Manjul Bhargava, Sanskrit, Indian Mathematics and a Question of Relevance.

Several readers understood my last blog, regarding how science diverged from philosophy and progressed beyond the ancient philosophical paradigms, Indian or Western, appropriately. The readers also understood that I was not rejecting a study of any philosophy but only rejecting the notion that modern science and knowledge could still function within those paradigms. However, several readers took issue with the blog and misconstrued that I was rejecting the contributions of Indian, specifically Hindu, philosophy. A reader pointed out to Manjul Bhargava, Indian-American recipient of Fields medal, crediting his knowledge of Sanskrit for providing key insights, based on ancient Indian works, into mathematics. Yes, that's true but that's not the whole truth.

First, let me categorically state that I agree with the many studies that point out to the importance of a knowledge of liberal arts for any graduate. Study after study has pointed out that students must have an introduction to classical literature, philosophy and music. University education in America, unlike India, lays a heavy stress on liberal arts. Indian students of engineering and medicine would do well to learn Kalidasa, the upanishad and many other local variants of literature and philosophy in addition to at least an introduction of Plato, Socrates and Shakespeare. 

Second, I fully and completely support books of unimpeachable academic quality that explore ancient India's contributions to science and arts. If a beautifully academic book on how Baudhayana's math presages Pythagoras can be written I'd happily buy it. 

That said, what irritates and angers me are twofold. One, wallowing in wooly mysticism and connecting everything modern in science to ancient wisdom turning a blind eye to tenuous connections. Two, showing an interest only in the jingoism of establishing what the world learned from India and not even bothering to inquire into the possibilities of any influence from outside on Indian wisdom.

India has arrived on the world stage as an economic power, a strategic partner and a key exporter of talent but Indians still belabor under an inferiority complex showing an undue and ugly eagerness to grab credit for achievements of not just Indian expatriates but even those of Indian descent. This ugliness becomes more despicable when achievements by Indians could be tied to Indian heritage of yore. 

Manjul Bhargava, born in Canada to Indian parents, enjoyed a tsunami of publicity when he won the very prestigious Fields medal, one of two highest honor in mathematics, awarded to mathematicians under the age of 40 who've made a significant contribution. The very boyish looking mathematician has a stellar resume that boasts of winning honors like he was collecting candy and a tenured professorship at Princeton at 30 years of age. 

Manjul Bhargava - Image Courtesy Wikipedia

Indians went crazy over interviews of Bharghava that mentioned how he was thrilled to find mathematical ideas from Sanskrit texts of ancient Indian mathematicians.When Bharagava said he saw mathematics in everything including Sanskrit and the tabla music he played Indians, to  put it mildly, almost had a collective orgasm. When Bhargava came to India he was feted and everywhere he went he was asked to speak on how great Sanskrit was. Sanskrit institute located in, where else, Mylapore felicitated Bhargava and had him lecture on, what else but, "Sanskrit and Mathematics".

Amidst the din what was lost is there's much more to the Bhargava story than just Sanskrit and tabla. Bhargava's grandfather was a Sanskrit scholar who had jotted down excerpts from ancient texts but, let us painfully remind ourselves, was nowhere close to winning a Fields medal. Bhargava is a typical product of western education and a story that's almost impossible to be replicated in India, under both its current and past education system.

Bhargava's mother was a mathematician at the Hofstra university in Long Island, NY and played an instrumental role in turning the boy's interest in mathematics into a career. Bhargava is not the first and nor would he be the last genius from the western world who takes a multi-disciplinary approach to the chosen subject. American university system lays a stress on diversified thinking and drawing inspiration from as many sources as  possible. This western approach is why a Schrodinger could easily see in Vedanta a spark for his quantum theory while no Indian philosopher or Indian scientist could connect the dots similarly. Bhargava's theory that won him the Fields medal was inspired by the Rubik's cube and was the result of a journey from Bhramgupta to Gauss. 

That Bhargava won prize after prize in America shows a society where meritocracy rules (along side affirmative action). A 27 year old Bhargava was a visiting scholar in that most American of research institutes, The Institute for Advanced Study. The Institute for Advanced Study was established in Princeton by Abraham Flexner who had played a vital role in reforming medical education in America. Flexner's article, published in 1939 in Harper's Weekly, titled "The usefulness of useless knowledge" is an intellectual tour-de-force and sets the objectives of the Institute where Fellows could indulge in anything that might fancy them without the pressure of having to invent anything or create anything in particular responding to any external demand. A Harvard professor , Flexner recalls in the article, who was given a stipend wrote to Flexner asking "what are my duties" and Flexner replied "you have no duties. only opportunities". This is where Bharagava flowered.

