The immeasurable gift of music, inspiring and soothing in its emotive content, woven around the fabric of devotion: the ancient and glorious tradition of carnātic music, while defying definitive descriptions even by the most erudite of scholars, is perhaps closer to the meloexpression of aesthetic emotion or bhāva than to a rigid, inviolable musical structure. Inseparable from the concept of bhakti bhāva or fervent devotion to the supreme reality of the cosmic race, carnātic music has been enriched for thousands of years by gifted saintly composers, preserved and nurtured by a quality of selfless dedication that has transcended material concern and transient emotion. A ladder of individual growth and evolution, a gateway into self-reflection and harmonization, it is said that the mind of the well-trained carnātic musician is a highly evolved one, laden with the power of meta-thinking and fortified with an innate penchant for balance and serenity.
My maternal grandmother, a great and ageless soul, who exuded a glow of wisdom and deep inner peace, firmly put me on a path to understanding carnātic music when I was three years old. Far too often in life, there comes a time when principles taught to us in our childhood do not make any sense until they are viewed in hindsight when we have unwittingly traveled a path we were put on by those whose foresight was cloaked in priceless and indivisible love. My grandmother commanded a prodigious mastery of the knowledge and practice of the values of devotion and dedication. Almost every day I spent with her saw us waking at the onset of dawn to chants of the suprabhatam or Sanskrit mantras to wake up the Gods, manifest and symbolized in virtues worthy of yearning for each and every day. The conversations we had were a great many, the ideas we exchanged were vast, probably so vast that it might take more than two lives for their complete realization. Of the many stories and instruction I received from my grandmother, one in particular deserves an exposition. The story of a carnātic singer whose voice carried the suprabhātam every morning.
Madurai Shanmukhavadivu Subbulakshmi or MS as she was affectionately known was of the greatest carnātic singers to walk this planet. Shimmering like a pole star for over seven decades in the musical firmament, Subbulakshmi’s luminous voice has and continues to inspire countless aesthetes of carnātic music. Listening to her voice is at times akin to immersing oneself in a transcendental space that represented the very beginning of time itself; her absolute and complete mastery of tone, pitch and pronunciation evoking a kind of vibration and impetus that spoke of a pristine, virtuous world, as if she was a bridge between a two identical quantum pairs existing in two parallel universes. My grandmother told me a story of a time when Subbulakshmi sang in the Kāmākśi temple in Kanchi in 1954, and how the gathered crowd were so moved with her performance that they exalted in unison that ‘her voice would be forever green and pristine, as long as the sun and the moon exist’. To my grandmother, the knowledge and yōga of music conferred the highest form of loving devotion, affection of virtuous people, the grace of the Sattva guna, the wealth of self-control, firmness of resolve and the attainment of mastery of enduring life skills. When the carnātic music singer had reached the state the Subbulakshmi had, they were so self-adjusted so as to be invariant to the vicissitudes of life.
It is in this grateful spirit, singing along the voice of Subbulakshmi, that I must give thanks this year to five noble souls that have impacted my life in mysterious, yet profoundly meaningful ways. They are each very ,very old souls, manifestly clear that this life is not their first rodeo on this planet, for it feels as if I know them for many millennia. How in the universe the forces of serendipity and effortless rapprochement could have made me the recipient of their boundless affection and love is a secret locked away in the misty eons of time and of space. Sometimes it is not necessary to look far into the misty eons of the future; it is sufficient to recognize and appreciate the bliss of the present, for meaning is the same golden thread that ties space and time as a continuum. I give each of them a Sanskrit name and associate them with a statistical distribution.
Catherine Kreatsoulas, Lalitā and the Dirichlet
Of all the connections I have forged during my time in Cambridge, none is more potent and powerful than the one with my great friend and colleague, Catherine Kreatsoulas. Often two paired realizations of a quantum particle are thought to exist in to two different universes, but one is hard pressed to imagine the pair existing in the same universe. The sheer number of things that we have in common is staggering; I sometimes see an image of myself in Catherine, and during others a reflection of my grandmother.
