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.


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:










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:













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

N. Roerich's Bridge of Glory

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.

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