Bhargava to his credit has been clear that while he'd like to see books about contributions of Indians he insisted that it should be accurate."It's not your agenda to show everything originated in India. It's your agenda to show what originated in India in an accurate and clear way". 

I wish Bhargava had been asked to speak about research topics in mathematics but Indians were interested in only thing, to get a Fields medal awardee to speak in glowing terms of an ancient heritage and nothing more.Once any Indian expatriate wins any award abroad the Indian government of the day will make a despicable show of awarding some Padma award. Bhargava was awarded the Padma Bhushan. V.S. Naipaul, most acerbic and acidic critic of India, wrote in his 'India: A wounded civilization' about how India treated Har Govind Khorana, "India invited him back and feted him; but what was most important about him was ignored. 'We could do everything for Khorana,' one of India's best journalists said,'except do him the honor of discussing his work.' "

A reader pointed to an interview by George Geverghese Joseph's interview in 'The Hindu' which spoke about how possibly work done mathematicians in Kerala could have traveled to Europe and influenced Isaac Newton's conceptualization of the infinite series. Incidentally I had bought Joseph's critically acclaimed book "The Crest of the Peacock: Non-European roots of mathematics", published by Princeton University.

Joseph's book speaks of ancient Indian mathematics and in addition has lengthy chapters on Egyptian and Chinese contributions but the interviewer from 'The Hindu' chose to ask him only about how great Kerala's mathematicians were. My reader complained, borrowing from Joseph, about a Euro-centric view on the history of sciences that ignores contributions, probably more significant, by non-Europeans.

Many Indians who are critical of India's education system and yearn for what they consider the fabled past of ancient Indian education system without fail gnash their teeth about Macaulay's imperialist comment that a shelf of European literature is worth more than a library of oriental literature. A recent controversy over Professor Sheldon Pollock, editor of the Murty library of Indian literature, cited a passage from a speech of his that appeared insulting to India. The protest letter was signed by professors from all and sundry universities of India including professors of Sanskrit who, unlike Pollock, had no publication. A simple google search revealed that Pollock's statement was deliberately torn out of context and twisted. The age of colonial imperialists like Macaulay is long gone but Indians, including Joseph, recycle statements of a bygone century to present a world at war. 

Indians do not realize that many books that document India's rich heritage are courtesy of Westerners. A sharp reviewer of Joseph's book points out that Joseph draws a connection between Euclid's legendary book 'Elements' and Panini's grammar but he fails to credit Frits Staal who first wrote about such a connection.  The reviewer also accurately picks issue with Joseph broad generalization every unsympathetic view as "western" and almost intentionally ignoring other westerners who worked to give a more honest history of ideas. It is also unfair to charge that but for an Indian author like Joseph the oriental contributions would not receive their due. The reviewer points to several examples by European authors in that regard.

To circle back, demanding an accurate history to be written is fair and necessary too. However, it appears that Indians are more interested in writing history, that too an exaggerated one, than in worrying about the pathetic state of Indian education and academics today. Several of the signors on the protest letter against Pollock teach in IITs and JNU, including Makarand Paranjape, and all of them are just plain guilty of witch hunt of a good professor of unimpeachable academic credentials. 

Bhargava is also the recipient of the "Ramanujan Prize" from SASTRA university (my alma mater). While 3 Indians figure on the list of Ramanujan Prize since it was instituted in 2005 not one of them did their work in any Indian university. Ironically, at SASTRA a tech festival was held for which a computer science student wrote a blog about how a weapon used in Mahabharata was the precursor of modern day Inter-continental-ballistic-missile. This is how Indian universities are being run.

While India went insane over Bhargava and his love of Sanskrit it was conveniently ignored that there were 3 other awardees for the Fields medal. Amongst the other awardees were an Iranian woman and a Latin American mathematician. I'm sure that those two have no idea of Sanskrit or Tabla and still won the Fields medal. 

When Indian's count Indian Nobel laureates they often include Amartya Sen, Venky Ramakrishnan, Har Govind Khurana and S. Chandrasekhar. Though Sen won the prize as an Indian, unlike the others, he too did his work in foreign universities and was, like the others, a product of western universities. 

