NUMEROLOGY OF METAPHYSICS: Archaic Mathematics of the Occult Science

The understanding of cosmology depends predominantly on the language and practice of the four ancient intellectual disciplines (arithmetic, geometry, music, astronomy). Arithmetic evaluates number. Geometry (our cosmological mind map), “earth measure,” is the basic science of natural law, which evaluates number in space. Music evaluates number in time. Astronomy evaluates number in space-time.

The practice of geometry functions only on a certain level of reality, the archetypal consciousness (the internal/spiritual realm). Experience results from immaterial, abstract, geometrical archetypes (essential concept/ideal/geometric symbol) composed of harmonic waves of energy, nodes of integrity, and melodic forms springing forth from the realm of geometric proportion (unchanging heaven/metaphysical). The archetypal consciousness is channeled through the human mind as ectypal consciousness (formal model/sign). The typal (actual specific instance) is subject to sensory perception (changing earth/physical). (Lawlor)

To Plato (427 BCE), reality consisted of essential archetypal ideas, and physical perceived phenomena are only mere reflections. Archetypal ideas could only be perceived by pure reason alone, therefore Plato subscribed that geometry was the clearest language to describe the metaphysical realm. Geometrical knowledge is innate within the higher self (god-head) of humanity. The passage from creation to procreation, from idea to form, can be mapped by geometry and experienced through the practice of geometry (rekindling of the soul’s fire through effort). (Lawlor) Taoists apply this geometrical practice metaphysically in the firing process of interior alchemy (neidan).

Depiction of Taoist Sage (zhenren), or anthropocosm, juxtaposing the sun and the moon with the yin and yang of his energetic being.

Ancient cultures may have symbolized eternal processes as gods, or lines of action through which the spirit condenses into energy and matter. These processes, archetypal activity, demonstrate the principle that energy is controlled, specified, and modified through the effects of angulation, which illustrate a fundamental relationship between two numbers. Thus, the archetypes, or gods, represent dynamic functions forming links between higher worlds of constant interaction and processes with the actual world of particularized objects. (Lawlor)

Information is energy. Physics refers to the basic unit of light as a photon that came into being from an electron that increased velocity enough to break out of atomic orbit about a nucleus. This photon, reflected off a viewed object, carries information that travels in waves through an eye to file an event-image as memory in the brain. Metaphysically, the perception of an event-image, or point on the wave of experience, received through photonic transmission, is interpreted as a symbol by the ectypal consciousness. These symbols of interpretation, frozen frames of understanding, are the crucial link between the typal and archetypal consciousness. The continuous flow of interpretations becomes the proportional harmonic feeling of moving through experience. In other words, a human interprets the proportional harmonic flow of experience event-by-event geometrically through the recognition of symbols.

The idea is created in heaven. The sign is discovered in the human mind. The specific instance is observed on earth. The actual sensations of earth originated ideally in heaven. The material senses function in response to their discovery of immaterial (spiritual) qualitative archetypal geometric proportions. The sense of smell responds to the geometry of molecule construction. The sense of hearing notices logarithmic, proportional differences between frequencies of sound waves. For sight, nerves in the retina are tuned into the same frequency range as skin. (Lawlor)

Pythagoras (560-490 BCE) said, “All is arranged according to number.”

The distance of the square’s diagonal or the circle’s circumference would never be known exactly because they make irrational functions (1:Ö2; 1:p). Irrational functions demonstrate graphically a level of invariable and universal experience, which is the key to opening a higher reality of number. Number has a definite, finite, particularizing power (quantity: exoteric/external; arithmetic), and a universal synthesizing power (quality: esoteric/internal; numerology). (Lawlor) Cosmology utilizes arithmetic for its structure and numerology for its meaning.




Level of Consciousness






Spiritual; essence; wisdom


Absolute unity; God-head; creation; circle



(number in space)

Intellectual; being; knowledge


Duality; power of multiplicity; self; first man (father)



(number in time)

Emotional; virtue; opinion


Trinity; mother; triangle



(number in space-time)

Physical; action; sensation


First born thing; material world; procreation; child; tetrahedron/square

This symbology of number, numerology, is reinforced mathematically with exponents, which represent the number’s dimension. Any number to the zero power is one, symbolically the unity womb. Any number to the first power is itself, expressed one-dimensionally. Any number to the second power is expressed as a plane, two-dimensionally. Any number to the third power is expressed as a three dimensional form.

The ascending dimensional progression expresses the creation of form from a point through the movement from heaven to earth. Reversing the movement (earth to heaven) is seen in the Buddhist alchemical process of renouncing the transient physical world and returning to the spiritual source (nirvana) (square-triangle-circle = earth-humanity-heaven = earth-fire-water). This progression moves from a four-point (three dimensional form) through a three point (two dimensional plane) to a one point (one dimensional point). This progression exemplifies the transformation from the material to the immaterial through the firing process of interior alchemy (neidan).

