“Ante omnia Punctum exstitit…”
“Before all things were, there was a Point.”
Anonymous, 18th century ‘Le Mystere de la Croix’
Sacred Geometry, to be fully appreciated and experienced, must be undertaken as a contemplative, or meditative exercise. From the initial act of putting pencil or compass point to paper each act of geometry is charged with meaning. The process of producing the forms, patterns and symbols of Sacred Geometry should be undertaken as a ritual act, where each line, curve, shape, gesture or operation takes on a significance far beyond the mere act itself, and reveals fundamental processes of creativity on a vast scale and range of phenomenon, from the geometry of atomic and molecular organization, through the forms and patterns of biological systems, to the scale of the cosmos itself and the very structure of Space and Time. Indeed, the emergence of the Universe from the unknowable and unfathomable void, before the very existence of Time and Space, was an act of Geometry. It is nothing less than this ultimate act of Creation which is replicated through the placing of pencil upon paper and from this point the drawing of a line or arc. From these simple operations, the Geometrician soon learns to generate an infinite variety of form and pattern, and is, thereby, following in the footsteps of Nature herself, such being the indispensable requirement for success on the Hermetic path.
To ancient masters and teachers geometry was seen as the definitive Holy Science from which emerged all other sciences. Masonic author Carl Lundy affirms this status when he says:
“All science rests upon mathematics, and mathematics is first and last, geometry… Geometry is the ultimate fact we have won out of a puzzling universe.”
“All science rests upon mathematics, and mathematics is first and last, geometry… Geometry is the ultimate fact we have won out of a puzzling universe.”
The presumed requirement on the part of Plato, the acknowledged greatest Metaphysician of the Hellenic world, that anyone seeking admission to his academy must be conversant with the principles of Geometry, affirms the importance of this form of mental training to anyone desiring to tread the path to Metaphysical Knowledge.
It should come as no surprise that ancient Mystics visualized God as a Geometrician. That concept is nowhere better portrayed than in William Blakes famous 1794 painting The Ancient of Days, depicting the Demiurge, the Creator God of the Universe, setting his compass upon the Face of the Deep, and through the turning of the compass bringing Order out of unformed Chaos. This depiction exemplifies the verses from the 8th chapter of Proverbs, wherein Wisdom establishes her priority in the hierarchy of Creation by proclaiming:
“I was set up from everlasting, from the beginning, or ever the earth was…While as yet he had not made the earth, nor the fields, nor the highest part of the dust of the world. When he prepared the heavens, I was there: when he set his compass upon the face of the deep.”
This concept of God as geometrician is also depicted in a number of medieval bibles. As an example, the frontispiece of the Bible Moralisée, ca. 1250, shows God about to impart order to the disordered primeval chaos within the circle by a rotation of the compass.
All geometric constructions begin with a single point, represented by the moment that the point of the compass or the point of the pencil contacts paper. The construction can commence with either a straight line or the arc of a circle. Through the combination of straight lines and arcs the entire edifice of geometry can be produced. To begin an exercise in Sacred Geometry four tools are required: A clean sheet of paper, a straight-edge of some kind, a pair of drawing compasses and a good sharp pencil. With these tools, and an appropriate state of mind, the geometrician can imitate the primordial process by which the Universe of Time and Space emerged into existence. In the compass itself we have symbolized the primordial duality of Rest and Motion, of stillness and action, for one point of the compass remains fixed while the other moves, generating the center and the circumference of a circle, generatrix of all subsequent form.
Metaphysical traditions have provided us with a variety of models to facilitate comprehension of the fundamental process of Creation. In the Pythagorean system, in the Tantric system and in the Kabbalah, this process commences with the manifestation of a single dimensionless point, a point, however, of infinite potentiality. Modern cosmology now concurs with the ancient models by postulating the existence of an ultimate singularity that preceded the Big Bang— or however one cares to describe the initial moment of existence — the difference being that the archaic model requires an act of Deity while the modern view dispenses with a creative intelligence.
Kabbalistic Scholar Z’ev ben Shimon Halevi describes the process of Creation from the perspective of Kabbalah, the ancient system of Jewish mysticism:
“…the EN SOF AUR, the Endless Light of Will, was omniscient throughout Absolute All. From God knowing All, God willed the first separation so that God might behold God. This, we are told, was accomplished by a contraction in Absolute All, so as to make a place wherein the mirror of Existence might manifest. The place that was vacated was finite in that it was limited in relation to Absolute All that held it. This act of contraction, or Zimzum, as it was called, brought about the void of Unmanifest Existence even though it was, we are told, the size of a dimensionless dot in the midst of the Absolute.” 1
In Kabbalah the point, or dimensionless dot in the midst of the Absolute, is understood to be the condensation, or distillation of Gods essence. It first appears against the background of negative existence, but this background is separated from the ‘Absolute.’ It is this separation that forms initial act of manifestation. The Absolute from which the infinitesimal point is contracted is beyond all words and definitions, it is beyond space and time, it is beyond Eternity, it is beyond Infinity. To speak of it is utterly futile; it is both everything and nothing simultaneously. Between this indescribable, unimaginable and incomprehensible state and the Universe of galaxies, stars, planets, atoms, molecules, gravity, radiation, life— in short— Creation as we experience it, lies the zone of negative existence. The same author, Halevi, in An Introduction to Cabala describes this zone:
“Negative existence is the intermediary zone between the Godhead and his creation. It is the pause before the music begins, the silence behind each note, the blank canvas beneath every painting and the empty space ready to be filled. Without this non-existent Existence nothing could have its being. It is a void, yet without it and its potential, the relative Universe could not come into manifestation.”2
However, according to the tenets of Kabbalism, this zone has a structure comprised of three ‘veils’. That veil which is nearest our relative universe is the veil of Limitless Light, in the terminology of Kabbalah, the Ain Soph Aur. This Limitless Light Halevi likens to cosmic rays which are everywhere throughout the Universe and can penetrate densest matter. The second veil is Ain Soph, simply that which has no limit. It is the zone where the Ultimate void begins to emerge into something, but something without limits, utterly without end. NO-thing lies beyond this, the veil called simply, Ain. Beyond Ain is the Absolute. Halevi describes the nature and quality of the three veils:
“These three stages constitute a condensing, a crystallizing out of the Being who permeates the whole of All; of a point in the centre of a circumferenceless sphere. This distillation, this point, is without dimension either in time or space, yet it contains all the worlds from the uppermost realm down through the ladder of creation to the lowest end…This all inclusive dot is called the First Crown, the first indication of the Absolute, perhaps better known as I AM, the first of many God names.” 3
The mention of the “First Crown’’ refers to the now famous Kabbalistic “Tree of Life,” which is represented graphically as a beautiful and elegant exercise in Sacred Geometry, where form and meaning are merged in a perfect synthesis, demonstrating the worlds and levels of creation emanating from the all inclusive “dot” through a process of geometrical evolution. The ladder is an important symbol of the Great Work, representing the linking of Heaven and Earth and is prevalent in the symbolism of Freemasonry. Again, Geometry provides the key to this cosmic synthesis, but that is a matter for another discussion.
