The Pythagorean School

Entries from Theosophical Glossaries

Pythagoras (Gr.). The most famous of mystic philosophers, born at Samos, about 586 b.c. He seems to have travelled all over the world, and to have culled his philosophy from the various systems to which he had access. Thus, he studied the esoteric sciences with the Brachmanes of India, and astronomy and astrology in Chaldea and Egypt. He is known to this day in the former country under the name of Yavanâchârya (“Ionian teacher”). After returning he settled in Crotona, in Magna Grecia, where he established a college to which very soon resorted all the best intellects of the civilised centres. His father was one Mnesarchus of Samos, and was a man of noble birth and learning. It was Pythagoras. who was the first to teach the heliocentric system, and who was the greatest proficient in geometry of his century. It was he also who created the word “philosopher”, composed of two words meaning a “lover of wisdom”—philo-sophos. As the greatest mathematician, geometer and astronomer of historical antiquity, and also the highest of the metaphysicians and scholars, Pythagoras has won imperishable fame. He taught reincarnation as it is professed in India and much else of the Secret Wisdom.—Theosophical Glossary

Pythagoreans The school founded at Crotona, Italy in the 6th century BC by Pythagoras of Samos. Pythagoras was an initiate not only into the Mysteries of his own native state, but also into those of the ancient Orient, where he had pursued extensive studies. His special work was to translate his esoteric knowledge into terms of the Grecian thought of that period. He shows the ultimate derivation of his wisdom and consequent teaching both by the content of his philosophical doctrines and by his insistence upon purity and self-mastery in life as a prime requisite to the attainment of wisdom.

His word metempsychoses is given as meaning the transference of the soul from one body to another; whereas by its Greek etymology it should mean the various highly occult transformations undergone by the soul-ego after death, and preceding the process of reensoulment — something of larger significant content than what the word reincarnation has mainly come to mean today, as implying merely soul-reimbodiment. It is the teaching of the various successive karmic transformations and imbodiments of a monad during its evolutionary cycle — not only in the larger sense of cosmic destiny, but also in the smaller sense of its karmic transformations between death and the succeeding physical birth.

Pythagoras is famous for his use of numerical and geometrical keys, which he illustrated by reference to the geometrical figures, the musical scale, astronomy, etc. He is supposed to have “discovered” the Divine Section, the regular polyhedra, and the proposition relating to the square of the hypotenuse; what he did was to show that these were keys to the interpretation of mysteries. Porphyry reports that the numerals of Pythagoras were “hieroglyphical symbols” by means whereof he explained ideas concerning the nature of things: (Vita Pythag) or, Blavatsky adds, “the origin of the universe” (SD 1:361). His tetraktys is a gem of condensed esoteric symbolism. The influence of his school may be traced in subsequent Greek history, inspiring such characters as Epaminondas; “It was Pythagoras who was the first to teach the heliocentric system, and who was the greatest proficient in geometry of his century. It was he also who created the word ‘philosopher,’ composed of two words meaning a ‘lover of wisdom’ —philosophos. As the greatest mathematician, geometer and astronomer of historical antiquity, and also the highest of the metaphysicians and scholars, Pythagoras has won imperishable fame. He taught reincarnation as it is professed in India and much else of the Secret Wisdom” (TG 266).—Encyclopedic Theosophical Glossary

Arithmomancy (Gr.). The science of correspondences between gods, men, and numbers, as taught by Pythagoras.

Monas (Gr.). The same as the term Monad; “Alone”, a unit. In the Pythagorean system the duad emanates from the higher and solitary Monas, which is thus the “First Cause”.

Quadrivium (Lat.). A term used by the Scholastics during the Middle Ages to designate the last four paths of learning—of which there were originally seven. Thus grammar, rhetoric and logic were called thetrivium, and arithmetic, geometry, music and astronomy (the Pythagorean obligatory sciences) went under the name of quadrivium.

Ten Pythagorean Virtues. Virtues of Initiation, &c., necessary before admission. (See “Pythagoras”.) They are identical with those prescribed by Manu, and the Buddhist Pâramitâs of Perfection.

Tetraktys (Gr.) or the Tetrad. The sacred “Four” by which the Pythagoreans swore, this being their most binding oath. It has a very mystic and varied signification, being the same as the Tetragrammaton. First of all it is Unity, or the “One” under four different aspects; then it is the fundamental number Four, the Tetrad containing the Decad, or Ten, the number of perfection; finally it signifies the primeval Triad (or Triangle) merged in the divine Monad. Kircher, the learned Kabbalist. Jesuit, in his Œdipus-Ægvpticus (II p. 267), gives the Ineffable Name IHVH—one of the Kabbalistic formulæ of the 72 names—arranged in the shape of the Pythagorean Tetrad. Mr. I. Myer … shows that “the sacred Tetrad of the Pythagoreans appears to have been known to the ancient Chinese”. As explained in Isis Unveiled (I, xvi.): The mystic Decad, the resultant of the Tetraktys, or the 1+2+3+4=10, is a way of expressing this idea. The One is the impersonal principle ‘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.

Theosophical Glossary

Number and Numbers, from the Encyclopedic Theosophical Glossary

Number People usually think of number as merely a varying multiplicity of units, a plurality of individuals, which is correct enough. Yet “Number lies at the root of the manifested Universe: numbers and harmonious proportions guide the first differentiations of homogeneous substance into heterogeneous elements; and number and numbers set limits to the formative hand of Nature” (Blavatsky) — a strictly Pythagorean vision and conception. Our reasoning minds lend a spurious reality to abstractions; and from this viewpoint the genuine realities appear in the guise of such abstraction. Number is such an apparent abstraction; we know it only by its effects in that world which seems to us so real, and of which we regard number as an attribute. Yet nothing can be more fundamental than number. As Balzac said, number is an entity, a divinity; the creative Logos itself is called the Number, meaning number one, arising out of no-number or the zero. After this we have the duad, triad, etc. For the Pythagoreans number was a creative, emanationally formative power, and the Hebrew Sepher Yetsirah (Numbers of Creation) gives out the whole process of evolution in numbers, while in China the I Ching speaks of celestial numbers. All esoteric systems set great store by numbers — some systems more so than others. For “we see the figures 1, 3, 5, 7, as perfect, because thoroughly mystic, numbers playing a prominent part in every Cosmogony and evolution of living Beings” (SD 2:35).

One. By itself the One represents not pure unalloyed spirit, which is signified by the zero — the all-containing womb of space and being — but is the First Logos or Pythagorean Monas monadum (monad of monads). From this monad of monads flows forth through emanation the duad, then the triad, and then the entire manifested universe of interlocking hierarchies, emanated from the cosmic womb of being or the zero through the First Logos or the One of primordial manifested spirit. “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 down 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” (IU 2:407).

The circle, zero, or nought is the symbol of the All, equivalent to Non-being, in contradistinction to being or the number One. With the Pythagoreans number One was equivalent to the cosmic monad, the Odd: odd numbers were considered by them to be perfect or celestial and the even numbers imperfect, manifested, or terrestrial. The cosmic One, the First Logos, alone was cosmic unity and therefore good and harmony, because no disharmony is to be found in the unitary One alone.

Yet “in all such numerical divisions the One universal Principle, — although referred to as (the) one, because the Only One — never enters into the calculations. It stands, in its character of the Absolute, the Infinite, and the universal abstraction, entirely by Itself and independent of every other Power whether noumenal or phenomenal” (SD 2:598). Here the cosmic One is intimately intertwined with the universal zero, the last being equivalent to the universal All. Analogies in different systems of thought are numerous; for instance, the cosmic zero corresponds to parabrahman-mulaprakriti, whereas the cosmic One or monad corresponds to Brahman. See also UNITY

Two The prime religious and mystical meaning in the science of numeration is finite completion, involving defined limits, and hence standing in sharp contrast to the indefiniteness associated with the nonfinite or cosmic; and therefore Pythagoras and his school looked upon two as beginning the series of even numbers, each one signifying a completion or a balance, suggesting the material worlds as contrasted with the spiritual. The binary was regarded as “the origin of differentiation, hence of contrasts, discord, or matter, the beginning of evil. . . . With the early Pythagoreans, however, the duad was that imperfect state into which the first manifested being fell when it got detached from the Monad. It was the point from which the two roads — the Good and the Evil — bifurcated. All that which was double-faced or false was called by them ‘binary’ ” (SD 2:574-5). It was represented geometrically as a line, because two is produced by the first motion from indivisible spiritual nature: the line also forms the tie or union between two points.

Two is the significant primal number of manifestation, of the famous pairs of opposites. Pure unmanifested spirit is in human understanding unitary, and not broken up into manifested and therefore contrasting minor points or units, and for this reason partakes of some of the attributes of non-finity, which becomes through manifestation finite points — generated by the duality emanating at the beginning of manifestation, which duality is expressible mathematically by the duad or the number two: “the Duad, although the origin of Evil, or Matter — thence unreal in philosophy — is still Substance during Manvantara, and is often called the third monad, in Occultism, and the connecting line as between two Points . . . And from this Duad proceeded all the Scintillas of the three upper and the four lower worlds or planes — which are in constant interaction and correspondence” (SD 1:618).

