Sacred Geometry

There is nothing in this universe apart from God.  ...  God is present at every point of the universe and can be approached and experienced at every such point.  ...  and, though the Deity is no doubt infinitely greater than the universe which is His creation, every part and particle of that universe, from the tiniest atom to the mightiest planet, is essentially, entirely and thoroughly divine.

J. J. Van der Leeuw
The Fire of Creation
 1976, The Theosophical Publishing House

 

Star TetrahedronFor the same reason, we can say that all geometry is sacred, along with all mathematics and the laws of physics, especially certain fundamental constants and relationships such as the golden ratio, the natural logarithm, pi, etc.

However, in the strict sense of the meaning, when we refer to sacred geometry we are talking about methods, ancient or modern, of representing the metaphysical relationship between our physical existence and the spiritual source of existence -- between the consciousness of the individual and the Universal Consciousness of the transcendental dimension.

This relationship is the seed of creation.  It is an interaction process that is the root cause of all forms, the source of the experience of "otherness", and the entire field of objective spacetime.

 

 

 

 

Modeling Multidimensional Geometries

Light-coneWhen we model a three-dimensional sphere on a two-dimensional page, we easily understand that the resulting circle is only a limited representation, and we have no problem visualizing the sphere within the conceptual space of our mind.  With the use of shading and perspective, 3-D models on flat paper can be very convincing, making it still easier to use the conceptual 3-D space of our mind to visualize what the model is trying to represent.  Modeling more than three dimensions gets a little more difficult since the conceptual space of our mind seems to be limited to the same three dimensions as the space of our objective experience.  However, the mind is perfectly capable of conceptualizing more than three dimensions even though they cannot all be visualized at the same time.

This is exactly what is done in the Minkowski diagram.  By "collapsing" one dimension of space, all of three-dimensional space is represented by a flat plane -- this way the dimension of time can be represented by the third space dimension.  As mentioned earlier, this flat plane is a timelike hypersurface which no individual observer can ever actually see in its entirety.  The three-dimensional space that we see is represented by the surface of the past light-cone, which can also be thought of as a continuous series of ever-widening rings, each ring representing a set distance away from the observer in all directions -- the surface of a spherical plane.  Imagine the spherical plane surrounding you at this moment at a distance of (with a radius of) one light-second, for example (about 186,000 miles -- most of the way to the moon!).  The surface of that sphere is repesented in a Minkowski diagram by a ring one second back along the past light-cone, because what we are seeing at that moment is light which left one second ago from that spherical surface on its way you.  The human mind is able to understand that such models are limited representations of more complex, extra-dimensional structures, and with some mental gymnastics, to better understand the extra-dimensional relationships represented in that limited way.

Often, in physics and metaphysics both, different geometric forms are used to represent the same state of reality, usually as representing different qualities, relationships, or perspectives of the same thing.  With a simple transformation of the defining coordinate system, for example, a geometric form can take on an entirely different shape.  As mentioned in "Realm of the Quasar", the hyperspherical model of a big bang universe with three-dimensional space visualized as the surface of an expanding balloon, can at the same time be thought of as being flat, or even hyperbolic, as far as relativistic geometry is concerned.  In fact, many different geometries have been used throughout history to represent cosmological relationships.

For in the view of the old Sumerian astronomical observers, the universe was neither flat nor a sphere, but in the form of a great mountain, ...

In a late Sumerian cuneiform text of ca 2000 BC  ...   the name of the goddess-mother of the universe, Nammu, is denoted by an ideogram signifying "sea", and she is given praise as "the mother who gave birth to Heaven-and-Earth [ama tu an-ki]." Moreover, a second tablet of about the same date   ...  tells that when this "Heaven-and-Earth" emerged from the primal sea, its form was of a mountain whose summit, Heaven (An), was male, and lower portion, Earth (Ki), female; further, that from this dual being the air-god Enlil was born, by whom the two were separated.  ...