Another modern Kabbalistic author, Charles Ponce, describes the process of Zimzum in similar terms as Halevi. (Although spelling it differently)
“The term tsimtsum originally meant ‘contraction’ or ‘concentration’, & appeared in the Talmud where it was used to describe God’s projection and concentration of his divine presence, his Shekkinah, at a single point…This voluntary contraction on the part of God, the En-Sof in this case, is the act which causes creation to come into existence. Without this act there would have been no universe. ” 4
The point, or distillation without dimension, to which Halevi and Ponce refer, has a precise correspondence in Geometry, for in any geometric figure a point is considered to be without any dimension whatsoever. The point lying on the center of a line, for example, divides the line into two equal parts whose sum is exactly the same length as the whole line. The point of division occupies no space at all, yet from such an utterly insignificant point, condensing out of the zone of negative existence, the whole edifice of Geometry emerges. The “blank canvas beneath every painting and the empty space ready to be filled”, is represented in the ritual of Sacred Geometry by the blank sheet of paper upon which the forms, figures and patterns are set down by the hand of the Geometrician, and, in the language of modern physics it represents the quantum vacuum from which a seething ocean of virtual particles springs forth to become the universe of infinitely varied form that we experience.
In the realm of Sacred Architecture the single point represents the omphalos, the position from which the physical form of the Holy Temple emerges, defined precisely by the sharp point of the plumb bob, suspended on the end of a cord and directed by the force of gravity to demarcate the vectorial line linking the celestial zenith with the center of the Earth. The construction of the Temple was perceived as a ritual act recapitulating the process of Divine Creation.
The construction of the Temple was perceived as a ritual act recapitulating the process of Divine Creation.
This idea of an infinite potential materializing out of an infinitesimal point is exemplified in the New Testament parable of the mustard-seed, Mark, 4th chapter:
“Whereunto shall we liken the kingdom of God? or with what comparison shall we compare it?
It is like a grain of mustard-seed, which, when it is sown in the earth, is less than all the seeds that be in the earth: But when it is sown, it groweth up, and becometh greater than all herbs, and shooteth out great branches; so that the fowls of the air may lodge under the shadow of it.”
These passages convey profound meaning on multiple levels simultaneously. The ‘mustard seed’ has meaning in the metaphysical/spiritual dimension, representing the ‘siva-bindu’ the point round which the kundalini serpent lies coiled; on the Hermetic/Alchemical level, it represents the germ of transmutation; on the level of nuclear physics, it is the extraordinary power contained within the atomic nucleus, and in the Cosmological dimension, the mustard seed represents the ultimate singularity containing the potential of the entire universe of Space and Time.
One of the pre-eminent Holy Books of Kabbalah is the Zohar, or Book of Splendor, dating from at least as far back as the Middle Ages, possibly much earlier, its origins are uncertain. Regarding the immeasurably small, infinitely potent point it has this to say:
“A dark flame issued from within the most hidden recess, from the mystery of the Infinite…It could not be recognized at all until a hidden, supernal point shone forth under the impact of the final breaking through. Beyond this point nothing is knowable, and that is why it is called reshith, beginning, the first of those creative words by which the universe was created.”5
Zohar, I, 15a
Reshith means ‘beginning’ as ‘In the beginning, God created the Heaven and the Earth’ the opening words of Genesis. The perspective of the Zohar on these verses opens a portal onto a vast underlying cosmology that is only accessible to those who employ the mathematical and geometrical keys to unlock the hidden teachings concealed below the literary imagery.
The perspective of the Zohar on these verses opens a portal onto a vast underlying cosmology that is only accessible to those who employ the mathematical and geometrical keys to unlock the hidden teachings concealed below the literary imagery.
“The primordial point . . . was taken to be the second sefirah or first departure from the divine nothing implied by the image of the point. It is the world seed, the supreme formative and male-paternal potency, which is sown in the primordial womb of the ‘supernal mother’, who is the product but also the counterpart of the original point.”6
The sefirah in Kabbalah are the “emanations” of force and form originating out of the Ain Soph Aur, the third veil of negative existence. The process of emanation of the sefirah corresponds to the unfolding of form, pattern and proportion through the process of Sacred Geometry, and results in the manifestation of the Tree of Life. How appropriate it is that the primordial point is conceived as the ‘world seed’ paralleling the imagery invoked by the Grain of Mustard-seed, and likened here by Scholem to male potency. The seed metaphor is echoed in the Sanskrit Pratyabhijnahrdayam, a 10th century sacred text of the Advaita Śaiva Philosophy of Kashmir, a secret doctrine of Yoga descended from the ancient Indus civilization:
“As the great banyan tree lies only in the form of potency in the seed, even so the entire universe with all the mobile and immobile beings lies as a potency in the heart of the Supreme.”
