Sri Ram An A

TOWARDS A MATHEMATICAL THEORY OF SPIRITUALITY BASED ON ADVAITA (Part III):

ON SRI RAMANA’S PRINCIPLE OF PERSONAL WILL - Raju Chidambaram, Ph.D SUMMARY Bhagawan Sri Ramana often taught his devotees that everything in the world happens at the Will of Ishwara only and not at the will of the individual jeeva. But there is one notable exception, Bhagawan used to observe: It is up to each jeeva to decide whether to identify with the world (i.e. Non-Self) or with the Self. The present paper -the third in a series- examines this principle in the context of the mathematical framework presented in the earlier papers at previous WAVES conferences by this author.

EXPERIENCER/ AWARENESS

INTRODUCTION Parts I and II of this series proposed a mathematical model of spiritual detachment based essentially on the teachings of Vedanta ( Ref 1). That model posited that all changes in the world are the result of the interplay of Prakriti’s Wish (expressed as probabilistic laws) and Ishwara’s Will. The spiritual evolution of a jeeva is captured in the model using a function θ(t), representing the jeeva’s degree of spiritual detachment at time t, varying in the range (0,π/2 radians). At the lowest level of detachment θ(t)= 0 and indicates that the jeeva is fully identified with the world or Non-Self. At the other end of the range, θ(t)= π/2 signifies that the jeeva is completely detached from the world and fully absorbed in the Self. The spiritual progress of a jeeva over its many life times can be shown by plotting (t, θ(t)) in polar coordinates (Fig 1). Fig 1: Spiritual Progress as (t, θ(t))

☼ Point where J3’s progress curve meets the vertical axis AB. J3 attains Perfection here.

☼ J2

B J2

D (t,θ(t))

t C

θ(t) A

E

EXPERIENCED O-E-T As a jeeva becomes increasingly detached from the world through sadhanas, it suffers less and less from worldly concerns and at the same time gains more and more in purity

of mind as its selfish desires are replaced by universal love. These twin effects of spiritual detachment on a jeeva’s life are described in the mathematical model by the complex function ζ(t) ζ(t) = ∫ e iθ(t) dt As elaborated in Ref (1), the real part of ζ(t), represented by τ(t), is a measure of the jeeva’s “suffering” cumulated over the period 0 to t, while the imaginary part, G(t) is interpreted as the jeeva’s accumulated merit over the same period. That is, ζ (t) = τ(t) + i.G(t) = ∫ e iθ(t) dt…… Eq. (1) A graph of G(t) plotted against τ(t) provides an overall view of the spiritual life or “path” of the jeeva (Fig 2). It was further explained using the model that a jeeva attains Realization when its detachment θ(t) reaches the maximum possible value of π/2 radians. ☼ Point where G(t)=Accumulated Merit

Fig 2: Path of Jeeva “J” as (τ(t), G(t))

B

tangent to J2’s path becomes vertical. J2 attains Perfection here. J2 endures no more changes.

☼ C

J A

E

τ(t) EXPERIENCED TIME; O-E-T The model viewed the material and spiritual domains somewhat differently. Changes in the material domain were incorporated using a probabilistic approach based on the Prakriti- Ishwara partnership mentioned earlier, whereas the spiritual evolution of the jeeva was modeled without any explicit probabilistic elements. However Sri Ramana’s teaching gives a large role to personal free will in a jeeva’s spiritual unfoldment. It was therefore conjectured that both material and spiritual domains could be, and should be, put on same conceptual footing. Presence of freewill introduces uncertainty and uncertainty implies probabilities. THE PROBABILISTIC APPROACH The possibility of solving Eq. (1) in some probabilistic sense is suggested by Sri Ramana’s assertion that the only decision left to the free-will of a jeeva is to “either identify with the world (i.e. Non-Self) or with the Self” (Ref 2). All other decisions, by virtue of which the world changes from moment to moment, are made as per the Will of

Ishwara, says the sage. The general implication of Sri Ramana’s profound insight is that a jeeva has no control over the external material domain of which Ishwara is the sole supreme ruler, but has control over its own spiritual destiny. To see how Sri Ramana’s Principle may be incorporated into Eq. (1), consider the complex variable z’(t) defined by z’(t) = {1-γ(t)}/cosθ(t) + i. γ(t)/sinθ(t)

