The Divinity Equation

Thanks to the vagaries of the Indian educational system, I believe I encountered recurring decimals a few chapters before I encountered fractions at the tender age of six. I distinctly recall the fact that I thought the teacher had a screw loose, since the concept of an infinite sequence of numbers seemed to make absolutely no sense to me. How, I argued, would 0.9999.... be any different from 1? You can't tell them apart, since if you try to, you have subtracted at a finite decimal position of the former, which should be impossible. Of course, by the time we'd gotten to fractions, I had forgotten all about the question. It was nearly ten years later that I came across the idea that

0.9999... = 1

and sad to relate, disbelieved it and had to be shown the proof. Since then, it has become an important part of my repertoire of math problems which I set teenagers in order to provoke some philosophical thought (much to the chagrin of their protective mothers, who would rather I kept my loopy ideas to myself).

The pathless land

Even though I have known the equation for a long time, it was not until very recently that its metaphysical connotations struck me. When they did, I realized that this equation can be used not just as a tool to get children thinking about mathematical infinity, but also adults about the concept of spiritual and existential infinity. This essay constitutes a brief exposition of the latter. Note that I'm not claiming any epistemological truth behind the equation, I am simply using its interpretation as a metaphor to clarify some aspects of the spiritual quest.

As the yogi delves deeper and deeper into the labyrinths of his mind, he receives (or appears to receive) deep clarifying insights into the nature of reality and his own existence. At times, this occurs as a blinding flash of comprehension and awareness followed by a gradual dissipation of the initial certitude of discovery once reason examines it and finds it irrational. At other times, the insight obtained is a rational understanding of previously unexplained insights, in which case, there is a greater sense of achievement, since the insight obtained is communicable. However, the yogi finds that as he goes deeper, the insights keep subsuming themselves, reaching eventually a stage where even the insights of reason seem to lose their certitude, since they appear to be simply statements made at a shallow plane of understanding when viewed retrospectively.

The same applies to the sense of Bliss and Joy the yogi obtains as part of his spiritual practice. Even as he finds deep and fulfilling bliss at a particular stage of his practice and decides that perpetuating this particular state of Being through every waking moment is the ultimate goal of his practice, a few short months later, he attains an even deeper sense of Bliss that makes the previous experience appear epi-phenomenal and ephemeral in retrospect. The continual subsumption of one's own deepest realizations appears thus, to be an important characteristic of internal inquiry.

Somewhat recursively, this particular insight in my own case has caused me to appreciate the significance of what I have called the Divinity Equation. It is conceivable that further practice will make me feel disinclined to speak of it, since the realization that at the moment appears to me to have some value will then appear to be quite trivial. The reason this particular insight seems non-trivial and communicable at the moment is that it appears to connect the normal consensual plane of human existence with the more esoteric ones I tend to deal with these days, and hence may have some value to others besides myself. I must , therefore, speak of it now before greater wisdom and/or laziness cause me to hold my tongue (and pen).

Metaphysics of the Divinity Equation

The desire to seek experiences and feelings beyond one's current state of awareness is the essential definition of spirituality. Lighting incense sticks, chanting, praying, meditating etc are activities that boost spiritual awareness through inward perception. Falling in love, climbing mountains, working professionally in a team, even drunken revelry are activities that boost spiritual awareness through outward perception. At different stages, however, practitioners realize that the goal they seek is too far away to meaningfully achieve and direct their motivations towards less idealistic goals. The motivation towards deeper spiritual awareness can then, with some anthropomorphism of the concept, be summarized by the slogan `God/Spirit/Meaning is near/realizable', while the existential angst, moral relativism and spiritual apathy that results from diminution in awareness is best summarized by the slogan `God/spirit/meaning is dead/unrealizable'.

