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The Tetractys is a rather unique symbol both because of its appearance and its history. It’s made up of 10 identical dots arranged in four rows forming a triangle. The bottom row includes 4 dots, the second has 3, the third 2, and the top row just 1 dot. The triangle they form is an equilateral one, meaning that its three sides are equally long and its angles are all at 60o. This means that the triangle looks the same regardless of which side you’re looking from.
As for the Tetractys symbol’s etymology, it comes from the Greek word for the number four – τετρακτύς or tetrad. It’s also often called Tetractys of the decad and it’s the geometrical representation of the fourth triangular number T4 (as opposed to T3 being a triangle with 3 rows, T5 being a triangle with 5 rows, etc.)
But why is the Tetractys symbol so important? What makes these 10 dots arranged in a triangle anything more than a simple “connect the dots” puzzle?
As a mathematical model, the Tetractys symbol was designed by the famous Greek mathematician, philosopher, and mystic Pythagoras. Throughout his life Pythagoras did much more than advance mathematics and geometry, however, as he also began and advanced the Pythagorean philosophy. What’s fascinating about the Tetractys symbol in relation to Pythagorean philosophy is that the symbol has multiple different meanings.
The Tetractys as the Cosmos in Musica Universalis
The different triangular numbers have different Pythagorean meanings and the Tetractys is no exception. While T1 or Monad symbolizes Unity, T2 or Dyad symbolizes Power, T3 or Triad symbolizes Harmony, T4 or Tetrad/Tetractys is the symbol for the Cosmos.
This means that according to the Pythagoreans, the Tetractys represented the universal geometric, arithmetic, and musical ratios upon which the entire universe was built. And that leads us to the several other interpretations of the Tetractys which lead to it being viewed as the symbol of the Cosmos.
The Tetractys as the Organization of Space
Much more intuitively, the Tetractys is also believed to represent the several known dimensions of space. The top row is said to represent zero dimensions as it’s just a single point, the second row represents one dimension as its two points can form a line, the third row represents two dimensions as its three points can form a plane, and the last row can represent three dimensions as its four points can form a tetrahedron (a 3D object).
The Tetractys as a Symbol of the Elements
Most philosophies and religions at the time of Pythagoras believed that the world was made out of four basic elements – fire, water, earth, and air. Naturally, the Tetractys was believed to symbolize these four natural elements as well, further cementing it as the symbol of the Cosmos.
The Tetractys as the Dekad
The simple fact that the Tetractys triangle is comprised of 10 points was also significant to the Pythagoreans as ten was a sacred number to them. It used to represent a unity of the highest order and was also called The Dekad.
Tetractys Meaning in Kabbalah
The Pythagoreans weren’t the only ones to ascribe meaning to the Tetractys symbol. The mystical Hebrew belief system Kabbalah also had its own view on the Tetractys. It is a fairly similar interpretation on the symbol, however, the followers of the Kabbalah had arrived at it on a purely mystical ground while the Pythagoreans had formed their view on the symbol through geometry and mathematics.
According to Kabbalah, the symbol was an illustration of all existence and the way the universe was structured. They believed that because they connected the Tetractys’ shape to that of the Tree of Life which was a significant symbol in Kabbalah as it is in many others.
Another line of reasoning for the followers of the Kabbalah was that the ten points of the Tetractys represent the ten Sephiroth or the ten faces of God.
In Kabbalah, the Tetractys was also linked to the Tetragrammaton – the manner in which the name of God (YHWH) is spoken. The followers of the Kabbalah made the connection by substituting each of the ten points in the Tetractys with a letter of the Tetragrammaton. Then, when they added the numeric value of each letter they got the number 72 which is considered holy as ait symbolizes the 72 names of God in Kabbalah.
Although simple in appearance, the Tetractys has complex symbolism and is a multi-faceted symbol with significance to both secular and religious groups. It symbolizes the ratios that can be found in the creation of the universe, outlining the sequences of creation and the fundamental aspects of what we find in the cosmos.