Three The first odd truly manifested number in the Pythagorean system, the second in emanation from the first odd number, the unit or monad. Because it was odd, like its grandparent the monad, it partook of the qualities and attributes of the latter and hence occupied a noteworthy place in the mystical numerative system of the Pythagorean school. It was designated as corresponding to a superficies because it is the first of all numeral causes generating a plane figure. Even a circle probably may in one sense be said to comprise a triad, for it has a center, a circumference, and a space contained within the latter. The number three, however, was commonly represented by the ancient thinkers by the triangle, the three sides making a complete plane figure. “This number is truly the number of mystery par excellence,” remarks Blavatsky; in order to understand the esoteric side of the mysteries connected with it, however, one is obliged to study the Hindu symbolism of numerals “as the combinations which were applied to it are numberless” (SD 2:575).

The Pythagoreans regarded the number seven as a compound of three and four: “On the plane of the noumenal world, the triangle was, as the first conception of the manifested Deity, its image: ‘Father-Mother-Son’; and the Quaternary, the perfect number, was the noumenal, ideal root of all numbers and things on the physical planes” (SD 2:582). The early Pythagoreans regarded the number three mystically as the vehicle of deity. If the duad was considered by these and other thinkers to be the first numerical element in cosmic manifestation, so following the same line the triad or three was considered the first number with which began the emanative series of hierarchies building all the planes inner and outer of the manifested worlds. See also TRIAD

Four The square of two, and the second even number, hence feminine in characteristics. It was regarded by the Pythagoreans with especial esteem, for it was the base number of the tetraktys. It corresponds to a solid figure, or a square — the quaternary although on the spiritual plane, as being the immediate successor of the triad, it became the symbol of immortality, and hence in this sense a perfect number, the ideal root of all subsequent hierarchical numbers on the lower planes including the physical. Thus there is the spiritual four as the mother-type of all productivity, and there was likewise the material four, the ideal root of all numbers on the astral and physical planes. It was called by the Pythagoreans the key-keeper of nature, but it was only so in union with the number three, for then the sum made seven — the perfect number of nature in our world. The Hermetists had the same idea: four was the symbol of truth when expanded into a cube, for when this cube is unfolded the production is seven. Four is the number “which affords an arithmetical division between unity and seven, as it surpasses the former by the same number (three), as it is itself surpassed by the seven, sincefour is by as many numbers above one, as seven is above four” (SD 2:582).

The number four is considered feminine on the planes of matter; it is considered to be masculine and energic only on the highest plane of abstraction. When united with three (spirit), “their union is the emblem of life eternal in spirit on its ascending arc, and in matter as the ever resurrecting element — by procreation and reproduction” (SD 2:592).

In ancient and modern occultism, 3, 4, and 7 are respectively held sacred as symbolizing light, life, and union — at least during our present manvantara; for the reckoning was somewhat as follows: unity, the One or the monad, was the generating point of spirit, from which flowed forth the first manifested stream of energy or the duad, which became in expressing itself the triad, the carrier and holder of cosmic wisdom and therefore light to our view. These three expressing themselves in the next stage of differentiation clothed themselves in a vehicle, the square or four, which thus became manifested life. Hence, when light and life conjoin in unitary action we have the complete septenary, the significant number of complete monadic being on this plane — the septenary individual.

Four also appears in the sacred key-numbers 4, 3, 2 (in this sequence): these are the basic numbers used in esoteric computations, and hence they form the numerical structure of the time periods of the four yugas of ancient India, which likewise were prominent in ancient Chaldean calculations — for the numerical science was the same in both lands. “The sacredness of the cycle of 4320, with additional cyphers, lies in the fact that the figures which compose it, taken separately or joined in various combinations, are each and all symbolical of the greatest mysteries in Nature. Indeed, whether one takes the 4 separately, or the 3 by itself, or the two together making 7, or again the three [4, 3, 2] added together and yielding 9, all these numbers have their application in the most sacred and occult things, and record the workings of Nature in her eternally periodical phenomena. They are never erring, perpetually recurring numbers, unveiling, to him who studies the secrets of Nature, a truly divine System, anintelligent plan in Cosmogony, which results in natural cosmic divisions of times, seasons, invisible influences, astronomical phenomena, with their action and reaction on terrestrial and even moral nature; on birth, death, and growth, on health and disease. All these natural events are based and depend upon cyclical processes in the Kosmos itself, producing periodic agencies which, acting from without, affect the Earth and all that lives and breathes on it, from one end to the other of any Manvantara. Causes and effects are esoteric, exoteric, and endexoteric, so to say” (SD 2:73-4).

As instances of the recurring of the sequence 4, 3, 2: the addition of 3 ciphers produces the length of the kali yuga, 432, 000 years; with 4 ciphers, the total of the four yugas or one mahayuga, 4,320,000 years; with 7 ciphers, the period of 14 Manus or 1,000 mahayugas, which is one Day of Brahma or a period of 4,320,000,000 years. When this latter figure is multiplied by two, in order to add the period of a Night of Brahma, and then multiplied by one year of Brahma (which is equivalent to 360 such days and nights) we have the basic figure of Brahma’s Life (which consists of 100 years). When 4320 is halved the result is 2160, which multiplied by 12 is the number of years in one turning of the precessional cycle; again 2160 is the period of the so-called Messianic cycle.

Five Because of its being one half of the perfect number (ten), five held the attention and study of all followers of the Pythagorean system of numerals. As we are now in the fifth root-race, the fifth principle (manas) takes an especially prominent position in human evolution. The five-pointed star, or again the pentagon, is the symbol of the microcosm, man, often referred to as a five-limbed man. Five “symbolizes at one and the same time the Spirit of life eternal and the Spirit of life and love terrestrial — in the human compound; and, it includes divine and infernal magic, and the universal and the individual quintessence of being” (SD 2:579).

The symbol of the kali yuga is the five-pointed star reversed, with the two points or horns of the star pointing upwards. This is also a sign of sorcery.

In the numerical mysticism of ancient Egypt five crocodiles, for instance, were represented as in the celestial Nile, and the emanating deity calls forth these crocodiles in his fifth creation. The number five, as well as other numbers, was sacred to the Gnostics, hence five words signifying the five mystic powers attained by the initiate were written upon the garment in their interpretation at the glorification of Jesus. In classical Greece the E Delphicum, a sacred symbol, was the numeral five. There were five ministers of Chozzar (the Gnostic Poseidon); and in the Hindu mythology Brahma is represented as uttering five words or vowels at the creation. From another standpoint, five is the “universal quintessence which spreads in every direction and forms all matter” (SD 2:583). See also PENTAGRAM

Six The number of manifestation; the ancients reasoned that since the basis of all manifested nature was sextal — such as six fundamental forces, planes, and hierarchies of beings — therefore nature throughout all its manifested structure and workings would be subordinate to this fundamental numerical key. Hence not only the structure of nature itself would be sextal, but so would cycles of time in their operation. Here is the fundamental reason the Hindus, ancient Babylonians, and the Mystery schools and teachers of other lands, adopted the sextal or sexagesimal keys as the numerical series of events in which time cycles repeated themselves, therefore corresponding to events in human and cosmic matters. Multiplied by itself, and then by ten (the perfect number), gives 360 — the number of the Hindu Divine Year, also of degrees in a circle and the basis of the Babylonian saros.

The combination with three (6+3) making nine, however, was looked at askance by the ancients, for “if number 6 was the symbol of our globe ready to be animated by a divine spirit, 9 symbolized our earth informed by a bad or evil spirit” (SD 2:581).

In Saint-Germain’s manuscript, six is regarded as the symbol of the animating or informing principle, and it was also the “symbol of the Earth during the autumn and winter ‘sleeping’ months” (SD 2:583).

In occultism six is represented by the cube representing the six dimensions — the four cardinal points, and the zenith and nadir; “while the senary was applied by the sages to physical man, the septenarywas for them the symbol of that man plus his immortal soul” (SD 2:591).

Six is also present in the double triangles, which when interlaced form a six-pointed star; “this is the reason why Pythagoras and the ancients made the number six sacred to Venus, since ‘the union of the two sexes, and the spagyrisation of matter by triads are necessary to develop the generative force, that prolific virtue and tendency to reproduction which is inherent in all bodies’ ” (SD 2:592). See alsoSENARY

Seven The fundamental number of manifestation, frequently found in the different cosmogonies as well as in many religious dogmas and observances of the different ancient peoples. Although ten was called one of the perfect numbers by the Pythagoreans, seven was unique in their series of numbers because it has all the “perfection of the Unit — the number of numbers. For as absolute unity is uncreated, and impartite (hence number-less) and no number can produce it, so is the seven: no digit contained within the decade can beget or produce it” (SD 2:582). Seven is the number of the manifested universe, while ten or twelve is the number of the unmanifested universe.

Pythagoras taught that seven was composed of the numbers three and four, explaining that “on the plane of the noumenal world, the triangle was, as the first conception of the manifested Deity, its image: ‘Father-Mother-Son’; and the Quaternary, the perfect number, was the noumenal, ideal root of all numbers and things on the physical plane” (ibid.). Further, seven was called by the Pythogoreans the vehicle of life for it consisted of body and spirit: the body was held to consist of four principal elements, while the spirit was in manifestation triple, comprising the monad, intellect or essential reason, and mind.