If the primordial point, the singularity, is the creative seed, what, might we ask, constitutes the womb of the ‘supernal mother’? Geometry provides the answer as we shall see. But whence comes the seed? In the Etz Chaim (Tree of Life) by Rabbi Isaac Luria (1534 – 1572), a discourse on concepts found in the ancient Kabbalistic text, the Bahir, we find a description of the process of the self-constriction of God’s light:
“Before all things were created. . . the Supernal Light was simple, and it filled all
Existence. There was no empty space. . . .
When His simple Will decided to create all universes . . .He constricted the Light to the sides . . . leaving a vacated space. . . .The space was perfectly round. . . .
After this constriction took place . . . there was a place in which all things could be created. . . . He then drew a single straight thread from the Infinite Light . . . and brought it into that vacated space. . . . It was through that line that the Infinite Light was brought down below. . . .”7
Modern Kabbalistic scholar Aryeh Kaplan gives a succinct explanation of this process in his introduction to the The Bahir Illumination:
“In its literal sense, the concept of Tzimtzum is straightforward. God first ‘withdrew’ His Light, forming a vacated space, in which all creation would take place. In order for His creative power to be in that space, He drew into it a ‘thread’ of His Light. It was through this thread that all creation took place.” 8
Metaphysical author Elisabeth Haich, in her book Initiation, describes the same process from the standpoint of the Egyptian mystic:
“In order for a force to emerge from the dimensionless state and manifest itself, it needs a point of departure. A point is dimensionless, has not yet emerged from unity, but is necessary for manifestation… When the force whose first manifestation was a point emerges from the dimensionless state and is effective for a period of time, the point moves and forms a line.” 9
“The point moves and forms a line.” The line may be straight or curved, but in either case we have the transition from the dimensionless point into dimensionality. In the simplest preliminary act of geometric construction the point of the pencil is first brought into contact with the drawing surface and is then moved along the straight edge. This first line drawn represents the ‘thread of light’ manifesting in the void during the process of Zimzum. In the drawing of a circle one first establishes the central point, and then through the turning of the compass a circumference is generated. The radius of the circle, at this stage of the work, is implicit but invisible. It is the drawing of the radius from the center to any point on the circumference that represents the first expansion phase of Zimzum, the projection of a thread of light into the vacated space of the void. This diagram conveys the idea Zimzum, with the single thread of light reaching into the void, the zone of Nothingness.
In Kabbalah we learn that the Universe in all its aspects is represented by the letters of the Hebrew Alphabet, but more than that, we learn that the letters not only represent forces and energies but are themselves actual signatures of elemental energies, and the combination of these letters into words and names is equivalent to the interplay of forces that brought about all of Creation. The letter Yod , the tenth letter, is considered the seed letter of the Hebrew alphabet. All other letters can be seen as combinations and permutations of the basic Yod, and the Yod begins with the appearance of its’ uppermost point, from which the remainder of the body of the letter flows forth. This point is the Singularity and the Yod itself represents the motion of that point through the first infinitesimally short increment of time and space.
19th century French occultist M. Encausse, writing under the pseudonym of Papus, authored a number of books on Kabbalah, Tarot, and kindred subjects of the Western esoteric tradition. In his book ‘The Tarot of the Bohemians’ he describes the role of the Yod in the development of the kabbalistic language.
“The Yod, shaped like a comma or a dot, represents the principle or origin of all things. The other letters of the Hebrew alphabet are all produced by different combinations of the letter Yod. The synthetic study of nature had led the ancients to conclude that one law only existed and ruled all natural productions. This law, the basis of analogy, placed the Unity-principle at the origin of all things, and regarded them as the reflections at various degrees of the Unity-principle. Thus, the Yod, which alone forms all the other letters, and therefore all the words and all the phrases of the alphabet, was justly used as the image and representation of this Unity-principle, of which the profane had no knowledge.
Thus also the law which presided over the creation of the Hebrew language is the same law that presided over the creation of the Universe, and to know the one is to know the other, unreservedly.”10
At this stage of commentary it would be valuable to mention that, prior to the advent of the Hindu-Arabic numeral system, in ancient Semitic alphabets such as Hebrew and Arabic, and in the Greek alphabet, each of the letters served a dual purpose, in that they were both letters of the literal alphabet, representing phonetic values, while at the same time representing numerical symbols. The 22 letters of the Hebrew alphabet, and their final values, were arrayed according to a denary system. The first nine letters Aleph through Teth, stood for the numbers 1 through 9, counting by ones. The second nine letters, Yod through Tzaddi stood for the numbers 10 through 90, counting by tens. The numbers 100 through 900, counting by hundreds, were achieved by ascribing final values to 5 of the 22 basic letters, thus giving a total of 27 values. In this manner all words, names and phrases comprising Hebrew sacred writings automatically had numerical values that could be derived simply by summing the values of the individual letters. The process of determining the numerical value of Hebrew words formed an important branch of Kabbalistic studies called gematria.
In this system is to be found the association between language and geometry. Through the agency of gematria, words, names and phrases of the sacred writings can be expressed as numbers and those numbers linked with geometric form. Words expressing key concepts or names could be expressed as numerical values and those values related to one another proportionally and thereby reveal corresponding geometric relationships. The system of gematria opens the door to a truly astonishing system of analogy between literary images and geometrical pattern and demonstrates that lying beneath the outer, literal forms of the sacred writings, beneath the stories, the parables, the moral teachings, resides another dimension altogether, one of pure geometry and mathematics. It could be said that the literary expression of the ancient, sacred writings serves as the vehicle or means of conveyance for the real teaching, which is another dimension of knowledge expressed through the Sacred Geometry that emerges from a numerical reading of Scripture. The hidden geometry of ancient sacred writings represents an amazing and profound dimension in the application of Sacred Geometry which is beyond the scope of this article but which I explore in depth in my advanced classes and will address in future articles.
