THEOSOPHY, Vol. 45, No. 1, November, 1956
(Pages 22-29; Size: 23K)

THE SYMBOLISM OF NUMBERS(1)

II

[Part 2 of a 4-part series]

PYTHAGORAS esteemed the Deity (the Logos) to be the centre of unity and "Source of Harmony." We say this Deity was the Logos, not the MONAD that dwelleth in Solitude and Silence, because Pythagoras taught that UNITY being indivisible is no number. And this is also why it was required of the candidate, who applied for admittance into his school, that he should have already studied as a preliminary step, the Sciences of Arithmetic, Astronomy, Geometry and Music, held as the four divisions of Mathematics. Again, this explains why the Pythagoreans asserted that the doctrine of Numbers -- the chief of all in Esotericism -- had been revealed to man by the celestial deities; that the world has been called forth out of Chaos by Sound or Harmony, and constructed according to the principles of musical proportion; that the seven planets which rule the destiny of mortals have a harmonious motion "and intervals corresponding to musical diastemes, rendering various sounds, so perfectly consonant, that they produce the sweetest melody, which is inaudible to us, only by reason of the greatness of the sound, which our ears are incapable of receiving."

In the Pythagorean Theogony the hierarchies of the heavenly Host and Gods were numbered and expressed numerically. Pythagoras had studied Esoteric Science in India; therefore we find his pupils saying "The monad (the manifested one) is the principle of all things. From the Monad and the indeterminate duad (Chaos), numbers; from numbers, Points; from points, Lines; from lines, Superficies; from superficies, Solids; from these, solid Bodies, whose elements are four -- Fire, Water, Air, Earth; of all which transmuted (correlated), and totally changed, the world consists."

The "great Extreme" of Confucius produces "two figures." These "two" produce in their turn "the four images"; these again "the eight symbols." It is complained that though the Confucianists see in them "Heaven, Earth and man in miniature," we can see in them anything we like. No doubt, and so it is with regard to many symbols, especially in those of the latest religions. But they who know something of Occult numerals, see in these "figures" the symbol, however rude, of a harmonious progressive Evolution of Kosmos and its beings, both the Heavenly and the Terrestrial. And any one who has studied the numerical evolution in the primeval cosmogony of Pythagoras (a contemporary of Confucius) can never fail to find in his Triad, Tetractis and Decad emerging from the ONE and solitary Monad, the same idea. Confucius is laughed at by his Christian biographer for "talking of divination" before and after this passage, and is represented as saying: "The eight symbols determine good and ill fortune, and these lead to great deeds. There are no imitable images greater than heaven and earth. There are no changes greater than the four seasons (meaning North, South, East and West, et seq.). There are no suspended images brighter than the sun and moon. In preparing things for use, there is none greater than the sage. In determining good and ill-luck there is nothing greater than the divining straws and the tortoise."

Therefore, the "divining straws" and the "tortoise," the "symbolic sets of lines," and the great sage who looks at them as they become one and two, and two become four, and four become eight, and the other sets "three and six," are laughed to scorn, only because his wise symbols are misunderstood.

Confucius, one of the greatest sages of the ancient world, believed in ancient magic, and practised it himself "if we take for granted the statements of Kin-yu," and "he praised it to the skies in Yi-kin," we are told by his reverend critic. Nevertheless, even in his age -- i.e., 600 B.C., Confucius and his school taught the sphericity of the Earth and even the heliocentric system; while, at about thrice 600 years after the Chinese philosopher, the Popes of Rome threatened and even burnt "heretics" for asserting the same. He is laughed at for speaking of the "Sacred Tortoise." No unprejudiced person can see any great difference between a tortoise and a lamb as candidates for sacredness, as both are symbols and no more. The Ox, the Eagle, the Lion, and occasionally the Dove, are "the sacred animals" of the Western Bible, the first three being found grouped round the Evangelists; and the fourth (the human face) is a Seraph, i.e., a fiery serpent, the Gnostic Agathodæmon probably. As explained, the "sacred animals" and the Flames or "Sparks" within the "Holy Four" refer to the prototypes of all that is found in the Universe in the Divine Thought, in the ROOT, which is the perfect cube, or the foundation of the Kosmos collectively and individually. They have all an occult reference to primordial Cosmic forms and its first concretions, work, and evolution.

