It is argued that "the human mind cannot conceive an indivisible unit short of the annihilation of the idea with its subject". This is an error, as the Pythagoreans have proved, and a number of Seers before them, although there is a special training for it, and although the profane mind can hardly grasp it. But there are such things as metamathematics and metageometry. Even mathematics pure and simple proceed from the Universal to the particular, from the mathematical, hence indivisible Point, to solid figures. The teaching originated in India, and was taught in Europe by Pythagoras, who, throwing a veil over the Circle and the Point – which no living man can define except as incomprehensible abstraction – laid the origin of the differentiated Cosmic matter in the basic or horizontal line of the Triangle. Thus the latter became the earliest of geometrical figures.

The Secret Doctrine, i 616

  The rigorous discipline of meta-geometry is concerned with the indispensable philosophical ideas required to construct the entire system of the manifested universe out of a single boundless Source. That inexhaustible Source, seen as a pervasive principle in the cosmos, vitalizes all planes and spheres and ceaselessly acts upon all forms, objects and subjects. Metaphysics, when rendered metaphorically and by analogy with the axioms and postulates of geometry, takes on much more than a merely theoretical relationship to the simple points, lines and constructions that are the basic elements of geometry. What at one level may appear to be merely geometrical relations between these elements are, at a metaphysical level, vital elements of the cosmos as a living geometry in repose. This is the deeper meaning of the systematic study of Euclid's elements, and it is a fundamental reality which constitutes the noumenal world. Numbers also interpenetrate the phenomenal world of objects and the complex relationships between them. Numbers, in all their possible combinations, give structure and order in an evolutionary universe to the totality of all that exists. So it is possible, through a highly precise and disciplined consideration of geometrical ideas – in effect, the study of meta-geometry at a preliminary level – to move beyond geometry, as generally understood, towards a true Buddhic insight into the underlying shape of metaphysics. Though a highly difficult discipline, this process is crucial to one who would awaken the metaphysical imagination.

  All knowledge arises because of the immense power of visualization. It draws freely upon familiar phenomena from the world of sense-perception, yet alters and modifies the sensory world. This process is exemplified by any artist, whether painter or sculptor, musician or mathematician. Likewise, the creative power of visualization is central to any true science. For this fertile power depends upon precise renderings of formal relations between ever more abstract notions. As an innate capacity of the immortal soul, this enormous power is given exercise and direction through the study of mathematics. It is this which makes the natural scientist capable, at one level, of performing notable and elaborate acts of abstraction. The natural sciences become capable of attaining a seeming stability in their operational concepts through the relationship of thought to number. And through systems of complex equations, theorems and models, some continuity of transmission in this body of knowledge is also achieved.

  At the same time, the power of visualization is limited neither by what one may know of objects nor by what one may know of procedures in logic and mathematics. The power of visualization must spring from the deepest core of subjectivity in every human being. Each and every man and woman, every Manasa, privileged to carry the sacred fire of self-consciousness, is necessarily capable of mental creation that transcends the limits not only of the seen but of the known. Thus every human being can, through the power of mental abstraction, ascend into the unknown ground and invisible origin that lies behind the entire phenomenal realm of existence. It is thereby possible through the power of visualization for the individual to transcend significantly all existing knowledge encapsulated in any set of equations, theorems and models.

  All human beings are more or less at ease in exercising this power in relation to various subjects and objects. Yet often the very ease with which human beings visualize becomes an actual limitation. Nowhere is this more true than in the twentieth century, when through the natural sciences we have inherited so many extraordinary analogies – linking, for example, the solar system and the atom. This bold insight, coming at the close of the nineteenth century, was both intriguing and confining. In a sense, it was the product of a system of thought which had become fortified and solidified through a narrow interpretation of the ideas of Newton, and so fast becoming an impediment. It took a rare scientist, Werner Heisenberg, to see that it was essential to break with the known ways in which people were visualizing the world, to overturn assumptions confined by an over-simplified view of motion, location and causality. In his attempt to visualize a new way to understand subatomic phenomena, Heisenberg introduced a fresh model of the migration of entities from one point in space to another. He did not mean that subatomic particles literally migrate from one point of space to another as a bird might fly from tree to tree. Instead, he depicted the migration or shift of subatomic particles in terms of certain types of transitions between different possible quantum states. In effect, he introduced a more abstract notion of space than that connected with ordinary Cartesian extension.

