A Mathematical Model of the Path of Initiation
by Jose' Becerra, M.D.

"All within the Ashram,  
except those of higher initiate status,  
fall short at times."

Discipleship in the New Age, Vol. II, p. 731

 
According to DK, the initiate Paul distorted some of Christ's teachings. We are told,

It is the creed of a crucified and dead Christ which rules Christianity and not that of the risen Master. One of the reasons for this travesty of the truth has been that St. Paul, that great initiate, prior to taking the third initiation which he did at the time he was functioning as related in The Acts of the Apostles, was potently under Martian influence and was born in Scorpio; a study of his horoscope would demonstrate this were you in a position to study as can we who are connected with the Hierarchy. It was he who gave the Scorpio-Mars slant to the interpretation and exposition of the Christian teaching and deflected its energy into channels of teaching which its Founder had never intended. Esoteric Astrology, p. 213

DK's words could be interpreted to mean that a third degree initiate may still be subject to personal bias. How could that be possible? Haven't third degree initiates overcome the illusions of the mental plane?

In this work we explore these issues by applying a mathematical model developed by others to describe two overlapping paths of spiritual development. One path aims at Truth and attains Unity; the other approaches Life itself and attains Synthesis.

Discernment

Perfect Discernment of the Soul is attained in the pursuit of Truth, as taught in the Eightfold Path of the Buddha. Full Identification with Life is attained by the Monadic realization of synthesis, as in Christ's promise of a "life more abundant."

To discern is to correctly assess pairs of opposites. The fundamental polarity of ordinary human experience is truth versus error. [1] 

 
A "signal detection theory" has been developed, applicable to fields of scientific research such as psychophysics. In short, it states that a "receiver" gets and "operates on" a signal to discern its accuracy according to the signal's "characteristics" (as observed by the receiver). Thus the name "receiver operating characteristic" (ROC) given to the graphical plot of a continuous curve of true positives (sensitivity or "hits") versus false positives (false alarms) for a signal.[2]

Figure 1
Source: http://www.nap.edu/books/0309084369/html/343.html

Figure 1 shows several ROC curves corresponding to increasing levels of accuracy (A) in detecting a signal. The diagonal line (A=0.50) corresponds to random noise. It is useless except to serve as the baseline from which to measure the receiver's accuracy. The closer a curve is drawn towards the point of perfection (100% hits; 0% false alarms) the greater its accuracy. 

The Soul serves as the reference standard of Truth. The personality serves as the receiver of signals operating in "shades of gray" (i.e., a mix of signals and noise). The more "integrated" (i.e., experienced) a personality, the more precise (less noisy) its observations (Figure 2A).

Figure 2A 
Discriminability index 
Source: http://www.cns.nyu.edu/~david/sdt/sdt.html

The more "soul-infused" a personality, the better it is at distinguishing truth from error (Figure 2B). As truth overcomes error we attain unity with the soul of things everywhere.

Figure 2B
Source: http://www.cns.nyu.edu/~david/sdt/sdt.html

Recognitions

"It is an occult truism to state that the aspirant is to be recognised by triplicity; the disciple [is] recognised duality and the initiate by unity." The Rays and the Initiations, p. 470 

"The initiated disciple is beyond registering triplicity and is occupied with the duality of manifestation, with life-energy as it affects or is related to matter-force, with spirit and substance." The Rays and the Initiations, p. 288

We recognize five planetary thresholds in the process of spiritual unfoldment as defined by the Path of Initiation. These five thresholds could be related to the ROC curves corresponding to accuracies of 0.70, 0.80, 0.90, 0.95 and 1.00, respectively (Figure 1).

We are told that an initiation "might be called 'stabilising points of crisis,' in which the 'occasional becomes the constant and the intended becomes the intentional.' " [Discipleship in the New Age, pp. 247] As we ponder on these words, we realize that the "occasional becoming the constant" defines a new average of accuracy for a given initiation. Thus, the ROC model may illustrate how an initiate of higher degree could fail where one of a lesser degree succeeds, while the average accuracy defined by each degree of initiation would still hold.  
 
