales other than the 21notes of the first 6 types consist of 42 pairs of intervals and their inversions and (21+62+1=84) inversions or unpaired intervals.

lists the numbers of notes, intervals and their inversions that can be paired, as well as the numbers of unpaired intervals and their inversions (black tone ratios are those of the Pythagorean scale, red tone ratios are those of notes in the other diatonic scales). There are 125 intervals of the first six kinds (21notes) but they have only 64 inversions (21 notes). As the inversion 729/512 appears once more often than the interval 1024/729, whilst each of all the other types of inversions appears less often than their counterparts, there are 63 notes & intervals


that can be paired with their inversions, leaving (125–63+1=63) other intervals that cannot be paired (see the last “Total” row in Fig. 72). Hence, the 189 intervals below the octave split naturally into three sets of 63: 1. 63 notes & intervals; 2. their 63 inversions, and 3. 63 intervals without their accompanying inversions. Notice that they consist of 21 notes of the first six types and 168 inversions & intervals (see the bottom of the table). As discussed earlier, the 21:168 split shown by the number 189 is characteristic of sacred geometries and non-geometrical holistic systems, such as the seven musical scales. As confirmation that chance is not involved here, notice that the 168 inversions & intervals consist of 42 pairs of intervals & their inversions, i.e., 84 intervals, and 84 inversions & unpaired intervals that comprise the 21 inversions paired with the 21 notes of the first six types, 62 unpaired intervals of the first six types & one unpaired inversion. This is another way in which the holistic division:

168 = 84 + 84

manifests in the seven diatonic scales. The two sets of 84 intervals are the musical counterpart of the two sets of polygons in the inner Tree of Life, each with 84 geometrical elements surrounding their centres.

11. Conclusion
Table 21 summarises the primary analogous divisions of the holistic parameters 336 and 168 in nine holistic systems:

Table 21. Comparison of two divisions in various holistic systems.

Sacred geometry or holistic system

336 = 168 + 168

168 = 84 + 84

Inner Tree of Life

The set of 7 enfolded polygons in each half of the inner Tree of Life has 168 intrinsic, geometrical elements outside the root edge.

84 intrinsic geometrical elements in the triangle, square, pentagon & dodecagon; 84 elements in the hexagon, octagon & decagon.

1st (6+6) enfolded polygons

168 yods other than corners of polygons in each set of 6 enfolded polygons.

84 yods line each set of 6 enfolded polygons outside the root edge.


168 yods other than corners associated with each joined, Type B dodecagon.

84 hexagonal yods at the centres of 36 tetractyses or on the 24 sides of the 12 sectors; 84 hexagonal yods or corners on 36 internal sides of tetractyses.

Sri Yantra

168 yods line the 21 triangles/tetractyses in each half of the 3-d Sri Yantra.

84 pairs of yods line the 21 triangles/tetractyses in each half.

64 hexagrams

168 solid lines & broken lines in the 28 off-diagonal hexagrams in each half of the 8×8 array of 64 hexagrams.

28 off-diagonal hexagrams comprise 84 solid lines & 84 broken lines.

5 Platonic solids

168 yods on average in each half of a Platonic solid surround the centres of faces & internal triangles.

These 168 yods comprise: 84 yods in the tetrahedron and on sides of tetractyses in the octahedron, cube & icosahedron; 84 yods either at centres of tetractyses in these solids or lining sides of tetractyses in the dodecahedron.

Disdyakis triacontahedron

168 hexagonal yods on edges above/below the central 12-gon perpendicular to an axis passing through two opposite A vertices.

1680 (=168×10) yods above/below the central 12‑gon for Type A triangles.

These 168 hexagonal yods comprise 84 pairs of hexagonal yods.

840 (=84×10) yods inside 84 internal Type A triangles and 840 yods either lining their sides or in faces in the upper/lower half of the polyhedron.

3-torus with {3,7} tiling

168 automorphisms & 168 anti-automorphisms of the Klein quartic form the group SL(2,7) with order 336.

168 hexagonal yods on sides of the 56 tetractyses in the 4 prisms & 6 antiprisms of the 3‑torus; 168 hexagonal yods on sides of the 56 tetractyses in the 3-torus turned inside-out.

84 sextactic points on the Riemann surface of the Klein quartic where 168sheets join in pairs.

84 pairs of hexagonal yods on 84 sides of the 56 tetractyses in the {3,7} tessellation of the 3-torus.

7 diatonic musical scales

168 rising intervals & 168 falling intervals other than the 21 notes of the first 6 types belonging to the basic set of 12 notes.


1. These 168 intervals comprise 84 repetitions of Pythagorean notes & 84 intervals that either belong to the basic set of 12 notes or are repetitions of non-Pythagorean notes.

2. 168 intervals comprise 42 pairs of intervals & their inversions and 84 inversions or unpaired intervals.


