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
1976, The Theosophical Publishing House
For the same reason, we can say that all geometry is sacred, along with all mathematics and all the laws of physics. The fundamental constants and relationships that science has found prevalent in the physical world are also fundamental clues to our relationship to the higher metaphysical dimensions. Geometric relationships such as the golden ratio and the natural logarithm, etc., as well as science's view of the time scale of the Big Bang universe and its connection to the physics of the subatomic world, are all important to metaphysical geometry.
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, a dynamic process at the root of our existence. It is the 'first cause' of all forms of being and is experienced as consciousness and time within the individual -- the source of the experience of "otherness" and the entire field of objective spacetime.
Sacred Geometry, then, is a way of conceptualizing and illustrating the fundamental principles of a spiritual universe: Transcendental Omnipresence, the One Source of all realities, and Polarity, its intrinsic creative aspect, the Force of Creation.
Modeling Multidimensional Geometries
When 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, and the third space dimension can be used to represent time. 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 represented in a Minkowski diagram by a ring one second back along the past light-cone (and defined by where the plane of the timelike hypersurface of one second ago intersects the light cone). The human mind is able to understand that such models are limited representations of more complex, extra-dimensional structures, and the model can help us 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.
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.
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 cosmological time T=0 of the Big Bang or the center point of a timeless 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, the center being the transcendental spiritual dimension and timeless source. 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.
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.
The 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.
from Flower of Life Research
The Seed of Life
The Flower of Life
The Fruit of Life (lighter blue circles) and Metatron's Cube (red lines),
representing the male (rays) and female (circles) movements of Creation
The circles of this sacred geometry pattern 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.
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.
1963, The Theosophical Publishing House