Integration Formulas and Identification Functions

Teachings on Initiation, Formula Three
("...the seed of all philosophies..."):

"There is that which transmutes knowledge into wisdom within a flash of time; there is that which changes sensitivity into love within an area of space; there is that which alters sacrifice into bliss where neither time nor space exists." -DINA II

I. Math background [adapted from Wikipedia/calculus]

In mathematics, a function is a formal statement defining how the elements of one domain are mapped into another. For example, the expression f(x)=x+2 describes a function, f, that relates a number, x, with the results of an operation, x+2. Thus, an input of 3 is related to a value of 5, and can be expressed as f(3)=5.

The properties of functions may be further described with the tools of differential and integral calculus. The word "calculus" stems from the nascent development of mathematics: the early Greeks used pebbles arranged in patterns to learn arithmetic and geometry, and the Latin word for "pebble" is "calculus," a counting unit.

Calculus is built on two major complementary ideas, differentiation and integration. Differential calculus "derives" the instantaneous rate of change of a mathematical function's value with respect to changes in the input variable. Such "derivative" can be illustrated by the slope of a function's graph. For instance, speed is the "instantaneous rate of change" of the "difference quotient" of distance over time.

$\frac{dy}{dx}$

Integral calculus, on the other hand, is an extension of the concept of a sum (Greek letter Sigma). The process of finding integrals is called integration and is used to find a measure of totality, such as an area. For instance, the area under a speed function curve represents the spatial distance traveled in a given time interval.

$\int_a^b f(x)\, dx$

II. Integration Formulas and Identification Functions on the Path of Return to the Source:

I AM THAT I AM

 Identity (I am): 1 = 1 (All-thing) I am ONE with every-thing Source (THAT): 1-1 = 0 (No-thing) That is no-thing There is THAT which: Function: x F(x) Transmutes Knowledge Wisdom Flash Time Light Right (cyclical) Relations (Manas) Changes (Transforms) Sensitivity Love Area Space Love Good Will (Buddhi) Alters (Transfigures) Sacrifice Bliss Infinity Being Life Will-to-Good (Atma)

F(knowledge) = Wisdom
[past + present + future] ~ infinitely small measure of TIME ["flash"]

F(sensitivity) = Love
[group consciousness] ~ infinitely great measure of ["bounded"] SPACE

F(sacrifice) = Bliss
[Logoic Purpose] ~ Unfathomable Monadic PRESENCE

III. Agni Yoga: GROUP Revelation of the Purpose (THAT)

A. The (manifest) UNI-VERSE is derived by DIFFERENTIATION.

B. The SOURCE of All is known by (Monadic) INTEGRATION .

I am the ONE,
Begotten by the ZERO,
Differentiated into INFINITY,
Integrated into the conscious SYNTHESIS
Of LIGHT, and LOVE and LIFE,
For the GLORY of the ONE.

***

The Gayatri

O Thou Who givest sustenance to the universe,
From Whom all things proceed,
To Whom all things return,
Unveil to us the face of the true Spiritual Sun
Hidden by a disc of golden Light
That we may know the Truth
And do our whole duty
As we journey to Thy sacred feet.

2006-11-14