The 3 fundamental variables are coupled pair-wise

In the “Silence of the La Madeleine” I talked about a perfect spring day in Paris and my experience inside the church known as the La Madeleine which looks like a Greek temple from outside.  La Madeleine church is dedicated to Mary Magdalene.

On that day there were hundreds of people sitting outside the church but only few tourists inside and only two people praying or meditating including myself. When I meditate I never think. Meditation is opposite of thinking. Normally, I try to enter into the silence of meditation. Intuition, ideas or inspiration come after meditation. On that day it was different. My meditation was interrupted with ideas regarding the mystery of 3. I could not continue my meditation and I sat there about an hour turning various thoughts in my mind. The silence of the church was amplifying my thoughts.

Prior to this experience I wrote few articles on the the significance of the 3 fundamental variables. The most important one was: Golden Biquaternions, 3 Generations and Spin

Message from the spirit of the La Madeleine was that I have to do a better job of explaining the significance of the 3 fundamental variables and communicate the SRT hypothesis clearly:

SRT hypothesis

• The 3 fundamental variables (gunas) cannot be expressed in terms of each other.
• The 3 fundamental variables (gunas) are coupled pair-wise.
• There is a conservation law for gunas:

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

where $\mathbf{S}$ is the Sattvaguna, $\mathbf{R}$ is the Rajoguna, $\mathbf{T}$ is the Tamoguna. This equation makes the pair-wise coupling of gunas explicit.

Assuming S, R, T are continuous variables, the geometrical shape implied by the equation $\mathbf{S R T = S^2 R^2 + R^2 T^2 + T^2 S^2}$ is known as the Steiner’s Roman surface (the image shown above). It is called Roman surface because Jacob Steiner was visiting Rome when he came up with the idea of this geometrical shape.

How I came up with the SRT hypothesis

When I wrote the “Conservation Law of Three Gunas” I was thinking in terms of logical requirements for the 3 gunas:

• As the Rajoguna (mutative guna) increases, if the Tamoguna (static guna) is increasing the Sattvaguna (sentient guna) must decrease
• As the Rajoguna (mutative guna) decreases, if the Tamoguna (static guna) is decreasing the Sattvaguna (sentient guna) must increase
• The totality of the 3-gunas must be strictly conserved

At that time I was not aware of the significance of the pair-wise coupling. These logical requirements led me to the equation $\mathbf{S R T = S^2 R^2 + R^2 T^2 + T^2 S^2}$

Later, I realized that there are biquaternions that obey the golden condition (g-1/g=1) and the same equation $\mathbf{S R T = S^2 R^2 + R^2 T^2 + T^2 S^2}$ emerges naturally from the mathematics of those golden biquaternions.

The confluence of two independent approaches resulting in the same equation is truly amazing!

Physics implications of the SRT hypothesis are explained in Golden Biquaternions, 3 Generations and Spin. A particular solution of the golden condition 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 condition is more than a mathematical/physical requirement. It is a universal principle. I refer to that principle as the Primordial Generator.

The primordial fabric of the universe has a fundamental invariance.

The golden condition

$g-1/g=1$

is the symbol of this fundamental invariance. The golden condition is telling us that if the primordial fabric is distorted it will be distorted in such a way that the physical manifestation and its inverse will maintain unity. Any distortion in the primordial fabric has to have a dual distortion as to leave the unity unchanged. You can read more about this in Primordial Generator.

Reminder 1: Steiner’s Roman surface is a deformed tetrahedron.

There is only one geometrical structure that can model the pair-wise coupling of 3 fundamental variables: Tetrahedron. The pair-wise couplings can be represented by the angles between the edges of the tetrahedron. The “angle” is a perfect concept to represent “coupling.” There is much more to say on this angle.

Tetrahedron has 6 edges of equal length, 4 faces (equilateral triangles), 4 vertices (3 triangles meet at each vertex).

Steiner’s Roman surface has 4 faces and 4 vertices too. Suppose we place a Roman surface inside a  tetrahedron, then the  4 lobes of the Steiner’s Roman surface would be under the 4 vertices of the tetrahedron. Similarly, the 4 faces of the Steiner’s Roman surface would correspond to the 4 faces of the tetrahedron.

Reminder 2: Tetrahedron is a Platonic solid

I would like remind you that tetrahedron is one of the Platonic solids

There are only 5  geometric objects (convex polyhedra) that satisfy the following properties?

• All vertices touch the circumsphere
• The insphere touches all the faces.
• All faces consist of identical polygons.
• All the vertices are surrounded by the same number of faces.
• All the dihedral angles are equal.
• All the solid angles are equivalent

Such geometric objects are known as Platonic solids. The 5 Platonic solids are: Tetrahedron, Octahedron, Cube, Icosahedron, Dodecahedron.

The mystery of 3 is so profound!