  Every such remarkable exercise of the enormous power of visualization, whether in the natural sciences or elsewhere, can free the imagination from limiting past patterns. In a society where so much consciousness is concentrated on physical phenomena, virtually any effort to abstract from the phenomenal world will yield some degree of transcendence. What is striking in the case of Heisenberg, and others like him, is that they were able both to transcend the limits of their perceptual models and yet to maintain a continuity with previous thought. So, as soon as his colleagues began to grasp the difficult Uncertainty Principle which Heisenberg had introduced into their science, they began to expand upon it. In Japan, for example, Hideki Yukawa joined the ideas of uncertainty and relativity together to formulate the model of the meson, an entity representing the rest mass of the nuclear binding force.

  From the standpoint of meta-psychology, every human being as a subject is capable of drawing from the infinite resources of universal ideation, Akasha. What some mathematicians refer to as mind-space is itself only one aspect of the infinite Akasha. The capacity of the human being to extend the range of possible thoughts in all sorts of ways not previously imagined is essentially an application of the power of visualization in this mind-space. Far more is indeed possible. Such divine ideas and metaphysical possibilities go well beyond the entire system of visible and invisible manifested relationships.

  Since it is precisely this realm of the unmanifest that is the focus and root of Gupta Vidya, the true awakening of the spiritual aspects of the power of visualization depends upon the ability to maintain continuity of consciousness completely apart from any perception of differentiated subjects or objects. Hence, H.P. Blavatsky warned:

  Those unable to seize the difference between the monad – the Universal Unit – and the Monads or the manifested Unity, as also between the ever-hidden and the revealed LOGOS or the Word, ought never to meddle in philosophy, let alone the Esoteric Sciences.

And again:

  Draw a deep line in your thought between that ever-incognizable essence, and the, as invisible, yet comprehensible Presence (Mulaprakriti), or Shekinah, from beyond and through which vibrates the Sound of the Verbum, and from which evolve the numberless hierarchies of intelligent Egos, of conscious as of semi-conscious, perceptive and apperceptive Beings, whose essence is spiritual Force, whose Substance is the Elements and whose Bodies (when needed) are the atoms.

Ibid., 629

  The fundamental idea which the student of Gupta Vidya must initially grasp is that we can never relate the One to the many unless we first recognize that the One is by its nature unconditioned, without attributes, and so without any relationship to anything else. There is an unbridgeable abyss separating that Unconditioned One or Parabrahman from the differentiated world of manifestation. We cannot, therefore, reduce the multiplicity of manifestation to a primordial or primeval unity simply by invoking TAT or Parabrahman – the absolute, attributeless One. Rather, we can at best, in the dawn of manvantaric manifestation, find that which mirrors the One within a primordial field. This then becomes what is sometimes called the Second One, or more commonly, the Unmanifested Logos. The Unmanifested Logos is not Parabrahman, but it does, in a transcendental way superior to all formulatable conceptions of relationship, mirror Parabrahman. Since Parabrahman is out of all relation to space and time, not only as they are ordinarily known to finite minds but also in reference to all possible limits known even to the most developed minds, the Unmanifested Logos may be treated as the First Cause.

  If Parabrahman were an infinite ocean consisting of centres of inconceivable potentiality, it is as if one of those centres became the Unmanifested Logos, mirroring and reflecting the absolutely inexhaustible nature of the whole in relation to all subsequent stages of manifestation subordinate to that Logos understood as a cause. Even here, however, it is crucial not to overlook the abyss between TAT, the unconditioned, attributeless Absolute, and the Unmanifested Logos. The degree to which an individual appreciates this truth of arcane metaphysics is the degree to which an individual is ready to apprehend a similar analogical relationship between the Unmanifested Logos and the manifested Logos. There is a conceptual abyss between these two, though it is neither so intense nor so vast, nor can it serve as a model whereby one may reduce the gap between the Unmanifested Logos and Parabrahman. Abstract though it is, the cognitive leap from the realm of the Unmanifested Logos to that of the manifested Logos is a less stern test of the power of metaphysical visualization than the "awesome mystery of Parabrahman ".

  Put in another way, the cornerstone of a real comprehension of the ancient science of spirituality is a proper grasp of the difference between what are called the Universal Unit and the manifested Unity. There is a fundamental difference between the supreme, Cosmic Monad – the Pythagorean Monas and the vast aggregated Host of all the monads that spring forth like rays from the original Logos. Though this cannot be understood outwardly, it must be made a stimulus to meditation. Between Non-Being and even the vastest concept of Being there is a fundamental difference. Only when a human being is able, through meditation, to create a degree of voidness in relation to all other beings, all subjects and all objects, can the real relationship between the Logos and the monads be grasped. It is necessary to negate all finite attributes, even of the subjective self, and come to something like a pure apprehension of "I am" that is consubstantial with, and corresponds to, the cosmic "I am" – the Logos in the cosmos. Having attained that preliminary threshold, one must go farther, entering into the realm of Non-Being without any possible reference to any possible concept, thought, form, event or object. This realm, beyond any differentiated field, is, of course, extremely difficult to describe. Mystics, poets and men of meditation have tried by analogy and correspondence to evoke in the minds of those who are drawn in this direction some sense of what it is possible to experience in the way of the ineffable in the realm of Non-Being.

