Adapted from “The Elegant Geometry of Our Inner Path to Enlightenment”, Page 100-101
Please Note: The Alpha and Omega in the mathematical model do not have the same meaning as used in Christian theology where they often refer to the beginning and end of the world. As should be clear from the following excerpt, the equation A = Ω emerges when discussing the state of consciousness of a Realized Jiva. Such a jiva has transcended “samsar“, the world of births and deaths or starts and ends. Hence the equation, though just an unanticipated coincidence due to choice of symbols used in the mathematical model, still is meaningful.
” 9.5 Case of the Incarnate (Avatār) and Realized Jīva (Mukta)
A jīva attains Realization when it is vāsana-less and sheds even the “I AM” state of ego. The vāsana distribution function of the Realized jīva is the limiting form of Fig. 9.2, as ε → 0. The limiting form, shown in Fig. 9.3, has a singularity at x= 1, with V’(1) = 1/ε as ε → 0. The infinitely large singularity indicates that the jīva, released from its finite existence attains the infinite, the abode of Īśvaraḥ. It is remarkable that a finite, infinitesimally small jump from ε to zero takes the jīva from the finite to the infinite.
The vāsana distribution function in Fig. (9.3 ) applies to Īśvaraḥ
(Figure 9.3 Yet to Be Downloaded)
Fig. 9.3 The Vāsana Distribution Function of a Realized Jīva
and also to the incarnates (Avatāra Puruṣas) who have “descended” from the abode of Īśvaraḥ to accomplish some particular divine mission. From the results derived in the previous section for the yogī, and letting ε → 0, we get
E’In,k(t) = 1-ε/2 → 1 and hence E’0,k(t) = 1-E’In,k(t) → 0.
D(t) =0 as before.
Plotting the coordinates (1,0) in Fig. 7.4, we arrive ata fact well known in Vedānta: The realized one is ever content and satisfied. (“santuṣta satatam yogī” Gītā, Ch.12, v.14).
Considering both objective and subjective experiences we get (from Eq. 9.1 with ε → 0) the noteworthy result
A= Ω at all times (for the Incarnate and Realized)
or it is always total bliss for the Realized. The incarnate beings revel in the bliss even while actively engaged in their mission on earth. For Īśvaraḥ, Ω is infinite and hence the bliss A is also infinite.
It should be noted that Ω itself may change as a jīva transcends its finite individuality and reaches a realm where it fully identifies in unconditional love with the entire creation, much as Īśvaraḥ does. As explained in Sec 5.10 here we can distinguish between two schools of thought: The advaitic school which defines realization as one where the individuality merges totally with Brahman. In this view Ω, the sentiency of the individual should be considered to end by becoming undefinable like the sentiency of Brahman itself. A is also consequently undefinable in the case of the realized jīva.
In the view of Viśiṣtādvaita, the jīva continues to have individuality after realization with Ω > 0. This jīva continues to experience bliss but which is finite compared to that of Īśvara’s infinite bliss. “