THEOSOPHY, Vol. 44, No. 12, October, 1956
(Pages 551-559; Size: 25K)



[Part 1 of a 4-part series]

THERE is a canon of interpretation which should guide us in our examination of every philosophical opinion: "The human mind has, under the necessary operation of its own laws, been compelled to entertain the same fundamental ideas, and the human heart to cherish the same feelings in all ages." It is certain that Pythagoras awakened the deepest intellectual sympathy of his age, and that his doctrines exerted a powerful influence upon the mind of Plato. His cardinal idea was that there existed a permanent principle of unity beneath the forms, changes, and other phenomena of the universe. Aristotle asserted that he taught that "numbers are the first principles of all entities." Ritter has expressed the opinion that the formula of Pythagoras should be taken symbolically, which is doubtless correct.

The key to the Pythagorean dogmas is the general formula of unity in multiplicity, the one evolving the many and pervading the many. This is the ancient doctrine of emanation in few words. This, as we can see by the following quotation, is purely Hindu and Brahmanical: "When the dissolution -- Pralaya -- had arrived at its term, the great Being -- Para-Atma or Para-Purusha -- the Lord existing through himself, out of whom and through whom all things were, and are and will be, resolved to emanate from his own substance the various creatures" (Manava-Dhama-Sastra).

When we speak of the Deity and make it identical, hence coeval, with nature, the eternal and uncreate nature is meant, and not your aggregate of flitting shadows and finite unrealities. We leave it to the hymn-makers to call the visible sky or heaven, God's Throne, and our earth of mud His footstool. Our DEITY is neither in a paradise, nor in a particular tree, building, or mountain: it is everywhere, in every atom of the visible as of the invisible Cosmos, in, over, and around every invisible atom and divisible molecule; for IT is the mysterious power of evolution and involution, the omnipresent, omnipotent, and even omniscient potentiality.

Read the superb Kabalistic poem by Solomon Ben Jehudah Gabirol, in the Kether-Malckut, and you will understand: "Thou art one, the root of all numbers, but not as an element of numeration; for unity admits not of multiplication, change, or form. Thou art one, and in the secret of Thy unity the wisest of men are lost, because they know it not. Thou art one, and Thy unity is never diminished, never extended, and cannot be changed. Thou art one, and no thought of mine can fix for Thee a limit, or define Thee. Thou ART, but not as one existent, for the understanding and vision of mortals cannot attain to Thy existence, nor determine for Thee the where, the how and the why," etc., etc. In short, our Deity is the eternal, incessantly evolving, not creating, builder of the universe; that universe itself unfolding out of its own essence, not being made. It is a sphere, without circumference, in its symbolism, which has but one ever-acting attribute embracing all other existing or thinkable attributes -- ITSELF. It is the one law, giving the impulse to manifested, eternal, and immutable laws, within that never-manifesting, because absolute LAW, which in its manifesting periods is The ever-Becoming.

Were we to exclude the Omnipresent Principle from one single mathematical point of the universe, or from a particle of matter occupying any conceivable space, could we still regard it as infinite?

He who has studied the speculations of Pythagoras on the Monad, which, after emanating the Duad, retires into silence and darkness, and thus creates the Triad, can realize whence came the Philosophy of the great Samian Sage, and after him that of Socrates and Plato. The mystic Decad (1+2+3+4=10) is a way of expressing this idea. The One is God; the Two, Matter; the Three, combining Monad and Duad and partaking of the nature of both, is the phenomenal World; the Tetrad, or form of perfection, expresses the emptiness of all; and the Decad, or sum of all, involves the entire Kosmos.

In the Epinomis is fully stated the doctrine of the Pythagorean numbers in relation to created things. As a true Platonist, its author maintains that wisdom can only be attained by a thorough inquiry into the occult nature of the creation; it alone assures us an existence of bliss after death. The immortality of the soul is greatly speculated upon in this treatise; but its author adds that we can attain to this knowledge only through a complete comprehension of the numbers; for the man, unable to distinguish the straight line from a curved one will never have wisdom enough to secure a mathematical demonstration of the invisible, i.e., we must assure ourselves of the objective existence of our soul (astral body) before we learn that we are in possession of a divine and immortal spirit. Iamblichus says the same thing; adding, moreover, that it is a secret belonging to the highest initiation. The Divine Power, he says, always felt indignant with those "who rendered manifest the composition of the icostagonus," viz., who delivered the method of inscribing in a sphere the dodecahedron.

According to Plato, the Universe is built by "the first begotten" on the geometrical figure of the Dodecahedron. The four-fold Dodecahedron on the model of which the universe is said by Plato to have been built by the manifested Logos, synthesized by the unmanifested First-Born, yields geometrically the key to Cosmogony and its microcosmic reflection -- our Earth.