  What it even means to speak of experience in this sense is almost impossible to convey. One cannot reduce zero to one, or one to zero. It is impossible to state the relationship between the One without a second, in the phrase of the Upanishads, to all that follows from it by multiplication and duplication, by permutation and combination, in the realm of numbers. There is a fundamental incommensurability between No Number and the world of numbers. When the Vedic sages spoke of the mysterious bond of Being in Non-Being, they did not refer to any ascertainable relationship. This truth must be apprehended, even in the early stages of the Path, for it is essential to the development of Manas through universalization. It is impossible for the mind to reach the plane of Mahat or the universal mind until it is willing to forego its addiction to finitizing tendencies. Put more mystically, one must learn to recognize the fundamental difference between the Soundless Sound, the unutterable unmanifested Sound or Logos, and that which is partially uttered or revealed and is sometimes characterized by the sacred syllable AUM. Without understanding this difference it is impossible to become a true apprentice to Adepts, Magicians and Initiates, and to commence the progressive transmutation of all life-atoms.

  Unless a person can to some extent understand this at a preliminary level, making it the basis of abstraction and meditation, he or she should leave Gupta Vidya alone. For, a person ill prepared for Gupta Vidya will be in constant danger of dragging the Teachings downward, concretizing them either through images of language or of perception. The same point was made by Nicholas of Cusa, in saying that no one would be entitled to have a meaningful conception of God who has not thoroughly mastered the idea of infinity. Human beings do, it is true, have a natural attraction to the unknown – one might even say to the Unknowable – and to the divine. But very few are actually willing to take the trouble to make a fundamental break in cognition with the world of visible things. This is why Socrates said in Phaedo that many bear the emblems, but the Initiates are few. Few are ready to enter into the invisible world in which they must progressively ascend towards the realm of the Divine Darkness, the realm of the noumenal Reality.

  If the manifested cosmos in its invisible form is difficult for ordinary human beings even to conceive, how much more difficult must it be for them to distinguish that invisible but manifested universe from the absolutely ideal universe of the unmanifest? Where the highest metaphysical discrimination requires the capacity to negate even Mulaprakriti if one would not do violence to the mystery of Parabrahman, most human beings are not even prepared to cognize, much less negate, those aspects of prakriti that lie immediately beyond the physical, visible plane. The visible solar system, for example, is nothing but a superficial appearance upon the waves of space. That space, however, is not a blank abstraction, but rather a sphere pervaded by the Vaishvanara fire on the invisible plane of objective consciousness. Though invisible to the naked eye, this magnetic solar fire is the pre-genetic basis in metaphysical substance of the objective solar world. The solar magnetic fire, which is omnipresent throughout the solar system, is itself an emanation from an even more ethereal plane – the realm of the radiant Hiranyagarbha or Golden Egg of the solar world. This, in turn, is a differentiation of the eternal germ on the plane of sutratman that exists in latency within the bosom of Mulaprakriti. The entire range of possibilities inherent in that eternal and all-potent germ gives way to the Golden Egg of the invisible astral realm, itself connected with the objective magnetic fire omnipresent within the solar system. All these gradations of the invisible world lie on what one might call the near side of the unmanifest, forming together the cosmic differentiations of Mulaprakriti. Mulaprakriti itself is nothing but a veil over Parabrahman. Meta-geometry provides a series of powerful aids in comprehending this fundamental distinction upon which so much depends in meditation, mysticism and magic. Meta-geometry is, in effect, an archetypal record of the Mysteries.

