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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 (?tman) 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.

"?tman, smaller than the small, greater than the great, is hidden in the hearts of all living creatures."18

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 Sahasr?ra chakra, gateway to the thousand petaled lotus, these linked by the line of force called Sushumna, the pathway followed by the Kundalin? ?akti 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 Sv?dis?hana as a lotus of 6 petals, the Man?p?raka 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.

Chakra Geometries

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 ?akti coiled round ?iva, making one point (Bindu) with it, is Kundalin?-?akti . . . 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 Kundalin?-?akti is that which, when it moves to manifest itself, appears as the universe . . . This ?akti coiled round the Supreme ?iva is called Mah?-kundali, ("The great coiled power"), to distinguish it from the same power which exists in individual bodies, and which is called Kundalin?."19

The Serpent Power is a translation and commentary upon two Tantric texts originally written in Sanskrit. One of the texts, ?at-cakra-nir?pana or ‘Description of the Six Centers' describes the zone of Para Bindu in verse 48:

"Within its middle space shines the Supreme and Primordial Nirv?na- ?akti; 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, former head of the Typhonian 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

I think we are here justified in asking whether or not Hawking and Penrose were merely recovering an insight into the most fundamental processes of Creation which long ago were entertained by the Egyptians, or the Masters of Kabbalah, or Tantra, or Freemasonry, or the authors of the Vedas?  Whatever the answer, the parallels between ancient and modern, between sacred and scientific are indeed compelling; and consistent with the fundamental ideas of dynamic symmetry and scale invariance in Sacred Geometry, that the proportions of any whole structure, system, or composition is reflected in its parts and vice versa, 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.  This structure comprised of singularity and event horizon was christened with the now familiar term ‘black hole' by astrophysicists and cosmologists. ' 25

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 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." –Shelley, Prometheus

Sincerely Yours,



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

Image by European Southern Observatory, courtesy of Creative Commons license.