It should be noted that there is a Kabbalah of the Greek sacred writings as well, for example, the New Testament was originally written in Greek and displays the same principles of underlying geometric meaning as can be found in the Hebrew of the Old Testament. It should also be noted that the method of numerical substitution leading to mathematical and geometric insight into hidden dimensions of meaning is not by any means confined to the Bible, but can be found in various kabbalistic works such as the Sepher Yetsirah and the Zohar, in Gnostic writings, such as the Pistis Sophia, the Clementine Homilies and others. Sufism incorporates a parallel method of numerical substitution, called the Cipher of Abjad, in the interpretation of sacred works composed in Arabic. See the works of Idries Shah for an elaboration on this tradition, most especially see The Sufis (1964). Papus goes on to elucidate further significance of the letter Yod.
“The numerical value of the yod leads to other considerations. The Unity-principle, according to the doctrine of the Kabbalists, is also the Unity-end of being and of things, so that eternity, from this point of view, is only an eternal present. The ancients used a dot in the center of a circle as the symbol of this idea, the representation of the Unity-principle (the dot) in the center of eternity (the circle, a line without beginning or end.)” 11
The dot within the center of a circle is now generally considered a symbol for the Sun, but certainly also represents the fundamental act of geometry, the simple drawing of the circle with the compass. Again, the numerical value of the Yod is 10. In this number we have the symbol for Unity, the All, represented by the number 1, paired with the symbol for Nothing, the zero, but also implying Eternity, for the circle has no beginning and no end. Here we have simple ideograms expressing the the All and the Nothing, the ultimate duality, conjoined symbolically by the numerical value of 10, signified by the Yod, or seed from which all manifested existence springs, including all the words comprising the sacred writings of the ancient Hebrew seers. The fundamental duality represented by the All and the Nothing is recapitulated in the act of geometry, for in every turn of the compasses there is a stationary fixed limb and an active moving limb, displaying the dynamic factor necessary for Creation to take place. This is also the same duality symbolized in the I Ching by the contrasting pairs of fixed and moving lines forming each of the 64 hexagrams. In astronomical terms the fixed limb corresponds to the axis of any rotating spherical body, such as a moon, a planet, a star or a galaxy while the moving limb corresponds to any point rotating on the equatorial circle.
Albert Pike, in his Masonic tome Morals and Dogma, explains the significance of the Yod from the perspective of Freemasonry:
“In the East of the Lodge, over the Master, inclosed in a triangle, is the Hebrew letter YOD. In the English and American Lodges the Letter G∴ is substituted for this . . . YOD is, in the Kabalah, the symbol of Unity, of the Supreme Deity, the first letter of the Holy Name; and also a symbol of the Great Kabbalistic Triads. To understand its mystic meanings, you must open the pages of the Zohar and Siphra de Zeniutha, and other kabalistic books, and ponder deeply on their meaning. It must suffice to say, that it is the Creative Energy of the Deity, is represented as a point, and that point in the centre of the Circle of immensity. It is to us in this Degree, the symbol of that unmanifested Deity, the Absolute, who has no name.”12
The Holy Name to which Pike alludes is the name of the Old Testament deity, commonly known as Jehovah, but originally considered to be the unpronounceable name of God, represented by the 4 letters Yod, He, Vau, and final He, yielding a formula known as the Tetragrammaton. A future article will delve into the significance of this name from the standpoint of Pythagorean Sacred Geometry. Note also that Pike discloses the fact that in certain Masonic lodges the Yod is enclosed in a triangle, in this case an equilateral triangle, the simplest of the polygons and the first to emerge from the circle through the process of geometric construction. In Masonic lodges the symbol of the point within the circle is usually depicted with two parallel lines lying tangent to and on opposite sides of the circle. When represented this way the symbolism invokes not only geometric significance but geographic and astronomic as well. Pike elaborates on further depths of meaning in the Yod.
Yod is termed in the Kabalah the opifex, workman of the Deity. It is, says the Porta Cælorum, single and primal, like one, which is the first among numbers; and like a point, the first before all bodies. Moved lengthwise, it produces a line, which is Vau, and this moved sidewise produces a superficies, which is Daleth. Thus Vau becomes Daleth ; for movement tends from right to left; and all communication is from above to below . . .Yod is the most occult of all the letters; for he is the beginning and end of all things. The Supernal Wisdom is Yod; and all things are included in Yod, who is therefore called Father of Fathers, or the Generator of the Universal. The Principle of all things is called the House of all things: wherefore Yod is the beginning and end of all things; as it is written: “Thou hast made all things in Wisdom.”13
The other two Hebrew letters to which Pike refers, the Vau and the Daleth, when added to the Yod, represents the spelling out of the letter, because, in the Hebrew alphabet each letter is a name which is actually spelled out in full. Contrast this with the Latin alphabet in use for modern English, the letter D, for example, is never spelled out as if it were a word, i.e. Dee.
But in the Hebrew the letter Yod is actually spelled out Yod, Vau, Daleth, or Y, O, D. Rich symbolism can be drawn from this spelling, in that, as already mentioned, the value of the single letter Y is 10, but the value of the Vau is 6 and the value of Daleth is 4. Therefore the total numerical value of the letter Yod when spelled out in full is 20, or 2 times the value of the individual letter, suggestive of the idea that a doubling of the potential is latent in the seed. In the Tantric system the seed point of infinite potential is the ‘Bindu.’ One of the indispensable works on Tantra for English readers is The Garland of Letters, by Sir John Woodruff, wherein he discusses the Bindu.