  From the very beginning of Aeons – in time and space in our Round and Globe – the Mysteries of Nature (at any rate, those which it is lawful for our races to know) were recorded by the pupils of those same now invisible "heavenly men", in geometrical figures and symbols. The keys thereto passed from one generation of "wise men" to the other. Some of the symbols, thus passed from the east to the west, were brought therefrom by Pythagoras, who was not the inventor of his famous "Triangle". The latter figure, along with the plane cube and circle, are more eloquent and scientific descriptions of the order of the evolution of the Universe, spiritual and psychic, as well as physical, than volumes of descriptive Cosmogonies and revealed "Geneses"

Ibid., 612

  The Pythagorean Triangle was derived from India. In the Pythagorean school it was the basis of understanding something fundamental about the elements of geometry, which are prior to both space and time. They are metaphysical principles, and to grasp them in their pure essence is to understand them in relation to metaphysical space. The first great idea in the series of meta-geometric glyphs is that of the mathematical point within the circle, representing the universal and absolute Deity. The point presupposes the boundless plane of existence, represented by the plane of the boundless circle, which gives rise out of its infinitude and incognizability to that which becomes the pre-genetic basis of all manifestation. That root is the Pythagorean Monas or Point, which emerges out of the Divine Darkness, initiates a series of transformations and then withdraws again into the bosom of the Divine Darkness from which it came. Simultaneously with the disappearance of the Point within the Circle of its origin, the Point is transformed into a line or diameter, and then the diameter becomes the cross. Such meta-geometric transformations are not intended to create a logical or empirical relationship between the unconditioned and the conditioned. Rather, they are meant to help individuals reach out in imagination, in consciousness and through meditation, to the unconditioned.

  Next in the series of meta-geometric glyphs comes the hierogram, or equilateral triangle, within the circle. Moving from the absolute unity of the Divine Essence, exemplified by the plane of the boundless circle and the point which represents the universal and absolute Deity, one comes to the Pythagorean Triangle.

  What it really meant was the triune co-equal Nature of the first differentiated Substance, or the con-substantiality of the (manifested) Spirit, matter and the Universe – their "Son", who proceeds from the Point (the real, esoteric LOGOS) or the Pythagorean MONAD. For the Greek Monas signifies "Unity" in its primary sense.

Ibid., 614

  This Triangle is the unmanifest production of the first Point within the Circle. The Point retires and merges back into the Circle after having emanated the first three points and connected them with lines, thus forming the first noumenal basis of the Second Triangle in the Manifested World.


  Once the primordial Point has radiated its triadic ray to form the equilateral triangle and then disappeared, the apex of that Triangle takes on a Logoic role in relation to the subsequent stages of manifestation.

  The Monad – only the emanation and reflection of the Point (Logos) in the phenomenal World – becomes, as the apex of the manifested equilateral triangle, the "Father". The left side or line is the Duad, the "Mother", regarded as the evil, counteracting principle (Plutarch, De Placitis Placitorum); the right side represents the Son ("his Mother's husband" in every Cosmogony, as one with the apex); at the basic line is the Universal plane of productive Nature, unifying on the phenomenal plane Father-Mother-Son, as these were unified in the apex, in the supersensuous World. By mystic transmutation they became the Quaternary – the triangle became the TETRAKTIS.


  Thus, it is the reflection of the original Point within the Circle which becomes, at a later stage, that which generates the Pythagorean Triangle, whose base line serves as the point of emanation for the countless hosts of gods, monads and atoms in the manifested worlds.

  These successive hierarchies of beings are represented within the Pythagorean Triangle by the Pythagorean Decad, the set of one, two, three and four points. It consists of ten points inscribed pyramid-like (from one to the last four) within its three lines, and it symbolizes the Universe in the famous Pythagorean Decad. The upper single dot is a Monad, and represents a Unit-Point, which is the Unity from whence all proceeds, and all is of the same essence with it. While the ten dots within the triangle represent the phenomenal world, the three sides of the equilateral triangle which enclose the pyramid of dots are the barriers of noumenal Matter, or Substance, that separate it from the world of Thought.

Ibid., 616

Within the Decad, the four points at the base indicate the connection between the Triangle and the world of solid geometry. The Triangle itself may be seen as a tetrahedron or pyramid, transformable into the cube and then into the other five Pythagorean or Platonic solids.

  The Decad within the Triangle is sometimes referred to as the Tetraktys, a mystical term having many meanings. These ten points contain the potential of all manifestation, providing the basis for everything that is possible in the vast multiplicity of the universe. Everything is prefigured within the ten points. The ten points inscribed within that "Pythagorean triangle" are worth all the theogonies and angelologies ever emanated from the theological brain. For he who interprets them – on their very face, and in the order given – will find in these seventeen points (the seven Mathematical Points hidden) the uninterrupted series of the genealogies from the first Heavenly to terrestrial man. And, as they give the order of Beings, so they reveal the order in which were evolved the Kosmos, our earth, and the primordial elements by which the latter was generated. Begotten in the invisible Depths, and in the womb of the same "Mother" as its fellow-globes – he who will master the mysteries of our Earth, will have mastered those of all others.