Taoist sage (zhenren) arrays a cuboctahedron (vector equilibrium: energetic model of balance) (60x) from the middle elixir field (dantian), or heart center, by projecting subtle sound vibrations (thoughts) at a harmonic frequency which opens a celestial vortex.

The entire perceptible universe is composed of vibrations, wave-forms. Waves, pure temporal patterns, can only be understood through number. All life physically vibrates, while all elemental or inanimate matter vibrates molecularly. The notion that every vibrating body emits sound is the key to understanding the universe (ie.harmonics). (Lawlor)

Qualities of matter are actually differences in periodicity. In biology, geometrical proportion illustrates that every atom of every molecule is being changed and replaced. Genetic coding is a vehicle of replication and continuity. The DNA helix is a set of fixed geometrical proportions.


The genetic nucleic acids form chains on chromosomes arranged in base pairs, in a double helix formation. At conception, after the sperm enters the egg, the double-helixes separate, and one strand from the male recombines with one strand with the female, to form a new double-helixed DNA strand of the offspring.


Analogos Note (genetic design; of hybrid human; Anunnaki-Homoerectus ): the Deoxyribonucleic Acid (DNA) strand, the essential spiral of life [sim.Sumerian: “breath-wind-life” (shiimti); Hebrew: “spirit/soul” (nephesh) in the blood] consists of a pentagonal (5) sugar phosphate [corresponds with nature; Vedic: dodecahedron (organism essence spinning/unfolding tangibility along the spiral of time); mother of form (prakriti); Sumerian: Of Earth’s Soil/One Made of Blood (Adapa/Adam)] connected to a hexagonal nitrogenous amino acid base pair, which are bonded by hydrogen [corresponds with: Sumerian: Righteous Ones of the Rocketships (Dingir); aka: Those of Heaven Who Are on Earth (Anunnaki)]. Furthermore, the 12 nucleotide (locations of) DNA strand, consisting of 6 bonded nitrogenous base pairs, corresponds numerologically with the zodiac houses of astrology (event portent synchronicity for information transmission).

Genetic Engineering: An offspring’s fate (eg.disease, death) [sim.Tantric: karmic debt (rnanubandhana)] was determined at the moment of conception, through the assimilation of congenital data that recombined within the complete genetic code (genome). According to the Babylonian priest, Berossus (c.3rd BCE), who compiled Sumerian history and knowledge (mythology) for the Greeks, the genetic design (gene splicing) of the human being, a hybrid between the hominid of Earth and the Anunnaki of Heaven, was a process of trial and error (eg.defects, sickness, monsters) (Enki and Ninmah: The Creation of Mankind). The genome, the totality of genetic data, consisting of infinite combinations of nucleic acid code [ie.ADENINE (A)-CYTOSINE (C)-GUANINE (G)- THYMINE(T)], directs organic function (eg.aging process, longevity, memory, reasoning, intelligence), and consequently facilitates its connection with the cosmos.

According to the Sumerian creation myth, the “seed of life” was imparted to Earth from Nibiru during the Celestial Battle, the cosmic cataclysm, giving the hominids and the Anunnaki the same seed; therefore trans-genic manipulation was possible (as Enki was aware). Apparently, the Anunnaki also had knowledge of what genes were responsible for longevity/immortality, withholding it from humanity (adapa). Also, initially, humanity was unable to procreate (only 22 basic chromosome pairs); later X-female and Y-male chromosomes were added through genetic manipulation (not just for gender determination). Eventhough humanity was deprived of immortality (Tree of Life), wisdom (Tree of Knowledge; extra dose of intelligence genes) (The Legend of Adapa) was granted through secret initiation by Anu in heaven and Ninkarrak on Earth.


The 64 codon sets correspond to 64 hexagrams of the Yijing arrayed in the magic square of Mercury inherent in the bone oracle code (eg.chess board). Theoretically the Yijing is the philosophical code that guides the transmutation of the soul (alchemical process).

The genetic language consists of nucleotide (DNA) strands (ie.A-T-C-G), which store vast amounts of information (represented mathematically by binary numbers, with countless variation in “0” and “1”) [sim.Sumerian: (me)] within fundamental components, codon sets (paired three letter words; A links with T, C with G). DNA computation (like a computer, which also utilizes binary mathematics) involves the activity of messenger RNA, that decodes, transcribes, and recombines the DNA (“letters into words”), at lightning speed, to formulate codon sets (three letter words), spelling the biochemical language of the 20 amino acids found in all living organisms. Similarly, words in the Hebrew language are based on three letter root words, quite a departure from its mother Akkadian language. ”Death and life are in the language.” (Proverbs 18:21)


Bodily existence is determined by an invisible immaterial world of pure form and geometry, the archetypal essence. Photosynthesis occurs when carbon, hydrogen, nitrogen, and the magnesium of the chlorophyll molecule are arranged in a complex twelve-fold plan, the innate geometry of life.

