What do we understand as “archetype”? The definition we can find on the internet is: “the original pattern or model from which all things of the same kind are copied or on which they are based; a model or first form; prototype”. In Jungian psychology: “pattern of thought, image, universally present in individual psyche”.

 

In our understanding “archetype” is a pattern of thought which becomes a model for the creation/manifestation of any form in the universe. All forms of life are created through the mechanism of holography using the archetypes of the Universal Thought of the creating Spirit as perfect patterns for manifestation. Our human consciousness as co-creator of the Creator’s Universal Consciousness, when perceiving such an archetype, is able to modify it from the standpoint of our experience, and to produce a new archetype.

 

An example is the “Vitruvian Man” by Leonardo da Vinci. Marcus Vitruvius Pollio (born c. 80–70 BC, died after c. 15 BC), commonly known as Vitruvius, was a Roman author, architect, and civil engineer during the 1st century BC perhaps best known for his multi-volume work entitled De Architectura. Vitruvius explained his perception of the harmony of human body which he set up as a model for building temples. Leonardo (1452-1500 AD) made a drawing which became an archetype.

 

Why do we speak about mathematical archetypes? Because the archetypes reflect the order of Creation, and it appears that humans from ancient times onwards are seeing this order through number and pattern. We call the order – mathematics. The order of the pattern we call – geometry. Mathematics is the way of orderly division of the One. It defines the order of division. In geometry – the pattern of division. This provides the Creation with the variety of forms. Not accidental, but orderly forms.

It happened that two different and yet complementary books contributed to our understanding of the origin and mechanism of the archetypes in nature, art and science: Kalagia by a Russian author Alexander Naumkin, published in 1993, and A Beginner’s Guide to Constructing the Universe by an American mathematician and educator Michael S.Schneider, published in 1994.

 

Interestingly enough, A.Naumkin wrote his book after climbing the sacred mountain Belucha in Russia and living there in seclusion for several years. M. Schneider composed his book after studying ancient mathematics in India. Both books appeared almost simultaneously, but on different continents.

 

Kalagia has been published only in Russian, and though eagerly studied since by the spiritual students of Russia, has been never completely translated into any language other than Russian. Some excerpts of it translated into English, you can find in our book The Laws of Life.

 

Kalagia is one of those rare books dictated directly to a chela by an Ascended Master. This is the book of “The Teaching of Evolution of a Human Being and Universe accepted on the Mahasatyana’s Ray from the teacher of Humanity Jesus Christ – Maitreya by the chela A.P.Naumkin in the mountains of Altai”, in 1992.

 

Actually, Kalagia is a book of metaphysics. In auxiliary, we can see 52 tables, full of diagrams of unknown and incomprehensible content. The editor of Kalagia Nikolai Sijanov later described in his book The Echo of Kalagia the process of receiving and drawing of some of these diagrams by a group of spiritual students under the leadership of Naumkin.

 

Unexpectedly for us, we have found in Kalagia and in the Schneider’s book some identical diagrams.  A diagram titled in Schneider’s book “Harmonically decomposed square”, in Naumkin’s book meant “The first experiences of Crystallizing the Void and Formation of the Substance of Space”.

 

This gave as the key. By analyzing the diagrams of Kalagia, we came to the conclusion that the tables of Kalagia depicted the geometry of some archetypes of Involution/ Manifestation and Evolution of our universe.

 

The simplest archetypes, however, we have found in “A Beginner’s Guide to Constructing the Universe”. The first archetype, the dot in a circle, symbolizes the unity of Spirit, and its essence, its core, or “seed”.

 

Spirit is in a condition of complete Unity. Life is born in and from this Unity and is manifested holographically through the medium of Light.  That’s why every part and particle reflects the whole. The “seeds” of creation in all the seemingly separate beings are unified in their essence. Hence arises the power of attraction which we can call magnetism. The magnetic forces in each essence, from a sun to an atom, take their beginning in their core. Agni Yoga calls this attraction of the parts of unity – the “Cosmic Magnet”. The Spirit’s Cosmic Magnet becomes the real source of any magnetism and attraction, including gravitation, which is perhaps the most familiar aspect of this principle to us.