Without throwing any discredit upon time-honoured beliefs, in whatever direction, we are forced to draw a marked line between blind faith, evolved by theologies, and knowledge due to the independent researches of long generations of adepts; between, in short, faith and philosophy. There have been -- in all ages -- undeniably learned and good men who, having been reared in sectarian beliefs, died in their crystallized convictions. For Protestants, the garden of Eden is the primeval point of departure in the drama of Humanity, and the solemn tragedy on the summit of Calvary, the prelude to the hoped-for Millennium. For Roman Catholics, Satan is at the foundation of Kosmos, Christ in its centre, and Antichrist at its apex. For both, the Hierarchy of Being begins and ends within the narrow frames of their respective theologies: one self-created personal God and an Empyrean ringing with the hallelujahs of created angels; the rest, false gods, and fiends.

Theophilosophy proceeds on broader lines. From the very beginning of Æons -- 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." 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.

Whatever ignorance, pride or fanaticism may suggest to the contrary, Esoteric Cosmology can be shown inseparably connected with both philosophy and modern science. The gods of the ancients the monads -- from Pythagoras down to Leibnitz -- and the atoms of the present materialistic schools (as borrowed by them from the theories of the old Greek Atomists) are only a compound unit, or a graduated unity like the human frame, which begins with body and ends with spirit. In the occult sciences they can be studied separately, but never mastered unless viewed in their mutual correlations during their life-cycle, and as a Universal Unity during Pralayas.

La Pluche shows sincerity, but gives a poor idea of his philosophical capacities when declaring his personal views on the Monad or the Mathematical Point. "A point," he says, "is enough to put all the schools in the world in a combustion. But what need has man to know that point, since the creation of such a small being is beyond his power? A fortiori, philosophy acts against probability when, from that point which absorbs and disconcerts all her meditations, she presumes to pass on to the generation of the world."

Philosophy, however, could never have formed its conception of a logical, universal, and absolute Deity if it had no Mathematical Point within the Circle to base its speculations upon. It is only the manifested Point, lost to our senses after its pregenetic appearance in the infinitude and incognizability of the Circle, that made a reconciliation between philosophy and theology possible -- on condition that the latter should abandon its crude materialistic dogmas. And it is because it has so unwisely rejected the Pythagorean Monad and geometrical figures, that Christian theology has evolved its self-created human and personal God, the monstrous Head whence flow in two streams the dogmas of Salvation and Damnation. This is so true that even those clergymen who would be philosophers and who were Masons, have, in their arbitrary interpretations, fathered upon the ancient sages the queer idea that "the Monad represented (with them) the throne of the Omnipresent Deity, placed in the centre of the Empyrean to indicate T.G.A.O.T.U." -- read "the Great Architect of the Universe." A curious explanation this, more Masonic than strictly Pythagorean.

Nor did the "hierogram within a Circle, or equilateral Triangle," ever mean "the exemplification of the unity of the divine Essence"; for this was exemplified by the plane of the boundless Circle. 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. Those unable to seize the difference between the monad -- the Universal Unit -- and the Monads of 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. It is needless to remind the educated reader of Kant's Thesis to demonstrate his second Antinomy. Those who have read and understood it will see clearly the line we draw between the absolutely Ideal Universe and the invisible though manifested Kosmos. Our Gods and Monads are not the Elements of extension itself, but only those of the invisible reality which is the basis of the manifested Kosmos. Neither esoteric philosophy, nor Kant nor Liebnitz would ever admit that extension can be composed of simple or unextended parts. But theologian-philosophers will not grasp this. The Circle and the Point, which latter retires into and merges with the former, 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, have ever been an insuperable obstacle to theological flights into dogmatic Empyreans. On the authority of this Archaic Symbol, a male, personal god, the Creator and Father of all, becomes a third-rate emanation, the Sephiroth standing fourth in descent, and on the left hand of En-Soph. Hence, the Monad is degraded into a Vehicle -- a "throne"!

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; 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.

This transcendental application of geometry to Cosmic and divine theogony -- the Alpha and the Omega of mystical conception -- became dwarfed after Pythagoras by Aristotle. By omitting the Point and the Circle, and taking no account of the apex, he reduced the metaphysical value of the idea, and thus limited the doctrine of magnitude to a simple TRIAD -- the line, the surface, and the body. His modern heirs, who play at Idealism, have interpreted these three figures as Space, Force, and Matter -- "the potencies of an interacting Unity."

But to the average physicist, as remarked by a Kabalist, "Space, Force, Matter, are, what signs in algebra are to the mathematician, merely conventional symbols"; or "Force as force, and Matter as matter, are absolutely unknowable as is the assumed empty space in which they are held to interact." As symbols representing abstractions, "the physicist bases reasoned hypotheses of the origin of things ... and sees three needs in what he terms creation: (a) a place wherein to create; (b) a medium by which to create; (c) a material from which to create. And in giving a logical expression to this hypothesis through the terms space, force, matter, he believes he has proved the existence of that which each of these represents as he conceives it to be."