There are innumerable instances of sevening — the seven days of the week, the seven colors of the spectrum, the seven notes of the musical scale — while special emphasis is placed upon the seven human and cosmic principles; the seven senses (five senses now in manifestation and two more to be attained in the future through evolutionary unfolding); the seven cosmic elements; the seven root-races and seven subraces; the seven kingdoms, human and below; the seven rounds; the seven lokas and talas; the seven manifested globes of the planetary chain; the seven sacred planets; the seven racial buddhas; the seven dhyani-bodhisattvas and -buddhas; the seven Logoi; etc.

Man as well as nature is called saptaparna (seven-leaved plant), symbolized by the triangle above the square. While the senary was applied to man in all ranges from the physical to the spiritual, when completed by the atman, thus making the septenary, the latter signified the entire range of the constitution, whether of man or nature, crowned by the immortal spirit.

In Hindu literature the number seven continually appears: the saptarshis (the seven sages), the seven superior and inferior worlds, the seven hosts of deities, the seven holy cities, the seven holy islands, seas, or mountains, the seven deserts, the seven sacred trees, etc. In Greece seven was often connected with the gods and goddesses: Mars had seven attendants, seven was sacred to Pallas Athene and to Phoebus Apollo — the latter with his seven-stringed lyre playing hymns to septenary nature as well as to the seven-rayed sun; Niobe’s seven sons and seven daughters, etc.

Apart from mythological considerations, in physical life manifestations of the number seven occur continuously: “if the mysterious Septenary Cycle is a law in nature, and it is one, as proven; if it is found controlling the evolution and involution (or death) in the realms of entomology, ichthyology and ornithology, as in the Kingdoms of the Animal, mammalia and man — why cannot it be present and acting in Kosmos, in general, in its natural (though occult) divisions of time, races, and mental development?” (SD 2:623n).

Seven is indeed the sacred number of life, and with the circle and the cross it forms a triad of primordial symbols of the ancient wisdom.

Eight Although infrequently used in occultism, one of the important numerical stages in nature and, therefore, in all occult systems of reckoning and computaton. An inaccurate use of 8, or a use springing from ignorance, can very easily mislead the student of archaic numerology as to its ancient computational value and numerical signification. After remarking that the ancients always referred to seven planets (the sun being included in the septenary), Blavatsky says: “These ‘seven’ became the eight, the Ogdoad, of the later materialized religions, the seventh, or the highest principle, being no longer the pervading Spirit, the Synthesis, but becoming an anthropomorphic number, or additional unit” (SD 2:358n).

However, the ogdoad of the ancients had a special significance, among other things referring to the addition of the linking unit, whether of a superior or inferior hierarchy, to the septenary hierarchy envisioned at the moment. Furthermore, when the seven sacred planets of the ancients were considered in connection with their relations to earth, this conjoining of the eight units was often called an ogdoad. Hinduism takes cognizance of eight great gods, namely, the eight adityas, and on some of the oldest monuments of India, Persia, and Chaldea one may see the eight-pointed or double cross.

When the figure 8 is placed on its side . . . it symbolizes the eternal and spiral motion of cycles “and is symbolized in its turn by the Caduceus. It shows the regular breathing of the Kosmos presided over by the eight great gods — the seven from the primeval Mother, the One and the Triad” (SD 2:580). In modern mathematics, it is the symbol for infinity, or for the approach to infinity.

Nine Especially significant when regarded as a triad of triads, it is the number which reproduces itself in multiplication. “It is the sign of every circumference, since its value in degrees is equal to 9, i.e., to 3+6+0. It is a bad number under certain conditions, and very unlucky. If number 6 was the symbol of our globe ready to be animated by a divine spirit, 9 symbolized our earth informed by a bad or evil spirit” (SD 2:581).

As nine is one less than ten, in a denary hierarchy it is all the units except the first, the first being regarded as the origin or synthesis of the emanated nine. Thus one and nine may represent spirit and matter, or unmanifest and manifest, a logos and its rays. In the Stanzas of Dzyan svabhavat is the numbers one and nine, which make the perfect ten; and the same is seen in the ten Sephiroth of the Qabbalah, where Kether the Crown is often considered apart from the other nine. It was an especially favorite number in Norse mythology, appearing continuously throughout the Eddas.

In a denary system of hierarchies, in which the ending of one is the beginning of the subsequent hierarchy, we have actually a series or scale of nines. Many properties assigned to nine pertain to its position in the decimal scale. In many languages the word for nine is similar to that for new — Sanskrit navan, nava; Greek ennea, neos; Latin novem, novus; German neun, neu — which apprises us that nine has been considered from immemorial time the number of change or renovation, for it is followed by the complete number making 10, or springs from the monadic unit also making 10 — in either case the reckoning enters upon a new decimal series.

Ten One of the most sacred fundamental numbers in occultism, for ten — or more accurately perhaps twelve, as Plato pointed out — is the key of the numerical structure upon which the universe is laid and built. Where seven represents the manifested universe or brahmanda, ten or twelve includes the unmanifested aspects as well. Ten is the foundation of the decimal system and because of this is universal in its relations. With the Pythagoreans ten was the most sacred number, the mystical dekad involving and expressing the mysteries of the entire kosmos, “the absolute All manifesting itself in the Word or generative Power of Creation” (SD 2:553); and among certain other schools, as in the Orient, ten was symbolically synthesized by the vertical line traversing the circle.

The early Gnostics also considered ten to contain the knowledge of the universe, both metaphysical and material. The Pythagorean dekad “representing the Universe and its evolution out of Silence and theunknown Depths of the Spiritual Soul, or anima mundi, presented two sides or aspects to the student. It could be, and was at first so used and applied to the Macrocosm, after which it descended to the Microcosm, or Man. There was, then, the purely intellectual and metaphysical, or the ‘inner Science,’ and the as purely materialistic or ‘surface science,’ both of which could be expounded by and contained in the Decade. It could be studied, in short, from the Universals of Plato, and the inductive method of Aristotle. The former started from a divine comprehension, when the plurality proceeded from unity, or the digits of the decade appeared, but to be finally re-absorbed, lost in the infinite Circle. The latter depended on sensuous perception alone, when the Decade could be regarded either as the unity that multiplies, or matter which differentiates, its study being limited to the plane surface; to the Cross, or the Seven which proceeds from the ten — or the perfect number, on Earth as in heaven” (SD 2:573).

A great deal of the highly mystical and occult meanings of the dekad were symbolized by the Pythagoreans in their sacred tetraktys, which was considered by them so holy that their most binding oath was made upon it. Other symbols of the number ten are two interlaced triangles — for the septenary and the triad are there present at the same time — and the line within the circle line through circle, unity within zero (cf SD 2:581).

“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 Decade, 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-stones of Occult Cosmogonies. This decade and its thousand combinations are found in every portion of the globe” (SD 2:321).

See also DECAD

Encyclopedic Theosophical Glossary


Iamblichus’ Life of Pythagoras, or Pythagoric Life


Life of Pythagoras


Pythagoric Life

Accompanied by

Fragments of the Ethical Writings of Certain Pythagoreans in the Doric Dialect

and a

Collection of Pythagoric Sentences from Stobaeus and Others

Translated from the Greek by

Thomas Taylor

Full Text Online

Pythagorean Ethics and Virtues  (Fragments of the Writings of Certain Pythagoreans)

Golden Verses of Pythagoras

Golden Verses of Pythagoras

Full Text Online

The Extant Pythagorean Sentences

The Pythagoric Symbols, with the Explanations of Iamblichus

The Life of Pythagoras, with his Symbols and Golden Verses, Together with the Life of Hierocles, and his Commentaries upon the Verses, by M. Dacier, tr. N. Rowe (1707)

The Golden Verses of Pythagoras and Other Pythagorean Fragments, Selected and Arranged by Florence M. Firth (1904)

See Also

Pythagoras: His Life and Teaching, a Compendium of Classical Sources, by Thomas Stanley (1687)

Lore and Science in Ancient Pythagoreanism, by Walter Burkert (1972)

The Pythagorean Sourcebook and Library: An Anthology of Ancient Writings Which Relate to Pythagoras and Pythagorean Philosophy, by David R. Fideler (1987)

Pythagoras and the Early Pythagoreans, by Leonid Zhmud (2012)

Pythagoras and the Pythagoreans: A Brief History, by Charles H. Kahn (2001)

Pythagoras: His Life, Teaching, and Influence, by Christoph Riedweg (2005)

Plato and Pythagoreanism, by Phillip Sidney Horky (2013)

Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages, Christiane Joost-Gaugier (2007)


The School of Pythagoras at Crotona, by A. Cervesato

Life and Teachings of Pythagoras, by F. S. Darrow

Pythagoras and His School

Pythagoras and His School

Hermes, November 1977

Pythagoras was revered in India as Pitar Guru, Father and Teacher, and as Yavanacharya, the Ionian philosopher. He was known by other names in ancient Egypt where he spent twenty years in preparation before, at the age of fifty-six, he founded the School at Crotona in Magna Graecia, with great deliberation and in accord with the wisdom and the vision of the mighty Brotherhood he represented. He taught an entire emerging community, seeking four hundred pure souls who might constitute a small brotherhood for the sake of making that polis a city of souls in search of wisdom in harmony with the larger fellowship of man. His School was based upon the most stringent rules for admission, including a probation lasting five years and a requirement of total silence in the presence of those in the assembly who had been longer in the school. He initiated those who had passed all the preliminary trials, making themselves channels for the divine fount of omniscience, towards which he always pointed and upon which he enjoined an absolute, reverential silence.

