Mathematics of Spirituality

The webpage on ‘WAVES PAPERS‘ lists several papers which together provide a mathematical theory of spirituality based on the Advaita Vedanta philosophy. It may help to be aware of the important features and results of the theory highlighted below before reading the details in the papers:

1. The model is based overall on a view best expressed in modern times by Sri Ramana: While the world that a jeeva encounters moment after moment is totally under the controlling Will of Ishwara, the manner in which it faces that world is up to the jeeva to decide. The jeeva may meet the world in attachment to the Non-Self (bhoga) or established in Self (yoga.) As a bhogi, the jeeva suffers; as a yogi, it takes one step further towards Perfection. This choice is available to the jeeva every moment.
2. The Cosmic Mind space (Mahat) is the space in which the “triputi” of all possible worlds experienced, all experiencing jeevas, and all conceivable experiences exist. This space is described mathematically in polar coordinates (t,θ) where t denotes the experienced worlds at time t, and theta denotes a jeeva with detachment theta. (t,θ) together denote the experience of the jeeva at time t. An interesting feature of this representation is that only one-quarter of the Mahat space (namely the first quadrant) is required to denote all possible worlds and experiences; the other three quadrants remain undefined, beyond anything objectively experienced. This is quaintly reminiscent of the famous opening mantras of Purusha Sooktha.
3. The analysis reveals an unexpected and unexplained similarity between the Mahat space and the four dimensional time-space continuum of Relativity Theory. Past, present, and future co-exist in the time-space continuum, according to Einstein. Mahat also is beyond time. That is, time is in Cosmic Mind, but Cosmic Mind is not in time. Further, in parallel with the famous relationship in special relativity theory between (ordinary) space and time, there is a mathematically identical relationship between a jeeva’s state of spiritual evolution and its worldly suffering. This relationship, demonstrated using Minkowski’s metric, can be stated in words thus: “As a jeeva gains more and more in Universal, Unconditional Love and Understanding, it suffers less and less in the world”. This statement is a first and immediate result of the model and hence it may qualify as the “fundamental result of mathematical spirituality”, especially since Love is acknowledged as a supreme, necessary virtue in almost all religions.
4. θ= 0 characterizes a jeeva fully attached to the world. Increasing value of theta denotes spiritual progress. God-Realization occurs when theta reaches the maximum possible value, namely π/2. A result that is likely to be very gratifying to mathematicians is the relevance of the Euler’s equation, namely e^i.π + 1 = 0, to the model in describing Realization. This equation - acknowledged by many as the most famous and beautiful of all equations in higher mathematics- has held a mystical significance for mathematicians since its discovery nearly 250 years ago.
5. The jeeva can choose to identify with the Self or to identify with the Non-Self at any time, according to Sri Ramana. A probabilistic equivalent of the model is derived to reflect this freedom which gives a new interpretation for the variable θ(t), the spiritual detachment at time t. The a priori probability that the jeeva will identify with the Self is sin²θ(t), implying higher probability of identifying with Self with higher detachment θ(t). Upon Realization, the probability of identifying with Self becomes 1, as one would expect. Jeevas with low detachment are more likely to identify with the Non-Self if left to their usual nature. But even such a worldly Jeeva can identify at any time with the Self provided its will power is strong enough to overcome the pull of its lowly vasanas.
6. A theory of vasanas has been proposed which integrates well with the overall mathematical model of detachment and spiritual evolution. Vasanas of a jeeva at time t are represented as a function V(x,t) indicating the energy with which the jeeva’s mind responds to vasana stimulus x. The variable x ranges from 0 to 1 with value 0 corresponding to lowest tamasic vasanas (e.g. survival instincts associated with the muladhara in Kundalini Yoga) and the value x=1 corresponding to the highest satwa (i.e. the “tatwa” associated with sahasrara and Realization). Based on this representation, the mathematical relationship between spiritual detachment θ(t) and the vasana function V(x,t) has been derived. In essence, it relates θ(t) to the mean value of V(x,t). More satwic the mind, higher is its detachment.
7. Mathematically speaking, spiritual sadhana (practice) involves the re-shaping of the vasana function V(x,t) so that its mean value gets increasingly closer to 1. From this perspective, questions such as limits to spiritual evolution and the nature of Realization are discussed leading to observations consistent with Vedantic teachings.
8. The model permits incorporation of the Advaitic views on how jeevas derive happiness (or its opposite) by contact with objects of the world. This leads to a final result showing how the “suffering” of jeeva at any time can be expressed as the product of three factors: 1) the level of alertness of the jeevas mind, 2) the degree to which the jeeva accepts good and bad outcomes with equanimity, and 3) its spiritual detachment. The karma, bhakti, and jnana yoga recipes for reducing suffering are reflected in this result.

The results presented are not, by and large, new or unknown to Vedanta. Nor is the modeling approach the only one possible. In fact, others better skilled in mathematics and better endowed with Vedantic knowledge may propose more comprehensive mathematical approaches. The work presented in the papers is only a “proof of concept” of the proposition that mathematics can indeed play a helpful role in clearly understanding our spiritual nature. The language of mathematics may finally provide that elusive link between spiritual science and material science.