For unsurprising reasons Venky Ramakrishnan's name is rarely mentioned unlike Bhargava's name. Ramakrishnan, as usual, was feted by India after he won the Nobel and he too was given the Har Govind Khorana treatment. Ramakrishnan was invited to attend the Indian Science Congress, a venerable institution that stretches back to the Colonial era actually. Aghast at seeing paper presentations about how ancient Indian epics had the precursor of modern flights Ramakrishnan said "the Indian science congress is a circus" and that he'd never ever attend it again. After his Nobel prize it was rumored that Ramakrishnan took up a job in a premier Indian lab, he vehemently refuted it saying "Nobody has approached me about an offer to work in India. However, I can categorically state that if they did so, I would refuse immediately".

It is laughable when an Indian author, known for his militant fundamentalist outlook in favor of Hinduism, called Hindutva, asserted that J.C. Bose could arrive at the conclusion that plants respond to stimuli because his Indian worldview is, unlike the western, is a holistic one. Andrea Wulf's critically acclaimed biography of Alexander Von Humboldt quotes Humboldt, "In this great chain of causes and effects no single fact can be considered in isolation". Wulf, continues, "with this insight he invented the web of life, the concept of nature as we know it today". Humboldt, Wulf points out, influenced a wide array of intellectuals. Thomas Jefferson, Charles Darwin, William Wordsworth, Coleridge and Henry David Thoreau were influenced by Humboldt. Wordsworth, incidentally, also was in awe of Isaac Newton. Goethe, who admired Humboldt, wrote 'The Faust', laid the foundations of morphology and a treatise on light, "Theory of colors". Vladimir Nabokov wrote 'Lolita' and researched butterflies. Nabokov's theory on the evolution of butterflies was recently proved correct. While it is difficult to list Indian thinkers who showed diverse interests or achieved in diverse fields it is common to see such personae in the western intellectual tradition.

Alexander Von Humboldt - Image Courtesy Wikipedia

Write history all you want but the more urgent need for India today, is not in proving that Bhaudhayana was better than Pythagoras but in creating an institutional framework that can produce a Manjul Bhargava. 

References:

1. Manjul Bhargava https://en.wikipedia.org/wiki/Manjul_Bhargava
2. SASTRA Ramanujan Prize https://en.wikipedia.org/wiki/SASTRA_Ramanujan_Prize
3. Fields Medal https://en.wikipedia.org/wiki/Fields_Medal
4. Institute for Advanced Study https://en.wikipedia.org/wiki/Institute_for_Advanced_Study
5. Abraham Flexner https://en.wikipedia.org/wiki/Abraham_Flexner
6. Flexure's article "The usefulness of useless knowledge" https://www.ias.edu/ideas/usefulness-useless-knowledge
7. "The Crest of the Peacock" by George Gheverghese Joseph https://en.wikipedia.org/wiki/The_Crest_of_the_Peacock:_Non-European_Roots_of_Mathematics
8. Review of "Crest of Peacock" by Clemency Montelle http://www.ams.org/notices/201311/rnoti-p1459.pdf
9. Venky Ramakrishnan on Indian Science Congress http://www.firstpost.com/india/indian-science-congress-is-a-circus-wont-attend-it-nobel-laureate-v-ramakrishnan-2572268.html
10. "I'll not accept any job in India" - Venky Ramakrishnan http://articles.economictimes.indiatimes.com/2009-10-13/news/27645273_1_nobel-laureate-venkatraman-ramakrishnan-venki-ramakrishnan-nobel-prize
11. Goethe's Scientific work https://en.wikipedia.org/wiki/Johann_Wolfgang_von_Goethe#Scientific_work
12. "Nabokov Theory on Butterfly Evolution is Vindicated" - New York Times http://www.nytimes.com/2011/02/01/science/01butterfly.html?_r=0
13. "The Invention of Nature: Alexander Von Humboldt's New World" - Andrea Wulf
14. Manjul Bhargava's Theory (an explanation) https://www.quantamagazine.org/20140812-the-musical-magical-number-theorist/
15. About Bhargava's award http://www.business-standard.com/article/beyond-business/a-professor-who-sees-common-thread-in-sanskrit-music-and-mathematics-114081400051_1.html
16. "India has to be its own cultural ambassador, but it has to be scientific about it" - Manjul Bhargava -- Lecture on "Connection between Sanskrit and Mathematics" http://thewire.in/2016/01/19/india-has-to-be-its-own-cultural-ambassador-but-it-has-to-be-scientific-about-it-manjul-bhargava-18524/
17. Another blog on the same lecture http://varahamihiragopu.blogspot.com/2016/01/manjul-bhargava-on-sanskrit-and.html
18. "Nobel, Nationality and Venky Ramakrishnan" - My blog in 2009 http://contrarianworld.blogspot.com/2009/10/nobel-nationality-and-venky.html
19. Alexander Von Humboldt https://en.wikipedia.org/wiki/Alexander_von_Humboldt
20. George Joseph's interview in 'The HIndu' http://www.thehindu.com/features/friday-review/history-and-culture/dr-george-gheverghese-joseph-tsays-the-work-of-kerala-mathematicians-influenced-their-european-counterparts/article7818063.ece