For Pythagoras, philosophy was a purgation of the mind and emotions so that the pure light of the immortal soul may freely shine through the limited vestures common to all men. The purification must begin by preparatory reverence—becoming truly worthy of relationship through silent worship of the immortal Gods with the transcendental order which holds everything in the universe in a divine harmony. This order could be seen in the heavens and be studied with the help of geometry and mathematics of the most archetypal form. Through the honouring of heroes and peers, profound reverence may emerge for the whole of life when seen in the context of a vast universe. Pythagoras was the first to use the word ‘cosmos’. The universe is a cosmos, not a chaos. It represents the majesty of a vast intelligible ordering of immense magnitudes through the application of an over-brooding architectonic principle in a rounded but boundless perspective. It is bounded in time and space but unbounded in its peripheral transition to the realm of the potential. Apprehending this, a person begins to deepen his or her feeling for the mystery of life and all the multitudinous forms of matter, and thereby comes to have a true and rectified respect for those forces that are ceaselessly at work, even in the simplest acts such as the handling of objects. The person who is thus prepared would naturally honour the noble heroes, the forerunners of every race and every civilization who, though they are imperfect individuals, are yet capable of elevating the moral tone of human culture. Throughout history their name is legion. Anyone who has thought about these matters fosters a view of human nature that is enormously expansive, and comes to see human beings in terms of opportunities, not limitations, in terms of powers and possibilities rather than handicaps. Then, according to the Pythagorean teaching in the Golden Verses, any person can come to show fearlessness in relation to fate, having already acquired a mature self-respect that is rooted in an understanding and a reverence for all of life.

Self-respect means here very much more than in current usage and in our ordinary languages. It is the key to what is said in the Golden Verses about proper self-examination, which is an activity very different from offering a confessional before a priest, or going to a psychiatrist and having oneself analysed, or engaging in one or another form of tedious, furtive and repressive discussion of the shadow. In the Pythagorean teaching, the shadow cannot understand itself. The shadow is void of the very possibility of self-knowledge. Real understanding can come solely through the light of self-awareness which is inherent in every human being. The light of understanding can dispel the shadow of the personality only when, in lunar consciousness, a fruitful connection is made—metaphorically withdrawing to Metapontum where Pythagoras passed away, some say around the age of a hundred. Having built a bridge in personal consciousness towards the latent potential self, one sees that in this larger selfhood there are no differences between oneself and every other human being and also the inner light and essence of anything and everything. The same luminous essence is to be found in a piece of paper, a table, a stone, in each single atom in space, in every animal form, in each vegetable and mineral, and the same is also to be found in every constituent of that vast and complex universe that we call the human body. The same is also to be found in each thought-form entering into and leaving the human mind through its affinity with appropriate centres of excitation in the brain, or when self-consciously drawn from an abundant cosmic storehouse.

All who want to come closer to the spirit of the Golden Verses must prepare and purge themselves as Pythagoras taught, thereby coming to be known as a trainer of souls. When human beings seek to learn, in the privacy and solitude of their own solemn undertaking, the serious business of truly elevating a human life, they must begin to ask questions about themselves: “Who am I?” “What am I?” “Why did I do this then?” “Do I always say what I intend?” “Did I think before I acted this morning, and what do I now think I am supposed to do tomorrow, next week, next year?” It is significant that the only phrase occurring twice in the Golden Verses is: Think before you act. It is precisely because human beings with the best intentions in the world, with access to the profoundest ideas and sharing the noblest of feelings, are not able to deliver themselves in public life with the dignity of divine monads, that they need to give themselves a chance, by making time within the space of every day for looking back in review. By continually reflecting the standpoint of the immortal Self, they will surely come to understand others and increase their real confidence through recognizing what is good in themselves; this in turn gives the courage to notice what in themselves is left-handed and must be discarded.

It is well known, though little understood, that in the Pythagorean School the psychological disciplines were joined to the study of mathematics. If one really wanted to understand this, one would be well advised to meditate deeply upon the Pythagorean Triad and the Tetrad. When one truly does so, one will find that the mystery deepens further, because what is esoteric and what is exoteric are relative. What is hidden to one is not unknown to another. What is hidden at one time is not inaccessible at another time. Unfortunately, many people are victims of an Aristotelian-Baconian view of knowledge where thoughts are seen as bits of information transmitted from the outside and impressed upon the brain, itself misconstrued as a kind of tabula rasa. In contemporary culture many people erroneously believe that true knowledge has got to do with the information revolution, and hence all that is needed is to find proper ways of giving access to information to each and all. In the School of Pythagoras, if people sought to know the Mysteries, they were fairly and squarely told what were the rules that must be respected. These time-honoured rules have always been observed. Great Teachers make fresh applications of these enduring rules according to the exigencies of the age in strict obedience to the Fraternity on behalf of which they act, and of which they are faithful members.

In teaching the divine wisdom relevant to his time, Pythagoras, the great Master, followed very strict rules. In one mythic version the story is told of how this was done. If individuals sought admission into the School, having already found inspiration in daily life from the ethical teaching of the Golden Verses, then they were invited to put themselves through a preliminary set of freely chosen and strictly administered tests. One of these required that the candidate be conducted to some secluded place and left with bread and water. He was requested to remain there for a night and to think intently upon a single symbol such as the triangle. Having prepared properly and taken whatever steps were needed to gain calmness, the candidate then set down ideas on the subject in relation to the whole of life. The following morning, the candidate was invited to the assembly of those who had already passed through these stages and asked by Pythagoras, who presided, to convey his observations to the entire group. A common practice during those days was that various members of the assembly were instructed to make it difficult for the candidate to state what he had to say by ridiculing his ideas. Naturally, a new candidate was liable to be nervous though the assembly was really on his side, yet nonetheless no concessions were made to his limitations, ambiguities and mixtures of motive. This was for his own good. Unless one could maintain one’s composure under these circumstances, it was clear that life in the School would prove too much for a candidate who was unduly sensitive to criticism. Something of this ancient tradition still persists, for example in Holland and Germany at the time of the defense of dissertations, although without the compassionate purport of the trial the ceremony becomes censorious and even absurd.

What was crucial for Pythagoras was the authenticity of self-knowledge in relation to the application for the sake of other men of the holy and sacred teaching in relation to the divine Triad. The Triad itself could not be comprehended except in relation to the Point. The Point could not be grasped except as a One in relation to the Duad. The Monad and the Duad could not be understood completely unless they were also seen in terms of the Triad. And so the number series proceeds. Underlying it is the difficult problem which has to do with form, the meaning of the Pythagorean Square. If all of these are to be put together, something is involved which is rather like squaring the circle, securing the elixir of life, the key to the Mysteries of life and death. Pythagoras taught that unless the Mysteries are found within oneself, they cannot speak to one. All must make their own experiments with truth. They must make their own exercises in the calming of the passions, the controlling of the mind, the concentration of the thinking principle, and above all, the purgation and purification of their motives, intentions, feelings, likes and dislikes. This must be done for the sake of fusing the whole of one’s being into an overriding thought-feeling, one keynote vibration which becomes a sacred verbum, moving and animating the entire manifested self. All human beings have a unique and privileged access to the verbum within the sanctuary of their own consciousness in deep sleep, in daily meditation, in waking life, in golden moments, but, above all, when they begin to enter into a current of continuous thought and meditation upon the holiest of all subjects, which has to do with the fons et origo of all living things and beings. When they do this, then they will begin to understand the Tetraktys or sacred Quaternion, the Number of numbers.

Intuitive individuals will come to see that all these numbers point towards five, the Pythagorean pentagon, and six, which was used later in the Kabbalah but for Pythagoras was a six-pointed star where there was an eagle at the top and a bull and a lion below the face of a man. They will also begin to sense something about the significance of seven as the basic principle of division of not only colours and sounds, but of all manifestation. The seven in turn cannot be understood without the eight and Pythagoras taught how harmony may be produced when tuning the high and the low notes in the octave, thereby laying the basis for many of the theories and teachings that have come down through musical traditions. What he illustrated in music could also be applied to medicine, which means we cannot leave out the number nine. Nine has great meaning as three sets of three, but it also spells the ending of all things—incompletion. The wise take this into account in advance, thereby preserving the inviolable image of what since Pythagoras has come to be called the perfect number—ten—without seeking for its exact visual replica on earth. What is hidden in the Triad has been glimpsed by great architects, sculptors and craftsmen. The Chinese, when creating vases, abstained from making them perfectly symmetrical. Contemporary architects like Jacobsen after conceiving a fine building do not care to come to the opening ceremony as they are absorbed in the designing of the next. Truly creative minds have known that there is a joy in creativity which is constricted and cancelled by attachment to results. The criteria of the world which accommodate the concerns of the mediocre also act as a brake upon the ascent to those levels of excellence which are relevant to all cultures. In the Pythagorean tradition, a proper answer to any question about the Mysteries must throw one back upon oneself so that each will do his own meditation and reflection upon the Tetrad as well as the Tetraktys.