This selfless and generous soul, the first in her entire extended family to go to school no less becoming faculty at Harvard, represents an esoteric culmination of the choicest strengths and vulnerabilities that one can hope for in any human being. That she is a gifted and accomplished piano musician, a forensic scientist in a previous life before becoming a clinical epidemiologist and a gifted statistical methodologist is but testament to her pursuit of passion, away from the societally defined parameters of contrived success and the games required to achieve them. I have seen few people with this the type and depth of her insight, and I cannot even begin to count the number of occasions when she has helped me, often at a time when no one else did.
The Sanskrit word Lalitā represents divine graciousness and playfulness that is at the heart of the cosmic order. It has eight meanings, namely brilliance, manifestation, sweetness, depth, fixity, energy, grace and generosity; eight human qualities that constitute her faculties up and down. For this reason alone, I cannot think of a better name and I christen her Lalitā.
Conjugate prior to the multinomial, pristine and multifaceted, whose stick-breaking construction makes the entire world of Bayesian non-parametrics, the Dirichlet distribution has been my friend and ally for as long as I can remember. Of all the members in the exponential family of distributions, the Dirichlet for me has the most profound meaning. The Dirichlet process in many ways is the precursor to many generative models and the laden with meaning and insight that began the advent of variational inference and to me, a new life. For this alone, Catherine Kreatsoulas is Lalitā and Lalitā is the Dirichlet.
Gunther Weil, Chandraśēkara and the Beta
Many a time, the grand designs of the universe bend the locus of serendipity to bring aid when it is needed the most. Introduced to me by a dear mentor under the auspices of dealing with repressed-alpha personalities, Gunther Weil is quite by far the most knowledgeable and awe-inspiring human being I have had the great fortune of meeting. A doctoral student of Timothy Leary at Harvard psychology in the 1960s, hand-picked by none other than Abraham Maslow himself for his first job, Gunther is a scholar that embodies in personage and in spirit, the ageless concept of guru-śiśya, whose mastery of the Vēdas , Upanishads, Qigong and principles of developmental psychology denote a level of breadth and depth that only be described as a shimmering polymath.
Under his steadfast mentorship and guidance over the years, I have participated in and witnessed countless dialogues, from the epistemological foundations of contemporary machine learning to the nonduality characteristics that seem to define quantum physics. It is also inspiring the work I hope to do once I graduate early next year. Gunther has masterfully picked me up from a state of near frailty and placed me in a space where one feels the simultaneous escape of gravity and sense of firm earthly groundedness at the same time, a clay pot trained and meticulously made by a fearsome zen warrior.
Chandraśēkara in Sanskrit is the amalgamation of chandra (the cresent moon) and śekara (crown), denoting he who wears the moon in his crown, a symbol of Shankara himself. There was once a time when I was four years old when my grandmother and I were sitting outdoors on a calm summer night when the full moon shone brightly above us. Upon asking her why the moon seemed to shine differently everyday, my grandmother replied that the moon merely reflected the light of sun. When asked where the sun got its light from, I was told that the sun was svayam-tējasvi or self-radiant, and that the moon, reflecting the light of the sun, was a reminder that there is always light, even in the dark, and hence the name chandraśekara signified a reminder of luminosity even in the face of a dearth of light. For this reason alone, Gunther Weil is Chandraśekara.
In Bayesian statistics, the Beta is the conjugate prior to the binomial, Bernoulli and the geometric distributions. The Beta has a special property laden with meaning in order statistics. The distribution of the kth smallest item from a sample of size n from a continuous uniform distribution is a beta distribution, denoting that invariance to transient emotions and self-control is, in fact a state that can be parameterized at a completely different exponential family. This in my mind completely mirrors and merits why Gunther is Chandraśēkara and why Chandraśēkara is the Beta, and a reminder that only upon achieving uniformity of clarity, stillness and an expanding liberal spirit can we parameterize ourselves into something higher.