Computer model of Carbon (C60) molecule

The innate intellectual quality, which perceives spiritual archetypal idea was called ‘pure reason’ by the Greeks, ‘heart-mind’ by the Hindus, and ‘intelligence of heart’ by the Egyptians. Geometry is the tool, which allows the understanding of the origins of form and the principles of evolution. Through the practice of geometry, thought patterns can be raised to the archetypal level.

“The student’s concentration on sacred geometry was a discipline to assist in seeing, the metaphysical realities beneath all appearance; the crystallization of perception.” –Robert Lawlor

The physical world has a secondary reality. Its knowledge is imprecise. Nothing can exist without a cause. The creator of anything focuses on the eternal unchanging (complete archetypal heaven) and uses it as a pattern for form and function for good results. If creation is a result from focusing on the changing existence (incomplete) the results will be poor. The changing earth is the likeness of the unchanging complete eternal perfect heaven. (Plato)


Anatomy of the Soul:

The body of the cosmos is composed of five elements, earth, water, fire, air, and ether (Chinese: earth, water, fire, metal, wood). The spherical shape (extremes equidistant in all directions from the center) of the cosmos revolves on axis. The cosmos is a single complete whole consisting of parts that are wholes. The body of the cosmos contains all possible figures within it. Nothing can be taken from or added to it. It is designed to supply its own nourishment from its own decay. (Plato)

The soul of the cosmos is the ultimate cause of all motion of its body, because the soul was created before the body. The soul of the cosmos is composed of three layers of paired actions.


Quantitative (Log2)

Qualitative (Log3)

Indivisible Existence

Intermediate Existence

Divisible Existence

Indivisible Sameness

Intermediate Sameness

Divisible Sameness

Indivisible Difference

Intermediate Difference

Divisible Difference

The soul’s ingrained mathematical structure can be expressed in seven numbers within a compass like model, progressing at logarithms of 2 and 3. One represents the indivisible and the intermediate, or 20 or 30. Logarithm 2 (corresponds with Ö2; 2d) represents the quantitative linear structure of destiny (the function of heaven; calculated by divination mathematics). Logarithm 3 (corresponds with Ö3; 3d) represents the qualitative circular details filled in by fate of divine intervention (function of earth; described by cosmological mythology). The intersection of log2 and log3 (corresponds with Ö5; 5d; sim.Taoist numerology: power0»5) expresses the free will, or the ability to change fate through decision (function of human; resolved through alchemical medicine).

It is always the qualitative realm that links the opposing realms of the quantitative (Plato with Pythagorean origins). Yijing numerology (divination mathematics) unfolds the structure of the quantitative realm (heaven:destiny) which philosophically guides the attitude of the sage (human:free will; alchemy) through the intermediary experience of the qualitative realm (earth:fate) to the indivisible existence (immortality). Taoist alchemists meticulously used free will to change fate, yet follow destiny, in order to attain immortality.


Folding and Unfolding:

When analyzing the quantitative realm (log2) of destiny [Sumerian: (nam) the predetermined course of events which is unalterable (eg.planetary orbits; laws of physics)], the exponents (0, 1, 2, 3, 4) define the cosmological level of progressive external creation, while the products (1, 2, 4, 8, 64) define the level of physical multiplicity and diversity, which can be expressed geometrically as polygons (circle-square-octagon) within the three realms upon a central axis;


[void (hundun) (20) ® heaven (tian) (21 ) ® earth (di) (22 ) ® human (ren) (23 ) ® human quantitative application (Yijing) (26)]


When analyzing the qualitative realm (log3) of fate [Sumerian: (namtar); “cut,” “break,” “change” (tar); the predetermined course of events which could be altered (eg.planetary stations, zodiac houses, ages)], the exponents (0, 1, 2, 3, 4) define the metaphysical (philosophical) level of progressive internal observation (towards immortality), while the products (1, 3, 9, 27, 81) [sim.Taoist symbolism: using thunder (3 = alchemy) to attain fire (9 = immortality)] define the level of spiritual multiplicity and diversity, which can be expressed as overlapping circles of heaven (abodes of deities) within the three realms upon a central axis;


[heaven (tian) (30) ® three heavens (santian) (31 ) ® nine heavens (jiutian) (32 ) ® three levels of nine heavens (33 ) ® human qualitative application (neidan) (34)]; [sim.Vedic: trinity/complexity of universal mind (chitta)]


External creation and internal observation are interconnected through the discovery of their exponential growth similarity (0, 1, 2, 3, 4).