The idea that "numbers" possessing the greatest virtue, produce always what is good and never what is evil, refers to justice, equanimity of temper, and everything that is harmonious. "The numerals of Pythagoras," says Porphyry, "were hieroglyphical symbols, by means whereof he explained all ideas concerning the nature of all things."

Pythagoras taught that the entire universe is one vast system of mathematically correct combinations. Plato shows the deity geometrizing. The world is sustained by the same law of equilibrium and harmony upon which it was built.

"God geometrizes," said Plato. "The laws of nature are the thoughts of God," exclaimed Oersted, 2,000 years later. "His thoughts are immutable," repeated the solitary student of Hermetic lore, "therefore it is in the perfect harmony and equilibrium of all things that we must seek the truth." And thus, proceeding from the indivisible unity, he found emanating from it two contrary forces, each acting through the other and producing equilibrium, and the three were but one, the Pythagorean Eternal Monad. The primordial point is a circle; the circle squaring itself from the four cardinal points becomes a quaternary, the perfect square, having at each of its four angles a letter of the mirific name, the sacred TETRAGRAM. It is the four Buddhas who came and have passed away; the Pythagorean tetractys -- absorbed and resolved by the one eternal NO-BEING.

The term "God" -- unless referring to the Unknown Deity or Absoluteness, which can hardly be supposed acting in any way -- has always meant in ancient philosophies the collectivity of the working and intelligent Forces in nature. The word "Forest" is singular, yet it is the term to express the idea of thousands or even millions of trees of different kinds. Materialists have the option of saying "Nature," or still better -- "Law, geometrizes" if they so prefer. But in the days of Plato, the average reader would hardly have understood the metaphysical distinction and real meaning. The truth, however, of Nature ever "geometrizing" is easily ascertained. Here is an instance: Heat is the modification of the motions of particles of matter. Now, it is a physical and mechanical law that particles or bodies in motion of themselves, assume a spheroidal form -- this, from a globular planet down to a drop of rain. Observe the snowflakes, which along with crystals exhibit to you all the geometrical forms existing in nature. As soon as motion ceases, the spheroidal shape alters; or, as Tyndall tells us, it becomes a flat drop, then the drop forms an equilateral triangle, a hexagon and so on. In observing the breaking up of ice-particles in a large mass, through which he passed heat rays, he observed that the first shape the particles assumed, was triangular or pyramidal, then cubical and finally hexagonal, etc. Thus even modern physical science, corroborates Plato and justifies his proposition.

The Rosicrucian theory, that the whole universe is a musical instrument, is the Pythagorean doctrine of the music of the spheres. Sounds and colors are all spiritual numerals; as the seven prismatic rays proceed from one spot in heaven, so the seven powers of nature, each of them a number, are the seven radiations of the Unity, the central, spiritual Sun.

"Happy is he who comprehends the spiritual numerals, and perceives their mighty influence!" exclaims Plato. And happy, we may add, is he who, treading the maze of force-correlations, does not neglect to trace them to this invisible Sun!

All systems of religious mysticism are based on numerals. With Pythagoras, the Manas or unity, emanating the duad, and thus forming the trinity, and the quaternary or Arba-il (the mystic four), compose the number seven. The sacredness of numbers begins with the great First -- the One, and ends only with the nought or zero -- symbol of the infinite and boundless circle which represents the universe. All the intervening figures, in whatever combination, or however multiplied, represent philosophical ideas, from vague outlines to a definitely-established scientific axiom, relating either to a moral or a physical fact in nature. They are a key to the ancient views on cosmogony, in its broad sense, including man and beings, and the evolution of the human race, spiritually as well as physically.

The number seven is the most sacred of all, and is, undoubtedly, of Hindu origin. Everything of importance was calculated by and fitted into this number by the Aryan philosophers -- ideas as well as localities.

Now Pythagoras says that "The number eight, or the Octad, is the first cube, that is to say, squared in all senses, as a die, proceeding from its base two, or even number; so is man four-squared or perfect." Of course few, except the Pythagoreans and kabalists, can fully comprehend this idea; but the illustration will assist in pointing out the close kinship of the numerals with the vedic Mantras. The chief problems of every theology lie concealed beneath this imagery of fire and the varying rhythm of its flames. The burning bush of the Bible, the Zoroastrian and other sacred fires, Plato's universal soul, and the Rosicrucian doctrines of both soul and body of man being evolved out of fire, the reasoning and immortal element which permeates all things, and which, according to Herakleitus, Hippocrates, and Parmenides, is God, have all the same meaning.

"The figure 8 or 00 indicates the perpetual and regular motion of the Universe," says Ragon. But if perfect as a cosmic number it is likewise the symbol of the lower Self, the animal nature of man. Figure 9 represents the earth under the influence of an evil principle. Three times three is the great symbol of corporisation, or the materialisation of spirit according to Pythagoras -- hence of gross matter.