But this, almost to the letter, is the myth preserved in the classical [Greek] legend of Earth and Heaven, Gaia and Ouranos, separated by their son Kronos.  We recognize it also in the ancient Egyptian representation of the separation of Heaven and Earth by the air-god Shu, or  ...  by a god bearing on his head a mountain sign -- except that in Egypt the sexes of the world-parents are reversed, Heaven (Nut) being female, and Earth (Geb) male.

Joseph Campbell
 The Mythic Image
 1974, Princeton University Press

In these ancient examples, the tip of the cosmic mountain corresponds to the spiritual dimension, and thus to the Universal Singularity (at the instant of the Big Bang or in the center of the hypersphere), and the tip of the individual's light-cone is a point at the foot of the cosmic mountain, in the physical dimension.  In the Vedic tradition, the unfoldment of creation from the spiritual to the physical is generally represented by a series of concentric spheres, usually seven, the center being the unchanging spiritual dimension.  Transcending the universal chakras to the spiritual source is often described as climbing a cosmic mountain.  This theme is also reflected in the general form of the mandala, with the center of the motif representing the spiritual source of creation.

In fact, the circle or sphere is the most common spiritual motif, used throughout history to represent the infinity and oneness of creation.

An Archaic Manuscript....is before the writer's eye.  On the first page is an immaculate white disk within a dull black background. On the following page, the same disk, but with a central point.  The first, the student knows to represent Kosmos in Eternity, before the re-awakening of the still slumbering Energy...   The point in the hitherto immaculate Disk, Space and Eternity in Pralaya, denotes the dawn of differentiation.  It is the Point in the Mundane Egg..., the germ within the latter which will become the Universe, the ALL, the boundless, periodical Kosmos....The one circle is divine Unity, from which all proceeds, whither all returns.

Helena Blavatsky
 The Secret Doctrine, Vol.1, Cosmogenesis
 The Theosophical Publishing House

 

 

We should always keep in mind that metaphysical geometries are a way of modeling higher-dimensional relationships that are more real than the geometries themselves.  What is most important is to develop an intuitive understanding of the metaphysical relationship or principle being modeled, and as powerful as they are as teaching tools, we must not get too hung up on the models themselves.  The realization of transcendental unity is the goal of any metaphysical system or spiritual teaching.

When the mind of the Yogi is in harmony and finds rest in the Spirit within, all restless desires gone, then he is a Yukta, one with God.

Then his soul is a lamp whose light is steady, for it burns in a shelter where no winds come.  ...

He sees himself in the heart of all beings and he sees all beings in his heart.  This is the vision of the Yogi of harmony, a vision which is ever one.

Bhagavad Gita
6,18-19-29

 

 

 

A Matter of Perspective

There are many books which cover the details of the parallels between the new physics and mysticism, but few help us to actually visualize what this great integration means to our worldview. Surprisingly enough, there is an easy way to quickly integrate the ancient mystical connections into our current worldview, although it seems so bizarre to our normal "common sense" way of looking at things that it is not as easy to assimilate as it is to say.  A basic understanding of the new vision of reality provided for us by modern physics will help it to seem less unbelievable, as does a familiarity of the ancient schools of sacred geometry.  It basically comes down to a matter of perspective, and requires a totally new understanding of space and time -- new at least for most of us in the West.  (As we will see, there is a much older understanding of space and time that has been preserved for us in the ancient metaphysical systems of teaching.)

From where we are now, we look out upon an apparently expanding Universe, and we project this image back in time, way back in time, about 15 or 20 billion years, toward that singular point of origin called the Big Bang.  This Universal Singularity is thought of as infinitely dense, our entire Universe compressed to a single point, where the laws of physics do not apply -- infinitely dense matterenergy and no spacetime.  (Actually, physics breaks down just 'before' the Singularity itself.)  The concept of the Big Bang represents a singular point of origin for our entire Universe, a state of pure and infinite potential, and the whys and wherefores of the origin of that state completely transcend spacetime and are beyond the scope of physics.  Modern cosmology and common logic tells us that this is a past state of the Universe which has since evolved into what we see now, so we tend to think of it as no longer existing as such.  Now, imagine that this is not exactly the full picture.

