Universe according to Pythagoras – pt. 1 – Tetractys

The mystery of creation and our place in it – a subject probably as old as the homo sapiens, and the one that was highly revered by the wise men whose thoughts left a permanent imprint on the foundations of our civilization. A very ancient belief stated that the universe is a result of an interaction between the four (or sometimes five) elements. But what the ancient Greek philosophers wanted to know was which of these elements was the “arche” – the first, and the origin of everything. Thales believed that it was the water, while for Anaximenes it was the air… but Pythagoras, he had some different ideas when he proclaimed: “All things are number”.

Pythagoras had a very simple and elegant manner of explaining his theory – he would draw a triangle in which 10 dots were placed in the 4 rows. This figure became known as  Tetractys, a sacred symbol for many centuries to follow.


Tetractys, Wikipedia commons


The four rows symbolize the four stages of creation. The first dot, known as the Monad, represents the Creator – the first cause. Pythagoreans used many epithets to describe it: “the first, the seed, the essence, the architect, the foundation“. Everything that is, was created from it and contained inside of it.

If we add two even numbers, the result is always an even number, and if we add two odd numbers, the result is an odd number. This rule does not apply only if one of the numbers is 1. For Pythagoreans, this was the proof that number one is two-gendered – a hermaphrodite, as they described the odd numbers as male and the even numbers as female.

This “two-gendered” nature of number one was a proof that besides being limitless, the creator is capable of self-reproduction. The same idea is represented by Ouroboros, a symbol much older than Pythagoras, as we see it depicted on religious artifacts of ancient Egypt, India and even of ancient Mesoamerica. Ouroboros represents eternity, as well as the interaction of the male and female principles, symbolized respectively by its tail and its mouth.


Ouroboros in Alchemical tract, Wikipedia commons

For an obvious reason, Pythagoreans considered Monad as the most important element of Tetraktys, and it was the one that they least discussed. A similar view existed in Orphism:

“Originally there was Hydros (Water), he [Orpheus] says, and Mud, from which Ge (Gaea, the Earth) solidified : he posits these two as first principles, water and earth . . . The one before the two [Thesis, Creation], however, he leaves unexpressed, his very silence being anintimation of its ineffable nature.

Orphica, Theogonies Fragment 54 (from Damascius) (Greek hymns C3rd – C2nd B.C.)

Monad is not discussed as it was believed that it cannot be comprehended by the means of a rational thinking. The word “rational” signifies a process of deduction based on the contrast of two opposites, a contrast that does not exist in a perfect unison that is Monad. A famous Zen Kōan relates to the same thing: “What is the sound of a one hand clapping“? For this reason, Pythagoreans used only a dot in a circle to represent Monad.



Therefore, Monad is a dot, but also the all-encompassing circle. A similar view existed in the Upanishads:

“This whole universe in Brahman…

…He is my self within the heart, smaller than a grain of rice, smaller than a corn of barley, smaller than a mustard seed, smaller than a canary seed or the germ in a canary seed.

Chandogya Upanishad 3.14. 1-4


The “rationality” begins with the Dyad, the second row. In this phase, the light separates from the darkness, male from the female, active from the passive… The word “Dyad”, as well as the number two, are related to the meanings “god” and “light” in most IE languages. For example in Sanskrit: “deva” – god, “dve”- two, and “div” – to shine, words related to Slavic “div” – a giant, “dva” – two, but also Latin “Deus” – God and “duo” – two, English “day” etc.

Dyad is related to the separation of the opposites, the darkness and the light, and in the later mysticism it is usually represented by the two pillars. In Vedic terms, it would be the realm of Vishnu, but we see the same idea in Yin-Yang symbol and other dualistic beliefs such as Zoroastrianism, where it is particularly emphasized. In the “more recent” times, a Christian sect of Bogomils believed that Jesus Christ and Satan were twin “brothers”.

But another reason that the Dyad is comprehensible, is that its two dots form a line, and therefore the first dimension in space.


Pythagoras believed that the laws of Tetractys are applicable to the whole of creation, from astronomy to music. He believed that the movement of the planets creates “music of the spheres”, whose sound we are not able to hear, even though its melody affects us. He used a one string instrument known as Monochord to develop further this theory. By doing so he discovered the musical intervals that we still use to this day, and which are simply the ratios between the rows of Tetractys: 4:3 (perfect fourth), 3:2 (perfect fifth), 2:1 (octave), 1:1 (unison).