Ellen Weil, Padma and the Gamma
An inherent import and latent power resides in the practice of meditation, of silent contemplation of truth and non-duality, accessing deep recesses of the mind; an act of meta-thinking by astute observation and by parameterizing progress by the degree of freedom from needless thoughts and by the degree of focus on a single one. When the practice of meditation is juxta-postioned with disciplined compassion, it awakens several layers in the deep stack of our own consciousness, equipping us with a set of powerful lenses for self-inquiry. A denizen hailing from New York city, Ellen Weil is something akin to a maternal force in my life, responsible for a series of epiphanies and self-discoveries each of which have made me a more resilient and stronger person. I often wonder where she comes from, which stardust she’s made of, and what it must be to have meditated for so many decades, a complete voluntary control of galvanic skin responses and a spiritual force capable of being the kindler of compassion in others and yet glowing like the effulgent and self-luminous sun in a planet so bereft of mindfulness.
Ellen has over the years has mentored and guided me, and many a time it has felt as if we’ve groked the rich and detailed hologram of my psychological conditioning and during others, pinpointed where the conditional probabilities need to be surgically removed; and during others a method of stochastic variational inference for the realization of a dream hologram.
The pure and unsullied lotus, emerging from the depth of the waters and fso ar from the banks of the river bank, is associated with the idea of purity which arises from the law-of-conduct (dharma) and wisdom (jñāna). The Lotus is also symbolic of the enlightened mind. It rises in the mud of material existence gradually growing through the waters until it reaches the surface and then opens up to the efflugent sun in all its glory. Water splashed upon a lotus leaf never remains but immediately slips off. In the same way the dirt of worldliness never stains the enlightened being. For these reasons alone, the Sanskrit name for this great soul is śrī Padma.
The gamma distribution is a conjugate prior to many other distributions, the Poisson, normal, pareto to name a few. The gamma function, which plays a role in both its probability and cumulative density functions, has the peculiar self-recursive property that I always found quite mysterious when there were proofs associated with L’Hopital’s rule in high school. But it is perhaps this simple, yet powerful capacity for recursiveness that is associated with the ability to act as an observer of one’s own mind, from afar as if power to meta-think comes from the consciousness pervading all things, just as Ādi Shankara repeatedly says. This feels a lot like Padma, and Padma sounds exactly like Ellen, a force reminiscent of glittering stars.
Joost Bonsen, Natarāja and the Wischart
When generosity of spirit and purity of intent, combines with acumen for Cartesian association of ideas, it gives rise to a mind capable of forging structural similarities in fields that often have no apparent connecting links. Conceived in pristine San Diego and raised in the Bay Area, Joost Bonsen is a Dutch-American of enormous import and influence at MIT, earning the name of ‘oracle of MIT’. A dialogue with this man is seldom devoid of excitement, for he has in him an innate skill of kindling the latent variables waiting to be awakened in those that are engaging him. I cannot speak to the countless souls he has mentored, and the dozens of startups that have found funding and a path to success because of his sage advice. I can however vouch unequivocally that he has been a stoic and brilliant mentor for me over the years, protecting me, often from myself and sometimes letting me know in utter honesty that I probably had my thumb up my posterior if a project or a collaboration could be ‘dialed up’ and failed to see it.
I will never forget a time when I was with him in the Muddy Charles, crestfallen about an aspect of my work that didn’t seem to be going anywhere. A fireplace in the deep of winter surrounded us, and he steered the conversation towards the work of the astrophysicist Fritz Zwicky, and the discovery of dark matter, and Zwicky’s methods of ideation and possibility spaces. As I groked his exposition of Zwicky, I remember glancing at the fireplace and feeling as if he was unlocking a gate in me as he continued to tell me why my despair was in fact quite foolish. Anyone who is the recipient of Joost’s mentorship at a depth at which he has given me is genuinely blessed and lucky soul.