Geometry of Experience: Intermediary Progression between the Quantitative and Qualitative

When the Nile flooded annually, the people of ancient Egypt were reminded of chaos. But when it receded, chaos was replaced by order. This event demonstrates the geometric law of proportion. When the laws of nature are perceived, inner conflict can be removed, and harmony is restored between the body, mind, and spirit.

The goal of geometry is to enable the mind to channel abstract cosmic tendencies of heaven into spatial ordered form upon earth. This is the conversion of number patterns into spatial arrangement: geometric proportion. Geometric symbols reveal still moments of time-continuum universal action that is hidden from sensory perception. Plato expresses that geometry and number are the most simplified expressions, and therefore the most ideal philosophical language. (Lawlor)

In Buddhist and Hindu philosophy time is represented as a necklace of square beads (mala), tangible moments or events. To be absorbed by this succession of limited frames is an illusion (maya). It is the inner thread, the unimaginable continuum that is real.

Our experience results from immaterial, abstract, geometrical proportions that spin to compose an arrangement of harmonic energy waves. Proportion is formed from ratio, a comparison of two different dimensions, quantities, or ideas (qualities; a : b). Sensory faculties respond by measuring the difference. Gregory Bateson said that the world is made up of patterns of ‘differences which make up difference.’ Comparison (‘analogos’ in Greek) is the basis of conceptual judgment.

Discontinuous proportion, used by the Pythagoreans, manifests the finite with two different ratios; [a : b :: c : d], [2 : 4 :: 3 : 6]. Continuous proportion expresses threeness through the reduction of number terms by introducing a mean term [a : b :: b : c]. Geometry can be used as a symbol, but ultimately it is the most simplified expression of innate pattern. In the continuous proportion, the perceiver does not stand outside the perceptual process as portrayed in the Pythagorean discontinuous proportion. Instead, the perceiver becomes apart of the perceptual process. The perceiver (b) forms the equivalency or identity between observed differences (a and c). Humanity is the geometric mean between heaven and earth.

The constant awareness of the integration of the external vibratory field with the internal field of perception, Sri Aurobindo referred to as “knowledge by identity,” which means the fusion of the self with the world, and is necessary for spiritual development. The continual flow of experience is a continuous proportion illustrated through the relationship between cognition, faculties of perception, and the external object:

[cognition : perception :: interpretation :: perception : external object].

“Whether we know it or not, all things take on their existence from that which perceives them.” -Upanishad

Nothing would exist without perception. Perception is relationship. To be is to relate. (Lawlor) Perception, the scope of experience, sifts through sensory information to ultimately remember an eternal concept. At the core of perception, created symbol is the key for understanding (returning to the innate concept) the interpretation of sensory data:

[sensory data : symbol :: symbol : concept].


Golden Proportion (F): (phi)


[sim.Chinese: "middle; center" (zhong)]

Continuous proportional thought approaches the sense of unity when the three-termed (trinity) proportion becomes possible with two terms (duality). The continuous proportion with two terms [a : b :: b : (a + b), or b/a = F] is the ‘golden proportion,’ and designated as phi, ‘F,’ the 21st letter in the Greek alphabet. There are two considerations (mysteries) for relating phi with unity. This proportion is larger than unity when b is equal to 1, so unity expanding is expressed by adding a to it. 

1)       First Mystery of Holy Trinity (the three that are two): [the whole is more than unity (a + b > 1)]

?         First term = a = 1/F

?         Second term = b = 1

?         Third term = a + b = a + 1 = 1/F + 1

?         a/b : a/a + b,  or b/a + 1

2)       Second Mystery of the Holy Trinity (the three that are two that are one): [the whole is equal to unity (a + b = 1)]

?         If the value of unity is shifted so that the whole is equal to one, a unique characteristic of the quantity of F (1.618) is discovered as the only geometric partitioning of unity.   

?         When the third term is (a + b = 1), then (1/F + 1/F2  = 1).

Thus, the ultimate reduction of proportional thought from the three termed continuous proportion is a mathematical metaphor for the trinity: “the three that are two that are one.” Unity (a : b :: b : 1) is the goal of progressive meditation. Phi, derived from an irrational (intimate) geometrical relationship, is the only possible creative duality (proportional existence) within unity. Therefore, phi was referred to as the ‘golden proportion,’ or the perfect division. In Christian mysticism, F is the ‘son of God.’

Olmec head with superimposed golden mean rectangle proportions to derive acupuncture points at key intersections.