Interestingly, the ROC curves are drawn in the direction of an arrow sent towards the One. As we develop spiritual discernment, the discernment of differences becomes an increasingly exacting science. As the signals become less noisy and detectable, the difference in Space-Time between the Real and the Unreal also narrow. Thus the need for ROC curves closer to perfection. Such perfection is finally attained on the Fifth Planetary Initiation of Monadic Integration.  
 
However, we know that spiritual unfoldment does not stop at the Fifth Initiation. For a Master to keep growing in ever more inclusive spiritual dimensions, what would be the counterpart for His attainment in the pursuit of Truth? It seems reasonable to propose that a Master develops further in the Life dimensions of Being. As Truth converged towards Unity (the Monad) in the Soul dimensions of Consciousness, the Master would work toward synthesis in the Life dimensions of Being.

The perfect discernment of the Real (1) from the Unreal (-1) reveals the ZERO (1-1=0), a new fulcrum of creative synthesis, the source of Life itself. There are no rational standards to operate (i.e., multiplication and division) with the zero as the center of synthesis. Synthesis‒like the zero--is indivisible. The simplicity of the infinite additive scale refuses to be reduced to complex reasonings (ratios).  
 
The Void of No-Thingness is infinitely beyond reason. Such Void is the Source of All Things in the UNI-verse (1-1=0), the fountain source of Life, the Life more abundant promised by Christ 2,000 years ago.

The reappearance of Lord Maitreya-the Christ will be accompanied by the revelation of a new fiery yoga of synthesis: Agni Yoga. It is the state of consciousness (or rather consciousness without a state) that opens the door to the dimensions of Life ‒AGNI‒ in our spiritual unfoldment.

Agni Yoga encompasses a definite and sustained effort to sense the (Monadic) Presence throughout the Universe in all forms and in all presentations of truth. Only after sensing the (Monadic) Presence‒not theoretically but in vibrating response to its Existence‒can the synthetic Purpose of Shamballa be ascertained. [3]

The Christ or the Buddhic Principle is our Way into Shamballa. We were told then: "I am the Way, the Truth and the Life." He is coming again to fulfill His promise and lead us into the Mysteries of the Path of Initiation.

I would suggest that there has never been a better description of the nature of love than that given by the initiate Paul, even though the translation of his words is faulty at times. Study those passages in the New Testament in which he defines love.  Discipleship in the New Age, Vol. II,, p. 736

It is in the realm of so-called mind that the great principle of separateness is found. It is also in the realm of mind that the great at-one-ment is made. The words of the initiate Paul have here a fitting place, wherein he says: "Let this mind be in you which was also in Christ," and adds in another place that Christ had made "in himself, of twain, one new man". It is through the mind that theory is formulated, truth distinguished and Deity apprehended. When we are more advanced upon the Path, we shall see naught but spirit everywhere, and the aphorism, enunciated by that great disciple, H.P.B., that "matter is spirit at the lowest point of its cyclic activity" and "spirit is matter on the seventh plane," or the highest, will be a realised fact in our consciousness. Esoteric Astrology, pp. 16-17  

References

1. Becerra, JE. A Mathematical Approach to Spiritual Discernment. 1997.  
[http://agni-yoga.org/IHF-TP-1D.htm]

2. Heeger, D. Signal Detection Theory. 2003. [http://www.cns.nyu.edu/~david/sdt/sdt.html]

3. Becerra, JE. Agni Yoga: The Practice of the Presence [http://agni-yoga.org/IHF-TP.htm]

Acknowledgment

Quotations from the books Discipleship in the New Age (DNA) and Treatise on the Seven Rays (TSR) by Alice A. Bailey were reprinted with the permission of Lucis Trust, which holds copyright.