Eq. (2)

where γ(t) is a random variable which takes the values 1 or 0 with probability sin2θ(t) and cos2θ(t) respectively; 1 if the jeeva identifies itself with the Self and 0 if it is attached to Non-Self. z’(t) is a random function of t. With this definition we see that the expected value of z’(t), denoted by E{z’(t)}, is cos θ(t) + i.sin θ(t) or eiθ(t). Hence E{z(t)} =E{ ∫ z’(t) dt }= ∫ E(z’(t)) dt = ∫ e iθ(t) dt…. Eq (3) Comparing Eq.(3) with Eq.(1), the expected path of z(t) in the probabilistic case and ζ(t) in the deterministic case are seen to be the same. Therefore we conclude that ζ(t) can be viewed as the expected path of a jeeva which, at time t, identifies itself with Non-Self and Self with probabilities cos2θ(t) and sin2θ(t) respectively. At any point in time, the gradient with respect to time of the path ζ(t) (or expected path in the probabilistic case) is cos θ(t) + i. sin θ(t). Of this complex number, the real part cosθ(t) is the time derivative of τ(t) and the imaginary part sinθ(t) is the time derivative of G(t). A plot of G(t) against τ(t) is what we call as the “jeeva’s path”. The tangent of this path at any point is the derivative of G with respect to τ and is equal to G’(t)/τ’(t) = sinθ(t)/cosθ(t) or tanθ(t). This simply confirms the sense in which we have been using the function θ(t) in the deterministic case, namely, as giving the “direction of the path” at time t. Figure 3 below can be used to visualize geometrically the two cases.

G(t)= Accumulated Merit

Path (G(t),τ(t)) Figure 3

Tangent at P to the Path Two possible directions in prob. case

Q

P(G(t),τ(t)) O

θ(t) S

τ(t)= Experienced Time

T

In the above diagram, let P be a point corresponding to time t in the path of a jeeva with coordinates G(t),τ(t). PQ is the tangent to this path. The gradient at P is dG/dτ = tanθ(t) = tangent of the angle QST. Thus, in the deterministic case, the direction of the jeeva at time t is PQ. In the probabilistic case, as per Eq. (2), the gradient z’(t) is either {1/cosθ(t) +i. 0) if γ(t) = 0 or {0+i/sinθ(t)} if γ(t) =1. As before, since the real part of z’(t) is dτ(t)/dt and imaginary part is dG(t)/dt, the gradient dG/dτ is either 0/(1/cosθ(t)) = 0*cosθ(t) = 0 (1/sinθ(t))/0 = ∞

if γ(t)=0 OR if γ(t) = 1

That is, the gradient of G with respect to τ is either 0 or ∞, implying that in the probabilistic case the instantaneous direction of the jeeva at any time t is either along the horizontal axis or the vertical axis. As seen before, the expected direction is along PQ which is the same as in the deterministic case. THE MEANING OF γ(t) IN EQUATION (2) The freedom to choose between Self and Non-Self is presumably available to jeevas all the time. It is reasonable to assume that a jeeva’s choice at time t between these two alternatives depends on its spiritual detachment θ(t): higher the detachment, more likely that it will choose to identify with the Self. Choosing to identify with Self, the jeeva is a pure witness, saakshi, untouched by suffering at that moment. Choosing to identify with the Non-Self it becomes the suffering jeeva. The random function γ(t) in Eq. (2) represents this fundamental, and (according to Sri Ramana) only, freedom a jeeva has. It takes the value 0 when the choice is Non-Self and the value 1 when the choice is Self. The probabilities of taking these values are cos2 θ(t) and sin2 θ(t), which does imply higher probability of identifying with the Self as θ(t) increases. θ(t) is a variable ranging between 0 and π/2 radians and, if and when θ(t) reaches π/2, the probability of choosing the Self becomes 1; i.e. the jeeva attains Realization at that time. Further, since we have assumed based on scriptural teachings that θ(t) does not revert to a lower value once it reaches π/2, the jeeva remains in Self only thereafter. Eq. (2) implies that a jeeva can be in the witness mode (“saakshi bhava”) even if it has not yet attained final Realization. But the likelihood of assuming the witness mode will be low when θ(t), spiritual detachment, is small. Further, abidance in this mode is not permanent, as is the case of a Realized jeeva. What exactly is required of a jeeva to identify with the Self? Sri Ramana would say that it requires only the exercise of its “will power”. A jeeva with a low degree of detachment will need very strong will power to lift itself up and identify with the Self, since such a jeeva has to contend with the very strong attachment it has for the world. But a jeeva that

