Universe according to Pythagoras – pt. 1 – Tetractys

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, for Anaximenes it was the air… But Pythagoras had some different ideas when he proclaimed: “All things are number”.

Pythagoras had a simple and elegant manner of explaining his theory. He would draw a figure that became known as  Tetractys, a sacred symbol for many centuries to follow. It is an equilateral triangle, made out of ten dots arranged in four rows. Each row (and each dot) carry different symbolism.



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 number one to the even number, the result is always an odd number. And if we add number one to the odd number, the result is an even number. For Pythagoreans, this was proof that number one is two-gendered – a hermaphrodite. They described the odd numbers as male and the even numbers as female.

This “two-gendered” nature of number one proved that besides being limitless, the creator is capable of self-reproduction. The same idea exists in the Ouroboros symbol, much older than Pythagoras. We see it on religious artifacts of ancient Egypt, India, and even ancient Mesoamerica. Ouroboros represents eternity, but also an interaction of the male and female principles, symbolized respectively by its tail and its mouth.

Ouroboros, Tetractys, Pythagoras, Monad

Ouroboros in Alchemical tract, Wikipedia commons

For an obvious reason, Pythagoreans considered Monad as the most important element of Tetraktys. It was also the one that they least discussed. A similar view existed in Orphism. Orpheus lists the earth and water as first elements, but

“The one before the two he leaves unexpressed, his very silence being an intimation of its ineffable nature.

Monad is not discussed as it cannot be comprehended by the means of rational thinking. The word “rational” signifies a process of deduction based on the contrast (ratio) of two opposites. This contrast does not exist in 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.

Monad, Tetractys


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 the 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 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, in the later mysticism usually represented by the two pillars. In Vedic terms, it would be the realm of Vishnu, but we see the same idea in the Yin-Yang symbol and other dualistic beliefs such as Zoroastrianism. 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”. This is a 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 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 make a perfect triangle with a base of three. It is an idea very similar to the concept of the Holy Trinity of Christianity. We often see it as a triangle in religious iconography and sometimes even they call it the Triad. Therefore, the Triad represents the “Holy Spirit”, while in the much older pantheon of the Vedas it would stand for 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, four cardinal directions, four seasons, etc.

And just as the sound of an open string represents the Trinity, the pressed string represents the material realm. If we press it in the middle (2:1), we get the octave, the most natural interval. It is 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.

Vedic origins of Tetractys?

Because of its symbolism, it is very likely that the Pythagoreans envisioned Tetrad as separate from the Triad – an image that is familiar to from the dollar bill. The basic idea 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. The Vedic caste system, Wikipedia commons

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

Who was Pythagoras really?

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, with the most common idea being “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. But perhaps even the Sogdian Panchekanth (five cities) is not far in meaning. Also, a popular Italian city of Cinque Terre still has the same meaning to this day. It is a fact that the term “Greek” was used loosely in those days. Even Thales was an offspring of the Phoenician parents.

Pythagoras, Scythian, Tetractys

A deeper meaning

But back to Tetractys. Another place where we see its meaning 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 comes from the Alchemical traits of the renaissance. It is not a secret that the Alchemists were influenced by the teachings of Pythagoras. On the following images, we see the creation of the world  – 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. Their names make a root in opposites such as “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

Part 2



  1. “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.“
    7+5=12 even number 3+7=10 even etc.


    • True, thanks for pointing that out, I read that explanation somewhere and took it without analysis. In any case, their view of odd and even numbers was definitely as described, but obviously not for this reason.

  2. The ten points are the ten decimals, corresponding to the ten sefirot. This means that the tetractys is the cosmic tree (the tree of life) defining the digital structure of the universe.

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