Robert Lawlor says, “In proportional thought there are no fixed quantities, only fixed relationships.”

The continuous progression of F represents the external universe regenerated from the creative dream of God, the abstract (internal values divisible within 1) to the visible (external values greater than 1), the replication of God (unity), or the evolution of consciousness.

[…1/F3 : 1/F2 :: 1/F2 : 1/F:: 1/F : 1 :: 1 : F :: F : F2 :: F2 : F3…]

The geometrical implications of the golden proportion are written by St. John,

“In the beginning was the word [internal progression of the abstract dream of God; Holy Spirit; F2, F3],

and the word was with [in] God [external progression of the concrete universe; Son of God; 1/F3, 1/F2],

and the word was God [unity; God the father; 1].”

(In Greek, ‘logos’ translates as ‘word’ or ‘idea,’ meaning a three-termed proportion.)

The continuous progression of
Ö2 is a procreative power functioning generatively on the external plane [1 : Ö2 :: Ö2 : 2].

Johannes Keplar said, “Geometry has two great treasures: one is the Pythagorean theorem, and the division of a line into mean and extreme ratios, the golden mean (F).”


F Series of Fibonacci:

Fibonacci, a 13th century Italian mathematician, drew attention to this series, which seems to control the laws governing the patterns of natural growth; branching. Some examples of these laws can be seen in: the conch shell nautilus pompilius, multiple reflections of light through mirrors, gains and losses of radiation, breeding patterns of rabbits, ratio of males to females in honeybee hives, philiotaxis (leaf arrangement on the stem of a plant), sunflower, cactus, pine cones, biometry (body measurements and bone lengths), etcetera.







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


Two successive terms are added together to derive the third term;

Any two successive terms tend to relate as 1: F;

Any three successive terms relate 1: F: F2;

Fourth term: 1+2=3

89/55=1.61818=approx. F;

144/55=2.61818=approx. F2


1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364

Successive ratios will tends toward F;

Corresponding terms of series A and B tends toward Ö5;

Twelfth term: 521/233=2.23605=approx.Ö5


1, 5, 6, 11, 17, 28, 45, 73, 118, 191, 309, 500, 809, 1309, 2118

Whole numbers tend to be half the decimal expression of the Golden Ratio;

1/F= .618

Twelfth term: 309x2=618


(C x 2)

2, 10, 12, 22, 34, 56, 90, 146, 236, 382, 618, 1618, 2618, 4236




F-5, F-4, F-3, F-2, F-1, 1, F1, F2, F3, F4, F5;

.090, .1458, .236, .3819, .618, 1, 1.618, 2.618, 4.236, 6.854, 11.090

Logarithmic progression




The Birth of the Cosmic Volumes: Elemental Polyhedra

“The five elements: wood, fire, earth, metal, water, encompass all the phenomena of nature. It is a symbolism that applies itself equally to man.” –Suwen


Construction of the Polyhedra: Trinity of Roots (Ö2, Ö3, Ö5)

Intelligent design (F)  gives birth to the trinity of roots to construct the pentology of elemental polyhedra.  Hence, phi (F)  is related to Ö5. (see below) The trinity within unity constructs the envelopes of consciousness.  


Trinity of Transformative Roots (Ö2, Ö3, Ö5): Construction of the Polyhedra

The trinity of simple root powers (Ö2, Ö3, Ö5) are geometric metaphors for the supra-rational (irrational function), or supernatural, moment in three various modes of transformation:

Ö2 Generative [Root of Destiny (Heaven)]: Diagonal of Square; Squaring the Circle- Mandala

Ö3 Formative [Root of Fate (Earth)]: Diagonal of Cube; Vesica Piscis - Generator of Form- Eye of the Vortex - Axis Mundi- Anthropocosm- Internal Alchemy [sim.Sumerian Tree of Life/Judaic Mystic Kabballah, Vedic Tantra, Taoist Neidan]

Ö5 Regenerative [Root of Free Will (Human)]: Golden Proportion

 These roots are considered the trinity of generative principles. These three root relationships are all that are necessary for the formation of the five regular polyhedra, which are also representational of the five elements.


Ö2 defines the mandala [sim. cross, swastika, medicine wheel]


Tibetan Mandalas: Wheel of Time (Kalachakra);


Han Dynasty silk; Vedic suvastika; Romanesque and Bavarian swastikas; Pueblo medicine wheel; Vedic suvastika  


Indus valley seals; crucifix; Hasegawa coat of arms

Mayan cross


Squaring the Circle: [Sanskrit: "circle, arch, section" (mandala)]

The process of creation is the ritual for destruction [sim.Tibetan sand painting]

Unity is represented by a circle. By squaring the circle, unity is now represented by the square, symbolizing the transformation of energy into matter. The square with four primary orientations (N, S, E, W) makes space comprehensible. Two pairs of equal yet opposite linear elements (axis of Taijitu) fulfill the universal nature. A square is made of four equal straight lines joined at right angles. Any number multiplied by itself is a square. Multiplication, symbolized by a cross, generates a square surface. Crossing is an action principle. Nature means “that which is born,” (multiplicity) which requires a crossing of opposites in order to represent the earth.