has acquired a high degree of purity of mind through sadhanas over many lives will do it relatively more easily. Eq. (2), as discussed below, conforms to this principle. CHOICE, WILL POWER AND PROBABILITIES Concepts such as disorder, entropy, chance events, and intelligent effort have been the subject of discussion among physicists and philosophers alike for over a century. It is generally accepted that states of disorder have a higher probability than states of order. Therefore systems will generally assume states of higher disorder with progress of time. However, there are many situations where intelligent and willful efforts can restore a measure of order at least to a part of the system. In such instances the degree of order found in the (sub)system reflects the amount of willed effort spent on it. Since the degree of order is also inversely related to the probability, the amount of willed effort implicit in the state of a system is inversely proportional to the a priori probability of that state. Higher effort will be required to bring about a low probability state. This principle is particularly suitable to decision-making situations involving multiple choices. It applies equally to Ishwara making choices affecting the state of the world and to jeevas making choices affecting their spirituality. As an illustration, consider a situation where the laws of Prakriti dictate that one of two events, A or B, happens with probabilities 99.99999999999% and 0.00000000001%, respectively. In the ordinary course of events A is far, far more likely than B. Which of the two events will actually happen is dependent on Ishwara’s Will. Should B happen in spite of these great odds, we recognize a “miracle” i.e. a display of Divine Will at work. On the other hand, when A happens there is less recognition of that Ishwara’s Will, though in reality neither A nor B can happen without that. It is that the display of Ishwara’s Will is much stronger- and hence more discernible- when the lower probability event happens. Let us apply this reasoning to the decision-making situation facing the jeeva which must choose between the “attached mode” { i.e. γ(t) = 0}and “witness mode” {γ(t) = 1}. The a priori probability of these two modes are cos2 θ(t) and sin2 θ(t) respectively. If θ(t) is low, sin2θ(t), the probability of identifying with the Self, is low. The jeeva can nevertheless still choose to be in the witness mode, but the will power required is correspondingly high; in fact the will power required varies inversely with sin2θ(t). Similarly, for a sagely jeeva (like Sri Ramakrishna) with deep vairagya, θ(t) is high and the will power needed to stay identified with the Non-Self is high. Since sin2θ(t) itself varies as sinθ(t), it is inferred that the will power required to stay in the witness mode varies as{1/sinθ(t)}. Similarly, the will power needed to stay attached to Non-Self varies as {1/cosθ(t)}. Eq.(2) can be therefore rewritten as z’(t) = {1-γ(t)}WPns + i. γ(t) WPs…. Eq.(4) where the weights WPns and WPs are quantities related to the will power needed to identify with the Non-Self and Self respectively. z’(t) itself is now seen as a random

variable which takes on one of the two values WPns or WPs. Since z’(t) is also representative of the direction of the spiritual path as seen in Fig 3, we have in Eq. (4) a mathematical representation of Sri Ramana’s Principle that a jeeva’s will power is an essential determinant of its spiritual growth 1. It is worth noting in conclusion that the main result of this paper plays a key role in proving a relationship between vasanas and spiritual detachment in the sequel (Ref 3.) ACKNOWLEDGEMENT The author acknowledges his indebtedness to Brahmaleen Gurudev Sw. Chinmayananda, Sw. Tejomayananda, Sw. Dheerananda and several other acharyas and friends of the Chinmaya Mission from whom he learnt Advaita Vedanta. In particular, Mr. Benjamin Root was involved from the beginning as the concepts underlying this paper slowly took shape. I thank him for patiently reading several versions of the paper and providing comments regarding both the mathematical and Vedantic aspects discussed here. This paper is one of a series which are to be incorporated into a book forthcoming from the author. Excerpts from these papers may be quoted with due acknowledgement to the author and the source. REFERENCES: 1. Chidambaram, Raju “Towards A Mathematical Theory of Spirituality Based on Advaita (Parts I and II)”- Presented at the Fifth International WAVES Conference, Houston, TX, July 2006 2. Mudaliar,A. Devaraja “Gems from Bhagavan” Sri Ramana Ashram, India (2000) 3. Chidambaram, Raju “Towards A Mathematical Theory of Spirituality Based on Advaita Vedanta (Part IV)”- To be Presented at the Sixth International WAVES Conference, Orlando, FL (June 2008)

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In the Bhagavad Gita (VI.35), Arjuna famously notes that the fickle (“chanchala”) mind is as difficult to control as the wind (“tasyaaham nigraham manye vaayoriva sudushkaram”.) By what means can one bring such a mind to single pointed attention on the Self? To this question from Arjuna, the Lord answers simply “abhyaasena tu kaunteya vairaagyena ca grihyate” (by repeated practice and detachment does one hold the mind.) Since will power is a prerequisite to diligent practice, it can be surmised that both will power and spiritual detachment are required for identifying with the Self.