“This ‘Point’ is one of the world’s religious symbols and is set in the center of a Satkona or in a circular Mandala or sphere . . . Where does the Extended universe go at the Great Dissolution (Mahaprajaya)? It collapses so to speak into a Point. This point may be regarded as a mathematical point in so far as it is without any magnitude whatever, but as distinguished from it, in that it has in fact no position. For there is then no notion of space. It need hardly be said that this is a symbol, and a symbol borrowed from our present experience cannot adequately represent any state beyond it. We only conceive of it as a point, as something infinitesimally subtle, which is in contrast with the extended manifested universe which is withdrawn into it. This point is Bindu.”14
The limitless potential within the Bindu is suggested by Viśvanātha in his Commentary to the Satcakra:
“Within the Bindu is a space a hundred million Yojanas in expanse, and bright with the brightness of ten million suns.” 15
(A Yojana is about 8 miles in length.) The duality inherent in the Bindu is described in The Serpent Power, also by Sir John Woodroffe:
“Where does the Universe go at dissolution? It is withdrawn into that Śakti which projected it. It collapses, so to speak, into a mathematical point without any magnitude whatever. This is the Śiva-Bindu, which again is withdrawn into the Śiva-Śakti-Tattva which produced it. It is conceived that round the Śiva-Bindu there is coiled Śakti, just as in the earth centre called Mūlādhāra-Cakra in the human body a serpent clings round the self-produced Phallus. This coiled Śakti may be conceived as a mathematical line, also without magnitude, which, being everywhere in contact with the point round which it is coiled, is compressed together with it, and forms therefore also one and the same point. There is one indivisible unity of dual aspect which is figured . . . in the Tantras as a grain of gram, which has two seeds so closely joined as to look as one surrounded by an outer sheath.” 16
In the Vedanta, the metaphysical system originating in the Upanishads, considered the preeminent scripture of Hinduism, we find a description of the primordial duality expressed as the infinitesimally small and the infinitely great conjoined as a single entity, and having both an internal and an external aspect.
“Verily this universe is Brahman . . . it is to be worshiped in silence . . . Spirit is its material, life is its body, light its form; its resolve is truth, its self is endlessness. . . this is my soul (ātman) in the innermost heart, smaller than a grain of rice, or of barley, or of mustard-seed, or of millet, or a grain of millet’s kernel;—this is my soul in the innermost heart, greater than the heaven, greater than these worlds.”17 – Doctrine of Candilya
Here we have a duality of dualities, ‘As Above, so Below’ and ‘As the Inner, so the Outer,’ for those who traverse the path of Metaphysical Knowledge come to understand that there is an inner Universe as vast as the Outer universe, and the two are linked by a common geometric harmony, reflecting one another in a fourth dimensional symmetry. The fundamental duality is present in the act of Zimzum, which produces a line defined by its two end points, one of which is the point of inception, the Singularity at the center of the circle, and the other any point lying on the circumference, the two connected by a radius. Again, the Upanishads conveys an awareness of the ultimate cosmic seed as an implicit function of Life.
“Ātman, smaller than the small, greater than the great, is hidden in the hearts of all
Here is expressed an important idea lying at the core of Spiritual science: That there is a locus of infinite potential and power within living organisms, and according to the teachings of Tantra this is most concisely represented as the Bindu. In the systems of occult anatomy addressed in Tantra this duality imaged by two endpoints of a line has its counterpart in the form of Siva Bindu, lying at the base of the spine in the Muladhara chakra, and the Para Bindu, concealed within the pericarp of Sahasrāra chakra, gateway to the thousand petaled lotus, these linked by the line of force called Sushumna, the pathway followed by the Kundalinī Śakti when she awakens and ascends through the chakras, or vortices of subtle energy lying along the 33 vertebrate of the spinal column. The chakras themselves are always imaged with precise geometric attributes, for example, the representation of the Muladhara chakra as a 4-petaled lotus, the Svādisţhana as a lotus of 6 petals, the Manīpūraka chakra as a 10 petaled lotus, and so forth. Understanding the geometry of the chakras is as important as understanding the sound vibration emitted by each chakra, the colors, the god names and other attributes.
In The Serpent Power, quoted above, the author goes on to expound on the Bindu and in doing so affirms its dual nature in that there is an internal, spiritual meaning to Bindu as well as an external, cosmic meaning:
“. . . the Śakti coiled round Śiva, making one point (Bindu) with it, is Kundalinī-Śakti . . . She is spoken of as coiled; because She is likened to a serpent, which, when resting and sleeping lies coiled; and because the nature of Her power is spiraline, manifesting itself as such in the worlds—the spheroids or “eggs of Brahma”. . . and in their circular or revolving orbits and in other ways . . . In other words, this Kundalinī-Śakti is that which, when it moves to manifest itself, appears as the universe . . . This Śakti coiled round the Supreme Śiva is called Mahā-kundali, (“The great coiled power”), to distinguish it from the same power which exists in individual bodies, and which is called Kundalinī.”19
The Serpent Power is a translation and commentary upon two Tantric texts originally written in Sanskrit. One of the texts, Șat-cakra-nirūpana or ‘Description of the Six Centers’ describes the zone of Para Bindu in verse 48:
“Within its middle space shines the Supreme and Primordial Nirvāna- Śakti; She is lustrous like ten million suns, and is the Mother of the three worlds. She is extremely subtle, and like unto the ten-millionth part of the end of a hair. She contains within Her the constantly flowing stream of gladness, and it the life of all beings.” 20
The analogy of the ten-millionth part of the end of a hair illustrates the utter minuteness of the Bindu which, nevertheless, can radiate with the luster of ten million suns.
Western occultism recognizes a cognate symbol in the form of Hadit, typically associated with the Egyptian god Set in various magical lodges. Kenneth Grant head of the British O.T.O and author of numerous works on occultism defines the term:
“Hadit represents the infinitely small yet supremely potent point or bindu which, in union with Nuit, generates the manifest Universe.” 21
Nuit, or Nut, is the Egyptian goddess of the night sky, and is typically depicted in papyri and on coffin lids as a woman arched over the Earth in the form of a semicircle, with numerous stars showing forth from her body. Her two arms and two legs form the four pillars upon which the celestial vault is supported. Beneath the arched body of Nuit is seen the supine figure of Set, or Seb, from whose embrace she has just become disengaged. In this occult interpretation Hadit is understood to be the infinitely potent seed impregnating the goddess of the heavens through her union with Seb. This idea brings us into the realm of exobiology, for modern research is proving the veracity of the Archaic model of life propagation, that the terrestrial biosphere was the product of cosmic fertilization of the primordial Earth. However in the image of coitus between Seb and Nuit we see the converse of the celestial seeding of life onto Earth, for here the seed, after germinating in the Earth for multiple Eons, is being transferred back to the Cosmic domain.