Pythagoras said, “The purpose of life was to discover and manifest supernatural existence within the finite.”


Root of Destiny:

The finite perfection is represented by limited whole number arithmetic (ie. square = earth, nature). The division of unity occurs when the supernatural is manifested within the natural [ie. the square is divided by its diagonal (Ö2)]. The side of the original square is called its ‘root’ and is given the value of 1. The area of the square is also 1. The diagonal gave rise to 2 because square 2 is implied (grows out of the original square). The diagonal of square 1 becomes the root of square 2 (twice the area of square 1). (Lawlor)

Ö2 divides the surface of the square (2d)


Ö3 divides the volume of a cube, and is the length of the vesica pisces axis (3d),

Vesica Pisces: Generator of Form; Eye of the Vortex

Literally, ‘vesica’ is a bladder when filled with air would be in the form of a fish, ‘pisces,’ was the predominant sacred geometry utilized in Medieval Christian mysticism. The vesica pisces is the fish shaped juxtaposition of two circles with their centers on each other’s circumference (known as the eye of the vortex to the Greeks; mouth of the word becoming flesh or window of Christ to the Christians; eye of Ra to the Egyptians). It is the two circles and their juxtaposition (vesica pisces) that establish the trinity, which the Chinese call the Great Triad (Santian) of heaven, humanity, and earth.

“The father’s divine eye is the pattern of creation behind creation.”-Key 316:5 Book of Enoch

The upper circle represents heaven, universal consciousness (mind), the gold solar source, the unchanging, and the archetypal symbol. Heaven is one, the whole, odd, yang, and unchanging because it is always present. The unchanging quality of the whole is that its parts are always changing.

“Everything a human being creates, is already there.”- Antonio Gaudi   

The lower circle (inscribing a square) represents earth (body), empirical consciousness, the silver lunar reflection, the changing, and the typal object particular to the event experienced. When the one divides it becomes two parts. Dependent upon the circumstances of interaction, dichotomy gives birth to the three, and the three to the 10,000 things that are always changing, yet still parts of the one.

The vesica pisces (juxtaposition of the two circles) represents the region of humanity, eye of god, balancing consciousness (spirit), and the ectypal comprehended product of memory and present event interpretation. The spirit (humanity) connects the mind (heaven) with the body (earth).

The Piscean Age (started 60 BCE-2100 CE) is characterized as the formal embodiment of spirit, manifesting a deeper penetration of spirit into form; this is the materialization of spirit. This idea is demonstrated with the length of the axis, between the two intersecting points of the overlapping circles, acting as the midline of the vesica pisces, which is equal to Ö3. Thus, Ö3 is linked with the formative process (the embodiment of spirit; or manifesting the supernatural within the finite). A vesica pisces succession is the mother of all the regular polygons.

The triangle is the first and simplest polygon construction derived from the vesica pisces (balancing consciousness, the ectypal realm of human perception and interpretation).

 “In India the triangle is called the mother, for it is the birth channel through which all the transcendent powers of unity and its initial division into polarity must pass in order to enter the manifest realm of surface. The triangle acts as the mother of form.”- Robert Lawlor

The human spirit relates with other living things, perceives the archetypal consciousness, via the heart chakra (fourth or middle chakra), or middle dantian, on the central channel. Recalling above, the Egyptians referred to the perception of the innate archetypal as the “intelligence of heart,” and “heart-mind” for the Hindus [sim.Vedic: universal mind (chitta) consisting of inertia (tamas), activity (rajas), purity (sattva)]. Furthermore, the Chinese designate the fire element with the heart, as well as the triangle.

Qi Bo said, “...joy is a vacuum and is the emotion of the heart.” (Huangdi neijing as quoted in Veith)

Joy, or happiness, the accomplishment of the spirit, which resides in the heart, is a vacuum of relationship through which all form is manifested (perceived).

Angles (triangles) become a bridge between heaven and earth. A triangle is three angles, or angels. Heliobiology is the study of the angle as a specification of the influences of celestial patterns (angels) on earthly events. For instance, the angular position of the moon and the planets does affect the electromagnetic and cosmic radiations, which impact with the earth, and in turn these field fluctuations affect many biological processes. Leverage is the principle that states that forces are controlled, specified, and modified through the efforts of angulation. Also, light is refracted through substances at different angles.

