Pythagoras establishes Unity as the principle of all things and said that from this Unity sprang an indefinite Duality. The essence of this Unity, and the manner in which the Duality that emanated from it was finally brought back again, were the most profound mysteries of his doctrine; the subject was sacred to the faith of his disciples and the fundamental points were forbidden them to reveal.

Fabre d'Olivet

  The golden light of the candles blurred into incense-laden shadows which thickened in the corners of the small village church. The walls displayed the flickering images of saints whose bodies oozed dampness from the sodden earth outside. Their sad eyes gazed from the gloom, their faces boldly Hellenic with narrowed noses and arching brows. Only their pose lacked the distinctive fluidity of pagan heroes and sages. Muted thus, and obscured by the shadows and soot, they witnessed the re-enactment of an ancient ritual laden with arcane symbolism and mystery. An old priest with tangled grey hair knotted behind his decorated crown stood before a low square altar hewn from the native rock and bedecked with hierophanies displayed for the occasion. To his left and his right in front of him stood a bride and a groom, their bowed heads crowned with wreaths of white satin ribbon and flowers. The mended and altered gown of the young bride was darkened at the seams with the yellowing of a previous generation, but the fresh flowers of her crown reflected the soft glow of the candle. It shone in response to its companion which encircled the buoyant locks of the groom's unruly hair. Behind them stood a row of witnesses in a horizontal line of maids and men. They created a threshold separating the actors of the ritual mystery and the gathered crowd, which stood in dusky silence, transfixed by the illuminated scene.

  In a small darkened dome of the church, the Angel Gabriel looked down upon them. His practised eyes, gazing from the orbs of a peeling fresco, traced the lines of the pattern below him. The old priest was the apex of a triangle that stood before the square. The hierophanies, arranged in a mystic triad upon the altar, marked its prototype and the line of witnesses formed its base. The bride and groom stood at the left and right angles of the triangle, and a radiant satin ribbon connecting their crowns strengthened the suggestion of their union. As the apex of the triad, the old priest acted as a solitary liaison between the altar and the couple. Only he understood the use of the sacred objects and the names that would enliven their power. Only he could make the gestures that would transmit their spiritually unified essence in the unification of the man and woman before him. Old and grizzled as he was, his heart was filled with the sanctity of this responsibility, and his gnarled hands imparted faithfully the blessing from on high. Smiling, Angel Gabriel saw the hidden current of light flow through the humble priest and unite the simple pair. He knew that from their merger another triad would be born, another division and union in an endless chain of such, and he laughed as he withdrew. The crowds below sighed and, at the completion of the ritual, mingled and mused upon former weddings and those yet to come. They wept in recalling and comparing notes on dowries and bride-wealth. They gossiped and speculated upon the prospects of the newly-weds and basked unconsciously in the luminousness of the magic that had just taken place.

 Simple villagers that they were, how could they know that millennia before their time the ancients, perhaps even some of their own Greek ancestors, had openly recognized this magic in an oath taken by disciples of Pythagoras. Being unfamiliar with such mysteries and sensing their presence only through an intuitive understanding of recurring patterns in nature, they did not realize the significance of the triad and the square. They glimpsed the beauty of spiritual transmission through union but could not grasp the immensity of the pattern nor its noumenal source. If in a dream an ancient ancestor came to them and spoke that sacred oath, their soul's memory might be aroused, but would they recognize the symbol of the Tetraktys? Would they know that it had been represented in their humble village church?

By Him who gave to our Soul the Tetraktys
Which hath the fountain and root
Of ever-springing Nature.

  The real significance of the Tetraktys is suggested in the portion of the Pythagorean Oath which describes it as containing "the fountain and root of ever-springing Nature", It is not merely symbolic of static relations, such as might be imagined to exist between priest and bride and groom, but enshrines the cosmogonical movement of life "evolving out of primal unity, the harmonized structure of the whole". In this way it is a fountain of ever-flowing life. It is also the measure of all things. The One becomes the many without losing its essential Unity, expressed in a bond of proportion running through manifestation. Porphyry tells us how followers of Pythagoras swore by the Tetraktys given by their Teacher as a symbol applicable to the solution of problems in nature. They believed that the nature of all things could be grasped through the decad as expressed in the symbol of the Tetraktys. They asserted that it would be impossible for the orderly and universal distribution of things to subsist without it. Resulting from an infinite series of quaternaries was a world geometrically, harmonically and arithmetically arranged, containing the entire range of number, magnitude and form. The Pythagoreans thus used an Oath with a key which applied to the assimilation of all things into number.

