Let’s look at the significance of √2 and √3 but before that let’s capture the philosophical significance of Progression and Proportion:
· The whole world is conceptualized as wave harmonics of the primordial rhythm with a progression and proportion. Philosophically the Proportion which does not change / which is constant is the immutable component and the progression which changes / is volatile is called as the Mutuable component in the process of evolution. The whole universe is the progression and God is the proportion. So if I know the God’s proportion and the formula behind it I can create anything in this universe including a universe. This secret is called as the Brahma Vidya / Sree Vidya (Knowledge of Brahman, Sree) in Indian texts. What we are going to see further are very minor parts of the Brahma Vidya. J
· In the last part we saw, that the primordial square multiplied itself to be a larger square (progression of squares) using the proportion √2. The diagonal of the square 1 (ABCD) forms the root of Square 2 (AGHJ). This is very profound if you get the concept.
· If we consider square 1 as the cause then its diagonal is the effect. This diagonal is the root for the next square (AGHJ) and hence the effect of Square 1 is the cause of Square 2, this cause results in square 2’s diagonal which is its effect and this is how the progression or evolution happens. If you can see glimpses of Cause and effect cycle and the famous law of Karma in this analogy then you can pat yourself. J
· A square halved by the diagonal (square 1 with area 1) produces a square twice its area (square 2, area = 2). The mystery of biological growth from cellular division or the different musical notes from the base tone is contained in this.
· Robert Lawlor in his book “Sacred Geometry” very nicely puts it as the root of a plant (like the root in a square) is causative and embedded in the earth (and embedded in the square). These are very heavy and profound concepts just let it sink into you.
· When you divide the full height of the human being considering the total height as unity then belly as called as Hara in Japanese, Dantein in Chinese, Nabhi in India which is below the navel will measure (2- √2) from the soles of the feet to belly and (√2 -1) from navel to the head. In Yoga, Zen and Chinese meditation techniques this point corresponds to the transformative and generative aspects of the individual that involves rooting techniques for self transmutation. So Lao Tzu said, “To seek the root is the goal”.
· Hence √2 signifies the power of multiplicity. Hence the Generative aspect of this rhythm is attributed to √2. This represents the principle of transformation.
· Remember √2 is a proportion in the progression of squares and a square does not become a higher form. We have seen that the diagonal of the cube (sides of unit length) is √3. It is this √3 which divides the volume form of a cube and the diagonal of the cube becomes a root for the higher shapes like pentagon, hexagon etc.
· Hence √3 signifies the formative power of the rhythm while √2 signifies the generative power of the nature.
We will touch the same using Vesica Piscis in the next part which shall take us to √5 and the golden meanF. I am not going to touch upon important topics like Gnomic spirals and the relation between various progressions and hence I would request you to Google them if you are interested.
There are many books on this topic and I would recommend “Sacred Geometry – Philosophy & Practice” by Robert Lawlor which I found easy to read and understand.
You tube and Internet is replete with tons of images, articles and videos on this topic and you can learn a great deal from them.