A string of the Monochord, stretched between two points would represent the Dyad. But in order to hear its sound, we need to make it vibrate. By doing so we are determining the third point, the one which is not as clearly defined, as the sound of the string will always be the same, no matter where we touch it.

For Pythagoreans, this was the mystical Triad, represented in the third row of the Tetraktys. They believed that number three represents the spirit, motion, light, sound, vibration, time… It is a force that brings back the harmony between the two opposites, describing the nature of their interaction in the process.

In this way, the first three rows of Tetraktys create a perfect triangle with a base of three, an idea very similar to the concept of the Holy Trinity of Christianity, which is often represented by a triangle in religious iconography, and sometimes even referred to as Triad. Therefore, the Triad can be seen as the “Holy Spirit”, while in the much older pantheon of the Vedas it would represent Shiva.

  1. The eye of providence 2. Shiva with his trident, Wikipedia commons

This triangle formed by the first three rows of Tetractys consists of the 6 dots, a number of days needed for the creation of the world. Six is also the first perfect number in mathematics, as it equals the sum of its proper positive divisors (6=1+2+3). And naturally, Triad also represents the second dimension in space.


Tetrad, the final row of four dots, represents the three-dimensional world in its material form. Number four relates to the four elements, the four cardinal directions etc.

And just as the sound of an open string would represent the Trinity, the string that is pressed down would represent the material realm. If we press it in the middle (2:1), we get the octave, the most natural interval – a sound that is the same as that of the string, but one octave higher. The symbol for the octave is a dot in a circle, the same as for the Pythagorean Monad. In Alchemy this symbol represents gold, the accomplishment of the Great Work.

In this way, the four lines of Tetraktys depict the “music of the spheres”, and since there are 12 intervals and 7 notes in music, it is not hard to see how this idea would relate further to the astronomy.

Because of its symbolic, it is very likely that the Pythagoreans envisioned Tetrad as separate from the Triad – an image that would be familiar to us from the dollar bill. The basic idea behind this representation of the “New world order” is that the “enlightened” ones are separated from the other layers of society. But this is just a modification of a very ancient idea. The Vedic society consisted of the four castes, and this division matches perfectly the symbolic of Tetractys:

  • Monad – Creator: Brahmins (priests,  scholars, and teachers)
  • Dyad – Opposites: Kshatriyas (rulers, warriors)
  • Triad – Spirit, Fertility: Vaishyas (merchants)
  • Tetrad – Material: Shudras (laborers and service providers)
  1. Dollar pyramid 2. Vedic caste system, Wikipedia commons

To me, it is very clear that the ancient Vedic society was aware of the meaning of Tetraktys, and that their goal was to replicate the harmony of the cosmic order. If I am correct, it would also mean that even Pythagoras was only reusing the ancient Vedic knowledge.

Indeed, many things that we know about Pythagoras could easily classify him as a Vedic Brahmin: He wore exclusively white, he was a vegetarian, he believed strongly in reincarnation, and we now know that even his theorem had already existed in the Baudhayana sutras of the Vedic India.

Also, his name is probably not Greek. Its etymology was often a question of debate for the later authors, and the best they could come up with is “the marketplace of Appolo”. (Pythios =Apollo + agora=marketplace). But to me, this sounds like a forced etymology. Perhaps this name could be related to Pyatigorsk, meaning “a city between five hills.” – a name that Scythians could have easily used for the other cities in the past? One such example is Phanagoria. I am aware that I risk getting crucified for such a claim, but it is a fact that the term “Greek” was used loosely in those days, as even Thales was an offspring of the Phoenician parents.

But back to Tetractys. Another place where we see its symbolic is the masonic sign square and compasses. A compass represents a triangle and a circle – the spiritual realm, while the square represents that which is measurable, material.


Square and compasses, Wikipedia commons

This symbol is derived from the Alchemical traits of the renaissance and it is not a secret that the Alchemists were highly influenced by the teachings of Pythagoras. On the following images, we see the creation of the world according to them – with Adam and Eve inside of the final circle.

The law of Tetractys in the Alchemical traits

The final circle is a reflection of the incomprehensible Monad, and that reflection is us. Indeed, the names of Adam and Eve are coded deeply in the English language, in the same way that Pythagoreans saw the opposites – odd / even, day / evening, god / devil, good / evil… Adam and Eve are the reflections of the Dyad in the material realm, in which even God gets a human form becoming Krishna or Christ. Or as Protagoras would put it: “Man is the measure of all things

(to be continued)