Pointing to the Alchemical nature of this process is the fact the Seb is positioned so that one hand is raised to the heavens while the other is touching the Earth, again, symbolizing the Great Work, the linking of Heaven and Earth in Cosmic Union, the meaning behind the Masonic ladder encountered earlier. A noteworthy tradition that should not be neglected has its source with a Sub-Saharan people of Mali, West Africa.
This would be the now well known Dogon tribe, the subject of several scholarly and popular works. The Dogon have developed an exceptionally sophisticated and detailed cosmology that appears to defy the notion that advanced scientific awareness was the sole prerogative of Western European culture. The definitive work on the Dogon and their traditions is The Pale Fox, by the two eminent French anthropologists, Marcel Griaule and Germaine Dieterlen, who spent years in their company, learning their philosophy, beliefs, and eventually, in the case of Griaule, being initiated into their most sacred mysteries. The Pale Fox was originally published in France in 1965 and was not published in English until 1986. However, around the time of its first publication in France, an article was authored by Griaule and Dieterlen which appeared in a book entitled African Worlds that was subsequently brought to the attention of scholar and Orientalist Robert K. Temple by the inventor and philosopher of Consciousness Arthur M. Young.
A passage in the article caught Temple’s attention and led him on a nearly decade long quest that culminated in the 1976 publication of his research in a work entitled The Sirius Mystery. The passage that so gripped Temple’s imagination read thusly:
“The starting-point of creation is the star which revolves round Sirius and is actually named the “Digitaria star”; it is regarded by the Dogon as the smallest and heaviest of all the stars; it contains the germs of all things.” 22
What Temple realized was the significant fact that the star which revolves around Sirius, now called Sirius B, is, in fact, a star completely invisible to the naked eye. It was not discovered until well into the 19th century with the aid of a powerful telescope and was not even photographed until 1970. Yet not only did the Dogon know of its existence, they were also aware of the fact that its orbital period is 50 years and had preserved this knowledge for many generations. Their traditions included an extraordinary wealth of sophisticated astronomical knowledge which makes for a profoundly interesting study. In recent years controversy has arisen over the validity of some assertions made by Marcel Griaule, which has caused defenders of orthodoxy to dismiss all claims to scientific knowledge on the part of the Dogon.
Without getting into the question of alien contact invoked by R. K. Temple, it certainly does appear that the Dogon had a very sophisticated astronomy as documented by Temple. Their cosmology appears consistent with other traditions such as we have discussed. Specifically they visualize Creation as emerging from an egg within which is the “po” the seed of all things. To quote from Griaule and Dieterlens major study of Dogon mythology and cosmology The Pale Fox we learn that “When Amma broke the egg of the world and came out, a whirlwind rose.“ The po, which is the smallest (thing), was made, invisible, at the center. . . it is the po which Amma let come out first.” Amma’s creative will was located in the po, the smallest of things . . . it is called po, a word considered to have the same root as polo ‘beginning.’ Indeed, due to its smallness, it is the image of the beginning of all things. “All the things that Amma created began like the little (seed of) po.” And, beginning with this infinitely small thing, the things created by Amma will form themselves by the continuous addition of identical elements:
“Amma makes things begin (by creating them as) small as the po: he continues to add (to the things created) little by little. . . As Amma adds that . . . the thing becomes large.”23
The image of the breaking of the egg and the emergence of the whirlwind are extremely evocative, especially from the standpoint of the very unique geometry of ellipsoids and the spiraling movement of matter and energy in a diverse range of phenomenon from the dance of neutrinos in a bubble chamber, through the intertwined helixes of the DNA molecule, through weather systems, through the movement of planetary bodies in space, to the structure and motion of galaxies. By immersing ourselves in the study of Ancient Cosmology through a variety of sacred traditions and then turning to Modern Cosmological thinking, we experience a sense of familiarity, for lying at the heart of both are models of Creation that are strikingly similar. Whatever the origin of the ideas represented by Zimzum, or Hadit, or Bindu, or Yod, or Po, or the Grain of Mustard Seed, in modern cosmology the SpaceTime Singularity emerged as an inevitable consequence of Relativity theory. In a treatment of the principles of quantum physics and cosmology for the general reader, author John Gribben discusses the work of physicist Stephen Hawking in following the implications of Einsteins general theory:
“One of Hawking’s major achievements . . . was carried out in collaboration with mathematician Roger Penrose, who was then working at the University of London. Together they proved that the equations of General Relativity in their classical form…absolutely require that there was a singularity at the birth of the Universe, a point at which time began.”24
the emerging evidence now leads to the realization that probably every galaxy has at its core a super massive, super dense singularity surrounded by a spherical event horizon, mimicking the ultimate Singularity that presided over the birth of the universe.
In an early popular treatment of Black Holes, Astrophysicist William J. Kaufman describes the beast:
“As seen by a distant astronomer, a black hole has formed once a dying star has shrunk inside its event horizon. But there are still no forces in nature that can support the star. So it continues to contract under the relentless influence of ever-increasing gravity. The strength of the gravity and the curvature of spacetime around the imploding star continue to grow until the entire star is crushed down to a single point! At that point there is infinite pressure, infinite density, and, most importantly, infinite curvature of spacetime. This is where the star goes. Every atom and every particle in the star is completely crushed out of existence at this place of infinite spacetime curvature. This is the heart of a black hole. It is called the singularity.” 26
What is an ‘event horizon‘? The event horizon surrounding a black hole is the boundary within which the gravitational attraction of the collapsing stellar mass becomes so powerful that nothing, not even light, can escape, hence the plunge into total darkness that gives these bizarre objects their name. How does one even conceive of infinite pressure, infinite density or infinite curvature of spacetime? Kaufman continues his account by emphasizing the very basic arrangement of matter and energy that comprise a black hole “It is interesting to note that black holes are very simple…a singularity surrounded by an event horizon. And that’s all!” 27
The structure of a black hole can, therefore, be symbolized very effectively by the simple geometric act of drawing a circle, the central point representing the singularity and the circumference its event horizon. The diameter of the event horizon is directly related to the mass of the black hole, the more massive the dying star the greater the event horizon. Our Sun is not massive enough to form a black hole when it reaches the end of its life cycle. A star 10 times as massive would, however, be of sufficient mass to terminate its existence by collapsing into a black hole. A star of this size would disappear behind the dark veil of the event horizon when it reached about 37 miles (60 km) in diameter. In 1975 Astrophysicist and Noble Laureate Subrahmanyan Chandrasekhar wrote,
“In my entire scientific life . . . the most shattering experience has been the realization that an exact solution of Einstein’s equations of general relativity . . . provides the absolutely exact representation of untold numbers of massive black holes in the universe.”