The vital essence of the Pythagorean teaching was to encourage the emergence of whole men and women. They cannot be manufactured, but must truly create themselves. Great Teachers assist in the self-production of whole human beings by making a holistic teaching come alive. Pythagoras was an originator of true science, religion and philosophy in the Near Eastern cycle which he initiated. The teaching of Pythagoras was also that of the Buddha and later on of Shankara. Two thousand five hundred years ago the Buddha taught his disciples first to become shravakas, listeners. When they had spent a sufficient time in listening and learning, as in the earlier Hindu tradition with its emphasis upon brahmacharya, a period of probation, then they could become sramanas, men of action. We find this also in the Pythagorean tradition, where neophytes are acousticoi, those who listen. This has reference not to something mechanical or rigid and therefore false, but to a balanced training in the art of perfecting through wisdom the conservation of energy. The purification of thought, the calming and harmonizing of feelings, was undertaken for the sake of the appropriate manifestation of the Inner Self through proper speech and fitting conduct.

Pythagoras taught a threefold division of humankind and a threefold division of desire. All men may be compared to people who attend a festival. There are those who are motivated by the love of gain and who go to buy and sell. There are those motivated by the love of honour and they go to compete with and emulate each other in attaining standards of excellence. Then there are those who are concerned with neither gain nor glory because they have either worn out these toys or thought through these illusions, or they are born with a natural indifference to them. Such are wholly concerned with the love of wisdom. Lovers of wisdom may be compared to those who at festivals are like spectators, not participating but at the same time not making external judgements, not buying and selling, not comparing and contrasting, but merely learning what is common to all men, learning something about the noble art of living. They do not do what is unnecessary. They try to find out what is intimated behind the forms in the vaster human drama in which all the world is a stage and men and women merely players. The play is the thing. Quiet attention is the beginning of the way to wisdom in the Pythagorean tradition.

Reincarnation, the philosophy of palingenesis, is also fundamental. Every human being has been involved as a spectator in a variety of spectacles, has played a multiple diversity of roles. In this perspective, all learning is recollection, and much of what is seen is the restoration of Soul-memory. What people think is new is mostly a recollection from where and whence they know naught, but which nonetheless acts as a divine prompting within them and sometimes saves them, in times of trouble and of trial, from making mistakes which would propel them further back than when they made them before, because by now they should have learnt something. The School which Pythagoras founded was one in which every kind of learning could be pursued, not for the purpose of integrating the isms and the sects of the time, but rather for coming down, from above below, so as to be able to see the synthesizing principles, in theoria and praxis, contemplation and conduct.

After the passing of Pythagoras, the pupils of his School separated out. Schisms ensued between the so-called scientific people, who spent their time making claims, arguing and attacking each other, and those who initially espoused simple enthusiasms and were mocked by the others. The latter were left solely with their disarming trust, faith and devotion, which helped to continue the transmission of the tradition. All of this was known in advance by that wise Promethean called Pythagoras. He wanted separation and self-selection to take place not only among the many who were influenced, but equally among the few who were experiencing the rigours of training, those who had the moral fibre to endure the extremely difficult ascent to wisdom. The claim that the path is easy is the facile excuse of those who do not truly intend to make the ascent, because they have failed many times before and are inwardly so terrified of failure before they start that they would rather not risk even the first test.

There is much protection in the time-tested moral codes of every true community of seekers. This is suggested in the proverbs and the folklore of all societies. Pythagoras taught that there must be an inward quiescence of the soul, a stilling of the mind in which the true receptivity of the heart can enable real learning to take place. A person concentrating while learning carpentry, or while training for athletics, is quiet. Individuals who concentrate while preparing and studying for anything are quiet. Could any less be required of a person who would study and persevere while seeking the divine science of the dialectic, as Hierocles called the Pythagorean teaching? The art of free ascent of the soul towards the upper realms, indicated in the concluding words of the Golden Verses, is portrayed as the unveiling of latent perceptions of realities that are hidden. Anyone who is in earnest must give Nature time to speak. It is only upon the serene surface of the unruffled mind that the visions gathered from the invisible may find true and proper representation.

In ancient India, classical Greece and in early America it was well understood that without veneration for forefathers, nothing worthwhile can happen to a human being, a group or a society. This tradition was partly preserved under the influence of the Theosophical Movement in the nineteenth century and the subsequent short-lived Platonic renaissance in a variety of fraternities and movements. Some are still doing well, but most other fraternities, which took Pythagorean rules and adapted them for the purpose of self-discipline, true friendship and self-respect, are not in the same position. While many have closed down, there are others that have held on though they lost the original impulse. There are also those few which have remained, and unknown to the many, have tried to be true to the original impulse. In some cases the impulse goes back not merely to the time of Benjamin Franklin or to the original societies of Philadelphia started at the time of the signing of the Declaration, but even earlier. As Burke suggested, any generation which fails to show respect to its ancestors will deserve nothing of posterity. Those who show little respect to those who have gone before them—their parents, grandparents, teachers and their teachers’ teachers—will be repudiated in turn by their children. The law of Karma does not discriminate between persons, societies and generations.

The question came up among the early Pythagoreans, regarding the injunction to honour one’s parents: What is one to do if one’s parents are unworthy? The answer given at the time by wise Pythagoreans was: First ask yourself whether you really have paid sufficient homage to the immortal gods, to the heroes of all time, and to the earth’s good geniuses. If you have done all of these, then you are entitled to ask whether you should show honour to your parents. But you will find, if you have observed all that is prior, that you will always find some reason to honour your parents while at the same time you do not have to blindly follow their ways. That is because, as the later Golden Verses stress, all people must think for themselves. Each must make up his own mind and choose his own way. This does not require any recommendation or advertisement in our time. It is part of our very constitution. It was also the deathbed utterance of the Buddha. This is the oldest teaching, and it is common sense. There is hardly a human being who does not know it.

Human beings forget. All selfishness is rooted, Pythagoras felt, in thoughtlessness. It is hardly ever the case, even in the age of inversion, that people deliberately intend consistent and systematic inversion of reverence to the immortal gods, even though they may not know what that means, or to the heroes even though they may have demythologized them. They do not deliberately intend to flout the law taught by an Initiate a long time ago: “God is not mocked; as ye sow, so shall ye also reap.” Every man knows all of these things. Why then did Schweitzer put so much emphasis upon reverence for life? He knew that if something is worth doing, it is worth emphasizing, because men think they know it, but act as though they never did. Men forget and therefore in the Pythagorean doctrine of anamnesis, as in the Platonic teaching, everything has to do with remembering and forgetting. All human souls, when they have drunk of Lethe’s waters, have become identified with forms and come under the influence of the lower languages transmitted to them by the world through their relatives and those near to them. They forget, and as they forget, the babies that stare and smile and greet the world in mystic wonder, in a very short time, in the process of learning how to toddle, to stand straight and to move, become confused in noticing the scorn and the scepticism, the cynicism and the distrust, the self-hatred that is all around. And by the time children are ready for the precious time of puberty, they have received no inspiration or help in learning to handle the sheer joy of using eros under the control of a calm and cool head. They are completely at war with others and with themselves.

We live in the age of Zeus, wherein it is difficult to understand the greatness, let alone the inner meaning, of the Pythagorean invocation of Brihaspati, Jupiter or Zeus—he who knows and can show the genius of every living being. Honour and reverence involve something more than the ordinary understanding of these words. They require what Pythagoras teaches in the closing stanzas of the Golden Verses, which collectively were called Heiros Logos, the Sacred Discourse. Pythagoras taught that discrimination and discernment are needed. One must learn not just to make distinctions but to show discrimination, to recognize nuances, sub-tones, sub-colours, shades of meaning, to recognize the immense diversity of forms of life but also to see the ordering and the structure under which they could be understood. It is necessary to recognize similars, notice opposites, identify counterfeits, cherish intimations, but above all, to see the continuity and the connection between all of these. Then it will be possible, when hearing opinions, to discriminate among them and to go for the good and the gold in all, even in the most foolish observations. One can learn and note down what is of value in anything and everything that one comes across. But if one comes across a lot that is not worth entering into a notebook, one can let it go and remain calm in the presence of its utterance. All of this points to a conception of manhood, a magnitude of self-possession which combines with compassion and love, magnanimity as well as prudence, and which is truly rare in any age, but wholly admirable in our epoch.