Ibid., 612, 613

  To understand the seven hidden points, one should attend to the six small triangles that can be formed within the Decad surrounding its central point. Each of these triangles has a central point of its own, and in addition, the midpoint at the base represents a seventh hidden point. The alchemical significance of these hidden points relates to the creation, through Deity Yoga, of a permanent divine vesture or Buddha-body. Sometimes misleadingly and loosely called the permanent astral, this vesture is an exact replica of the inmost causal body of the perfected man.

  Certainly, a conception so central to mystical training cannot have a merely mechanical or external interpretation. Thus, the seven hidden points within the Pythagorean Decad must, like all meta-geometric conceptions, be understood in relation to the concept of metaphysical depth. In addition to length, breadth and thickness, which are accessible in the realm of sensory perception, there is depth. Whatever the objective dimensions of an entity, they can yield no direct sense of the mystical meaning of depth. No merely visual representation, however subtle, can reveal the dimension of depth which has to do with Mulaprakriti, primordial root substance, the one element and force in the undifferentiated realm. Mulaprakriti is a paradigmatic plane upon which the Logoic constructions of meta-geometry arise. One cannot approach this realm through any kind of inductive process based upon phenomenal conceptions of length, breadth and thickness. Such a below-above approach to meta-geometry can yield only a useless collection of lifeless truisms. The real breadth, depth and points of meta-geometry are living abstractions that embody first on the unmanifest planes and then on the manifest the boundless potential of the Divine Darkness.

  The cosmic creativity represented in the glyphs of meta-geometry is inseparable from the Fohatic force of the cosmos, the vast reservoir of energy latent in Mulaprakriti. Meta-geometric diagrams are capable of endless duplication through transformation, translation and reflection along the axes of metaphysical space. Thus, each of the infinite points in space is capable of becoming and generating all that is displayed in the Pythagorean Triangle. This universally distributed potency is a key to understanding the process of manifestation itself. It must not be conceived in terms of staccato movements or static images, but rather in terms of a series of Fohatic unfoldments of pre-cosmic divine ideation within Mulaprakriti. Finally, at the third stage this brings about the synthesis of the seven Logoi, the seven Sons of Light, and then it becomes the basis of the vast manifestations of the forces at work in invisible and visible Nature. The natural sciences, which seek at once to understand these forces in relation to the phenomenal realm and to transcend them, will never succeed if they remain content in tracing out mere shadows or ghosts of supersensuous matter in motion. Limiting their study to the effects of the activity of that primordial field, they cannot understand very much about perpetual eternal motion. Cut off conceptually from the primordial field of undifferentiated energy, they cannot reveal anything about the infinitudes of latent energy within Parabrahman, which have no reference to any period of manifestation.

  Nevertheless, each individual human monad in its pilgrimage throughout the seven kingdoms of manifested Nature has an intimate connection to that primordial field. Each and every human being has a living link, through the seven Sons of Light, to the most potent of all realms – that of absolute negativeness. All the scintillas of manifested life emerging through the base line of the Pythagorean Triangle into active manifested existence are ensouled by the divine energies radiating from the noumenon of the seven states of undifferentiated cosmic substance. The divine Dhyani energies arise in that zero realm as the differentiated aspects of universal motion, the Great Breath.

  When Fohat is said to produce "Seven Laya Centres", it means that for formative or creative purposes, the GREAT LAW (Theists may call it God) stops, or rather modifies its perpetual motion on seven invisible points within the area of the manifested Universe. "The great Breath digs through Space seven holes into Laya to cause them to circumgyrate during Manvantara."

Ibid., 147

  The endless spinning of these seven invisible points in seemingly empty space is supremely potent in relation to the entire manifested realm. This hebdomadic activity of the One Logos makes possible, within any manifested system, the capacity to visualize its eventual disintegration and decay. At the same time, within such a manifested system, it is also the basis of the possibility of ultimate transcendence. Krishna, the Logos in the cosmos and the God in man, creates all these worlds through the mysterious power of maya, causing them to revolve upon the universal wheel of time. Krishna, as the divine Avatar, exists in all the invisible interstices and points hidden in the phenomenal world. Through devotion to Krishna, each pilgrim soul can find the breadth of heart and the depth of understanding needed to realize a relationship with the Logos within. Far beyond even the loftiest conceptions of modern thought, this is the true aim of Gupta Vidya, the hidden science, and the final goal of meta-geometrical insight, deep meditation and inward transformation.

Hermes, March 1986
by Raghavan Iyer