The Pythagorean Science of Numbers
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 the Tetraktys 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.