The hexagon, a progressive generative form from the vesica pisces, is seen in carbon bonding patterns, which allow the formation of organic substances. It is the hexagonal construction that leads to the formation of the regular polyhedra.

“There is no god which is not all gods.” -Koran


Axis Mundi: Conduit of the Anthropocosm (Cosmic Human)

The oneness of heaven may be discovered after establishing the axis of the world (axis mundi), which is a vertical axis linking the over-world (heaven/stars; reason) with the underworld (earth; chaos) via a particular still point that represents the center. It is the axis mundi (within the educating human) that brings order (expanding heaven) to chaos (changing earth). This still point is observed as the center of gravity (navel; umbilical hole) in the human being when practicing internal alchemy. The human being as axis mundi has been called the cosmic human (homomundus) in Leonardo’s famous drawing, known as the Vitruvian Man, illustrating the relationship of the navel to the golden proportion. The human being (a microcosm), like a tree, is an axis mundi, a conduit between heaven and earth (macrocosm).

Axis mundi superimposed on earthen mound in Shiloh, Tennessee.

St. Bernard of Clairvaux asked, “What is God? He is length, width, height, and depth.” (as quoted in Lawlor)

This statement defines God through the four directions, up and down (the vertical axis which links heaven with earth), which is axis mundi. Thus, axis mundi provides a system of measurement for earth (geometry). In geo-physics, this statement is expressed as a cube (earth: material earth) stabilized by two tetrahedrons spinning in opposite directions (fire: polarity of electro-magnetic/energetic earth) (star tetrahedron; merkaba).

Merkaba and star tetrahedron: sacred geometry visualization for transcendent consciousness at the heart.

Architectural microcosms (expansions of human microcosms) express axis mundi through nomadic dwellings (ie. teepee; yurt; kiva), temples (ie.Sumerian ziggurat), and mandala cities.

In geometric cosmology, the mystic doctrine of creation, the main anthropocosmic principle is that humanity is not a mere part of the universe but rather it is both the final summarizing product of evolution and the original seed, from which the universe germinated.

Analogos: [seed is to tree as the cosmic man is to the universe].

The tree grows from the seed but also creates more seeds. This is said another way in the kabalist expression, “In kether is malcut, and malcut is in kether.” The tree is the universe, which is the actualization of the seed, which is the cosmic man. Thus, the cosmic man, or true man (zhenren) to the Taoists, is the source of the universe. This notion reinforces the idea of the Upanishad, “nothing exists without perception.”  Humanity is not seen as the child of mother earth but earth is contained in the character of the cosmic man. The notion of the cosmic man being a part (origin) of the universe demonstrates that each fragment of the whole contains the constituents of the overall structure of the whole. The anthropocosm, or mystic anatomy, is the basis of astrological philosophy and internal alchemy [eg.Hebrew: kaballah; Vedic: tantra; Taoist: neidan]..

Buddha, Jesus, and Quetzalcoatl with Kabballah superimposition.

As Robert Dicke puts it, “The right order of the universe may not be, ‘Here is the universe, so what must man be?’ But instead, ‘Here is man, so what must the universe be?”

Thus, the body of the cosmic man contains universal proportions that are the basis for a canon of measurements used by many civilizations, which govern poetry, dance, architecture, art, etc. (ie. cubit, phi).


Kabballah: Tree of Life

The kabballah (Hebrew trans. “to receive” life), tree of life, or divine lightning rod of remote antiquity found in Sumerian mythos, and Judaic mysticism, is a highly definitive axis mundi. According to legend, it is a cosmological teaching from the Sumerian King Melchizedek to his faithful servant Abraham. Kabballah can be applied to all phenomena, further defining the cosmology and processes of the anthropocosm (cosmic man).

The creative process of life begins in the void (ain), or unmanifested consciousness of negative existence, which contains the endlessness of the unknown (ainsoph), which channels limitless light (ainsophaur) through the condensation of the crown (kether) to eventually manifest the physical existence (malcut). Energy descends (divine lightning flash) and ascends (Jacob’s Ladder) the kabballah in a specific path through ten spheres of light (sepherot), which are connected through twenty-two pathways [corresponds with 22 letter Hebrew alphabet and Chinese Ganzhi system (see geomancy)]. (Halevi), (Sankey)


Because the number of letters in the Mosaic-Semitic alphabet corresponds directly with the number of nuclear chromosome pairs (22) (prior to the second manipulation; before X and Y were added to make 23 pairs; prior to the insertion of the “priest gene” in Adapa), [reflecting in the pathways of the Kaballah; Chinese Ganzhi system of astrology consisting of 10 Heavenly stems and 12 earth branches, which when interplayed five times generates the cycle of 60 (Sexagenary Cycle)], many believe that the alphabet contains “secret knowledge” with the sophistication of the genetic code.