It now appears that like billions of raindrops, nucleating around minute specks of particulate matter in order to fall to Earth as a Life giving rainfall, billions of black holes serve as the nuclei for the accumulation of stellar mass into galaxies and metagalaxies, pouring out of the Ultimate singularity at the heart of Creation to bring Life and Consciousness into the Infinite Void of Absolute Nothingness. In trying to wrap their minds around ideas of such profundity Cosmologists have had to concoct a number of conceptual models that can provide at least partial analogies for the events and processes under consideration. One of the most useful models has been termed the ‘Cosmological Principle.’ The fundamental idea behind the ‘Cosmological Principle’ is that the universe can be likened to an expanding sphere, with the bulk of visible matter of the universe arranged into galaxies— the largest structure of matter and energy observable, for now, from our human vantage point—and these are visualized as dots on the surface of the sphere.
The analogy is frequently presented of an expanding balloon with dots painted upon its surface. As the balloon expands the dots move away from each other. To an observer stationed at any one of the dots all the other dots would appear to be receding, not only from the observer but from each other as well. While it may appear to the observer that he or she is at the center of the system, it would be obvious to an observer looking at the balloon from the outside that no dot would actually occupy a center any more than any other dot. Relative to the surface of the balloon, the center would be both everywhere and nowhere simultaneously. However, a center of the expansion process could be hypothesized. If the balloon was perfectly spherical it would have a central point from which it was uniformly radiating as it expanded. What interests us in the context of this discussion is the initiation of the process of expansion. If we reverse the process, visualizing the balloon shrinking to an ever diminishing radius, at what point will we have reached the absolute beginning? Is there a lower limit beyond which we can no longer decrease the radius of the sphere, or does it ultimately shrink to zero, which is, in effect, inverse infinity? This is the assumption behind the idea of the singularity. But, according to the precepts of relativity, it is not only Space, but Time as well, that has its genesis in the Singularity.
Of course the expanding model is only a means to provide some kind of analogy to reality as we experience and observe it within the limitations of our unique human centered, Earth centered vantage point. In effect, as we attempt to visualize the process of Creation, it becomes necessary to visualize the origin of Time and Space simultaneously, implying that the universe, rather than being an expanding three dimensional sphere, is an expanding fourth dimensional hypersphere. By observing the present rate of expansion of the universe, it is possible to infer the time span since the expansion began. By imagining the spherical universe spreading out radially in all directions, then reversing the process so that the sphere begins to collapse upon itself, in the nature of the ‘Great Dissolution’ or Mahaprajaya as referenced earlier in The Garland of Letters, and accelerating the rate of this contraction to account for the effects of gravity, one can obtain an approximate span of time since the expansion commenced, the moment in which all of Creation had its genesis.
Cosmologists have performed this hypothetical reversal and derived an age of about 15 billion years, with a margin of error of a few billion years more or less, owing to the fact that there is a large degree of uncertainty regarding the precise rate of expansion. In any case, at some point going backward in time, all the matter of the universe would eventually have been compressed into a state of infinite density. Some moment, just preceding the collapse of all matter in the universe into an infinitesimally small dot with a radius of zero, marks the very beginning of Space/Time. Cosmologists have reckoned this moment to have been 10-43 part of one second subsequent to the Absolute, unfathomable beginning of Reality.
In The Quickening Universe author and astronautical engineer Eugene Mallove has written on the subject of the origins of the universe and of human destiny as an implicit function of the universe. He describes the ultimate primordial condition from the cosmological perspective:
“The beginning occurred about 15 billion years ago. The universe came out of the Big Bang expansion of all space-time starting then. All matter didn’t explode from a highly compressed state into an infinite void. Rather, space-time itself blew up from a virtually infinitesimal point, continuing to expand and allowing galaxies of stars to evolve and grow ever further apart. Moreover, this point is infinitesimal in the almost unimaginable sense of a spherical surface that shrinks ever smaller toward a point, or an infinite volume that squeezes down to oblivion…” 28
Will the universe as we know it continue to expand forever, or will it eventually, at some inconceivably distant future time, begin to undergo a contraction, returning ultimately to its primordial state, where all spacetime as we know it is compressed out of existence, from whence it might once again undergo cosmic expansion?
No one knows.
However, even a cursory consideration of ancient and modern cosmological models underscores their striking correspondence. Did Ancient masters of Kabbalah, Tantra, or Hermetic Science have access to a level of knowledge of which modern science has only recently come into possession? Vedic models of cosmology postulate the occurrence of successive Creations, the great lifetimes of Brahma, reckoned according to the vast cycles of the Kalpas.
Did Archaic science grasp the idea of a relativistic universe? If so, what was the source of this knowledge?
Is such knowledge evidence for the existence of a technologically advanced society at some time in the past, now forgotten to history, which was capable of studying the macroscale structure of the cosmos? Or is it an implication regarding the metaphysical architecture of Human consciousness itself? Or is it some combination of both? Whatever the answer, we are left with the Singularity, either as the beginning of it All or the End of it All, perhaps both. That single point, the infinitesimal dot, marks the beginning of our journey into the kingdom of Sacred Geometry, and a truly astounding kingdom it is to those who can successfully navigate its trackways.
The practice of Sacred Geometry opens to the mind’s eye an analog of alternate worlds, higher dimensions representing the ultimate creative process and an unfolding evolution from Unity to multiplicity, and it demonstrates the fact that this unfolding on a cosmic scale is governed by the laws and relations of geometry.
