A Book Review


The Metaphysical Significance of Pi:
An Investigation into the Esoteric Nature of the Pi Constant.
[A Work in Progress, 2008]
by Patrick Mulcahy

Reviewed by JB



EOH 289: The Fact of God. This is the truth that Being is God Immanent and God Transcendent; it involves the recognition of the great Whole and the related part; it is the knowledge of divinity, ascertained through right relationship and identity of origin. It is the revelation of the life of God, pervading all that is (God Immanent), and of that same life, providing that still greater cosmic relation (God Transcendent) which is the final guarantee of all progress and of progressive revelation. "Having pervaded this whole universe with a fragment of Myself, I remain" is the challenge of Deity and the eternal hope of humanity. This is the answer of Life Itself to the demands of humanity, to the enquiries of science and to the whole world problem. God is here, present among us and in all forms of expression; He includes, pervades and remains beyond. He is greater than all appearance. He reveals Himself progressively and cyclically as man gets ready for further knowledge.


[JB] Transcendental mathematics, a Fourth Ray field of esoteric research, is instrumental in the development of the abstract mind and in the unfolding of the intuitive sense. Both abstract thought and the intuition serve as essential components of a revelatory "bridge" --also called the  "antahkarana"-- needed to ascertain the purpose of Life on Earth and in the Universe.

Patrick Mulcahy's book, a fine contribution to transcendental mathematics, focuses on precisely one of the best metaphors for the gap that this bridge is expected to unite, the PI remainder 0.141593...  I'm not a kabbalist, so I will not address this aspect of the work, limiting myself to review its more general esoteric approach.

Mulcahy launches his exploration from a mathematical fact: after having pervaded a whole universe (circle) with a three-fold fragment (3 diameters) of itself, 0.141593... remains. Thus, there is a gap of 0.141593..., a kind of "precession of the returning point," that needs to be bridged in order to understand the cyclic evolutionary purpose of Life in the Universe. 

It is not known if the value of this constant PI --the ratio of the circumference to its diameter--  has remained fixed throughout the history of the manifested universe. The intuition may lead us to assume that the currently calculated value of the PI remainder is just an approximation of its unmanifested (archetypal) value: 1/7 (0.142857). This is exactly the course chosen in Mulcahy's exploration of this "basic universal threefold cycle."

Let a diameter represent SPACE. Let its corresponding circle represent (motion in) TIME. In this metaphor, linear consciousness would be depicted by the sequence of time events that spiral out from the center. Non-linear consciousness would correspond to the rays orthogonal (perpendicular, i.e., at a 90 degree angle) to the direction of the motion of the events.  In Mulcahy's words: "... radiating monadic force (0.142857) is applied to an otherwise repetitive circular cycle (3.0) and causes it to become an evolving spiral (3.142857)."

Accordingly, our "common-sense" tools of causal inference are based on sequential linear methods along the spiraling path. Esoteric research on the purpose of Life, however, requires a non-linear "orthogonal" consciousness (referred to as "lateral" consciousness by Mulkahy).

The orthogonality of the non-linear approach is crucial to reveal its meaning. Each additional dimension of consciousness is orthogonal to its precursor. A 2-dimensional plane is orthogonal to its corresponding 1-dimensional line; a 3-dimensional space is orthogonal to its corresponding 2-dimensional plane; a 4-dimensional consciousness must be orthogonal to its corresponding 3-dimensional experience. This last orthogonal component we call TIME in our 3-dimensional brain consciousness. The 3.142857 (or 22/7) may represent a fractal value of the fourth dimension as perceived from the third.  

Summing it up, in Mulkahy's own words, "These twenty-one subtle but powerful nonlinear influences represent the lateral force of the seven rays (i.e. symbolised by 0.142857) as it interacts  with the twenty-one components of the linear  spiral (i.e. three on each ray symbolising 1 + 1 + 1 = 3) to form Pi (i.e. 3.142857). The combined sum of this interaction between the seven rays and the spiral of linear consciousness is thus: 7 x 3.142857 = 22 that is, the twenty-two ―methods of activity."

An important key to decipher the esoteric significance of Euler's Identity 

e^{i \pi} +1 = 0.\,\!

is thus explored in this fine book on transcendental mathematics. 

EP I, 415: RAY METHODS OF ACTIVITY. These are twenty-one in number, making in their synthesis the twenty-two methods which are the expression of the great Law of Attraction.

TCF 1222:  ... we are really studying the twenty-one vibrations of the Law of Attraction or motion, with the basic vibration, which is the synthesis of the twenty-one added, thus making the twenty-two...

Book Review

by JB

for NGSM.org


The Intuitive Heart

ANTAHKARANA: 22/7 Words of Power



  I [3]


  WITH  ONE [3]





THE , AND , WITH [3]

I [1]


[22] non-repeating words (out of a total of 30 words) in 7 sentences.

geometry pattern


Sentence Subject Verb Predicate     R
I  ASSERT THE  FACT I to assert fact I (pure Will) Unqualified affirmation (fact of God) I
I  SEE THE GREATEST  LIGHT I to see light I AM (the Eye) Maximum ring-pass-not (universe) II
PURPOSE  ITSELF  AM  I I to be purpose I AM THAT Recursive identification (itself) III

The Point (I), the Circle (II) and the Diameter (III) set the stage for Motion:

TWO  MERGE  WITH  ONE no person to merge no object

synthesis (pairs of opposites) IV - III
THREE  MINDS  UNITE no person to unite no object synthesis: universal, higher, lower V - III
THE  HIGHEST  LIGHT  CONTROLS no person to control no object As Above,
So Below
Implicit "lowest" sight VI - II
THE  HIGHEST  AND THE  LOWEST   MEET no person to meet no object Highest/Lowest Will VII - I




(317993695 = 52 = 7)

Lost am I in light supernal,
yet on that light I turn my back.

After nine Labors of Hercules (Aries through Sagittarius, with Leo through Sagittarius corresponding to the five stages of occult meditation), there are three signs of SYNTHESIS where the task of building the antahkarana is completed. The mysterious glyph of Capricorn may contain a key to this bridging work. -JB


[ 1 + 4 + 7 + 10 = 22 ]

Affirmation of the Disciple

I am a point of light within a greater Light.
I am a strand of loving energy within the stream of Love divine.
I am a point of sacrificial Fire, focused within the fiery Will of God.

And thus I stand.

I am a way by which men may achieve.
I am a source of strength, enabling them to stand.
I am a beam of light, shining upon their way.

And thus I stand.

And standing thus, REVOLVE
And tread this way the ways of men,
And know the ways of God.

And thus I stand.

[MONADIC IDENTIFICATION: Starting at e0 = 1, traveling at the velocity i relative to one's position for the length of time π, and adding 1, one arrives at 0.]


"The intuitive mind is a sacred gift and the rational mind is a faithful servant.
We have created a society that honors the servant and has forgotten the gift."
 - Albert Einstein



| English |