The Divinity Equation serves to place both these perceptions of the role of Spirit into perspective. 1, the Godhead, is infinitely far away from 0.9999, the aspirant at his 4th (or nth) level of understanding, if one chooses to count the number of steps of understanding one requires to attain identity with the Godhead. This view reflects existential sorrow and relativism in endeavor (`Spiritualism is a sham/cul-de-sac. Life has no meaning'). 1, the Godhead is infinitesimally close to 0.9999, the aspirant at his 4th (or nth) level of understanding, if one chooses to measure the extent to which one has approximated identity when compared to random existence, e.g. 0.5731. This view reflects faith, often anthropomorphized for cultural and historical reasons (`We are made in the image of Divinity/God. We must try to get closer still.'). Depending on one's perspective of reality and one's own place in it, the Divinity Equation can be used to show that God is both Near and Far.

Everyone is a yogi

Both these paradigms arise in every person's life, and are often intertwined. The young lady standing on the edge of the ocean looking into infinity feels the twinge of tears tug at her eyes, and she doesn't know why. It is the tug of the (n + 1)th 9, pulling her on into the vast progression of deeper and deeper insights that would draw her inexorably closer to Unity. The rock-climber perched precariously on a ledge in the Sierras, looking out upon the view beyond the craggy rock face feels the enormity of existence pour down upon him as a thrill of Life and vitality flows through his body. It is the thrill of the (n + 1)th 9, the flow of a purer current of Life than his body-mind has heretofore known, shredding the canopy of his current existential narrative with the promise of the ever-elusive `beyond'.

Think of a rock concert - thousands of bodies swaying in unison, thousands of minds letting go of their social inhibitions in one vast sea of supercharged rage and libido, the urgent spirit of Youth. Think of devotees chanting in an ashram, a shaman leading an incantation, scientists at a conference, all those brief flashes of social collaboration where the individual vanishes into the throb of the social creature that it has birthed. In each and every one of these instances, if there arises a sense of wonder and awe, it is that (n + 1)th 9 worming its way into the hearts of men, thrilling them with the promise of deeper understanding and a greater freedom than they have ever known.

And since all of us have felt that thrill, since all of us have felt that ennobling flash of intuition that makes life, if for one instant, worth living, we are all, in the deepest and truest meaning of the word, yogis. When one looks at oneself and sees 0.9999, there may arise, depending on one's perspective, a deep sense of unease and inadequacy. The solution, the Tao, the path of Raja Yoga, as far as the equation is concerned, is to merely pay attention to those little dots at the end. One of my heroes, Vivekananda, once said, `Not a sheep, but a lion thou art. Stand up and roar.'. Translated into the metaphor of the Divinity Equation, this should read, `Not 0.9999, but 0.9999... thou art. Stand up and recurse.'

When the music stops

The yogi who knows he is 0.9999..., ever growing, ever evolving, ever seeking after the next elusive 9 in all that he does, is already where he is trying to go, he is already the Divinity that he is trying to become, though he doesn't know it. Unfortunately, as soon as he stops to contemplate what he has accomplished, he is going to run into trouble. We have already talked about the two perspectives that accompany an awareness of the finitude of one's awareness. It then seems natural to presume that the yogi who stops to count how many 9s he has subsumed so far is going to end up doing one of two things (a) realize that he is never going to get where is he is trying to go, become depressed, get married and watch TV or (b) find that he is much farther along than the stupid ordinary mortals he is around, grow a beard and begin pontificating and sermonizing.

The former, the sense of inadequacy, loneliness and apathy, is best described by the statement, `0.9999999 is as many levels of understanding far away from 1 as 0.99. Why bother growing? Why bother learning?' It is something the vast majority of humanity believe in their darker hours, some perpetually. Gazing into infinity, in such cases, creates a sense of loss and existential meaninglessness that few can honestly stand. Thus, the young lady gazing at the sea breaks her reverie by transmuting her desire to see infinity into the desire to be close to her soulmate and lover, subsequently transmuted by practical circumstance into calling up her current boyfriend on her cellphone. The young man climbing and gazing at the view transmutes his desire to lose himself into infinity into the desire to take a picture and move on, further transmuted eventually into a desire to put the picture up on his web album to demonstrate his virility and fitness to his peers. The concert-goers, full of the vigor of life transmute their desire to climb the crescendo of music up into infinity into a desire to head-bang, anon into a desire to climb up over their fellow concert-goers and shout loudly.

