।।तरति शोकमात्मवित्।।

Functions of a Complex Variable;

Open and Closed Contours --

Pure and Applied Mathematics.

--

A Sequel to the last post :

"Real and Unreal"

--

The 7 Dimensions of the Universe --

Have been defined in the earlier post. 

Just like as on the Real Plane represented by (X, Y) there exists the 

Conjugate Imaginary Plane (X, iY).

The Functions of a Complex Variable could be expressed on either or both of the two planes. Here we are concerned with the two dimensional imaginary plane :

(X, iY) only,  which could be further extended in application to the :

Whole 7-Dimensional Universe.

Now, as an example, let us consider the standard equation of a Circle :

On the Real plane (X, Y), the equation  x squared + y squared = r squared 

represents a Circle with a

Closed Contour

With respect to Real Numbers.

If we consider the equation :

x squared - y squared = r squared,

The same holds true in the case of the

Complex numbers (x, iy)

on the 

Complex Plane (X, iY).

What significance holds for 'i' ?

Could this be related by :

"t" where "t" denotes "time"?

The premise :

"The  Observer is the Observed"

Points out to the undeniable, irrefutable existence of :

"an observer",

as the Essential Underlying Principle.

This is evident that :

The consciousness of the individual, the attention and the Awareness are but the synonyms of the "Observer".

"The Observed" could be either of the two :

An object as a sentient being, or some insentient thing or object.

The premise, notion or the hypothesis of "time" in terms of "past" "present" or "future" too applies at the level of the individual, the collective entity named as the objective existence or the "world" and the essential factor / truth of the "observer".

As has been already pointed out above, in the bold italics, this is the same as :

The individual consciousness,  Attention,  Awareness, 

The Inevitable Reality  and 

The  Potential Possibility.

Not to be found in any Philosophy or any Philosophical Thought.

Here lies the practical Vedanta truth of The Dharma: The Sanatana Dharma.

आत्मानं विद्धि.. 

तद्विद्धि प्रणिपातेन परिप्रश्नेन सेवया।।

उपदेक्ष्यन्ति ते ज्ञानं ज्ञानिनस्तत्वदर्शिनः।।३४।।

- श्रीमद्भगवद्गीता अध्याय ४,

Gita Chapter 4, verse 34.

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