The Secret Teachings of All Ages · 72 of 236

The Symmetrical Geometric Solids

To the five symmetrical solids of the ancients is added the sphere (1), the most perfect of all created forms. The five Pythagorean solids are: the tetrahedron (2) with four equilateral triangles as faces; the cube (3) with six squares as faces; the octahedron (4) with eight equilateral triangles as faces; the icosahedron (5) with twenty equilateral triangles as faces; and the dodecahedron (6) with twelve regular pentagons as faces.

the right and the other to the left. The branch to the right was called Divine Wisdom and the one to the left Earthly Wisdom. Youth, personified by the candidate, walking the Path of Life, symbolized by the central stem of the Υ, reaches the point where the Path divides. The neophyte must then choose whether he will take the left-hand path and, following the dictates of his lower nature, enter upon a span of folly and thoughtlessness which will inevitably result in his undoing, or whether he will take the right-hand road and through integrity, industry, and sincerity ultimately regain union with the immortals in the superior spheres.

It is probable that Pythagoras obtained his concept of the Υ from the Egyptians, who included in certain of their initiatory rituals a scene in which the candidate was confronted by two female figures. One of them, veiled with the white robes of the temple, urged the neophyte to enter into the halls of learning; the other, bedecked with jewels, symbolizing earthly treasures, and bearing in her hands a tray loaded with grapes (emblematic of false light), sought to lure him into the chambers of dissipation. This symbol is still preserved among the Tarot cards, where it is called The Forking of the Ways. The forked stick has been the symbol of life among many nations, and it was placed in the desert to indicate the presence of water.

Concerning the theory of transmigration as disseminated by Pythagoras, there are differences of opinion. According to one view, he taught that mortals who during their earthly existence had by their actions become like certain animals, returned to earth again in the form of the beasts which they had grown to resemble. Thus, a timid person would return in the form of a rabbit or a deer; a cruel person in the form of a wolf or other ferocious animal; and a cunning person in the guise of a fox. This concept, however, does not fit into the general Pythagorean scheme, and it is far more likely that it was given in an allegorical rather than a literal sense. It was intended to convey the idea that human beings become bestial when they allow themselves to be dominated by their own lower desires and destructive tendencies. It is probable that the term transmigration is to be understood as what is more commonly called reincarnation, a doctrine which Pythagoras must have contacted directly or indirectly in India and Egypt.

The fact that Pythagoras accepted the theory of successive reappearances of the spiritual nature in human form is found in a footnote to Levi’s History of Magic: “He was an important champion of what used to be called the doctrine of metempsychosis, understood as the soul’s transmigration into successive bodies. He himself had been (a) Aethalides, a son of Mercury; (b) Euphorbus, son of Panthus, who perished at the hands of Menelaus in the Trojan war; (c) Hermotimus, a prophet of Clazomenae, a city of Ionia; (d) a humble fisherman; and finally (e) the philosopher of Samos.”

Pythagoras also taught that each species of creatures had what he termed a seal, given to it by God, and that the physical form of each was the impression of this seal upon the wax of physical substance. Thus each body was stamped with the dignity of its divinely given pattern. Pythagoras believed that ultimately man would reach a state where he would cast off his gross nature and function in a body of spiritualized ether which would be in juxtaposition to his physical form at all times and which might be the eighth sphere, or Antichthon. From this he would ascend into the realm of the immortals, where by divine birthright he belonged.

Pythagoras taught that everything in nature was divisible into three parts and that no one could become truly wise who did not view every problem as being diagrammatically triangular. He said, “Establish the triangle and the problem is two-thirds solved”; further, “All things consist of three.” In conformity with this viewpoint, Pythagoras divided the universe into three parts, which he called the Supreme World, the Superior World, and the Inferior World. The highest, or Supreme World, was a subtle, interpenetrative spiritual essence pervading all things and therefore the true plane of the Supreme Deity itself, the Deity being in every sense omnipresent, omniactive, omnipotent, and omniscient. Both of the lower worlds existed within the nature of this supreme sphere.