The latter view, the egotism, is best described by the statement, `0.9999 is better than 0.99', something a preacher might tell his parishioners, or an ecological conservationist might tell an oil-rig worker. The urge to proselytize and impose one's own understanding of reality on others occupies a significant proportion of the conceptual space of most spiritual movements in the world and, in my opinion, is one of the principal causes for the low opinion that rationalists and bright people everywhere hold of spiritual practitioners in general.

The Divinity Equation expresses the irrationality of proselytism and arrogance of understanding very well. 0.9999 believes he is closer to the Truth than all the foolish and superficial 0.99s he sees milling about. `Why won't you open your hearts to the Spirit and let it transform your lives? And why don't you give us some of your money so we can help you do so?', he piously clamors. Viewed from his perspective, he is absoutely right. 0.9999 is closer to 1 than 0.99. However, 0.99 believes that while he himself is really far away from 1, he also sees that 0.9999 is not much closer either. He, therefore, sees little point in listening to what 0.9999 has to say, since the latter's aggressive pronouncements come not from infinity but from the 4th decimal place.

The first of these two errors, the `just 0.9999' error, is the denial of the agnostic materialist, who looks at infinity, then averts his eyes and insists that all those who do not do the same are foolish and irrational, since however large a sequence of 9s they may subsume, they will still be infinitely far away from true understanding.

The second of these errors, the `look at me, I'm 0.9999' error, is the egotism of the spiritualist. The egotism of the spiritually advanced practitioner leads him to impose his view of the world on others, a process that has the advantage of benefiting several 0.99s who may employ 0.9999's advice to reach 0.999, but which has also the disadvantage of trapping 0.9999 at 0.9999, since he has defined and promulgated his view of the world at his existing level of awareness as the Truth and now cannot easily subsume it further without adopting either secrecy or hypocrisy (or both).

However, not realizing the infinity inherent in the Divinity Equation need not necessarily cause one of either disillusionment or delusion. The ability to perceive clearly the beauty of being `just 0.9999', the ability to silently accept the pain of being afloat on a little boat amidst an infinite ocean, is the causal source of all that humans create in the external world that lasts beyond them. It is what drives the tender ballet of copulation, the emotional agony of musical composition and the existential sadness of great literary creation. While there are some who equate artistic and creative endeavor with spiritual awareness, it should be clear from this exposition that while the first arises from a clear and courageous perception of what `is', the latter subsumes the former in arising from a clear and courageous perception of what is and what may yet be. Spiritual awareness will often manifest itself creatively, yet not all creativity will necessarily be spiritual.

The error of advaita

There is one final erroneous perception of Divinity that we can explain using the Divinity Equation. It is the denial of the ascetic, a subtle error in that it is equivalent to the statement `look at me, I know I am just 0.9999....'. This, while obviously an accurate understanding of the infinity of perception involved in the process of spiritual practice, partakes of both the errors we have discussed earlier. From the denial of the materialist, it takes the concept `just' and from the egotism of the spiritualist, it takes the concept `look at me'.

The advaitin claims that reality is illusory and that what truly exists is definitionally unknowable, unthinkable and unspeakable. He further claims, implicitly, that knowing this is equivalent to supreme understanding. It is difficult to pin down the error in this solipsistic denial of the necessity for inquiry beyond a functional understanding of the Divinity Equation using just the equation itself. Therefore, I must introduce the additional metaphysical statement that knowing that there is an infinite sequence of 9s in the chain that connects the aspirant to the Godhead is not equivalent to following that chain of understanding all the way up.

Building upon this latter view, at every level of awareness, when the thought arises, `This is what is', there must and does eventually follow a realization, `But this is not all that is'. This realization primes the quest for the next level of awareness. The `neti, neti' solipsism that follows from advaita would throw away the understanding `This is what is' as soon as it arises using the premise that it will eventually be refuted (with no understanding of how it will be refuted). The crux of the argument here is that unless the negation of the premise is allowed to arise naturally as a consequence of the aspirant's experience of reality, there will be no motivation to proceed further along the sequence, and the aspirant's level of understanding will remain fixed at its existing level, tied down by the metaphysical assumptions of advaita.

