10 – The Tetractys and Sacred Numerology
- The Tetractys (Triangular Number of 10) – Sacred geometry of divine order.
1+2+3+4=10
Bless us, divine number, thou who generatest gods and men! O Holy, Holy Tetractys, thou that containest the root and the source of the eternally flowing creation! For the divine number begins with the profound, pure unity until it comes to the holy four; then it begets the mother of all, the all-compromising, the all-bounding, the first-born, the never-swerving, the never-tiring holy ten, the keyholder of all. - Pythagorean Prayer
The Tetractys of Pythagoras
“Nature and humanity can be understood in terms of fourfold patterns. The solar year has four seasons, and the day is divided into four quarters. The compass has four main directions, and a circle can be divided into four 90-degree segments. Early Greek philosophers described four elements: earth, water, air, and fire. Modern science recognizes four states of matter: solids, liquids, gases, and ether. Nature itself reflects this fourfold structure through its kingdoms: mineral, plant, animal, and human. Human beings can also be seen as composed of four layers: the physical body, the etheric double, the emotional body, and the mental body. Pythagoras illustrated this principle in his famous Tetraktis—a triangle containing ten points or numbers from 1 to 10, arranged so that each side has four points, with one point at the center. The four points at the base symbolize the lower, material aspects of man, while the rows of three, two, and one above represent his higher spiritual dimensions. In this way, the Tetraktis captures the harmony between the material and the spiritual, showing the interplay of the fourfold and the threefold in both Nature and humanity.”
The Tetractys represented the organization of space:
- the first row represented zero dimensions (a point)
- the second row represented one dimension (a line of two points)
- the third row represented two dimensions (a plane defined by a triangle of three points)
- the fourth row represented three dimensions (a tetrahedron defined by four points)
Tetractys. The Greek word τετρακτύς signifies, literally, the number four, and is therefore synonymous with the quaternion; but it has been peculiarly applied to a symbol of the Pythagoreans, which is composed of ten dots arranged in a triangular form of four rows.
This figure was in itself, as a whole, emblematic of the Tetragrammaton, or sacred name of four letters, (for tetractys, in Greek, means four,) and was undoubtedly learned by Pythagoras during his visit to Babylon. But the parts of which it is composed were also pregnant symbols. Thus the one point was a symbol of the active principle or creator, the two points of the passive principle or matter, the three of the world proceeding from their union, and the four of the liberal arts and sciences, which may be said to complete and perfect that world.
This arrangement of the ten points in a triangular form was called the tetractys or number four, because each of the sides of the triangle consisted of four points, and the whole number of ten was made up by the summation of the first four figures, 1 + 2 + 3 + 4 = 10.
Hierocles says, in his Commentaries on the Golden Verses (v. 47): “But how mayst God to be the Tetractys? This thou mayst learn in the sacred book ascribed to Pythagoras, in which God is celebrated as the number of numbers. For if all things exist by His eternal decrees, it is evident that in each species of things the number depends on the cause that produces them... Now the power of ten is four; for before we come to a complete and perfect decade, we discover all the virtue and perfection of the decade in the four. Thus, in assembling all numbers from one to four inclusive, the whole composition makes ten,” etc.
And Dacier, in his Notes on these Commentaries and on this particular passage, remarks that “Pythagoras, having learned in Egypt the name of the true God, the mysterious and ineffable name Jehovah, and finding that in the original tongue it was composed of four letters, translated it into his own language by the word tetractys, and gave the true explanation of it, saying that it properly signified the source of nature that perpetually rolls along.”
So much did the disciples of Pythagoras venerate the tetractys, that it is said they took their most solemn oaths, especially that of initiation, upon it. The exact words of the oath are given in the Golden Verses, and are referred to by Jamblichus in his Life of Pythagoras:
Ναὶ μὰ τὸν ἁμετέραν ψυχὴν παραδόντα τετρακτύνΠαγὰν ἁενάου φύσεως, ἀλλ' ἔρρει δι' ἔργον.
i.e.,
“I swear it by him who has transmitted into our soul the sacred tetractys,The source of nature, whose course is eternal.”
Jamblichus gives a different phraseology of the oath, but with substantially the same meaning. We will find the sacred delta bearing the nearest analogy to the tetractys of the Pythagoreans.
The outline of these points form, it will be perceived, a triangle, and if we draw short lines from point to point, we will have within this great triangle nine smaller ones. Dr. Hemming, in his revision of the English lectures, adopted in 1813, thus explains this symbol:
“The great triangle is generally denominated Pythagorean, because it served as a principal illustration of that philosopher's system. This emblem powerfully elucidates the mystical relation between the numerical and geometrical symbols. It is composed of ten points, so arranged as to form one great equilateral triangle, and at the same time to divide it into nine similar triangles of smaller dimensions. The first of these, representing unity, is called a monad, and answers to what is denominated a point in geometry, each being the principle by the multiplication of which all combinations of form and number are respectively generated. The next two points are denominated a duad, representing the number two, and answers to the potential line which, consisting of length without breadth, is bounded by two extreme points. The three following points are called the triad, representing the number three, and may be considered as having an indissoluble relation to all superficies, which consist of length and breadth, when contemplated as abstracted from thickness.”— An encyclopaedia of freemasonry and its kindred sciences, c. 1924 by Albert Gallatin Mackey
”The Pythagoreans found the primacy of the universe in numbers. They saw creation as a cosmos, i.e., an ordered whole as opposed to chaos. In numbers, mathematical conditions and geometric figures, they saw the orderly principle in both the physical and the ethical world. Through the harmony of the spheres – sweet sounding, yet only heard by the higher mind – both macrocosm and microcosm are governed, and it is by viewing and contemplating external and internal things that we reveal the secrets of existence. The most sacred number was the tetractys, the ten enclosed in the series 1+2+3+4, which later became embraced in the Jewish and Christian alchemical traditions.” - (From Alchemy The Divine Work book)