The Superior World was the home of the immortals. It was also the dwelling place of the archetypes, or the seals; their natures in no manner partook of the material of earthiness, but they, casting their shadows upon the deep (the Inferior World), were cognizable only through their shadows. The third, or Inferior World, was the home of those creatures who partook of material substance or were engaged in labor with or upon material substance. Hence, this sphere was the home of the mortal gods, the Demiurgi, the angels who labor with men; also the dæmons who partake of the nature of the earth; and finally mankind and the lower kingdoms, those temporarily of the earth but capable of rising above that sphere by reason and philosophy.

The digits 1 and 2 are not considered numbers by the Pythagoreans, because they typify the two supermundane spheres. The Pythagorean numbers, therefore, begin with 3, the triangle, and 4, the square. These added to the 1 and the 2, produce the 10, the great number of all things, the archetype of the universe. The three worlds were called receptacles. The first was the receptacle of principles, the second was the receptacle of intelligences, and the third, or lowest, was the receptacle of quantities.

“The symmetrical solids were regarded by Pythagoras, and by the Greek thinkers after him, as of the greatest importance. To be perfectly symmetrical or regular, a solid must have an equal number of faces meeting at each of its angles, and these faces must be equal regular polygons, i. e., figures whose sides and angles are all equal. Pythagoras, perhaps, may be credited with the great discovery that there are only five such solids.* * *

‘Now, the Greeks believed the world [material universe] to be composed of four elements—earth, air, fire, water—and to the Greek mind the conclusion was inevitable that the shapes of the particles of the elements were those of the regular solids. Earth-particles were cubical, the cube being the regular solid possessed of greatest stability; fire-particles were tetrahedral, the tetrahedron being the simplest and, hence, lightest solid. Water-particles were icosahedral for exactly the reverse reason, whilst air-particles, as intermediate between the two latter, were octahedral. The dodecahedron was, to these ancient mathematicians, the most mysterious of the solids; it was by far the most difficult to construct, the accurate drawing of the regular pentagon necessitating a rather elaborate application of Pythagoras’ great theorem. Hence the conclusion, as Plato put it, that ‘this (the regular dodecahedron) the Deity employed in tracing the plan of the Universe.’ (H. Stanley Redgrove, in Bygone Beliefs.)

Mr. Redgrove has not mentioned the fifth element of the ancient Mysteries, that which would make the analogy between the symmetrical solids and the elements complete. This fifth element, or ether, was called by the Hindus akasa. It was closely correlated with the hypothetical ether of modern science, and was the interpenetrative substance permeating all of the other elements and acting as a common solvent and common denominator of them. The twelve-faced solid also subtly referred to the Twelve Immortals who surfaced the universe, and also to the twelve convolutions of the human brain—the vehicles of those Immortals in the nature of man.

While Pythagoras, in accordance with others of his day, practiced divination (possibly arithmomancy), there is no accurate information concerning the methods which he used. He is believed to have had a remarkable wheel by means of which he could predict future events, and to have learned hydromancy from the Egyptians. He believed that brass had oracular powers, because even when everything was perfectly still there was always a rumbling sound in brass bowls. He once addressed a prayer to the spirit of a river and out of the water arose a voice, “Pythagoras, I greet thee.” It is claimed for him that he was able to cause dæmons to enter into water and disturb its surface, and by means of the agitations certain things were predicted.

After having drunk from a certain spring one day, one of the Masters of Pythagoras announced that the spirit of the water had just predicted that a great earthquake would occur the next day—a prophecy which was fulfilled. It is highly probable that Pythagoras possessed hypnotic power, not only over man but also over animals. He caused a bird to change the course of its flight, a bear to cease its ravages upon a community, and a bull to change its diet, by the exercise of mental influence. He was also gifted with second sight, being able to see things at a distance and accurately describe incidents that had not yet come to pass.

Iamblichus gathered thirty-nine of the symbolic sayings of Pythagoras and interpreted them. These have been translated from the Greek by Thomas Taylor. Aphorismic statement was one of the favorite methods of instruction used in the Pythagorean university of Crotona. Ten of the most representative of these aphorisms are reproduced below with a brief elucidation of their concealed meanings.

I. Declining from the public ways, walk in unfrequented paths. By this it is to be understood that those who desire wisdom must seek it in solitude.