Thus, while knowing that there is an infinite hierarchy of understanding is an important part of the spiritual quest, it is also necessary to experientially climb this hierarchy in order to approach a deeper understanding of the true nature of the awareness that sustains reality. While losing sight of the mountaintop can cause climbers to either lose hope and slide down discouraged or set up tent and pontificate where they are, to claim that one can see where the top of the mountain is and hence need not climb up also appears somewhat unfruitful and is, in a nutshell, the error of advaita.

To conclude, from a simple children's exercise in conceiving and understanding mathematical infinity, we have drawn parallels to some of the metaphysical and spiritual issues that occasionally arise in our personal existence as we seek to assign probabilities to the infinite sample space of our understanding. I hope that it may prove to have had some value, if only as a source of amusement.

The Heart of Shiva

My deep and obsessive fascination with Shiva began as a young child, as the mythology of Shiva addressed the archetype I have always identified with most: the primal ascetic. As psychological growth led me to a more rational understanding of reality, I came to understand Shiva as a primitive archetype corresponding to entropy - hence the appellative mahakala. Shiva came to represent to me the arrow of time, the creative as well as destructive dimension of space-time. Cosmologically speaking, Creation then corresponds metaphorically with the Dance of Shiva, where at every level of complexity, beauty and salience are supported by comparatively large quanta of random permutations at lower levels. Much of my scientific motivation and interest in information-theoretic aspects of physics and biology stems from this metaphysical lemma.

A breakthrough in my understanding of both Shiva and reality was set in motion by my chancing upon an interesting definition of Shiva about nine months ago. Shiva, in some Vedantic tradition the name of which escapes my memory now (UPDATE: Its originally drawn from the Brihadaranyaka Upanishad), is defined as `that which is not'.

Shiva is defined as that which is not.

This thought, while innocuously koan-like in its statement, led to much thought and meditation for me, culminating in a post-rational cathartic experience this summer. It has led me very deep into questions concerning the relationship between the Physical and the Spiritual worlds, the one characterized by the passage of Time and the other by the increase in fullness of Joy. It has also brought together the intellectual and Sufi strands of my thought into a rather interesting synthesis of understanding, where Shiva is now the source of the undifferentiated Consciousness that, in turn, is the source of all reality. Not to put too fine a point to it, I now believe that the story of existence can best be told as being a meditative thought in the heart-mind of Shiva. All insights that we obtain into Nature and our internal selves are reflections of the heart-mind of Shiva; the very possibility of comprehensibility arises only because that which comprehends (awareness) is an instantiation of the heart-mind of Shiva.

I raise these autobiographical details to provide context for what follows here. The Shiva Rudrashtakam is a piece composed by Tulsi Das, one of the greatest and least respected intellectual giants of the Indian Middle Ages. It is written in Sanskrit and contains eight couplets in praise of Shiva. I must confess that my Shaivite tendencies caused me to be rather dismissive of Tulsi Das and his typically Vaishnava (dualistic) compositions when I was younger. The Rudrashtakam changed my views. In the course of eight couplets, Tulsi gradually traverses the philosophical spectrum from definitive non-duality to definitive duality in a shockingly elegant manner.

Here, I translate the Rudrashtakam from a completely non-dualistic viewpoint, thereby thwarting, in a sense, Tulsi's noble intent. I contend, however, that it is of some value to regard the Rudrashtakam as a non-dualistic characterization of the nature of Shiva rather than as an explanation of the essential unity of the dualistic and non-dualistic understandings of Shiva. While the latter is more intellectually salient and deep, the former is more emotionally charged and potent as a meditative aid.

Lastly, I am sure some grammarians might take offense at what they might consider liberties I have taken with the language in my translation and metaphysical innovations that I have sought fit to introduce. I therefore emphasize that this is a subjective translation by a scientist in the 21st century, not an objective one by a Vedic scholar. Without further ado, let us delve into it. Most lines are translated individually, making two notes per couplet. The seventh couplet is translated in one place.