Imagine that what we have conceptualized as the Singularity of the Big Bang does still exist in that initial state of pure potential, right at this moment -- we "see" it on the one hand (in a fragmented way) as the singularities of particles, every particle in the universe, and see it on the other hand (in a reversed way) in the infinity of space.

Now forget the idea that atoms are even particles at all.  Think of atoms as four-dimensional vortices of "past" spacetime that reach all the way back to the Singularity of the Big Bang, which is still there shining forth as it always has, providing the very substance of every "wherewhen of spacetime" that ever was or will be.  Of course, our surface consciousness of the physical world "floats" in the resonant state called the present, where we see only the top cross-sectional ring of each vortex (more like interacting sets of vortices), which appear to us as those strange tiny spheres called atoms.  In a sense, we could say that the center of every atom is in the same place -- and even more strange, this very same place is also seen as the infinity of space.

In this perspective, the Big Bang is not merely an event in the past which created matterenergy in spacetime (although this is still true from within our normal perspective on time), but is more precisely a continuous state which creates what we experience as matterenergy in spacetime -- the Big Bang is more like a "Big Shine".  In the light of what we know today about matterenergy in spacetime, such a view is not really that far out at all.  Modern physics knows that the quantum processes which form the substance of all matter completely ignore the rules of spacetime separation, and are actually manifestations of interacting force fields which are in turn aspects of a single universal Superforce.

 

This worldview sees every quantum process of the Universe -- past, present, and future, even anything that can be imagined -- as integral an part of a timeless state of the Universe that is equivalent to the Planck-time of Big Bang cosmology.  We can conceptualize this state as a hyperspherical condition of unified force, expressed as a polarity between the Universal Singularity and a higher-dimensional Infinity -- a Hyperspherical Polarity.

 

Polarity between Singularity and InfinityThe polarity between Singularity and Infinity manifests in our experience in a number of lower-dimensional forms, and is key to understanding our experience of time, space, consciousness, and how the entire Universe is tied together in our experience of matterenergy in spacetime.

In a manner of speaking, the hyperspherical polarity is "sliced up" into our experience of four-dimensional spacetime.  As space itself, it is the polarity between every single dimensionless point in space and the fully-extended three-dimensional infinity outward from that point.  As time itself, it is the polarity between the singularity of past and the infinity of future, between the singular course of deterministic events which led to the present moment and the infinite number of possible and somewhat predeterministic futures.  In matterenergy, the polarity appears in the dualistic nature of wavicles, which act as either point particles or waves.  Even in individual consciousness it emerges as the polarity between the singular localized reference frame and the infinite field of matterenergy in spacetime surrounding the experiencer.

We have seen that the Big Bang universe can be modeled as a hypersphere centered on the Universal Singularity at t=0.  In this model, time is a hyperspherical polarity and spacetime is an expanding hypersphere.  The hypersurface of the present is the expanding surface of the hypersphere.  Keep in mind, however, that the hypersurface of the present is a condition of universal simultaneity that is never seen as such, and the present quantum state of the universe that any of us ever sees is defined by our light-cone slicing through the hypersurfaces of the past.

In fact, the notion that the universal hypersurface of the present even exists as a physical condition of spacetime is a complete abstraction imposed upon reality by modern science.  Science presupposes the existence of space and time as universal absolutes, and assumes they exist whether or not there is a consciousness to experience them.   This, of course, was a natural assumption for science to make, and was necessary in order for the physical models of our universe to be formulated.

Reality divided by reason always leaves a remainder.  After everything has been said about the universe, after the entire world has been transformed on the basis of scientific knowledge into a hierarchical structure of ever-widening systems, we are still left with a profound sense of mystery.  ...