The physicist who regards Space merely as a representation of our mind, or extension unrelated to things in it, which Locke defined as capable of neither resistance nor motion; the paradoxical materialist, who would have a void there, where he can see no matter, would reject with the utmost contempt the proposition that "Space is a substantial though (apparently) an absolutely unknowable living Entity." Such is, nevertheless, the Kabalistic teaching, and it is that of Archaic philosophy. Space is the real world, while our world is an artificial one. It is the One Unity throughout its infinitude: in its bottomless depths as on its illusive surface; a surface studded with countless phenomenal Universes, systems and mirage-like worlds. Nevertheless, to the Eastern Occultist, who is an objective Idealist at the bottom, in the real world, which is a Unity of Forces, there is "a connection of all matter in the plenum," as Leibnitz would say. This is symbolized in the Pythagorean Triangle.

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. "Pythagoras considered a point to correspond in proportion to unity; a line to 2; a superficies to 3; a solid to 4; and he defined a point as a Monad having position, and the beginning of all things; a line was thought to correspond with duality, because it was produced by the first motion from indivisible nature, and formed the junction of two points. A superficies was compared to the number three because it is the first of all causes that are found in figures; for a circle, which is the principle of all round figures, comprises a triad, in centre -- space -- circumference. But a triangle, which is the first of all rectilineal figures, is included in a ternary, and receives its form according to that number; and was considered by the Pythagoreans to be the creator of all sublunary things. The four points at the base of the Pythagorean triangle correspond with a solid or cube, which combines the principles of length, breadth, and thickness, for no solid can have less than four extreme boundary points."

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 abstractions -- laid the origin of the differentiated Cosmic matter in the basic horizontal line of the Triangle. Thus the latter became the earliest of geometrical figures. The author of "New Aspects of Life" and of the Kabalistic Mysteries -- objects to the objectivization, so to speak, of the Pythagorean conception and use of the equilateral triangle, and calls it a misnomer. His argument that a solid equilateral body -- "one whose base, and each of its sides, form equal triangles -- must have four co-equal sides or surfaces, while a triangular plane will as necessarily possess five," demonstrates on the contrary the grandeur of the conception in all its esoteric application to the idea of the pre-genesis of Kosmos. Granted, that an ideal triangle, depicted by mathematical, imaginary lines "can have no sides at all, being simply a phantom of the mind (if sides be imputed to which, they must be the sides of the object it constructively represents)." But in such case most of the scientific hypotheses are no better than "phantoms of the mind"; they are unverifiable, except on inference, and have been adopted merely to answer scientific necessities. Furthermore, the ideal triangle -- "as the abstract idea of a triangular body, and, therefore, as the type of an abstract idea" -- accomplished and carried out to perfection the double symbolism intended. As an emblem applicable to the objective idea, the simple triangle became a solid. When repeated in stone on the four cardinal points, it assumed the shape of the Pyramid -- the symbol of the phenomenal merging into the noumenal Universe of thought -- at the apex of the four triangles; and, as an "imaginary figure constructed of three mathematical lines," it symbolized the subjective spheres -- those lines "enclosing a mathematical space -- which is equal to nothing enclosing nothing." Because, to the senses and the untrained consciousness of profane and scientist, everything beyond the line of differentiated matter -- i.e., outside of, and beyond the realm of even the most spiritual substance -- has to remain for ever equal to nothing. It is the AIN-SOPH -- the NO-THING.

Yet these "phantoms of the mind" are in truth no greater abstractions than the abstract ideas in general upon evolution and physical development -- e.g., Gravity, Matter, Force, etc. -- on which the exact sciences are based. Our most eminent chemists and physicists are earnestly pursuing the not hopeless attempt of finally tracing to its hiding place the protyle, or the basic line of the Pythagorean triangle. The latter is, as said, the grandest conception imaginable, as it symbolizes both the ideal and the visible universes. For if "the possible unit is only a possibility as an actuality of nature, as an individual of any kind," and as every individual natural object is capable of division, and by division loses its unity, or ceases to be a unit, it is so only in the realm of exact sciences in a world as deceptive as it is illusive. In the realm of the Esoteric sciences the unit divided ad infinitum, instead of losing its unity, approaches with every division the planes of the only eternal REALITY. The eye of the SEER can follow and behold it in all its pregenetic glory. This same idea of the reality of the subjective, and the unreality of the objective universe, is found at the bottom of the Pythagorean and Platonic teachings -- limited to the Elect alone; for Porphyry, speaking of the Monad and the Duad, says that the former only was considered substantial and real, "that most simple Being, the cause of all unity and the measure of all things."

(To be continued)


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THE SYMBOLISM OF NUMBERS
III
[Part 3 of a 4-part series]

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