The state of unity is a static condition. Spirit sacrifices Its unity for the manifestation of life that leads to the division of the One. This division could be graphically represented by a circle divided into two opposites, two intersecting identical circles.

Division into two circles represents the process of separation into any opposites: Light and Shadow, Feminine and Masculine, etc.

Spirit, though dividing Itself, nevertheless remains intact and forms together with the opposites a working Trinity. An archetypal pattern representing this trinity is the so-called “Cosmic Egg”. Ancient myths and religions direct us to the primeval opposites as to the “Great Father” (“Divine Father”) and the “Great Mother” (“Divine Mother”). The “Cosmic Egg” then is an image of the “womb” where the archetypes of Matter are born.

Let’s now go from the images to the mechanism of the process of “birth” of the archetypes. The division incurs polar tension – repulsion of division and attraction of magnetism simultaneously. The poles are repelling each other, but the Magnet of Unity is always there, as is the yearning to return, to unite. It is a shift which on the one hand disrupts the unity, but on another hand requires and makes possible further motion and creation of something new.

As Agni Yoga says: “The correlation of cosmic transformations is called cosmic creativity. When Cosmos shifts the forces, the balance of the spheres is disturbed. When the balance of these forces is upset, forces in the space are drawn into a new tension. Thus, when Cosmos shifts, all spheres are shaken. Indeed, all forces expand in response to an attraction, and the cosmic harmony is intensified by the Cosmic Magnet. Thus is Infinity created.”  (Infinity II, 223).

The opposites are swirling in opposite directions producing whirlwinds of energy (electromagnetic vibrations) which follow in their motion the harmony (order) of Spirit’s Thought. The pattern of this motion in the electromagnetic field can be likened to weaving or to making a spider web, where all connecting lines actually are “lines of force” of the electromagnetic field. The ancient Egyptians expressed their understanding of this process as “the Goddess Neith weaving”, where Neith was the goddess of weaving, wisdom and war.

The result is the matrix of archetypes which lays the foundation for all the shapes of created Matter. And the symbols shown in the diagrams  are some of the first archetypes as we human observers see and interpret them. The symbols may well be the observer’s conjecture. But, because “The Creator is inseparable from the Creation, the Creation is inseparable from the Creator” (Kalagia, auxiliary), so our thought is taking these images from the Creator’s Thought.

Spirit’s Memory is all-dimensional, and Spirit’s Thought is not limited when creating Its archetypes. That’s why the archetypes can be orderly shapes of different levels of complexity.

The question remains: what is the holographic mechanism manifesting Spirit’s Thoughts in the material world?

The medium for holographic manifestation are Rays of Light.

As physics knows and applies, information can be stored by an interference pattern of high frequency waves (vibrations), either of light, or of sound. The meaning of the process of creation (manifestation) is that the information of Spirit’s Thought gets turned into an image, which would be animated by Spirit enabling it to live.

The process of manifestation by Light is a holographic process producing holograms of Matter. The technology of holography is based on the interference of two beams of light. One of them is a high frequency beam which we call the initial ‘reference ray’.  In technology it is usually a laser beam diffused by a lens and directed to a photographic film.

 

The other is the ‘working ray’ which passes through an object or experience. It is split from the initial beam and directed to the object by a system of mirrors and a diffusing lens. Meeting, illuminating and interacting with the object, the ‘working ray’ receives an experience. After being reflected from the object, the ‘working ray’ also falls on the film.

Interference of the ‘reference’ and ‘working’ rays produces an interference pattern on the film. This pattern contains information about the object (or the ray’s experience), which can be decoded and read as an image by a ray of observation. When the film is illuminated by whatever coherent light (in technology the same laser light used for making the interference pattern), a three-dimensional image of the object appears in the air. This is the hologram, and it can be of whatever complexity depending on the object which the hologram is mimicking.

 Spirit manifests the universe through a similar process using Its own Ray of Light as a ‘reference ray’. This initial Ray becomes a ‘working ray’ after any encounter with an experience. Thinking is Spirit’s “experience”, and the “Cosmic Womb” reflects the process of Spirit’s thinking.

 

The ‘working ray’, in this case, contains all Spirit’s Consciousness, yet carrying the imprint of the experience of Spirit’s Thought. In this way, an archetypal potential for a hologram of Life is produced and recorded on the ‘film’ of Spirit’s inner Space which Kalagia calls Spirit’s Memory.