This luminous experience of the impenetrable mystery is common to all the scientists, philosophers, and mystics of the highest rank.  The scientist calls it the mystery of Nature.  The philosopher calls it the mystery of Being.   The mystic calls it the mystery of the Spirit.

Haridas Chaudhuri
 Being, Evolution, and Immortality
1974, The Theosophical Publishing House

 

With the ancient understanding of space, time, and consciousness firmly in mind, we can look at the hypersphere of the Big Bang in a "new light".   From a mystical perspective, the Big Bang of modern cosmology is a continuous process, an omnipresent condition which has always been the same no matter what we believed.  Western science, caught up in its purely objective view of existence, has imposed the concept of "universal time" on this timeless condition, projecting it into the past as a single event.

What a strange thing to do with the most beautiful mystical principle of all.  We have completely ignored the ancient message of nondualistic mysticism and have thus found our science of the universe bogged down in the "strangenesses" of relativity and quantum theory for most of this century.  We have certainly developed an extraordinary understanding of the physical universe, and this was no doubt the purpose of modern science, but perhaps now is a good time to re-integrate the sacred science of the ancients.

A mystical understanding of modern cosmology sheds a good deal of light on the strange aspects of both modern physics and ancient mysticism.  We can see an underlying order as the source for the chaos of the apparently random and probabilistic nature of the quantum world.  The perfect homogeneousness of the transcendental hypersphere is all possible realities in an unmanifest condition, all probabilities superimposed.  At the same time, it is more exciting than ever to study the ancient systems of metaphysical geometries.

 

 

Multidimensional Man

... it is shown in every ancient scripture and Cosmogony that man evolved primarily as a luminous incorporeal form, over which...the physical frame of the body was built, through, and from, the lower forms and types of animal terrestrial life.   "The Soul and the Form when descending on Earth put on an earthly garment," says the Zohar.  ...   "When Adam dwelt in the garden of Eden, he was dressed in the celestial garment, which is the garment of heavenly light, ... light of that light which was used in the garden of Eden."

Helena Blavatsky
 The Secret Doctrine, Vol.2, Anthropogenesis
 The Theosophical Publishing House

Just as big bang cosmology is paralleled within the quantum realm, just as the entire history of cosmological evolution (Cosmogenesis) is ever-present in the structure of the atom, the entire history of human evolution (Anthropogenesis) is ever-present in the structure of the body-soul vehicle.  The relationship between the heavenly light of the Garden of Eden and the earthly world of the manifest Universe, is reflected directly in the relationship between the soul and the body, mind and matter, consciousness and spacetime.  In each case, both realms exist simultaneously in an intricate web of interdependence, and in each case, the higher, more ethereal levels provide the primary substance for the lower, more corporeal realms.  In transcendental meditation, an increasing transcendence is a progression toward the source of conscious unfoldment and toward the central source of the Universe itself.

Consciousness thus proceeds from the more limited to the more comprehensive, from lesser to greater intensity, from lower to higher dimensions, and each higher dimension includes the lower ones by coordinating its elements in a wider and more intricate structure of relationships.  ...  Thus the reality of a lower dimension is not devaluated or eliminated by the higher one, but only relativized.

Lama Anagarika Govinda
 Creative Meditation and Multi-Dimensional Consciousness
 1976, The Theosophical Publishing House

 

 

The human body as a configuration of energy is made up of seventy-two thousand channels, the currents of energy which travel through them and the essential drops or units of consciousness and energy conjoined which reside in the channels.  By manipulation of the essential drops within the channels by way of the currents, we undergo different levels or states of consciousness.  The type of consciousness we now have based on our present configuration is one type, dream another, deep sleep another.  Fainting, heavy fainting or coma or when breath stops are all others.  The final level of consciousness, Clear Light, is made manifest at the time of death. This is the strongest and subtlest. Unused, it serves as the basis for revolving the round of birth, old age, sickness and death.