  One of the epithets used to describe the Tetraktys was 'key-bearer of Nature'. As the wise Platonist Thomas Taylor observed: "It is a God after another manner than the Triad, because in the triad the first perfect is beheld, but in the tetrad all mundane natures are comprehended according to the causality principle. From its all-comprehending nature likewise, it is a manifold, or rather, every divinity. As, too, it causally contains all mundane natures, it may very properly be called the fountain of natural effects. Because likewise it opens and shuts the recesses of generation, it is denominated, as the anonymous author observes, the key-bearer of Nature, as is also the mother of the Gods, who is represented with a key." Opening and shutting the recesses of generation, the Tetraktys stands like the altar before the bridal couple, containing all the potential effects which will manifest partially and idiosyncratically in the microcosmic process of meiosis resulting from their union.

 It is said that the One, by Itself, does not 'exist'. Only when It is united with the Monad and duad is Being produced. The One is No-number. It is the primary, undifferentiated soul of the universe, and numbers arise from it by a process of 'separating out', not as a collection of units built up by addition, but as minor souls, each possessing a distinct nature with certain mystical properties. The interblending of these distinct natures produces infinitely complex harmonies distinguished by the Greeks as replicating tetrachords consisting of three intervals and four sounds. They believed that the multiplex expression of these conveyed the music of stars and planets, and ultimately every expression of the replicating duad. The Pythagorean School, pursuing lines of thought akin to the teachings of Orpheus, considered the problem of the One and the many in terms of 'the Fall' of the human soul from the One. In myth it was said that the reign of Aphrodite, the Age of Love, was a state of bliss whose end was heralded by the Great Oath of the gods (the Tetraktys). Putting "trust in strife", certain daemons were then banished by the gods and caused to mix, as a cross within a circle, the two streams of love and strife.

  Love and strife – the Higher in the lower. Surely this is what awaits the rustic bride and groom. They bask for a moment beneath the reign of Aphrodite, whilst the greater part of their life involves the struggle to keep body and soul together and in harmony. But in the sacred moment of their union, the united ray of their Higher Self illuminates their vestures and empowers them with the ultimate creativity of their inner nature. The primary maxim of the Delphic Oracle was "Know Thyself", and Iamblichus tells us that the most difficult question posed by Pythagoras to his pupils required them to understand the Delphic Oracle as the Tetraktys. In terms of 'the Fall', one can grasp the idea of the Self enveloped in the strife of the lower vestures, but the Self that is to be 'known' is the Oath or Word itself, which initiates the strife inherent in the duad and its endless progeny. The duad doubled is four, or the tetrad, which when doubled or unfolded, is the hebdomad. Thus four retorted into itself results in the first cube, which is a fertile number. Philo Judaeus pointed out that four is the virgin number related to the sacred Tetraktys, whereas the seventh power of any number is a square and a cube. This potential fertility is expressed again in terms of 'the Son' of the immaculate Celestial Virgin, who, born on earth, becomes humanity. The triad becomes the Tetraktys, the Perfect Square and six (seven)-faced cube on earth. Though tracing this unfoldment from the plane of the abstract to the particular is difficult, students of Pythagoras began by identifying two basic quaternaries: one through addition (of the first four numbers) and a second through multiplication (of even and odd numbers starting from Unity). Odd numbers, symbolizing the limit and formal principle of universe, were set along one side of a triangle (3 – 9 – 27), whilst even numbers, or those which represented the tendency to divide according to their own nature, were arranged along the other side (2 – 4 – 8). In this way, by virtue of the numbers from this Tetraktys, growth proceeds from the point to the line, to the surface and the solid cube. It is these numbers which, in the Timaeus, Plato identifies with the human soul.

  There is a third Tetraktys which takes its point from the second and has the property of constituting any curved or plane magnitude through point, line, surface and solid. The fourth Tetraktys is comprised of the elements – fire, air, water and earth; the fifth is the pyramid, octahedron, icosahedron and cube; whilst the sixth involves the seed (point), growth (line), the quality of width (surface) and that of thickness (solid). According to Theon of Smyrna, the seventh Tetraktys is composed of man, family, village and city; the eighth of thought, science, opinion and feeling (parallel to Plato's Divided Line); the ninth of the four faculties of judgement; the tenth of the four seasons; and the eleventh of the four ages of man. From above below, each of these descending levels of the Tetraktys unfolds through odd and even (male and female) pairs in a process of multiplication that is ever true to the principles laid down by the first Tetraktys.

