Tetractys

The primary stage of  existence is ONE-Existence. This is represented as a POINT of the first row. This ONE existence of “Everything and Everyone” is represented by “Biṃdu or a POINT” even in TANTRA Śāstra. The reason for this is that, a POINT acts as a seed for the forthcoming creation. Just like in a seed, which has a blueprint of the would-be creation, a POINT has a blueprint of what ever that will be unfolding from it.

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Also, can you imagine a “point” ? A point has no dimension or we can call it ‘0D’. A non-dimensional entity is impossible to imagine. The moment we imagine, we attribute a dimension to it and hence it implies that we can not imagine. But still we can talk and think about such an entity! This is because, we all originated from POINT and hence we have the essence of POINT in us. So, instead of “analyzing” a point, one has to synthesize with it and become verily IT. This is the GOAL of any spiritual student. Anyways, so, the first stage of SPATIAL comprehension starts with the root i.e., The POINT.

The secondary stage is a set of two points as represented by the second row. What comes with a set of two points, that are not identical (i.e., the points are not one and the same)? We get a LINE SEGMENT. What does this segment suggest? It is a One-Dimensional object or ‘1D’ object. A 1D line segment is that stage of differentiation which lets us comprehend the aspect of “Length”.

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A length occurs only when one point is different from another and thus, we are speaking of “Manifested and Separated” Creation now. We are able to say “She” and “I” etc., due to this second stage of Tetractys. A distinction between “TWO” entities is suggested by the two points and a correlation between them is suggested by the “line segment” that joins them.

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So, in summary, the second stage of comprehension of SPACE occurs by the 1D line segment of the two points of second row of Tetractys. Again, can you imagine a line? The moment we imagine, we give a thickness to the line and hence we are not imagining it. So, even 1-D object can not be imagined by us nor can it be dealt/felt by us. Can we hold or touch a line? No!

The third stage gives us three points of the third row of tetractys. If three points are collinear, i.e., if they form a line, no new information is revealed to us (as we explored a LINE in previous stage). So, the three points must not be collinear. Then what is that,  that we get from these points? We get a 2-Dimensional PLANE formed by the triangle, having these three points as its vertices. A 2-D plane represents our comprehension in terms of “Areas”.

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The surface area of an object, the area of a plot, the plane of Earth’s surface that we see, surface of water beds, etc., are all being possible to comprehend by us due to this third stage of Tetractys. We are able to travel on waters, walk on Earth, watch movies on the screen and do what not because of this 2-D comprehension? So compared to 0D and 1D, ‘2D’ is giving us more interactive freedom with the space around us!

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But still, we can not imagine a plane in its complete ideality. If you try to imagine a plane, you will attribute a thickness to its edges by default (because we can not imagine a “no-thickness” ever!). This will defy our definition of a plane being 2D surface (as the thickness adds another dimension to the plane). So, not even 2D surface can be properly imagined by us! But we can touch a surface, unlike a line or point!

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The final and fourth stage of creation is represented by the fourth row of the Tetractys. This gives us 4 points that are not co-planar, for if they are, we won;t get any new information. So, what is the figure formed by the four non-co-planar points? We get a Pyramid or a 3-Dimensional Object. A 3-D object is very comfortable to imagine. We can not only touch the object, but we can also imagine and feel the object in our heads. So, this fourth stage represents completely manifested creation.

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Thus, the slow evolution of our comprehension of SPACE from a point to a line to a plane to a SPACE is described by the 1, 2, 3 and 4 dots of Tetractys. It is interesting to associate the present link to two of Vēdic concepts here:

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Vak or Speech

The number of stages of Vāk or Speech are given to be four: Parā Vāk, Paśyaṃtī Vāk, Madhyamā Vāk and Vaikharī Vāk.

• Parā is akin to point (1-dot) – it is imperceivable and hence represents an “impulse to speak”.

• Paśyaṃtī is akin to a line (2-dots) i.e., it represents a cloudy idea in our mind.

• Madhyamā is akin to a semi-perceivable plane (3-dots) and hence represents a mental blue print of the idea that we want to convey.

• Vaikharī, the final one, is the uttered physical word which is akin to the manifested pyramid or completely perceivable object (4-dots). 

Thus, the 4 rows of tetractys also represent the four stages of VĀK. This VĀK is what is uttered by the creator BRAHMA, as his daughter SARASWATHI. These four stages are symbolical to his four heads! So, his uttered creation also has four stages, in his likeliness, of perception as mentioned in previous paragraphs. 

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Purusa Sukta

In Puruṣa Sūkta, there is a line that says “Pādōsya Viśvā Bhūtāni Tripādasya Amṛtaṃ Divi“. It means that “three-fourths of the creation exists in immortal divine planes while the remaining one fourth of creation manifests as the physical perceivable cosmos“. 

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The “Spatial Dimensions“, “Vāk” and “Puruṣa Sūkta” are all linked! Can you see how?

• The three stages of spatial dimension – 0D, 1D and 2D are not perceivable by us in complete fashion. Also, they are kind of fictional for us, because we can not create a perfect point or line or a plane ever!