The Dalai Lama, 1980

 

 

The Cosmic Mandala

Cosmic Mandala

 The Cosmic Mandala is encompassed by a flaming circle.  At the Cosmic Center is a three-footed spiral symbolizing a first movement, surrounded by the rotating wind which condenses into the basic elements, representing the states of aggregation:

Wind or Air stands for the gaseous state.
Fire stands for transformation, and is usually depicted as a red triangle.
Water stands for the liquid state, and is represented by a half-circle or circle.
Earth stands for solid matter, and is symbolized a yellow square or cube.

The emerging forms of the elements are painted in the blue ring surrounding the Cosmic Center, in the lower sphere intimating the world continents-to-be.  The blue Ether represents the all pervading condition, the source of all elements filling the space of the Mandala.  On it circles are drawn, looking like ellipses in their dynamic intersection.  They portray the orbits of celestial bodies, painted in all the colors of the rainbow plus black and white and indicating the directions.  These twelve astrological circles of the upper sphere demonstrate the movements in the seasons of the sun, moon, and stars.

-- courtesy BuddhaNet

 

 

The Tree of Life
painting by Patricia Waldygo		  The Kabalistic Tree of Life 

  

The Sephiroth:

The 1st Sephirah
Kether, the Crown

The 2nd Sephirah
Chokmah, Wisdom

The 3nd Sephirah
Binah, Understanding

The Invisible Sephirah
Da'ath, Knowledge

The 4th Sephirah
Chesed, Mercy

The 5th Sephirah
Geburah, Strength

The 6th Sephirah
Tiphareth, Beauty

The 7th Sephirah
Netzach, Victory

The 8th Sephirah
Hod, Glory

The 9th Sephirah
Yesod, Foundation

The 10th Sephirah
Malkuth, The Kingdom

 

 

Right Eye of Horus

The Right Eye of Horus, representing consciousness, wholeness, unity, etc.
It is also reported to be the symbol for an Egyptian Mystery School of Sacred Geometry.

 

 

The Flower of Life

  Flower of Life

The code of the FLOWER OF LIFE actually contains all the wisdom found in the universe, similar to the genetic code contained within our own DNA.   This geometric code goes beyond ordinary forms of teaching and lies beneath the very structure of reality itself.  All the harmonics of light, sound and music exist within this geometric structure, which exists as a holographic pattern, defining the shape of both atoms and galaxies alike.  This image has been used throughout the world and has been found in all the major religions in all countries.  ...  The Flower of Life pattern was considered so sacred to the ancients, that it was kept secret and has only been found in a few known Egyptian sites.Flower of Life on Egyptian Temple, Abydos

Drunvalo Melchizedek
 from Flower of Life Research

 

 

 

Fruit of Life and Metatron
 
The circles of the Flower of Life and Fruit of Life actually represent spheres in a 3-dimensional pattern pervading all of space, representing the female elements of Creation.  This provides the field for Metatron's Cube, which contains the Platonic Solids, formed by the ray-like male movements of Creation.

This very same geometry probably underlies what modern physics is calling the quantum vacuum, and is fundamental to the creation process at the quantum level.

 

 

Merkaba, Star Tetrahedron

MerKaBa Meditation
 courtesy Vitalistic Health & Healing Network

 

 

 

Vajrayogini Mandala

Tibetan Buddhist Mandala

 

An evolution of consciousness is the central motive of terrestrial existence.  The evolutionary working of Nature has a double process:  an evolution of forms, and evolution of the soul.  ...

Man occupies the crest of the evolutionary wave.  With him occurs the passage from an unconscious to a conscious evolution.  ...  The nature of the next step is indicated by the deep aspirations awakening in the human race.

Sri Aurobindo
The Future Evolution of Man
 1963, The Theosophical Publishing House

 

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