Inspiring Metaphors (3): Triangle

Triangle and the 3 Gunas

In spiritual philosophy, in some religions, in most esoteric philosophies and in various metaphysical creation theories the triangle and the essence of triangle the number 3 is used as a metaphorical device to refer to the 3 fundamental tendencies (gunas).

Triangle according to Dan Brown

According to Dan Brown, the triangle symbol represents the spiritual enlightenment in Freemasonry. In my opinion Brown’s “enligtenment” corresponds to the “Mukti” concept in eastern philosophies regarding the merger of the human mind with the Cosmic Mind and release of the human mind from the cycle of rebirths.

Mukti and Moksha

Mukti is the stage before Moksha which is the final dissolution of ego in the infinite ocean of love and bliss (Nirguna Brahma, Infinite Existence, Absolute Being, Consciousness). When the human mind merges in the Cosmic Mind permanently human attains the eternal life of Saguna Brahma (Supreme Being) and become part of the Cosmic Mind (the mind of Saguna Brahma). When the soul (atman) unites with the Cosmic Soul (Atman) permanently the final human goal (Moksha) is reached. The word “permanent” is emphasized because before the “permanent” merger or union there will be temporary ones. The temporary experience is known as samadhi.

Triangle Symbology in Ancient Mystery Schools

According to Douglas De Long the ancient mystery schools taught the “law of 3” or the “law of the triangle” which said that 3 “essences” were required to create or manifest something. He also acknowledges that the “law of 3” was borrowed from ancient Hinduism. It is clear that the “3 essences” refer to the 3 gunas. Douglas De Long says that the triangle also symbolizes reincarnation and claims that this was the interpretation used by Jesus as well [1].

Ancient Egypt

According to Moustafa Gadalla [2]  the metaphysical role of the number 3 was recognized in Ancient Egypt:

each unity is a triple power and double nature

I like Gadalla’s summary of the ancient wisdom. This is a deeply meaningful phrase.

In the Bremner-Rhind Papyrus it is stated that:

“After having become one neter (god), there were [now] three neteru (gods) in me [i.e. Atum, Shu, and Tefnut]”

Sefer Yetzirah of Kabbalah

Sefer Yetzirah is the earliest text of Kabbalah. Sefer Yetzirah means “Book of Formation” in Hebrew. The origin of the text is unknown. In many of the Kabbalistic commentaries, verse 1:1 is translated as:

“…He engraved Yah…, the Living God,.. and He created His Universe with three books (Sepharim), with text (Sepher), with number (Sephar), and with communication (Sippur)”.

According to Aryeh Kaplan the “He” refers to the Infinite Being (Ein Sof) who is above all divine Names. Ein Sof of Kabbalah corresponds to the Nirguna Brahma of Tantra Yoga. Nirguna Brahma is the Unmanifested Consciousness which is the Absolute Being, the Infinite Existence, the infinite ocean of love and bliss.

It is also clear to me that “Sepher”, “Sephar”, and “Sippur” are related to the 3 gunas Rajoguna, Tamoguna, Sattvaguna.

Taoism

In Taoism the “I Ching” (Yi Jing) uses trigrams which represent the 3 gunas. A trigram is a simplified representation of the various combinations of the 3 gunas. In reality the number of combinations is infinite (uncountable) but “I Ching” comes up with 64 combinations using 8 fundamental trigrams.

Remember 8 is the number of combinations you can arrange 3 objects in different ways. Combining the trigrams in pairs produces the 64 hexagrams. The table of “I Ching” hexagrams is a representation of the quaternion group $\mathbf{Q_8}$ in mathematics.

The line place (first, second, third line) corresponds to the one of the 3 gunas. From the descriptions of the solid and broken lines it is clear that

solid line : yang =  Sattvaguna

broken line: yin = Tamoguna

transitions between yin/yang = Rajoguna

Tantra Yoga: Brahmacakra (Cycle of Creation)

The 3 gunas (sattvaguna, rajoguna, tamoguna) constitute the foundation of the Tantric Theory of Creation known as Brahmacakra which was modernized and reformulated by Shrii Shrii Anandamurti [3][4].