Pythagoras especially commends prudence, not cunning or what the world calls shrewdness, but the insight of wisdom in relation to the lunar realm, a region in which everything that begins will change and pass away. If one does not remember this, one cannot be prudent. To be imprudent is to be over-attached. Desires are of three kinds. There are those desires which when they first arise are ill-fitting, inauspicious, and will do no good from the very start. Often such desires are longings to do the impossible. If a person, before being able to walk the Sierras, wants to climb Everest next week, it is an ill-timed and inauspicious desire. A wise friend might urge him to go and find out what in fact he needs to know, that such learning could be very unpleasant. The second kind of desire is not inauspicious to start with, but makes sense, like the desire to finish something which one has begun, whatever it be, whether it has got to do with school or job or family. Yet herein lies the danger, of an immense inflation of that desire so that it becomes an obsession. It may become a virulent, over-mastering force, so that the person who has it is a slave and no longer a free human being. This kind of desire is not wholly bad, but it has got to be trimmed. The vehemence has got to be taken out of it until it runs like cool waters, consonant with the ocean of life into which it must eventually empty itself. Thirdly, there are desires which, though not unfitting to start with and though not vehement, become inappropriate in expression. A person might have a legitimate desire and a sense of proportion about it but not know how to express it appropriately, and hence become the frequent victim of bad timing. Bad timing is like bad faith, betokening a lack of total commitment and engagement in one’s own project, to use Sartrean language. One is never quite there when needed but is always just that bit ill-timed. After a point one gathers around oneself elemental forces that become an ill-omened angel of misfortune.

When Pythagoras spoke of prudence and magnanimity, he gave a critical test. One is becoming a man when there is an increase in one’s magnanimity. This teaching was so telling that even after Plato, with the decline of the Academy, Aristotle thought it fit to base his conception of the ideal man upon the quality of magnanimity. Every human being has access to magnanimity, but it cannot be secured instantly if one is mean, niggardly, fearful, selfish or contemptuous. Magnanimity is only released in the mind by large ideas and great visions. In the heart it is released only by a tremendous compassion for the sick and the suffering.

Pythagoras knew what was then to be judiciously chosen as a foundation stone for the culture of the future. At present when modern culture is nearly dying and giving a great howl while doing so—but barely concealing a rather pathetic whimper—and another culture has already begun to come into birth as the invisible dips into the visible, the Pythagorean teaching cannot now mean a mere return to the forms once given in Magna Graecia. It must be seen and meditated upon as the seed of self-regenerating institutions and the culture and etiquette of the soul. When the soul becomes established firmly like a statue motionless in mind, while at the same time entertaining the vast universe of thoughts, the whole is fixed immovably in contemplation, showing beauty of soul, beauty of mind, beauty of heart, beauty in every direction and every dimension. It thereby makes it possible for more and more human beings, with their imperfections, to come out of the multitudes for the sake of all and for the sake of self-transformation and self-actualization, culminating in self-transcendence.

Preparations are crucial for the Pythagorean school of the future. Anyone who studies the Golden Verses of Pythagoras, in any translation or edition, and seeks by reflecting upon them to draw some inspiration, can release a vital energy in inward consciousness which is causal in relation to the external realm of effects. Those who do this could constitute themselves as beings who come closer in spirit, thought and feeling to the inmost, ever-unmanifest Presence. In the days of Pythagoras many people knew that they knew him not. No great teacher ever incarnates or manifests except in proper conditions, and these are always hidden and always involve a few. When necessary he will manifest any relevant part of himself. Pythagoras spent a long time—twenty-two years—studying the Egyptian Mysteries, taking a projection of himself and letting it share all the ailments of the age. When he was ready to begin his work, he allowed people to see veiled appearances and partial expressions. His unmanifest and invisible Self, by its very nature (for those who apprehend the Golden Egg), can never be seen except by the light of the eye when the golden thread which is in every human being has been extended. This requires Buddhi. One who reads the Golden Verses in this reverential spirit can come closer to the Divine Being who was their wise author and gain inspiration which would be invaluable in times of trouble.

Ancient Landmarks: Pythagoras

Ancient Landmarks: Pythagoras

Theosophy, April, 1939

Twenty-five centuries ago the island of Samos was one of the garden spots of Ionia. Colonized hundreds of years before by a group of Arcadians under the leadership of the “great soul” Ancæus, it had now become the “voluptuous isle” where the Tyrant Polycrates spent his days and nights listening to the languishing odes of the poet Anacreon.

Down in the city beneath the Tyrant’s palace there lived a wealthy merchant named Mnesarchus. In the first quarter of the sixth century B.C. he and his wife Parthenis went to Delphi to consult the Oracle, who told Parthenis that she would bear a son who would surpass all men in wisdom and virtue. When Mnesarchus and Parthenis reached Sidon in Phoenicia on their way back to Samos, their son Pythagoras was born.

From Iamblichus we learn that even in childhood Pythagoras astonished all who knew him by the profundity of his wisdom. By the time he had reached the age of eighteen, he had already exhausted the cultural possibilities of his island home. Having heard of Thales and Anaximander, he set sail for the mainland on the first lap of a journey which lasted for almost forty years and took him into every country in the then known world. As soon as Thales conversed with Pythagoras he recognized the superior quality of his mind and advised him to go to Egypt to study with the wise men who had been his own instructors. Leaving Miletus, Pythagoras went first to Sidon, where he was initiated into the Mysteries of Tyre and Byblos. Then he proceeded to Egypt, making the journey with some Egyptian sailors who believed that a god had taken passage on their ship. On his arrival in Egypt Pythagoras at once put himself under the instruction of the teachers of Thales. He spent the next twenty-two years perfecting himself in mathematics, astronomy and music, and was finally initiated into the Egyptian Mysteries.

When Cambyses invaded Egypt, he made Pythagoras his prisoner and sent him to Babylon. Pythagoras utilized this seeming misfortune as an opportunity for growth, and for the next twelve years he studied with the Magi and was initiated into the Chaldean Mysteries. Leaving Babylon, he made his way through Persia into India, where he continued his education under the Brachmanes and imbibed the wisdom of the East at its original source.

At that time India was still feeling the effects of the great spiritual revival brought about by Gautama the Buddha. Although Pythagoras arrived in India too late to come into personal contact with the Buddha, he was greatly influenced by his teachings. Indeed, there is such a close and intimate relationship between the Buddhistic and the Pythagorean systems that the one cannot be fully understood without an acquaintance with the other. Although Pythagoras went to India as a student, he left it as a Teacher. Even to this day he is known in that country as Yavanâchârya, the “Ionian Teacher.”

Pythagoras was fifty-six years old when he finally returned to his native land. Thirty-eight of those years he had spent in foreign lands, fitting himself by study and discipline for his future work. When he arrived in Samos he found the island crushed and ruined, its temples and schools closed, its wise men fleeing from the tyranny and persecution of the great Persian conqueror.

Instead of being welcomed by his countrymen, Pythagoras found them indifferent to the wisdom he was so eager to impart. Despite his best efforts, he was unable to procure a single pupil. One day he saw a poorly dressed young man playing ball in the Gymnasium. Entering into conversation with him, Pythagoras offered to support him if he would consent to receive instruction in geometry. The youth accepted the offer, began his study, and received three oboli from Pythagoras for every problem solved. At last the young man became so interested in mathematics that he offered to study without financial remuneration. Taking the name of Pythagoras for his own, this student became his teacher’s most devoted disciple.

By this time Pythagoras had realized that the island of Samos offered him no opportunity for the development of his educational scheme. Accompanied by his one disciple, he went to southern Italy, settling in Crotona, a town situated on the Gulf of Tarentum. He chose this town because of the freedom of its constitution and the liberal-mindedness of its inhabitants, and also because Pythagoras hoped that his residence in Italy would enable him to spread his teachings throughout the whole of Greece.

Shortly after his arrival in Crotona, Pythagoras visited the Gymnasium, where he was soon surrounded by a group of young men. He reminded them of the solidarity which should exist between students, warned them of the self-control which must be cultivated during the years of adolescence, and urged them to acquire the philosophical knowledge necessary to good citizenship.

The young men listened respectfully to Pythagoras’ words, and when they returned home that evening they repeated his conversation to their parents. A few days later Pythagoras was invited to speak before the Senate of Crotona. On this occasion he advised the Senators to build a Temple to the Muses, whose harmony and interdependence should be a constant reminder of the primary virtues necessary to good government. He also spoke to them of the sanctity of marriage and of those simple family duties which, if faithfully performed, would give them experience for the larger duties of state. He reminded them also of the solidarity which must exist among those who are at the head of the government, stressed the necessity of being able to both give and receive advice and instruction, and gave them a standard of action which, if applied, would bring happiness into their personal lives and success to the country they served.

The Senators of Crotona were so impressed with the wisdom of Pythagoras that they decided to build him an Institute which would serve the several purposes of a school of philosophy and moral training, an academy of science, and a small model city. The School was situated on the top of a high hill overlooking the town, with a glimpse of the Gulf beyond. Although it was understood that it would be patterned after the Mystery Schools, there was nothing about the place suggesting secrecy save a statue of Hermes at the door of the inner school with the words on the pedestal: Let no profane enter here.

Students entered the Pythagorean School first as probationers, and for three years they were closely watched by Pythagoras without being aware of the fact. While they exercised in the Gymnasium Pythagoras would walk among them, carefully observing their natural movements, their facial expressions, and especially their laughter. For, as Pythagoras said, “Laughter is an infallible index to character, and no amount of dissimulation can render agreeable the laugh of an ill-disposed man.” (There are no known writings of Pythagoras. All statements attributed to him are from later accounts of his ideas.) The students exercised with quoits, javelins, and by racing. Pythagoras was opposed to wrestling, saying that men who intended to practice the virtues of friendship should not begin by throwing one another on the sand and rolling about like wild beasts. Such actions, he said, tend to develop hatred, which makes a man inferior to any opponent.