According to Max Muller "the two words 'cipher' and 'zero,' which are in reality but one ... are sufficient to prove that our figures are borrowed from the Arabs." Cipher is the Arabic "cifron," and means empty, a translation of the Sanscrit name of the nought "synya," he says. The Arabs had their figures from Hindustan, and never claimed the discovery for themselves. As to the Pythagoreans, we need but turn to the ancient manuscripts of Boethius' Geometry, composed in the sixth century, to find in the Pythagorean numerals the 1 and the nought, as the first and final cipher. And Porphyry, who quotes from the Pythagorean Moderatus, says that the numerals of Pythagoras were "hieroglyphical symbols, by means whereof he explained ideas concerning the nature of things."

Each metre in the Brahmanas corresponds to a number, and as shown by Haug, as it stands in the sacred volumes, is a prototype of some visible form on earth, and its effects are either good or evil.

There are words which have a destructive quality in their very syllables, as though objective things; for every sound awakens a corresponding one in the invisible world of spirit, and the repercussion produces either a good or a bad effect. Harmonious rhythm, a melody vibrating softly in the atmosphere, creates a beneficent and sweet influence around, and acts most powerfully on the psychological as well as physical natures of every living thing on earth; it reacts even on inanimate objects, for matter is still spirit in its essence, invisible as it may seem to our grosser senses.

So with the numerals. Turn wherever we will, from the Prophets to the Apocalypse, and we will see the biblical writers constantly using the numbers three, four, seven and twelve.

The use of geometrical figures and the frequent allusion to figures in all ancient scriptures (see Puranas, Egyptian papyri, the "Book of the Dead" and even the Bible) must be explained. In the "Book of Dzyan," as in the Kabala, there are two kinds of numerals to be studied -- the figures, often simple blinds, and the Sacred Numbers, the values of which are all known to the Occultists through Initiation. The former is but a conventional glyph, the latter is the basic symbol of all. That is to say, that one is purely physical, the other purely metaphysical, the two standing in relation to each other as matter stands to spirit -- the extreme poles of the one Substance.

As Balzac, the unconscious Occultist of French literature, says somewhere, the Number is to Mind the same as it is to matter: "an incomprehensible agent"; (perhaps so to the profane, never to the Initiated mind). Number is, as the great writer thought, an Entity, and, at the same time, a Breath emanating from what he called God and what we call the All; the breath which alone could organize the physical Kosmos, "where naught obtains its form but through the Deity, which is an effect of Number." It is instructive to quote Balzac's words upon this subject: "The smallest as the most immense creations, are they not to be distinguished from each other by their quantities, their qualities, their dimensions, their forces and attributes, all begotten by the Number? The infinitude of the Numbers is a fact proven to our mind, but of which no proof can be physically given. The mathematician will tell us that the infinitude of the numbers exists but is not to be demonstrated. God is a Number endowed with motion, which is felt but not demonstrated. As Unity, it begins the Numbers, with which it has nothing in common. ... The existence of the Number depends on Unity, which, without a single Number, begets them all."

The expression "All is One Number, issued from No Number" relates again to that universal and philosophical tenet. That which is absolute is of course No Number; but in its later significance it has an application in Space as in Time. It means that not only every increment of time is part of a larger increment, up to the most indefinitely prolonged duration conceivable by the human intellect, but also that no manifested thing can be thought of except as part of a larger whole: the total aggregate being the One manifested Universe that issues from the unmanifested or Absolute -- called Non-Being or "No-Number," to distinguish it from Being or "the One Number."

From the effulgency of light -- the ray of the ever-darkness -- sprung in space the re-awakened energies; the one from the egg, the six, and the five. Then the three, the one, the four, the one, the five -- the twice seven the sum total. And these are the essences, the flames, the elements, the builders, the numbers, the arupa, the rupa, and the force of Divine Man -- the sum total.

This relates to the sacred Science of Numerals: so sacred, indeed, and so important in the study of Occultism that the subject can hardly be skimmed. It is on the Hierarchies and correct numbers of these Beings invisible (to us) except upon very rare occasions, that the mystery of the whole Universe is built.

"The Three, the One, the Four, the One, the Five" (in their totality -- twice seven) represent 31415 -- the numerical hierarchy. Mathematically they represent the well-known calculation, namely, that the ratio of the diameter to the circumference of a circle is as 1 to 3.1415, or the value of pi, as this ratio is called -- the symbol pi being always used in mathematical formulae to express it. This set of figures must have the same meaning, since the 1 : 314,159, and then again 1 : 3 : 1,415,927 are worked out in the secret calculations to express the various cycles and ages of the "first born," or 311,040,000,000,000 with fractions.

