Pythagoras
The Pythagorean Tetractys
The Pythagoreans believed that the Tetractys was an illustration of existence, of the way everything is structured in the universe. Meditating upon the Tetractys symbol is believed to signify the desire to seek Divine understanding and a yearning to attain a close relationship with God.
From the contemplation of the order and progression of the Numbers out of the Monad may be discovered the true relationship between natures and their Cause.
He who understands this mystery is of all men the wisest.
Numbers are the keys to the flow of Universal Energy.
The tetractys or tetrad, or the tetractys of the decad is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the fourth triangular number. As a mystical symbol, it was very important to the secret worship of Pythagoreanism. There were four seasons, and the number was also associated with planetary motions and music.
The first four numbers symbolize the musica universalis and the Cosmos as:
Monad – Unity.
Dyad – Power – Limit/Unlimited (peras/apeiron).
Triad – Harmony.
Tetrad – Kosmos.
The four rows add up to ten, which was unity of a higher order (The Dekad).
The Tetractys symbolizes the four classical elements—air, fire, water, and earth.
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).
A prayer of the Pythagoreans shows the importance of the Tetractys (sometimes called the “Mystic Tetrad”), as the prayer was addressed to it.
“Bless us, divine number, thou who generated gods and men! O holy, holy Tetractys, thou that containest the root and 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-comprising, all-bounding, the first-born, the never-swerving, the never-tiring holy ten, the keyholder of all.”
As a portion of the secret religion, initiates were required to swear a secret oath by the Tetractys. They then served as novices, which required them to observe silence for a period of five years.
The Pythagorean oath also mentioned the Tetractys:
“By that pure, holy, four lettered name on high, nature’s eternal fountain and supply, the parent of all souls that living be, by him, with faith find oath, I swear to thee.”
It is said that the Pythagorean musical system was based on the Tetractys as the rows can be read as the ratios of 4:3 (perfect fourth), 3:2 (perfect fifth), 2:1 (octave), forming the basic intervals of the Pythagorean scales. That is, Pythagorean scales are generated from combining pure fourths (in a 4:3 relation), pure fifths (in a 3:2 relation), and the simple ratios of the unison 1:1 and the octave 2:1. Note that the diapason, 2:1 (octave), and the diapason plus diapente, 3:1 (compound fifth or perfect twelfth), are consonant intervals according to the tetractys of the decad, but that the diapason plus diatessaron, 8:3 (compound fourth or perfect eleventh), is not.
The Tetractys [also known as the decad] is an equilateral triangle formed from the sequence of the first ten numbers aligned in four rows. It is both a mathematical idea and a metaphysical symbol that embraces within itself — in seedlike form — the principles of the natural world, the harmony of the cosmos, the ascent to the divine, and the mysteries of the divine realm. So revered was this ancient symbol that it inspired ancient philosophers to swear by the name of the one who brought this gift to humanity.
In the work by anthropologist Raphael Patai entitled The Hebrew Goddess, the author argues that the tetractys and its mysteries influenced the early Kabbalah. A Hebrew tetractys has the letters of the Tetragrammaton inscribed on the ten positions of the tetractys, from right to left. It has been argued that the Kabbalistic Tree of Life, with its ten spheres of emanation, is in some way connected to the tetractys, but its form is not that of a triangle. The occultist Dion Fortune writes:
The point is assigned to Kether;
The line to Chokmah;
The two-dimensional plane to Binah;
Consequently the three-dimensional solid naturally falls to Chesed.
The relationship between geometrical shapes and the first four Sephirot is analogous to the geometrical correlations in Tetraktys, shown above under Pythagorean symbol, and unveils the relevance of the Tree of Life with the Tetraktys.
In a Tarot reading, the various positions of the tetractys provide a representation for forecasting future events by signifying according to various occult disciplines, such as Alchemy. Below is only a single variation for interpretation.
The first row of a single position represents the Premise of the reading, forming a foundation for understanding all the other cards.
The second row of two positions represents the cosmos and the individual and their relationship.
The Light Card to the right represents the influence of the cosmos leading the individual to an action.
The Dark Card to the left represents the reaction of the cosmos to the actions of the individual.
The third row of three positions represents three kinds of decisions an individual must make.
The Creator Card is rightmost, representing new decisions and directions that may be made.
The Sustainer Card is in the middle, representing decisions to keep balance, and things that should not change.
The Destroyer Card is leftmost, representing old decisions and directions that should not be continued.
The fourth row of four positions represents the four Greek elements.
The Fire card is rightmost, representing dynamic creative force, ambitions, and personal will.
The Air card is to the right middle, representing the mind, thoughts, and strategies toward goals.
The Water card is to the left middle, representing the emotions, feelings, and whims.
The Earth card is leftmost, representing physical realities of day to day living.
The Tetractys refers to a sacred symbol of the Pythagoreans, consisting of four rows of dots containing one, two, three, and four dots respectively, which form an equilateral triangle.