The moral nature of the student was then tested. Sometimes he would be highly praised, to see if pride arose. At other times he would be humiliated before his fellow-students, and his reactions carefully noted. During those early years every thread of the disciple’s moral fibre was tested and strengthened, for Pythagoras taught that true knowledge cannot be acquired until the lower nature is under control. He spoke disparagingly of those teachers who “infuse theorems and divine doctrines into confused and turbid natures, just as if some one should pour pure and clear water into a deep well filled with mud.” The probationary period in Pythagoras’ School, therefore, was closely patterned after the discipline of purification in the Lesser Mysteries.

The student next was tested along intellectual lines. Every mental capacity was carefully noted — the rapidity of his thought, the accuracy of his memory, his power of concentration, and particularly his intuition.

After three years of this probationary discipline, the students who had passed these preliminary tests were admitted into the first degree of the School, becoming known as “listeners.” The purpose of this degree, according to Iamblichus, was that they “should exercise themselves in hearing, in order that they might be able to speak.” For five years, therefore, the students observed silence. Pythagoras knew the power of sound. He taught that the Universe evolves from Sound, and that man creates a universe of his own through the mighty power of his own words. In this degree the students learned to subjugate their tongues, “that being the most difficult of all victories, as those have unfolded to us who instituted the Mysteries.”

The students in this degree were not permitted to ask questions. Questions were propounded by the teachers, but were not answered, every student being obliged to seek the answer within himself. These questions were usually on some abstract subject, such as: What is Harmony? What is the most powerful thing in the world? What is the most difficult thing in the world? Happy the student whose intuition told him that the most difficult thing in the world is for a man to know himself.

These five years of silence accomplished two things. First, they trained the student’s powers of self-reliance and intuition. Second, they gave him training in the secrecy obligatory for the higher degrees, wherein some of the secrets of the Mysteries were disclosed. Upon initiation every student was warned that “it is not lawful to extend to the casual person things which were obtained with such great labors and such diligent assiduity, nor to divulge the Mysteries of Eleusinia to the profane.”

Although the “listeners” were not allowed to discuss their instructions with their teachers or their fellow-students, they were encouraged to associate with one another, especially with older students. In this degree the Unity of all things was stressed: the fundamental Unity lying behind all the diversity of nature; the underlying unity of all religions; the unity and friendship which should exist among all men.

He unfolded the friendship of all things toward all. Indeed he delivered such an admirable friendship to his associates that even now [300 A.D.] those who are benevolent in the extreme towards each other are said to belong to the Pythagoreans. (Iamblichus.)

The story is told of a certain member of the School who fell ill at a wayside inn, and died without being able to pay his bill. Before his death, he asked the inn-keeper to place a certain symbol on the road outside the inn. Months later another Pythagorean passed that way, saw the symbol and discharged the debt of his unknown friend. So did the Pythagoreans understand friendship, not as a matter of personal affection, but as that invisible bond which unites all who study the occult sciences and practice the disciplines of the ancient school.

The daily life of a student at Crotona followed a definite schedule. Rising with the sun, his first thoughts were given to meditation. After pronouncing a mantram on a certain tone, he carefully reviewed all his actions of the previous day and planned the coming day in full detail. After breakfast he took a solitary walk, as Pythagoras did not think it proper to converse with others until one had “rendered his soul sedate, and harmonized his reasoning powers.” The student then repaired to the Gymnasium for his daily exercise, for he had learned that the body is the temple of the soul, and should always be kept in a condition worthy of its divine occupant. The rest of the morning was spent in study. At noon the students dined together in small groups, their meal consisting mainly of bread and honey. Pythagoras himself was a strict vegetarian and the members of his esoteric school were not allowed to eat meat. He was not so strict, however, with the probationers who had not yet commenced their study of practical Occultism. These were permitted to eat the flesh of certain animals, excluding, however, the brain and heart.

The moral discipline of the Pythagorean student steadily increased in intensity, and the line of discrimination between right and wrong became finer with every passing year. Disciples were warned not to be surprised by anything that might happen and trained to meet the greatest shocks with an equal mind. Anger was considered as one of the deadly sins and every student was cautioned not to make a decision or rebuke a servant while under the influence of this passion. The Pythagorean idea of duty might well have been taken from The Bhagavad Gita. Iamblichus gives it thus:

We should never do anything with a view to pleasure as an end.
We should perform what is right, because it is right to do so.

After a frugal lunch, the students received their relatives and friends in the gardens of the School. This was followed by another walk, this time in the company of others. At the close of the day they supped together and read aloud. Before retiring each student again engaged in meditation, following the instructions of Pythagoras found in the Golden Verses:

Never suffer sleep to close thy eyelids, after thy going to bed, till thou hast examined by thy reason all thy actions for the day. Wherein have I done amiss? What have I omitted that I ought to have done? If in this examination thou findest that thou hast done amiss, reprimand thyself severely for it. And if thou hast done any good, rejoice.

After this review, the student chanted his evening mantram, and in the peace and quiet of the soft Italian night he fell asleep.

During the first eight years of probationary discipline the student received no instruction from Pythagoras himself, nor was he permitted to mention the Teacher by name. Those who were unable to stand the discipline left the school and went out again into the world. Even in the higher degrees some occasionally failed by breaking their pledge of secrecy or some other rule which bound them. These were expelled from the School, and a tomb bearing their name was erected in the garden. If a loyal Pythagorean met one of these failures on the street, he did not greet him nor in any way indicate that he had once known him, for Pythagoras taught that such a man is dead. “His body appears among men,” he said, “but his soul is dead. Let us weep for it!”

The great and compassionate heart of Pythagoras ached with helpless pity for those weak souls who had strayed from the Path. But he rejoiced for those who were strengthened by the discipline, who trod the thorny path of discipleship without faltering. These were admitted to the higher section of the School, which corresponded to the Greater Mysteries. During the first eight years of probation, the students were known as Exoterics. Those who entered the higher sections were known as Esoterics.

Ancient Landmarks: The Pythagorean Science of Numbers

Ancient Landmarks: The Pythagorean Science of Numbers

Theosophy, May, 1939

It was an auspicious day for the student at Crotona when Pythagoras received him into his own dwelling and welcomed him as a disciple. The candidate could now look back upon his eight years of probationary discipline with gratitude, for he knew that they had prepared him for the study of Nature’s hidden secrets and placed him on the Path leading to Adeptship.

Pythagoras began his instructions by establishing certain universal principles, proceeding from them into particulars. The key to the whole Pythagorean system, irrespective of the particular science to which it is applied, is the general formula of unity in multiplicity, the idea of the One evolving and pervading the many. This is commonly known as the Doctrine of Emanations. Pythagoras called it the Science of Numbers.

Pythagoras taught that this science—the chief of all in occultism—was revealed to men by “celestial deities,” those godlike men who were the Divine Instructors of the Third Race. It was first taught to the Greeks by Orpheus, and for centuries made known only to the “chosen few” in the Mysteries. Just before the Mysteries began to degenerate, Pythagoras instituted this teaching in his School, thus preserving under the name of “philosophy” the ancient science which, as Plato truly says, is “the greatest good that was ever imparted to men.” In his Life of Pythagoras, Iamblichus repeats the statement of Plato that the study of the science of Numbers tends to awaken that organ in the brain which the ancients described as the “eye of wisdom”—the organ now known to physiology as the pineal gland. Speaking of the mathematical disciplines, Plato says in the Republic (Book VII), “the soul through these disciplines has an organ purified and enlightened, an organ better worth saving than ten thousand corporeal eyes, since truth becomes visible through this alone.”

The present mode of teaching mathematics does little to arouse the higher mind. Even geometry, although based on the Elements of Euclid, is studied only for the purpose of acquiring a knowledge of the other parts of mathematics dependent upon it,

…without having even a dreaming perception of its first and most essential use, that of enabling its votary, like a bridge, to pass over the obscurity of a material nature, as over some dark sea, to the luminous regions of perfect reality. (Thomas Taylor: Theoretic Arithmetic of the Pythagoreans.)

In the seventh book of the Republic Plato indicates the possibilities lying behind the knowledge of numbers. He would make it compulsory for those who manage the affairs of state to study mathematics, “not in a common way, but till by intelligence itself they arrive at the survey of the nature of numbers.” This science, he assures us, should not be used merely for buying and selling, but “for facility in the energies of the soul itself.”

The Pythagorean student approached the science of mathematics from the universal point of view. By applying mathematics to both the Macrocosm and the Microcosm he was able to grasp the secrets of evolution in their minutest details. Quoting from the Neo-Pythagorean Moderatus, Porphyry says that the numerals of Pythagoras were “hieroglyphic symbols, by means whereof he explained ideas concerning the nature of things,” or the origin of the universe.