 

Thus Spirit creates a potential for holograms. To form a real hologram, a whole trinity of rays is required. So, the third ray would be the Ray of the Observer, which in this case is Spirit. It observes Itself through experiencing Itself and thus all these three Rays exist in Spirit’s Memory, and produce the first hologram of Matter – Prima Materia.

 

Thus the primordial Light creates the potential for the ideas to be developed into the perfect pattern, the archetypal matrix, which forms the body of the Fiery and Fine Worlds. The archetypes of this matrix can then be manifested in the Solid World in which we consciously exist and act at the present time.

 

All the forms of life manifest Nature in form, colour and sound. We humans as observers manifest all that our collective mind can perceive and accept at this point of our development. In this sense we are co-creators with all the living beings and with the Creator in all of them. We are “drawing and painting” together this miraculous “coloring book” of Nature, using the archetypes to form its manifestations.

 

Where can we see the manifestations of the mathematical archetypes?

 

In different times, scientists observed the periodicity of such properties of elements of matter as atomic size, valences, melting points, reactivity and conversely inertness. Therefore they created different versions of the Periodic Table of Elements showing us that the patterns of the elements of matter are created not chaotically, but in a mathematical periodic order.

 

One of the most widely manifested archetypes in the Spirit’s Memory is the Spiral form. A spiral form reflects the periodic cyclic nature of universe’s life, including the gradient of its development.

 

As above, so below. We find manifestations of spiral structures everywhere in Nature, from a shell on a beach to a constellation of stars. We also find them in the spiral forms of embryos, horns, ears, fingerprints and many other forms of natural objects. We find a spiral in the shapes of whirlpools, cyclones and tornados, movement of planets, and in all types of trajectories of different objects, beginning from the wave of Light energy.

 

We find the spiral shape also in all kinds of plants. In the patterns of bracts in pinecones and small dry fruits in the kernels of maize. In the coils of climbing plants. These coils can be right-handed or left-handed, and however you try to change their direction, they will always eventually return into the position natural for the plant. We find the spiral archetype in the pattern of leaves on a stem for any plant as it provides the plant with the best conditions of exposure as to sunlight as to rain drops.

 

In our three-dimensional world of matter the maximum of dimensions in which we see material forms is three. So, for example, Plato saw the first archetypal expressions of three-dimensional nature in his so-called “Platonic solids”.

Mathematic calls them “regular polyhedra”, which means “many bases” and states that they are the only five types of three-dimensional forms equal in all directions. Plato identified the four of them with the states of matter (fire, air, water and earth), and the fifth – with cosmos (“Heaven above”).

The archetypes reflected by Platonic volumes are also widely applied in the Nature’s shapes. For example, crystals of salt are made up in the form of a cube. Capsids (protein shells of viruses) take the forms of different Platonic volumes, very often icosahedral (20 triangular faces) forms.

 

The archetypal patterns of the whole repeat in its parts because of the non-locality of a hologram. We can see the pattern of branching of a tree in the pattern of veins in its every leaf.

And the pattern of branching is also an archetype provided by the mathematics of the “Fibonacci sequence” (see A Beginner’s Guide to Constructing the Universe by Michael S.Schneider).

 

Fibonacci sequence starts from two numbers: 0 (No-thing/Every-thing) and 1(Unity, Monad). Their sum is the third to make up a Trinity: 0+1=1. If we continue adding every two last numbers together, we will receive the series of the Fibonacci sequence: 0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,…

 

Michael S.Schneider writes: “Look at these series. At the first glance we see a chain of numbers. But look beyond the visible numbers to the self-accumulating process by which they grow. The series grows by accruing terms that come from within itself, from its immediate past, taking nothing from outside the sequence for its growth. Each term may be traced back to its beginning as unity in the Monad, which itself arouse from the incomprehensible mystery of zero” (p.117). The same appears in any pattern of branching.

 

Michael S.Schneider also shows us that the average number of petals in the field flowers as well as the number of pine needles in the clusters of pine cones is following the numbers of the Fibonacci sequence. The self-accumulating process shows itself everywhere, and in all the periodic qualities we can notice.