According to the Book of the Secrets of Enoch, Eden’s Tree of Life “is more beautiful than any created thing; on all sides in appearance is like gold and crimson, transparent as fire.” From its root move four streams of honey, milk, oil, and wine, from Heavenly Paradise to the Paradise of Eden, making a revolution around Earth. This description suggests that the Tree of Life was as conduit between Heaven and Earth, paralleling the Chinese idea of the Kunlun mountains, and the microcosmic orbit functioning as an axis mundi.


Sumerian tree of life and caduceus wand (medical symbol) with kabballah superimposition.

The fruit of the Tree of Life, which was located in the Western Paradise of Eden parallels the mythological Chinese immortality peaches and mushrooms (lingchi) of the Western Paradise of the Kunlun mountains, where the immortals lived.


and Ö5 is the length of a diagonal bisecting two squares (4-5d).


The Relationship between Ö5, F and the Pentagon:

The diagonal of the double square (Ö5) is required to determine the Golden Section, from which the pentagon can be derived. Thus, phi has an association with flowers having five petals or a multiple of five petals. Five is the foundation for living forms, while six and eight are the foundation of mineral and inanimate forms. The pentagon is the symbol of life, particularly human life, thus the manifestation of the five elements.


The continuous proportion expressed that the universe is God creating himself, thus creation cannot exist without perception and to perceive is to relate. And to relate is to be. With the Golden Proportion being the only possible continuous proportion to create duality within unity, the construction of the pentagon came to represent divine manifested form (life derived from phi; man was created in God’s likeness). Pentagonal geometry manifests naturally in biological systems.


The Golden Triangle:

In Taoist cosmology, the pentagon represents the generative cycle of the five elements: fire® earth® metal® water® wood. Where as the pentagram inscribed within it represents the destructive cycle: fire® metal® wood® earth® water.



The ratio of the length of one of the lines of the pentagram and a side of the pentagon is F:1, respectively. Each line of a pentagram is bisected in two places creating three segments, two equally long segments at the ends and one shorter one in the middle. The ratio of the length of the longer segment to the shorter one is F. Interestingly, the sum of the lengths of the shorter segment and one of the longer segments is equal to a side of the pentagon.

The Golden Triangle is an isosceles triangle in which the ratio of either of the two equal sides to the shorter base is F. The two base angles are 72° and the vertex angle is 36°. Twenty Golden Triangles can be found within the pentagon-pentagram construction, 5 small, 5 large, and 10 medium. The base angles of 72° express the number of years to establish 1° of precession in the zodiac (72x30=2160; zodiac age).  The vertex angle is 36° shows a mathematical connection with all aspects of Taoist numerology, most particularly the sexagesimal calendar (60 x 60 = 3600 year epoch); [sim.Sumerian: Nibiru sun circuit].


The Golden Navel:

“Man is the measure of all things.” –Heraclitus

The navel is the center of the universe. The ancient Chinese character for ‘zhong,’ meaning middle, or center, and F (phi) are virtually the same.

By taking the human height as 1 (unity), the locus of the genitals is at ½ the height, and the distance from the feet to the navel is 1/F, and from the navel to the top of the head is 1/F2. In females the cut of the Golden Section is slightly above the navel, while in males, slightly below. Sexuality, expressed by ½ and Ö2, is the ever-expanding, halving-then-doubling, procreative function of man. At birth however, it is the navel that divides the child in half. Phi integrates part to whole by relating the child to its origin, its mother (the universe). Phi represents the relational power in the navel, which binds individual awareness with the totality of its origin to which it will return. The navel, center of the physical self, is what the mind focuses on to lay the foundation for spiritual accomplishment during meditation.

“I am that which binds. I am the golden navel of the universe. He who knows this knows Upanishad. Upanishad means 'near approach.’” –Upanishad


These roots are considered the trinity of generative principles. These three root relationships are all that are necessary for the formation of the five regular polyhedra, which are also representational of the five elements.


The meaning of the letter-number encryptions could be understood by seeing the archetypical pattern of mathematics expressing the vibratory frequency inherent to the observed phenomena within space-time continuum. In other words, mathematical expression (ie. numbers progressing through dimensions: 1. number in number- arithmetic, 2. number in space-geometry, 3. number in time-music, and 4. number in space-time-astronomy) became the methodology of code encryption.

Previous information was taken from DAOZHAN: Divination Resource for Daoist Calculation, © 2005., by Michael Hamilton.