The practice of Sacred Geometry opens to the mind’s eye an analog of alternate worlds, higher dimensions representing the ultimate creative process and an unfolding evolution from Unity to multiplicity, and it demonstrates the fact that this unfolding on a cosmic scale is governed by the laws and relations of geometry.
The Holy Kaballah represents this process by means of the Tree of Life symbol and the 10 emanations issuing there from as fruit, and these are elegantly exemplified by a unique geometry of simple intersecting circles.
Physicist John Wheeler asked “What else is there out of which to build a particle except geometry itself?” but the same question might well be asked of the macroscale— “What else is there out of which to build a Universe except geometry itself?” The modern master of Sacred Geometry, Keith Critchlow, recognized that the Sacred Temples of old encoded this cosmological geometry and could serve to integrate human consciousness on a collective scale, because, as Sacred Geometry demonstrates, we Humans, each of us, are the ultimate measuring rods of Creation, for encoded into out very anatomy are the fundamental proportions upon which the Universe is built.
Describing this geometric order underlying all of Creation, Critchlow says:
“This is cosmology in the original sense of an ordered universe, a creation unfolding from a single all-embracing source or reality. The study of the ratios of this unfoldment has the benefit of indicating similar ratios for the return journey from multiplicity to unity.”29
So, these are the concepts that must inform and illuminate the commencement of our practice of Sacred Geometry. In the performance of this ancient Art, we begin with simple forms, and move towards increasing complexity, even as does the Universe in its evolution, and as does living Nature as it evolves from a single cell through myriads of species into a Human Being with the capacity for self-cognition. As we grow in our understanding of the proportions and harmonies expressed through the geometric process, we can begin to perceive the hidden patterns of Creation that unite widely disparate phenomenon, Natural and Human, into a synthetic whole and we can understand the literal truth that, as the Inner reality and the Outer reality are but reflections of one another, and As it is Above, So it is Below — the geometry of the Universe is a reflection of the geometry of our Consciousness — and, by following the pathway from the unity of that single, ultimate point of conception to the magnificent diversity of form which emerges beneath our compass and straightedge, we transcribe into our Consciousness the map that will guide us on our return journey to the Cosmos, to wholeness and final integration with the Godhead, the Atman, the source of All.
“. . . plunge into eternity, where recorded time seems but a point.” - Shelly, Prometheus
If you are interested in learning the divine science of Sacred Geometry from independent scholar Randall Carlson please visit the following link
- The Alphabet of Sacred Geometry
- Proportion: The Foundation of Harmony
- Scale Invariance and Dynamic Symmetry
- Sacred Metrology
1 Z’ev ben Shimon Halevi (1977) A Kabbalistic Universe, Samuel Weiser, Inc. pp. 7 – 8
2 Z’ev ben Shimon Halevi (1972) An Introduction the Cabala: Samuel Weiser, Inc. p. 28
3 Halevi (1972) p. 29
4 Charles Ponce (1973) Kabbalah: An Introduction and Illumination for the World Today: Quest
Books, p. 79
5 Quoted in Gershom Scholem (1960) On the Kabbalah and Its Symbolism:, Schocken Books, English translation by Ralph Manheim, 1965, pp. 102 -103
6 Scholem (1960) p. 103
7 Quoted in Kaplan, Aryeh (1979) The Bahir Illumination: Samuel Weiser. Attributed to Rabbi
Nehuniah Ben Hakana, 1st century C. E., Translation by Kaplan, p. xiv
8 Kaplan (1979) p. xiv
9 Elisabeth Haich (1960) Initiation: Seed Center, translated from the German by George Allen & Unwin, Ltd, 1965 p. 229
10 Papus (89 ) The Tarot of the Bohemians: Translated by A. P. Morton. Republished by Wilshire Book Company, 1978. p. 19
11 Papus (89 ), p. 20
12 Pike, Albert (1871) Morals and Dogma of the Ancient and Accepted Scottish Rite of Freemasonry, p. 15
13 Pike, Albert (1871) p. 792
14 Woodruff, Sir John (1922) The Garland of Letters: Ganesh & Co. (Madras) Private Ltd. 5th ed. 1969. pp. 144 – 145
15 Quoted in Woodroffe, Sir John (1918) The Serpent Power. Translated from the Sanskrit by the Author, Ganesh & Companry, Madras, India. p. 413
16 Woodroffe, Sir John (1918) pp. 34 – 35
17 Deussen, Paul (1912) The System of the Vedanta, trans. by Charles Johnston, Republished by
Dover Books, 1973, pp. 152 – 153
18 The Upanishads, translated by Swami Nikhilananda (1963) Bell Publishing Co. p. 73 I. ii. 20
19 Woodroffe, (1918) pp. 35 – 36
20 Woodroffe, (1918) p. 447
21 Grant, Kenneth (1974) Aleister Crowley and the Hidden God. Samuel Weiser, p. 209
22 Temple, Robert K. G. (1976) The Sirius Mystery: St. Martins Press, Inc. p. 2
23 Griaule, Marcel & Dieterlen, Germaine (1986) The Pale Fox: Originally published in French as Le Renard Pâle, 1965. Translated from the French by Stephen C. Infantino, Ph.D., Continuum Foundation, pp. 130 – 131
24 John Gribben (1986) In Search of the Big Bang—Quantum Physics and Cosmology: Bantam
Books, p. 381
25 Shankar, Francesco (2009) The demography of supermassive black holes: Growing monsters at the heart of galaxies: New Astronomy Reviews, Vol. 53, pp. 55 – 77
26 William J. Kaufmann, III (1979) Black Holes and Warped Spacetime: Bantam Books, pp. 88 –
27 Kaufmann (1979) p. 89
28 Mallove, Eugene T. (1987) The Quickening Universe: Cosmic Evolution and Human Destiny: St. Martins Press. pp. 52 – 53
29 Critchlow, Keith (1977) Forward to Gematria, A Preliminary Investigation of The Cabala by Bligh Bond and William Simcox Lea (1917) Republished by Research Into Lost Knowledge Organization