 As Creator, the Tetraktys is the divine numerical series of one to four. In this sense numbers are gods. "But", asked Hierocles, "how does 'God' come to be four?" We are told that Unity, the Absolute One, possesses within it the potential aspect of Absolute Motion which, radiating as the Great Breath, manifests the duad, the doubling of Unity. This, accompanied by Infinite Space-Matter, comprises three, which is the first number having a beginning, middle and end, thus expressing multitude. From this springs Fohat, the number four which is sacred to Hermes and to the Oath of the gods. This four is expressed in the four syllables (one hidden) of the AUM. It is said that when the Ain-Soph manifested Itself in the First Logos, the latter uttered the first word of his name, a syllable of four letters. This was followed by second, third and fourth syllables which intoned the number of Deity manifested. One added to two, added to three, added to four, equals ten or the figured representation of ten as a triangular number. Four and ten were the numbers of divinities to the Pythagoreans. In The Sale of Philosophers Lucian represents Pythagoras as asking a prospective buyer to count. When he had counted to four, the philosopher interrupted, "Lo! what thou thinkest four is ten, and a perfect triangle, and our Oath." Perhaps it is for this reason that the triangular-shaped δέλτα. Δ is the fourth letter of the Greek alphabet, for the delta represents the issuing forth of the river of life which proceeds from the Monad till it arrives at the divine Tetrad, the mother of all things; the boundary is the sacred Decad.

 In Plato's dialogue of his name, Timaeus, a Pythagorean from the Italian city of Locri, speaks of the Tetraktys as a double four (an odd and even series of numbers) forming the cosmic psyche. These were produced by the Dyad (identified with Rhea or Isis) or the flow of the universe involving matter in a constant state of flux. It was held that the Tetraktys "completed the process of fluxion whereby physical objects are produced from points, lines, surfaces and solids". In this process the Dyad produces even numbers by multiplication and odd numbers by functions of limit, which acts to stop, equalize and stabilize the propensity of the Dyad to multiply. Pythagoras, in placing even and odd sequences on either side of the Tetraktys, revealed his awareness of this necessary interaction even in the construction of the World Soul.

  Between two square numbers there is one mean proportional number. This odd third number acts as the 'lock' or binder between what may be called the building blocks of the universe. This role cannot be played by even numbers which, when they are divided, are empty in the centre and therefore weak. Thus, in the building of the square, the odd number is always master. It moves beyond the Dyad to the three and the four and, eventually, the cube. The Dyad contains the One from which issues the Three (the Three-in-One). Put in a slightly different way, "Matter is the vehicle for the manifestation of soul on this plane of existence, and soul is the vehicle on a higher plane for the manifestation of spirit, and these three are a trinity synthesized by Life which pervades them all," From Parabrahm the Three-in-One issues forth. It is the Tetraktys (the Three and One) from which radiates the One in many – the Dhyani Buddhas. It is the Four-Faced Brahma, the Chaturmukha (the perfect cube) "forming itself within and from the infinite circle". Brahma is thus Hiranyagarbha, Hari and Shankara, or the Three Hypostases of the manifesting Spirit of the Supreme Spirit – the one plus three which equals four. The Greeks identified this Tetrad as the first manifest deity, and Orpheus said that all of the intellectual orders of gods were "astonished on surveying this deity unfold himself into light from mystic and ineffable silence".

  The one macrocosm is eternally hidden in the Absolute. The entire universe is a "microcosmic projection of that one and only macrocosmos". Every microcosmic reflection follows its parent – projecting itself and becoming the macrocosmos to its offspring. The Ray from the Concealed Deity falls into primordial cosmic matter, resulting in the Divine Androgyne or First Logos, which, projecting further, becomes the Second Logos or Tetraktys. From Parabrahm, Mulaprakriti emerges as the basis of objective evolution and cosmogenesis. Projecting forth, the First Spiritual Logos provides the basis of the subjective side of manifest being and the source of all individual consciousness. This highest Logos is expressed through Force, which is transformed into the energy of the supra-conscious Logoic thought, which is infused into objectivization. This Primal Impress defines the laws of matter, which are synthesized in the Second Logos or Tetraktys. In its universal form and idea the three become four, but still the Tetraktys is the formless square giving forth only the idea of universal order.

 In this one can see the results of the first creation depicted in the Linga Purana as Mahat-Tattwa, in that it is primordial self-evolution of that which had to become (Divine Mind – the Spirit of the Universal Soul or Maha Buddhi). The intelligible world proceeds out of the Divine Mind as the Tetraktys reflects upon its own essence and on its beginning. Once one, twice two, and a tetrad arises. At its top is the essence of Light which illuminates the world of Deity without burning. Its base becomes the square platform of a pyramid, rooted in the world. Looked at once again, this mystery is that of the double Tetraktys: the Higher and the lower. The Higher or Macroprosopus is the Absolute Perfect Square within the circle 'Pass-Not'. The lower Microprosopus is the manifest Logos who passes through the circle and becomes the triangle in the square which is sevenfold – the square which is a cube, which unfolds and becomes the cross of flesh.