The holistic parameters 336, 168 & 84 manifest in the UPA described by Annie Besant & C.W. Leadbeater because what they remote-viewed were E8×E8 heterotic superstrings whose 3-dimensional structure conforms to the very same universal pattern that this article has shown is embodied in sacred geometries and the seven diatonic scales.

1.  Article 62; see also:

2.  Article 42. “Comparison of the eight Church musical modes and the human skeleton as holistic systems.”

3.  Proof: the seven enfolded polygons with their 47 sectors turned into tetractyses have 264 yods. The dodecagon constructed from tetractyses has 73 yods, that is, 69 yods outside the four yods in the root edge. The number of yods in the first six enfolded polygons = 264 – 69 = 195 (i.e., 191 outside the root edge). The number of yods in H = 4 + 2×191 = 386.

4.  Article 18: “Encoding of planetary distances and superstring structural parameters in the I Ching table.”

5.  Article 1: “The Pythagorean nature of superstring and bosonic string theories,” p. 5.

6.  Article 14: “Why the ancient Greek musical modes are sacred.”

7.  Article 39: ”The correspondence between the inner Tree of Life, the Sri Yantra & the I Ching diagram and their realization in the seven musical scales.”

8.  Article 3: “The sacred geometry of the Platonic solids.”

9.  Article 11: “Plato’s Lambda — its meaning, generalisation and connection to the Tree of Life.”




13.; and:

14. Hurwitz, A. “Über algebraische Gebilde mit eindeutigen Transformationen in sich,” Math. Ann. 41 (1893), 403-442.

15. Murray Macbeath, A. “On a theorem of Hurwitz.” Proc. Glasgow Math. Assoc. 5 (1961). 90-96.

16. Murray Macbeath, A. “Hurwitz groups and surfaces.” The Eightfold Way. MSRI Publications, vol. 35, 1998, 11.

17. The Schläfli symbol {n,k} denotes the tessellation of a surface by polygons with n vertices, k polygons meeting at each vertex.

18. Article 15: “The mathematical connection between superstrings and their micro-psi description: a pointer towards M-theory.”

19. Article 43: “The Tree of Life nature of the {3,7} tessellation of the 168 automorphisms of the Klein quartic on the 3-torus.”

20. Proof: the number of yods in a Type B n-gon = 15n + 1. Given the (n+1) corners of its n sectors, 14n more yods are needed to create a Type B n-gon. Transformation of the 24 sectors of the four polygons in S1 or the three polygons in S2 requires (24×14=336) more yods. A Type B n-gon has 7n corners & sides surrounding its centre. Surrounding the centres of the seven separate Type B polygons are (7×48=336) corners & sides.

21. Ref. 12.





The two halves of the seven enfolded, regular polygons that constitute half of the inner Tree of Life were identified in Section 2 as the set S1, whose members are the triangle, the square, the pentagon & the dodecagon, and the set S2, whose members are the hexagon (with one sector missing because it is occupied by the triangle), the octagon and the decagon. S1 and S2 have 36 corners, where

36 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8.

This number is determined by the Tetrad (4) in two ways. Firstly, 36 = 62, where 6 is the fourth polygonal number of order 1. Secondly, 36 is the sum of the first four odd integers and the first four even integers:

36 = (1+3+5+7) + (2+4+6+8) = 16 + 20.

16 (= 42) is the number of yods in a 4×4 square array of yods, whilst a tetrahedron — the regular polyhedron with four vertices — has 20 yods in its faces when they are tetractyses. S1 has 16 corners outside the root


edge and S2 has 20 corners (Fig. 73). The odd and even integers making up the number 36 therefore divides the seven enfolded polygons, respectively, into the two halves S1 and S2. Picturing the eight corners of an octagon as those of two squares rotated through 45°, we see that one square (red) with the first four odd integers assigned to its four corners corresponds to S1 with 16 corners, whilst the second square (blue) with the first four even integers assigned to its corners corresponds to S2 with 20 corners.

Tetrad divides 7 enfolded polygons into S1 and S2

Figure 73. The odd/even division of the first 8 integers divides the 7 enfolded polygons (S) of the inner Tree of Life into its two halves S1 (red) & S2 (blue). The ordering of these integers into the Pythagorean subset (1, 2, 3 & 4) and the subset (5, 6, 7 & 8) divides S into the dodecagon and the first 6 enfolded polygons, both of which are holistic systems.

If, instead, the first four integers 1, 2, 3 & 4 symbolising the four rows of dots in the Pythagorean tetractys are assigned to the corners of one square and the remaining integers 5-8 are assigned to the corners of the second square, this generates the division:

36 = 10 + 26,


10 = 1 + 2 + 3 + 4


26 = 5 + 6 + 7 + 8

correspond, respectively, to the 10 corners of the dodecagon outside the root edge and to the 26 corners of the first six enfolded polygons. This ordering of integers divides the seven polygons into two parts, both of which are holistic in character (see Sections 3 & 4).

These two orderings of the integers 1-8 illustrate the beautiful, natural harmony between number and sacred geometry.

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