• Similarly, the first three stages of Vāk: Parā, Paśyaṃti and Madhyama are all in our head. They are impulse, cloudy idea and mental blue print  respectively, and thus exist inside our head. They are not manifested yet. So, they are not perceived by “another” human at all!

• Similarly, according to Puruṣa Sūkta, this whole cosmos has four stages – three stages are hidden or DIVINE i.e., imperceptible.

• But, only one fourth of cosmos is perceivable according to Puruṣa Sūkta just like the 3D object (fourth stage of spatial dimension) or the Vaikharī Vāk (fourth stage of Divine/Human Speech) of the above examples. 

Is this not a Beautiful link to be meditated upon?!!

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Cycles of Time

When one closely observes the Indian scriptures and Tetractys together, one can easily find a link in terms of cycles of TIME. The numbers 4, 3, 2, 1 are universally used to represent cycles of TIME – (go to Kabbalah or Vēdās for example). Here, let us see how Indian division of time cycles use these numbers of tetractys!

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4 3 2 forms the base number for the calculation of time scales. Mineral, plant, animal and humans — all evolve in different speeds and hence different time scales are used for each. For example, 432 Earth years gives historical periodicity or 4320 Earth years give the cycles of floods of World oceans, etc.

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The number that we know publicly as “432000 Earth years” represents the time taken for a cosmos to complete one unit of “YUGA” or a “Cycle of TIME”. This UNIT is called “KALI” and hence the duration of time of 432000 earth years is called “KALI YUGA“. The duration of this YUGA forms a base of measure of succeeding yugās and cycles of time. 

• Base Unit Kali Yuga                          = 1 x 432000 =    432000

• Dwāpara Yuga is twice Kali Yuga = 2 x 432000 =    864000

• Trētā Yuga is thrice of Kali Yuga   = 3 x 432000 = 1296000

• Kṛta Yuga is four times Kali Yuga = 4 x 432000 = 1728000

These are the four yugās that are spoken of in the scriptures of the East. Did you see the link to Tetractys yet? See the colored “Unit” that is multiplied to the base number of 432000. What do you see? 1 2 3 and 4, right! These are the same number of dots as in Tetractys.

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Let us now add these units i.e., 1+2+3+4. What do we get? 10. Add all the Yugās as mentioned above: 432000 + 864000 + 1296000 + 1728000. What do you get? You get the same base number with an added 0 at the end i.e. “4 3 2 0 0 0 0“ This is called one “Mahā Yuga” – “The Great Cycle of TIME”.

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So, Pythagoras gave out all this by just the diagram of “Tetractys”. The tetractys is sometimes called a “Decad“, for it has 10 dots. Its 4 3 2 1 dots and the total numerical-value of 10 are what constitute the whole set of cycles of TIME or Yugās. There is more to the yugās like Manvantarās, Days of Brahma, Age of Brahma, etc. This is important to know to study the “evolutionary patterns” on a cosmic scale. For example, one manvantara has certain kinds of humans while the other has different ones.

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These are hinted in our Purāṇās and Itihāsās in form of Gaints, Cyclopses, Ape-Men, etc. The same is also recorded by world scriptures, as proved in ” The Secred Doctrine” by H. P. Blavatsky. So, to understand this grand scale of evolutionary cycles, we need to have the key of TETRACTYS. Pythagoras used it as a simple tool to expound on that wisdom!

The musica universalis (literally universal music), also called music of the spheres or harmony of the spheres, is a philosophical concept that regards proportions in the movements of celestial bodies – the Sun, Moon, and planets – as a form of music. The theory, originating in ancient Greece, was a tenet of Pythagoreanism, and was later developed by 16th-century astronomer Johannes Kepler.

Read More Music of The Spheres click

Read More Kabballah Tree of Life Hierarchy of The Archangels click

Source: https://en.wikipedia.org/wiki/Musica_universalis 

Pictures Videos Music and Additional Reading

Tetractys

Source: https://en.wikipedia.org/wiki/Tetractys

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The tetractys (Greek: τετρακτύς), 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.

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Pythagorean symbol

1. The first four numbers symbolize the musica universalis and the Cosmos as:

   1. Monad – Unity

   2. Dyad – Power – Limit/Unlimited (peras/apeiron)

   3. Triad – Harmony

   4. Tetrad – Kosmos

2. The four rows add up to ten, which was unity of a higher order (The Dekad).

3. The Tetractys symbolizes the four classical elements—air, fire, water, and earth.

4. The Tetractys represented the organization of space:

   1. the first row represented zero dimensions (a point)

   2. the second row represented one dimension (a line of two points)

   3. the third row represented two dimensions (a plane defined by a triangle of three points)

   4. 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.

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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.

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Kabbalist Symbol

Symbol by early 17th-century Christian mystic Jakob Böhme, including a tetractys of flaming Hebrew letters of the Tetragrammaton. A tetractys of the letters of the Tetragrammaton adds up to 72 by gematria.

Read More Tetragrammaton 4 Letter Name of God click

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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:

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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.

Lyric Video.