Orthogonality

I will continue to elaborate on the $\mathbb{C}$ (Confinement) and $\mathbb{L}$ (Liberation) hypothesis mentioned in [1] [2] [3] [4] [5].

$\mathbb{C}$ acts and $\mathbb{L}$ reacts. This is a simplistic description. We have to consider the modalities of the { $\mathbb{C}$ , $\mathbb{L}$ } interplay. One of the most important modalities is orthogonality.

Let’s employ symbolism to gain insight. Circle symbolizes confinement, straight line symbolizes liberation (escape from confinement). Therefore, it is natural to represent $\mathbb{C}$ by a circle and $\mathbb{L}$ by a straight line.

Note that in the figure above the straight line is perpendicular to the plane of the circle. $\mathbb{C}$ and $\mathbb{L}$ are orthogonal. Orthogonality is a measure of independence. $\mathbb{C}$ cannot be expressed in terms of $\mathbb{L}$ and $\mathbb{L}$ cannot be expressed in terms of $\mathbb{C}$ either.

If there is perfect orthogonality there is no coupling. If $\mathbb{C}$ and $\mathbb{L}$ were perfectly orthogonal changing $\mathbb{L}$ would not change $\mathbb{C}$ . Similarly, changing $\mathbb{C}$ would not change $\mathbb{L}$ . Later, we shall see that the orthogonality between $\mathbb{C}$ and $\mathbb{L}$ is not perfect.

$\mathbb{C}$ has a double role. The main function of $\mathbb{C}$ is to form structures and cognitive cores. The second function of $\mathbb{C}$ is to couple itself to $\mathbb{L}$ .

$\mathbb{C}$ is relentless. $\mathbb{C}$ will surely introduce new types of coupling to counter the de-coupling caused by $\mathbb{L}$ .

$\mathbb{C}$ is relentlessly active and $\mathbb{L}$ is relentlessly reactive and they are both very innovative. The { $\mathbb{C}$ , $\mathbb{L}$ } interplay keeps evolving with many innovations in all stages of manifestations.

While $\mathbb{C}$ keeps breaking orthogonality $\mathbb{L}$ keeps restoring it.

How does $\mathbb{L}$ restore orthogonality? One of the $\mathbb{L}$ strategies is the replication of the center. One becomes many while a mysterious connection between the original center and the replicated center is maintained. I refer to this mysterious connection as the ‘reference’. One becomes many but the whole-connectedness is not broken because of the ‘reference’. In Yoga philosophy the ‘reference’ connection (soul connection) is known as the Ota Yoga.

As soon as the replication takes place the degrees of freedom increases. More independent degrees of freedom means more orthogonality. The terms “orthogonality” and “independent” are almost synonymous.

An analogy from the physical stage can illustrate the idea. Each particle in external space has 3 (orthogonal) degrees of freedom (up/down, left/right, forward/backward). When we have many particles the number of combinations for the degrees of freedom quickly increases. For a collection of a large number of particles the degrees of freedom of the system approaches infinity. But remember no physical object (lump of energy) can escape from the $\mathbb{C}$ expression known as gravity. Eventually, $\mathbb{C}$ establishes confinement (coupling) at a different scale. This confinement action is immediately countered by $\mathbb{L}$ reactions. The { $\mathbb{C}$ , $\mathbb{L}$ } interplay is never ending.

Replication is not the only freedom seeking mechanism for $\mathbb{L}$ . As mentioned above, $\mathbb{L}$ is very innovative. $\mathbb{L}$ comes up with various mechanisms and expressions to counter the relentless binding action of $\mathbb{C}$ .

It is extremely important to stress the fact that an expression (manifestation) is not final without the $\mathbb{L}$ reaction. $\mathbb{C}$ prepares the conditions by its binding action but $\mathbb{L}$ has to complete the act of manifestation through its freedom seeking reaction.

It is also important to point out that the { $\mathbb{C}$ , $\mathbb{L}$ } interplay is a non-equilibrium process. Without the initial perfect orthogonality between $\mathbb{C}$ and $\mathbb{L}$ the Cosmos could not start. Without the continual imperfect orthogonality between $\mathbb{C}$ and $\mathbb{L}$ the Cosmos could not evolve.

Follow-up articles

Coupling

Duality Rotation

References

1] Ignoring Agency is Ignorance

[2] Confinement and Liberation

[3] Individuality and Collectivity

[4] Semiotic Closure

[5] Tropes in Physics