If Pythagoras found himself transported to the modern world, he would have much to learn about technology, science, and human thought. But is there something Pythagoras can still teach us today in his symbol of the tetractys? What do the dots reveal? How is it significant to Freemasonry?
To start with, tetractys refers to a symbol of the Pythagoreans which consists of four rows of dots containing one, two, three, and four dots respectively which form an equilateral triangle. Many have found the tetractys full of sublime meaning.
Pythagoras was born in Samos in the sixth century B.C. Pythagoras was both a mystic and a scientist, although some scholars tend to praise his mathematical prowess while looking away with embarrassment at his perceived “mysticism.” For Pythagoreans, they were one and the same.
The Science of Number was the cornerstone of the Pythagoreans. It describes, if not yet everything, at least something very important about physical reality, namely the sizes and shapes of the objects that inhabit it.
The Pythagoreans influenced the world by the simple expression:
“All is number.” ― Pythagoras
What Did Pythagoras mean by this famous motto “All is Number?”
Is it possible to listen to this message today afresh, with Pythagorean ears?
Manly Palmer Hall dedicated an entire chapter in his work “The Secret Teachings of all Ages” to the both mystical and philosophical qualities of Pythagorean numbers.
Manly Palmer Hall wrote:
“The ten dots, or Tetractys of Pythagoras, was a symbol of the greatest importance, for to the discerning mind it revealed the mystery of universal nature.”
Hall states that if one examines the tetractys symbolically a wealth of otherwise hidden wisdom begins to reveal itself.
The Prestonian Lectures (1772) give us further insight into some of the possible masonic thinking on the tetractys in the 1800’s. It was the subject in one of the series of lectures written by Brother William Preston for instruction and education of the Lodge members.
An excerpt of the Lecture (1772) goes as follows:
“The Pythagorean philosophers and their ancestors considered a Tetractys or No. 4:
1st as containing the decad;
2nd as completing an entire and perfect triangle;
3rd as comprising the 4 great principles of arithmetic and geometry;
4th as representing in its several points the 4 elements of Air, Fire, Water and Earth, and collectively the whole system of the universe;
Lastly as separately typifying the 4 external principles of existence, generation, emanation, creation and preservation, thence collectively denoting the Great Architect of the Universe Wherefore to swear by the Tetractys was their most sacred and inviolate oath.”
In other words, it is taught to Freemasons that a four-fold pattern permeates the natural world, examples of which are the point, line, surface and solid and the four elements earth, water, air and fire. Musically they represent the perfect consonants: the unison, the octave, the fifth and the fourth.
The Divine Creator in Freemasonry is sometimes referred to as The Great “Architect” or Grand “Geometrician” always building the universe through the creative tools of the geometer. Tetractys itself can be interpreted as a divine blueprint of creation.
Some say that Pythagoras and his successors had two ways of teaching, one for the profane, and one for the initiated. The first was clear and unveiled, the second was symbolic and enigmatic. In order to achieve mastery of this universe, a person has to discover the veiled meaning of numbers hidden in all things.
I have often wondered if we could hypothetically peer into the mind of the Grand Geometrician, and the veil was lifted, what design would we see?
The Grand Design:
Perhaps we would see how the Master Builder has ordered all things by measure and number and weight. Throughout the structure of the universe the properties of number are manifested. Geometry is fundamental to the work of the masonic builders. It is engaged with the first configurations of the Plan upon which the form is erected and the idea materialized.
Examining numbers symbolically, they represent more than quantities; they also have qualities. Madame H. P. Blavatsky in the “Secret Doctrine” tells us the numbers are entities. They are mysterious. They are essential to all forms. They are to be found in the realm of essential consciousness. They are clues to our evolution.
Blavatsky emphasizes that the study of numbers is not only a way of understanding nature, but it is also a means of turning the mind away from the physical world which Pythagoras held to be transitory and unreal, leading to the contemplation of the “real.”
Personally, I find that the masonic teachings in all their many symbolic forms a good way to study numbers. The reason I continually come back to Pythagorean philosophy is the tradition of music theory. In music, the Divine patterns of the Grand Geometrician are expressed in musical ratios. Harmony through sound, therefore, can be applied to all phenomena of nature, even going so far as to demonstrate the harmonic relationship of the planets, constellations, elements and everything, really. The reason being that all life vibrates, like the string.
Why do Freemasons connect the dots? Like many symbols, the tetractys can lead a craftsman down a rabbit hole of self-discovery. By rabbit hole, I mean a portal into a mysterious and infinite wonderland of formulas filled with beauty, confusion and intrigue – a place to encounter all sorts of adventures with concepts beyond our wildest dreams that keeps us coming back for more.
“The more deeply we study the processes of nature the greater in every direction becomes our admiration for the wonderful work of Him who made it all.”
― Charles Webster Leadbeater