Thus, while in the metaphysical world, the circle with the one central Point in it has no number, and is called Anupadaka (parentless and numberless) -- viz., it can fall under no calculation -- in the manifested world the mundane Egg or Circle is circumscribed within the groups called the Line, the Triangle, the Pentacle, the second Line and the Cube (or 13514); and when the Point having generated a Line, thus becomes a diameter which stands for the androgynous Logos, then the figures become 31415, or a triangle, a line, a cube, the second line, and a pentacle.

Three, five and seven are mystical numbers, and the last and the first are as greatly honoured by Masons as by the Parsis -- the triangle being a symbol of Deity everywhere.

The circle was with every nation the symbol of the Unknown -- "Boundless Space," the abstract garb of an ever present abstraction -- the Incognisable Deity. It represents limitless Time in Eternity. The Zeroana Akerne is also the "Boundless Circle of the Unknown Time," from which Circle issues the radiant light -- the Universal Sun, or Ormazd -- and the latter is identical with Kronos, in his Æolian form, that of a Circle. For the circle is Sar, and Saros, or cycle, and was the Babylonian god whose circular horizon was the visible symbol of the invisible, while the sun was the ONE Circle from which proceeded the Cosmic orbs, and of which he was considered the leader. Zero-ana, is the Chackra or circle of Vishnu, the mysterious emblem which is, according to the definition of a mystic, "a curve of such a nature that as to any, the least possible part thereof, if the curve be protracted either way it will proceed and finally re-enter upon itself, and form one and the same curve -- or that which we call the circle." No better definition could thus be given of the natural symbol and the evident nature of Deity, which having its circumference everywhere (the boundless) has, therefore, its central point also everywhere; in other words, is in every point of the Universe.

The Seven was a Sacred Number with every nation; but none applied it to more physiologically materialistic uses than the Hebrews. Whereas with the Hindus and Aryans generally, the significance was manifold, and related almost entirely to purely metaphysical and astronomical truths. Their Rishis and gods, their Demons and Heroes, have historical and ethical meanings, and the Aryans never made their religion rest solely on physiological symbols, as the old Hebrews have done.

The seven Laya centers are the seven Zero points, using the term Zero in the same sense that Chemists do, to indicate a point at which, in Esotericism, the scale of reckoning of differentiation begins. From the Centres -- beyond which Esoteric philosophy allows us to perceive the dim metaphysical outlines of the "Seven Sons" of Life and Light, the Seven Logoi of the Hermetic and all other philosophers -- begins the differentiation of the elements which enter into the constitution of our Solar System.

The earliest forms of elementary geometry must have certainly been suggested by the observation of the heavenly bodies and their groupings. Hence the most archaic symbols in Eastern Esotericism are a point, a triangle, a plane, a cube, a pentacle, and a hexagon, and plane figures with various sides and angles. This shows the knowledge and use of geometrical symbology to be as old as the world.

Starting from this, it becomes easy to understand how nature herself could have taught primeval mankind, even without the help of its divine instructors, the first principles of a numerical and geometrical symbol language. Hence one finds numbers and figures used as an expression and a record of thought in every archaic symbolical Scripture. They are ever the same, with only certain variations growing out of the first figures. Thus the evolution and correlation of the mysteries of Kosmos, of its growth and development -- spiritual and physical, abstract and concrete -- were first recorded in geometrical changes of shape. Every Cosmogony began with a circle, a point, a triangle, and a cube, up to number 9, when it was synthesized by the first line and a circle -- the Pythagorean mystic Decad, the sum of all, involving and expressing the mysteries of the entire Kosmos; recorded a hundred times more fully in the Hindu system, for him who can understand its mystic language. The numbers 3 and 4, in their blending of 7, as those of 5, 6, 9, and 10, are the very corner-stone of Occult Cosmogonies. This decad and its thousand combinations are found in every portion of the globe. One recognizes them in the caves and rock-cut temples of Hindostan and Central Asia, as in the pyramids and lithoi of Egypt and America; in the Catacombs of Ozimandyas, in the mounds of the Caucasian snow-capped fastnesses, in the ruins of Palenque, in Easter Island, everywhere whither the foot of ancient man has ever journeyed.

(To be continued.)

COMPILER'S NOTE: The following is a separate item which followed the above article but was on the same page. I felt it was useful to include it here:


As a gift is one thing, the act of giving another, as a sailor is one thing, the act of sailing another, and, as a sick man and his disease are not the same thing although a sick man is not without disease, so a benefit is one thing, and that which anyone receives by means of the benefit another. The benefit is incorporeal, and is never rendered invalid. Blessings that we have received can cease to be ours, but they can never cease from having been ours; what has been, too, is part of a benefit, and, indeed, its surest part. No power can efface the fact that this man has given, and that one received. 


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(1) NOTE.--Collated from the works of H. P. Blavatsky.
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