  The Higher Tetraktys, whilst containing the noumenon of the potential square, is yet in essence the Triad out of which the Tetrad emerges. The Secret Doctrine describes how the point that appears in the circle emanates the first three points, connects them with lines and thus forms the noumenal basis of the second Triad of the manifest world before retiring into the silent depths of the circle. Thus the one contains three which, together, possess the potential quaternary. The emanation from the three points is the Monadic reflection in the phenomenal world of its invisible Logoic parent. It is this Monad which then becomes the 'parent' apex of the lower triad, the mother and son composing its lower angles. At the baseline they are unified on the universal plane of phenomenal, productive nature, just as they were unified in essence at the apex in the causal realm. By the same mystic transmutation which is mirrored in the marriage of the bride and groom, they – triune – become the Tetraktys.

  Plato called the Higher Triad 'Intellectual' and compared it to its lower intelligible counterpart. The Tetraktys, it is said "subsists at the extremity of the intelligible triad. . . . And between these two triads (the double triangle) . . . another order of gods exists which partakes of both extremes". The key idea here is that the Tetraktys 'subsists', which is to say, 'is kept in life', at the apex of the lower triad as the Monadic soul of mankind expressed as the One in the many. In its synthesis it bears the potential qualities of the Dhyani Buddhas or gods of "another order" and is the Higher Tetraktys. Expressed in the phenomenal world, it becomes the Seven Dhyanis out of whom issue the scintillas or souls in the form of Monads, atoms and gods.

  The Ray of the Higher Triad falls, and from its point a lower triad emanates. But even as this is resulting in phenomenal expressions, the lower triad has become inverted, pointing away from the triangle above. This is the downward-pointing triad of Vishnu, who is called Bhutesa, 'Lord of the Elements and All Things', and Viswarupa, 'Universal Substance or Soul'. This second creation proceeds along the triple aspect of ahankara, 'I-am-ness', which first issues from Mahat. This ahankara is first pure, then passionate and finally rudimental. When this last occurs, the second hierarchy of Dhyan Chohans appears – the Seven Rishis who are the origin of form. The down ward-pointing triad thus contains the reflected point of the Logoic Ray and so it is shown as overlapping and being overlapped by the upward-pointing triangle which contains the essence of the same Logoic point. This is the symbol of the interlaced triangles called the six-pointed star, which powerfully illustrates the dynamic relationship between Vishnu and Shiva, or Hari and Shankara, within the golden circle of Hiranyagarbha. In the centre of the upward- and downward-pointing triads is the six (hexagon) and one (point) or seven, which is man. One of the Masters of Wisdom has said that "The two interlacing triangles are the Buddhangams of creation. They contain the 'squaring of the circle', the 'philosophical stone', the great problems of Life and Death, and the mystery of evil."

  The Tetraktys is thus the three made four and the four made three. Put very simply, the upper Triad emanates the Quaternary (symbolizing by itself the sexless 'Heavenly Man') which becomes a septenary by emanating from itself the three principles of the lower nature, thus forming the Decad or total Unity of the universe. One can see this as separate units of 3, 4 and 3, but in trying to understand the Tetraktys, it is important to remember that the Triad of the Inner Man is the Three Hypostases of Atman, and Its contact with Nature and man is the Fourth, which makes it a Tetraktys or the Highest Self. The upper and lower triads are not separate, but their very existence on the heavenly and terrestrial planes is made possible by the connecting Monadic 'link', which makes in turn a quaternary out of either and carries forth the principle of Unity into generation. This is connected with the squaring of the circle, for this greatest of all mysteries takes place at the edge of the 'Ring Pass-Not' as it does within the Golden Egg of Brahma and within every egg made fertile on the worldly plane. The key to understanding the squaring of the circle is concealed in the androgynous nature of the Logos, whose Ray becomes the Tetraktys in man. He who is fully informed by this is an Adept, a Master-magician incarnate.

  Pythagoras, knowing these mysteries and being such an Adept, attempted to act as a Demiurge, informing those around him who desired to open their minds and hearts to the Higher. That this is a difficult task was borne out by the hostility his efforts aroused in many. But he was wise in the ways of both worlds, and he united in a marriage which produced an offspring, who later (at the death of her father), like a ray projected from the familial triad, went out into the world safeguarding the precious truths that had been entrusted to her. Brave and true, Theona was the indispensable keeper of the flame and embodiment of the Sacred Oath. The sweet bride standing in the dimly lit church does not possess her wisdom and courage, but she is conscious of its spiritual presence hovering over her, symbolically emanating from the altar through the priest and uniting her to the rustic lad by her side. In her simple fashion, she dreams that her son will be a prince amongst men, a gifted and gentle person, and maybe one through whom the Demiurgos speaks in noble accents.

The Divine Tetraktys was esteemed
By wise men who beheld in dreams
Its emanation from the Three-in-One.
And since the Inner Man of all
Basks in Its Monadic light,
Even the lesser dream bears
The impress of its sacred projection.