Ananda Sutram (the short text that explains the Ananda Marga philosophy in sutra format) has the following entries regarding the creation of the universe:

“The tri-attributional primordial force (progenitrix of creation) flows on in endless triangular forms.” – Ananda Sutram 4-1

“In the triangle of forces, the three attributes of Prakrti are locked in endless mutual transformation.” – Ananda Sutram 4-2

“In the first stage (not yet a stage of actual manifestation), Prakrti is called Shivánii, and the witnessing Puruśa at the nucleus is called Paramashiva.” – Ananda Sutram 4-3

“In the second phase, when the germ of evolution sprouts, Prakrti is called Bhaeravii, and the witnessing Puruśa is called Bhaerava.” – Ananda Sutram 4-4

“In the vibrational world there is a sequence of similarity of curvatures (homogenesis). Here Prakrti is called Bhavánii and the witnessing Puruśa is called Bhava.” – Ananda Sutram 4-5

“The process of creation starts from Shambhúliuṋga.” – Ananda Sutram 4-6

“In the ultimate state of crudification, the paráshakti lying dormant at Svayambhúliuṋga is called kuńd́alinii (‘coiled serpentine’).” – Ananda Sutram 4-7

“The kuńd́alinii is the (force of) fundamental negativity.” – Ananda Sutram 4-8

New Insights

I have been writing about my intuitions about the 3 gunas.  In the article titled Conservation Law of Three Gunas I came up with a mathematical expression to express the conservation law of 3 gunas.

$\mathbf{SRT = S^2 R^2 + R^2 T^2 + T^2 S^2}$

where S is the Sattvaguna, R is the Rajoguna, T is the Tamoguna. I showed that S,R,T reside on a Steiner’s Roman surface. SRT is always positive; either S,R,T are all positive or else exactly two are negative. I also put forward the hypothesis:

A physical process can be represented by the guna vector (S,R,T) whose trajectories always remain on a Steiner’s Roman surface.  The totality SRT is strictly conserved.  The zero vector  (0,0,0) is  not possible.

My goal in that article was to show that 3 gunas is not just philosophical or esoteric talk. The 3 gunas is relevant in the context of physics. In the very near future physicists will establish the connection between the 3 gunas and the mysterious 3 that shows up in particle physics. Now, let’s talk about the mystery of 3 in physics.

Physics

In physics there are exactly 3 generations (families or flavors) of fermions. Fermions are the constituents of matter. The quarks which are fermions carry exactly 3 “color charges”. Why only 3 generations? Why only 3 color charges? The reason is clear but it will take some time for physicists to establish the connection mathematically. The 3 fermion generations and the  3 color charges are manifested because the fundamental process behind the scenes is an interplay of 3 gunas.

You can read my findings in this context in the physics paper “Golden Biquaternions, 3 Generations, and Spin“.  In that paper I show that a particular solution of the golden condition (g – 1/g = 1) for biquaternions and its physical interpretation as the fermion predicts exactly 3 generations and 1/2, 3/2, 2 as the only possibilities for particle spin and hints at the composite nature of bosons. The ‘golden biquaternion as fermion’ idea works if there are 3 fundamental variables that are coupled in a pairwise fashion.

References

[1] Douglas De Long, “Ancient Teachings for Beginners”, Llewellyn Publications, ISBN 978-1-56718-214-9

[2] Moustafa Gadalla, “Egyptian Cosmology”, Tehuti Research Foundation, ISBN 0-9652509-3-8

[3] Avadhutika Ananda Mitra Ac., The Spiritual Philosophy of Shrii Shrii Anandamurti: A Commentary on Ananda Sutram, 2nd Edition, Ananda Marga Publications, ISBN 81-7252-119-7