 

For example, piano keyboard is a metaphor of accumulating vibration – structured by terms of the Fibonacci sequence: the black keys go in twos and threes, and the white keys are forming the eightfold scale – 7 keys, and the eighth is starting a new octave.

 

The Fibonacci sequence leads to the proportions of the “Golden Mean”: the ratio which we receive by dividing any number of the Fibonacci sequence by the previous number (for example, 3/2, 5/3, 8/5,etc). The Golden Mean ratio is usually symbolized by the Greek letter Phi (Ф). The ideal Ф is equal to the endless number 1.61803398875…, or rounded off to 1.618 or to 1.62. The further we go in the Fibonacci sequence into the bigger numbers the Ф is closer to the ideal.

 

If we divide a line at its Golden Mean, then the ratio of the whole line to the longer section is equal to the ratio of the longer section to the smaller (section). If we bend a line into a half- rectangle applying the Golden Mean, we receive the basis for a best balanced rectangular frame.

 

Nature widely applies these archetypal proportions in all of its shapes and structures. They provide these structures with perfect balance. The parts of human body are balanced by the proportions of the “Golden Mean”. The navel divides the body, the brow divides the face, the wrist divides the arm/hand, and the bones of our hand are divided at the Golden Mean.

 

It appears that the “body” of our Solar System (having in mind the distances of the planets from the Sun) is also structured roughly at a Golden Mean if we take into account the asteroid belt between Mars and Jupiter. (Roughly – because the planets are constantly moving against each other, and distances change).

 

The ratio of the “Golden Mean” has been applied by humans – the great architects and artists of the past – from the Egyptian pyramids and further up to the Gothic cathedrals and paintings of the Renaissance. The masterpieces based on this ratio are always powerful, harmonious and therefore beautiful.

 

All living beings carry the images of the archetypes of the Perfect Picture of Creation within their consciousness, but not all can yet consciously tap into the depth of Spirit for a pure and whole archetypal pattern, the crystal of Spirit’s Thought. Those mature Souls who went through the wholeness of experience and spiritual maturation in many incarnations, the great thinkers and sages of all times, the artists, composers and philosophers, the scientists making “the cutting edge” discoveries – it is they who “dig up” these jewels for the benefit of humanity.

 Our human consciousness transforms these archetypes into forms that conform to our human understanding and reflect our common visual perception. That’s why we can see in different cultures, in their myths, religions and fairy tales similar themes and images: the Father, the Great Mother, the Great Serpent, the Egg, etc. We are emulating these forms and through many lifetimes of experiences and learning of our lifestream are building ourselves into new forms that will eventually become archetypes themselves. Like Christ or Buddha.

The examples of archetypes that we know are also: Brahma the Creator, Siva the Destroyer of the old ways creating the possibility of new ways of development, and Vishnu the Protector of the new offspring.

Nowadays, in many places on the Earth, we can see fighting for religious or other ideals. The opposites are trying to unite through war. People are suffering and looking out for a Messiah.

The archetype of the Messiah is already there as a potential in the Memory of the Creator. However, people cannot manifest this archetype because they imagine a Messiah whom they would appropriate, who belongs only to them. That’s why tension is growing and will continue to grow until many of us will start seeing the Messiah with their heart, as Spirit that is within and for everyone. People are waiting for the Messiah to come to them whereas they have to come to the Messiah.     

 

 

Bibliography:

 

Naumkin Alexander, Kalagia. Kaunas: Gyvata, 1998, (Russian).

Sijanov Nikolai, The Echo of Kalagia. Moscow: Publishing House “Yachtsman”, 1996, (Russian).

Schneider M.S., A Beginner’s Guide to Constructing the Universe (The Mathematical Archetypes of Nature, Art, and Science). Harper, 1995.

Bentov, Itzhak, Stalking the Wild Pendulum. Rochester, Vermont: Destiny Books, 1988.

Riaikkenen, R.&M., The Laws of Life. Trafford Publishing, 2004.

Roerich H., Agni Yoga. New York: Agni Yoga Society, 1929 (Republished 1997).

Simblet, S., Botany for the Artist. London: Dorling Kindersley Limited, 2010.

 

If you wish to make a comment on this lecture or contact the author, please email: andrewrooke@hotmail.com