Shiva Rudrashtakam

namami shami shana nirvana rupam vibhum vyapakam brahma veda swarupam

We sing of Consciousness: the ontological fundament of the physical Universe, the contemplation of whose nature is the source of inexhaustible Joy. We sing of that which is all-powerful for those who meditate upon energy (latent motion), all-encompassing for those who meditate upon motion (activated energy) and the primal cause for those who meditate upon causation (source of motion-energy).

nijam nirgunam nirvikalpam niriham chidakasha makasha vasam bhajeham

We know that to be Shiva which is the devourer of the interior perception; that which is beyond categories, beyond qualities, beyond causality and differentiation. We know that to be Shiva which is the devourer of the exterior perception, the deconstructor of all narratives of external reality, who exists beyond the physical universe.

nirakaramonkara moolam turiyam gira gyana gotitamisham girisham

We know that to be Shiva that is formless yet forms the substrate for all levels of Consciousness, the generator of Turiya, undifferentiated Consciousness. We know that to be Shiva that transcends all these levels, beyond individuated comprehension.

karalam mahakala kalam kripalam gunagara samsara param natoham

Shiva is that which unfolds both the involution and evolution of the Universe. Shiva exists beyond the realm of physical reality.

tusharadri samkasha gauram gambheeram manobhuta koti prabha shri shariraram

Shiva manifests in external awareness as the perilous, blinding radiance of the mightiest snow covered mountains. Shiva manifests in internal awareness as a formless form verily defined by the reflections of countless rays of light.

sphuranmauli kallolini charu ganga lasaddhalabalendu kanthe bhujanga

From the creativity of Shiva springs the sustenance of all that lives. From the will of Shiva spring all mysteries and death.

chalat kundalam bhru sunetram vishalam prasannanam nilakantham dayalam

All archetypes of physical beauty stem from Shiva, all aestheticism is but the comparison of the percept of the object to the percept of Shiva. All archetypes of morality stem from Shiva, all virtues are judged relative to the anthropomorphized nature of Shiva.

mrigadhisha charmambaram mundamalam priyam shankaram sarvanatham bhajami

All asceticism finds its root in Shiva, all practices of yoga and meditation stem from the desire to perceive Shiva. We sing, therefore, of Shiva, the universally beloved.

prachandam prakrashtham pragalbham paresham akhandam ajam bhanukoti prakasham

The ferocity of storms, the luminosity of stars, the indivisibility of unity are all pale reflections of the potency of Shiva. Shiva sows the Seed for all of Creation, and appears in the perception of all that is created as the brilliance of a billion suns.

trayah shool nirmoolanam shool panim bhajeham bhavani patim bhavagamyam

The thought of Shiva heals suffering through alienation from the Source in the physical, subtle and causal realms. The thought of Shiva is accessible only when thought of the self dissipates through the arousal of Divine Love.

kalatita kalyana kalpanta kari sadasajjananda data purari

The thought of Shiva suspends awareness of Time, it generates deep insights and transformative catharses. The thought of Shiva always rejoices those who seek it sincerely.

chidananda sandoha mohapahari prasida prasida prabho manmathari

The interior representation of Shiva takes the form of supreme awareness and bliss, dispelling delusion. Therefore, we sing and embrace the thought of Shiva.

na yavad umanath padarvindam bhajantiha loke pare va naranam

na tavatsukham shanti santapa nasham prasida prabho sarva bhutadhivasam

A fascination with external categories and causalities associated with them inevitably leads to uncertainty, alienation and unhappiness which manifest themselves as deleterious transactions with the external environment. We sing and remain mindful of Consciousness that moves all thoughts and action so that they may always remain useful.

na janami yogam japam naiva pujam natoham sada sarvada shambhu tubhyam

Self-awareness requires no denominational practices or rituals. The only requirement is a continual and persistent mindfulness of the interior representations of Shiva.

jara janma dukhaugha tatapyamanam prabho pahi apannamamisha shambhu

It is miraculous that finite instantiations of the Infinite can hope to merge with it. We sing, therefore, in the hope of perceiving the heart of Shiva.

Thus concludes the Rudrashtakam, a metaphorical device that always helps me in my meditation and mood. As a matter of fact, during a period of ecstasy in summer, I recorded a musical version that continues to give me joy every time I listen to it. Among other things, it reminds me of the paltry few coins that I earned busking with this in my repertoire at the Vondelpark in Amsterdam.