We are now embarking upon the final phase of this study in which we shall expand the Lesser Maze, which was constructed in Part one, into its most complete form. This is the Great Maze in which we shall see certain of the geometrical solids repeated and reproduced in a most fascinating manner.
It will be best by way of preparation to undertake a quick review of the material covered in Part One. To study Part One in its entirety will well repay any student who wishes to undertake such study, because he may find that some points which might have been obscure to him previously will now become much clearer. For those who do not wish to do this, the following brief summary may suffice.
We started out with the concept of a moving circle (Figs. 1 through 4), representing the gradual process of the Universe awakening out of a state of pralaya into that of manifestation. When the circle had moved a distance of its own diameter, it was found that by the simple laws of geometry it had inscribed within itself a regular Decagon or ten-sided polygon. This was taken to represent the fact that the Universe (within the limits of our understanding) consist of ten planes of consciousness. The mathematical properties of the regular Decagon in its relationship to the Golden Section were discussed at length, and the ten points on the circumference of the circle were shown to b one form of the Tetraktys. The more usual form is that of an equilateral triangle composed of ten dots, and it was shown that we might consider the three dots at the corners to represent the three unmanifested planes, and the seven dots at the center the seven manifested planes. The concept of the seven manifested and the three unmanifested is basic in the Esoteric Philosophy.
The seven dots at the center of the Tetraktys were joined (Fig. 5) in such a manner that we have a three-dimensional Svastika, which we have called Thor's Hammer; and these three axes of rotation—as they turn out to be— are known to be most important in mechanics. Every rotating object moves about three axes mutually at right angles, as represented in this figure.
The three arms of Thor's Hammer were taken to represent three fundamental streams of consciousness: the Gods, the Monads, and the Atoms. Part Two was devoted to an expansion of the teachings concerning these.
Going back to the inscribed Decagon, which also included the ten radii of the circle, by joining alternate points we found that we had drawn on Icosahedron (Plate I). This is one of the five regular polyhedral, and it consists of 30 lines, 20 equilateral triangular faces, and 12 vertices. The 12 vertices may be thought of as being 12 points spaced about on the surface of a sphere.
We joined internally the points of the Icosahedron, and the resulting 30 lines formed a Dodecahedron (Plate 5), a regular polyhedron consisting of 12 faces and 20 vertices. Constructed in this manner, the vertices of the Dodecahedron may be thought of as being 20 points spaced about on the surface of a sphere which is smaller than that circumscribing the Icosahedron, and therefore within it. The Dodecahedron was drawn by joining the 20 points on the circumference of the sphere. The Icosahedron enclosing the Dodecahedron represented the dual nature of the Universe, the former representing the consciousness aspect, and the latter the corpuscular—or we might say, more briefly, Spirit and Matter. This is of course an over-simplification necessary in a review of the subject; the idea is more fully expanded in Part One.
Each of the 12 points of the Icosahedron was joined by a line with a vertex of the Dodecahedron, the resulting lines intersecting in 6 points within the Dodecahedron. The resulting figure was an Octahedron (Plate 7) a regular polyhedron consisting of 12 lines, 8 triangular faces and 6 points. Because this is formed by the union of the Icosahedron with the Dodecahedron, it was taken to represent the inmost essence of Man's consciousness; for he is a child of the Universe, both aspects of its duality contributing to Man. It is hoped that we can show at the conclusion of this study how apt a symbol is the Octahedron in demonstrating this relationship between Man and the Universe.
Since the Octahedron consists of 8 equilateral triangular faces, it is possible to consider each of these faces as the base of a triangular pyramid, or Tetrahedron (See Plate 1). These were constructed, and it was found that these 8 Tetrahedra combine to form two larger interlacing Tetrahedra with the Octahedron at the center of them. (A Tetrahedron is a regular polyhedron consisting of 6 edges, 4 triangular faces and 4 points.) The manner in which they intersect represents in a most graphic way the same principle long associated with the interlacing triangles, or the union of Spirit and Matter as it applies to the consciousness of Man. In this solid form, generated as it is from the Octahedron itself, it represents the principle that when the indwelling core of Divinity in Man seeks to manifest itself in the process of rebirth, it first emanates from itself sheaths of Spirit-Matter which in turn eventually produce the vehicles of the many-faceted being we call Man.
Now the points of the interlacing Tetrahedra touch just those 8 points of the Dodecahedron which were not occupied by the lines emanating from the Icosahedron in the process of forming the Octahedron. This beautiful bit of geometric construction, which is simply a fact of mathematical law, forms a most telling symbol of the inter-relationship between Man and the Universe. Where could one find a more graphic symbol than this?
To complete the construction of the Lesser Maze, we joined externally by 12 lines the 8 vertices of the interlacing Tetrahedra. The resulting figure was a Cube, or Hexahedron, a regular polyhedron consisting of 12 edges, 6 faces and 8 points. It follows that this Cube fits neatly within the Dodecahedron; in fact each of the faces of the Dodecahedron is crossed by a line of the Cube as shown in Plate 1.
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Fig. 12 — Circulations of the Cosmos
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Plate VI — A cluster of Five Cubes
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Plate VII — A Cluster of Five Tetrahedra
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Plate VIII — A Cluster of Five Paris of Tetrahedra
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Plate IX — A Cluster of Five Octahedra
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Plate X — Five Octahedra clustered about an Icosahedron
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Plate XI — Five Icosahedra Clustered about a central Icosahedron (white)
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So here is the completed Lesser Maze, a perfect symbol of Man within the Universe, or “the Jewel in the Lotus” (Plates II and III). Remember that it can all be drawn in the center of the Tetraktys.
One more point of importance which was brought out previously is that, just as we formed the Dodecahedron by joining internally the points of the Icosahedron, so we may form another Icosahedron within the Dodecahedron, and this process may be repeated indefinitely, alternating with the construction of an Icosahedron and a Dodecahedron; although they become ever smaller, one may never reach the center (Fig. 6). This was taken to represent the concept that this Universe is but one term in an infinitely repeating series of universes. Each such repetition, of course, implies the construction of an infinite series of Lesser Mazes.
It may be difficult for some minds to understand that these symbols are not interpreted arbitrarily — for it might be said that you can see anything you want to wherever you look; it is just a question of where your inclinations lie. If that is true, then how wonderful is the Universe to him who looks for the consciousness of the Divine, for he can see it everywhere. Yes, it might be truly said that all things are in the Universe. However, the case is really somewhat different where these geometrical figures are concerned. Their amazing inter-relationships cannot be denied by the most pragmatically minded, and even if he were to let it go at that, he would be amply rewarded by the study along strictly geometrical lines.
Yet to one whose mind is engrossed in the Theosophical teachings, these geometrical solids have a special meaning. For one thing, he feels that in studying them he undergoes a stimulation of his mind and his intuitions, which is a wonderful experience. He learns that not only do these figures represent to him many of the teachings that he has studied, but that they can serve as very real pointers to new understandings. Few if any of the teachings have been fully explained in the books. There is every reason why much should be left to the intuition of the student and to further study on his part; there would be little progress possible to us if we were told everything.
It has been my own experience that some understanding has become available to me through the study of Mathematical Symbolism which was latter corroborated by a further study of The Secret Doctrine. To be sure, the teachings were there all the time; yet it is a cause for some wonder how that which once seemed so illusive in the pages of a book could become so perfectly apparent as a result of this particular form of research. I unhesitatingly give credit to Mathematical Symbolism for its power to open new doors of understanding.
And why should these figures serve as guidelines? We go back to the statement that was made at the beginning of this book: “It is in the nature of things.” They actually contain within themselves the principles of the truths they symbolize.