Plato, summarizing the Pythagorean formula, says that “Deity geometrizes.” The universe evolves from within outward. From the “point” a radiation equal in all directions begins, establishing a circumference, or sphere, within which all activities of the “point” are confined. The point, extending horizontally, becomes a diameter dividing the sphere into positive and negative hemispheres—the basis for action and reaction. The vertical extension of the point into a line crossing the horizontal makes the cross within the circle, and so on ad infinitum. The eleventh Chapter of The Bhagavad-Gita is a dissertation on the Pythagorean Science of Numbers, couched in Eastern terminology. There Krishna shows Arjuna the “vital geometry” of his Divine Form, with all the living lines of force therein and the countless lesser forms produced by them, representing the powers and elements that go to make up the universe.

Pythagoras described the indivisible Unity lying behind all manifestation as “No Number,” in this way repeating the statement in the Stanzas of Dzyan that “there is neither first nor last, for all is one: number issued from no number.” The plane above, therefore, can be indicated only by the nought or Circle, which Pythagoras said is the most appropriate symbol of Divinity.

On the plane below, the Monad or first number appears, and from this number the geometry of the universe emerges. Pythagoras called the Monad, or One, the first odd and therefore divine number. It is through the misinterpretation of the Pythagorean Monad that the various “personal Gods” of the different religions arose, most of whom are represented as a Trinity. In the phenomenal world the Monad becomes the apex of the manifested equilateral triangle, or the “Father.” The left line of the triangle becomes the Duad or “Mother.” This represents the origin of all the contrasts in nature, the point at which the roads of good and evil bifurcate. This being the case, the Pythagoreans are said to have “hated” the Binary. Considering the number Two as a representation of the law of polarity, they stressed its positive aspect by entering a temple on the right side and by putting on the right shoe first. The right line of the triangle represents the “Son,” described in every ancient cosmogony as one with the apex or “Father.” The line at the base of the triangle stands for the universal plane of productive nature, in which “Father-Mother-Son” are unified on the phenomenal plane as they were united in the supersensuous world by the apex.

The triangle is the most profound of all geometrical symbols. As a cosmic symbol representing the Higher Trinity of the universe it became the root of the word Deity. The ancient Greeks called the letter D (the triangular delta) “the vehicle of the Unknown Deity.” The Boeotians wrote the word Zeus with a delta, from which came the Latin Deus. The triangle is also a basic form in Nature. When the molecules of salt deposit themselves as a solid, the first shape they assume is that of a triangle. A flame is triangular in shape; hence, the word pyramid from the Greek pyr, or fire. The triangle is also the form assumed by the pine, the most primitive tree after the fern period.

The Pythagoreans called the number Four the “Key-bearer of Nature.” As a cosmic symbol it represents the universe as chaotic matter before being informed by Spirit. The cross made by the intersection of the vertical line of Spirit and the horizontal line of matter represents spiritual man crucified in the flesh, while the four-pointed star is a symbol of the animal kingdom.

The five-pointed star, the pentacle, is the symbol of man, not only of the physical man with his four limbs and head, but also of conscious, thinking man, whose fifth principle is Manas. The Pythagoreans associated the number Five with the fifth element, Ether. They called Five the “beam of the balance,” which suggests the power of choice and perhaps the final “moment of choice” for our humanity in the middle of the Fifth Round.

The number six illustrates the six directions of extension of all solid bodies. The interlaced triangles picture the union of spirit and matter, male and female. The Pythagoreans considered this number as sacred to Venus, since “the union of the two sexes, and the spagyrisation of matter by triads are necessary to develop the generative force … which is inherent in all bodies.” (Rayon:Potency of the Pythagorean Triangles.)

Pythagoras called seven a perfect number, making it the basis for “Music of the Spheres.” Regarding seven as a compound of three and four, he gave a twofold account of its meaning: On the noumenal plane the triangle is Father-Mother-Son, or Spirit, while the quaternary represents the ideal root of all material things; applied to man, the triangle represents his three higher principles, immortal and changeless, while the quaternary refers to the four lower principles which are in unstable flux. Seven not only governs the periodicity of the phenomena of life on the physical plane, but also dominates the series of chemical elements, as well as the world of sound and color, as shown by the spectroscope.

The Pythagoreans called the number eight “Justice.” In that symbol we find an expression of the eternal spiral motion of cycles, the regular inbreathing and outbreathing of the Great Breath. They called the number nine the “Ocean” and the “Horizon,” as all numbers are comprehended by and revolve within it. If we consult the Table of the Yugas on page 125 of The Ocean of Theosophy,we shall observe that all the figures may be resolved into the number nine.

Ten, or the Decade, brings all these digits back to unity, ending the Pythagorean table. In both the Microcosm and the Macrocosm the three higher numbers of the Decade stand for the invisible and metaphysical world, while the lower seven refer to the realm of physical phenomena.

The Tetraktys of Pythagoras—composed of ten dots arranged in four rows to form a triangle—was the sacred symbol upon which the Pythagoreans took their most binding oath:

“I swear by him who the Tetraktys found,
Whence all our wisdom springs and which contains
Perennial Nature’s fountain, cause and root.”

Theon of Smyrna says that this symbol was honored by the Pythagoreans “because it appears to contain the nature of all things.” H.P.B. indicates the extraordinary philosophical value of theTetraktys in The Secret Doctrine (I, 612). According to Iamblichus, the Pythagorean Tetraktys had eleven forms, each one applying to some one particular phase of cosmic or terrestrial life.

Pythagoras applied the Science of Numbers to music, giving the Western world the mathematical basis of its present musical system. The abstract Circle of music is Sound. The mathematical point within that circle, from which the music of our earth emerges, is the “Tone of Nature,” called Kung by the ancient Chinese. The “line” of music, derived from the ratio 2:3, is what is now called the “perfect fifth.” The rotation of this line forms the “Circle of Fifths,” which gives the basis of all key relationships.

The music of this planet, according to Pythagoras, is but a small copy of the “Music of the Spheres.” The seven tones of the musical scale correspond to the seven sacred planets, each of which is characterized by a certain tone. As Shakespeare makes Lorenzo say in The Merchant of Venice, “There’s not the slightest orb which thou beholdest but in its motion like an angel sings.” The study of music was obligatory in the Pythagorean School, not only as a science but also as a healing agent. Iamblichus informs us that “Pythagoras believed that music greatly contributed to health, if it was used in the proper manner.” Pythagoras taught that the purest type of sound comes from stringed instruments and that wind instruments tend to excite the lower nature rather than to quiet it, an observation later corroborated by Plato.

The study of astronomy was a duty of the School. Pythagoras taught the heliocentric system and the sphericity of the earth; he declared that the moon is a dead planet which receives its light from the sun and described the composition of the Milky Way. More than a thousand years later both Bruno and Galileo derived their theories of astronomy from Pythagorean fragments.

The esoteric students of Pythagoras were given the Mystery teachings in regard to the nature of the soul, its relation to the body and its ultimate destiny. Pythagoras taught that the soul of man is derived from the World-Soul; hence is immortal and cannot be destroyed by death. The soul of man, he said, accomplishes its evolution by means of numberless incarnations on earth. He frequently spoke to his pupils about their own former lives, and when asked about himself said that he had come into the region of mortality to benefit mankind. He also taught the doctrine of Karma, saying that all the seeming injustices on earth are explained by the fact that every life on earth is but a reward or punishment for deeds performed in previous lives. No outside circumstances are to blame for our unhappy lives, he said, since “men draw upon themselves their own misfortunes, voluntarily and of their own free choice.”

Applying the Science of Numbers to the problem of good government, Pythagoras first made himself a “point” in which great spiritual forces were focused, and from that “point” the radii of their influence extended. The Pythagorean School eventually became a small model city, its form of government being adopted by Crotona. From Crotona the sphere of Pythagorean influence expanded to include the neighboring towns, where legislative systems based upon Pythagorean principles lasted for generations.

When Pythagoras was almost a hundred years old he went to Delos to attend the funeral ceremonies of an old friend. One evening, when the Teacher and forty of his pupils were talking together, some of his former pupils who had been expelled from his School set fire to the building where they were assembled, and Pythagoras, with thirty-eight of his pupils, were consumed in the flames.

After the death of the Teacher the School at Crotona was closed and the students departed from Italy. Fearing that the very word philosophy — a word which Pythagoras had coined—would disappear from the Greek language, some of these loyal disciples collected the writings of the older Pythagoreans and wrote down many things which Pythagoras himself had said. These writings were passed down from teacher to pupil, or from father to son, for many generations.

The direct successor to Pythagoras—if such a man could be said to have a successor—was his pupil Aristæus. After him came Pythagoras’ son Mnesarchus, who was named after his grandfather. The Pythagorean fragments were preserved by two hundred and thirty-five of his loyal disciples, two hundred and eighteen of whom were men, the other seventeen women. At the present day all that remains of his ethical precepts is found in the Golden Verses.

On Pythagoras, by Irene Croiset van Uchelen

Pythagoras’ Contribution, by I. M. Oderberg

The Secret Doctrine: In Pythagorean and Platonic Teachings

The Symbolism of Numbers

See Also

History of Philosophy, Chapter II: The Pythagorean School, by William Turner

Pythagoreanism (wiki)



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