Natarāja is Shankara in the form of a cosmic dancer, surrounded by a ring of flames denoting the expanding cosmic race. He stands on his right leg, crushing the demon of forgetfulness and ignorance with his left leg rises upwards denoting the balance gained with knowledge as one crushes ignorance. He has four arms, one denoting the gesture of fearlessness in nonduality, another denoting the importance of grace and conduct in life. His third hand carries the small drum whose sounds signifies the origin of time and his fourth carries a pot of fiery fire to denote the power that ends the cycle of life. This cosmic dance form, called ānanda tāndava or the ‘dance of the supreme bliss’ has energized countless physicists, even earning a huge installation at CERN. For the immense symbolism laden here alone, Joost Bonsen’s Sanskrit name is Natarāja.
The Wischart distribution arises in a very natural way as a matrix generalization of the chi-squared normal distribution. While the chi-squared distribution is used to denote the variance in a univariate Gaussian distribution, the Wischart is a generalization of the chi-squared, making hierarchical estimation of covariance matrices possible. For these reasons alone, Natarāja is the Wischart and the Wischart is Joost Bonsen.
Joicho Ito, Gunavēndra and the Pareto
When the mind assumes a disposition of calmness or prashāntāya, and the thoughts bear a quality of pristine clarity or nirmalāya, the individual experiences a broadening, expanding liberal spirit or vishālaya, an equilibrium made of harmonious melody. For most denizens on this planet achieving this state probably requires the expenditure of a significant amount of individual effort. But some people, blessed with the innate perfection of their deep inner psyche, assume this state with elegant ease, with a rationing of energies that can only be described as a soul that has orchestrated and perfected this state over the span of several thousands lives. For these individuals, no reading of nonduality or any philosophy is necessary, for they already embody a detachment from fear, and they become instruments used by the universe in furtherance of a cause.
The superposition that an quantum particle can assume, a dirichlet of probabilistic states where uncertainty itself encodes information, realized to an observable state only dependent on the observer is a fundamental golden strain running through the greatest meta-thinkers of our age, and it has given my life new meaning in the fearsome power of serendipity of the universe. There are far too many things that Joi has done for me personally, often during moments of terrible personal crises. I cannot enumerate all of them in this post, but it probably suffices to say that I feel as if I have known him since the origin of time, and there is probably a quantum pair at work in a parallel universe, which feels the same way. This self-made Japanese-American has been tasked with a cause and a responsibility that began when the great Vannevar Bush of MIT published his article ‘As We May Think’, and the great forces at work in the cosmos couldn’t have found a better human being for this task.
Gunavendra is an amalgamation of the Sanskrit words Guna, signifying 'string, thread or strand', or 'virtue, merit, excellence', or 'quality, peculiarity, attribute, property' and Indra, or the one in whom resides the power to bring light and power, that ignites the subtle consciousness in life. He who embodies the perfect balance of the three Gunas, assumes a quality of balance, harmony, goodness and luminosity. For these reasons alone, Joicho Ito is Gunavendra.
Related to the exponential distribution, the Pareto distribution is often described in terms of the Pareto principle, which enunciates that around 80% of the observable effects in a phenomenon comes from 20% of the causes, underlying why the size of sand particles and of meteors have the same Pareto distribution that is also the pattern of human settlements. Any distribution that models objects in astrophysics, geophysics and human behavior represents a kind of unalterable basic reality, a reminder that we all come from stardust, and we are each the rising and setting sun. For these reasons, Joi is the Gunavendra and Gunavendra is the Pareto.
Subbulakshmi sang an astonishing array of rāgas, but none more auspicious and prosperous than madhyamāvati. It is probably apt then that this exercise on thanksgiving ends with the singing of this noble upward crescendo. Great things are waiting on the horizon in 2017.