Isaac Newton and the Divorce of Philosophy and Science

A recent Tamil book makes the case that Erwin Schrodinger was inspired by Vedanta in formulating his theories on quantum physics. The authors then proceeded to speciously argue for the continued relevance of Hindu Philosophy, knowledge systems, to today's world. In this backdrop it is pertinent to trace the point at which science roared forward unmoored from philosophical speculations and in the process creating its own paradigms. Isaac Newton marks the clear point at which science divorced itself from what was hitherto called philosophy.

Concluding the chapter on Aristotle Will Durant wrote "all the world awaited the resurrection of philosophy". Starting with Roger Bacon in the 13th century Europe saw a fervid efflorescence of genius. Tyco Brahe, Kepler, Copernicus, Galileo, Vesalius and Harvey took human knowledge into new frontiers. "It was an age of achievement, hope, and  vigor; of new beginnings and enterprises in every field; an age that waited for a voice". The voice was embodied in Francis Bacon.

Isaac Newton(Image Courtesy Wikipedia)

The explosion of knowledge that accompanied what Durant called "Age of Reason" was unprecedented in human history. Sir Thomas Bodley who established the Bodleian Library (1598) in Oxford "obtained from the Stationers Company a grant whereby the Bodleian Library that he had established at Oxford (1598) was to receive a copy of every book published in England". France and Germany saw similar libraries. Germany made elementary education compulsory for both sexes in 1565, rapidly other European cities followed. The Church which receives a justifiable rap for its confrontation with science nevertheless played a vital role in furthering the goal of education. "In France every parish had to maintain an elementary school". "In 1685 the Christian Brothers opened what was probably the first modern institutions for the training of elementary school teachers". Nearly two hundred universities were opened between 1550s to late 17th century.

Isaac Newton, born on Dec 25th 1642 in Woolsthorpe, entered a world where slowly but surely science, thanks to Francis Bacon, was stepping out of the shadows of philosophy. Bacon, James Gleick's biography of Newton says, lamented "all the philosophy of nature which is now recieved, is either the philosophy of the Grecians, or that other of the alchemists...The one is gathered out of a few vulgar observations, and the other out of a few experiments of a furnace. The one never faileth to multiply words, and other ever faith to multiply gold". Bacon, Gleick points out, "argued for experiment".  When the Royal Society was established in 1660 with the motto 'Nullius in verba" Bacon was adopted as the patron saint. The age of telescope and microscope had arrived. "It (the Royal Society) exalted communication and condemned secrecy".

Robert Hooke who served as the Curator of Experiments in the Royal Society wrote in his "Microphagia", tat science should now "return to the plainness and soundness of Observations" and away from what it was hitherto, a "work of the Brain and Fancy".

A society for science dedicated to communicate faced the question of which language to use. Though Latin was the obvious choice the members felt "it was time for plain speaking, the most naked of expression, and when possible this meant the language of mathematics". The Royal Society was not alone, soon Europe saw a host of societies established where, most importantly, men of science congregated and debated without the constraints of social status. Gleick quotes an entry from Samuel Pepys's diary on how the Society organized science exhibitions for Londoners. This was a quantum leap. Let's return to Newton's story.

Thanks to Stokes, the schoolmaster at Grantham where Newton attended school, and his uncle, a rector, Isaac Newton was sent to Trinity college at the University of Cambridge for further studies. A civil war, plague, a rebellion and a regicide (if hanging Cromwell's corpse could be called so) formed the climate in which Newton attended college. Newton read avidly, particularly Aristotle. Aristotle idea of "motion" was elastic enough to consider a "piece of bronze becoming a statue" as motion. That meant, Gleick says, "philosophers were not ready to make fine distinctions between velocity and acceleration". Aristotle had famously said "Plato is my friend, but truth my greater friend". Newton added Aristotle to that and wrote in his notebook "Plato amicus Aristoteles magic amica veritas".

Descartes had earlier married algebra to geometry yielding a new discipline. "He treated one unknown as a spatial dimension, a line; two unknowns thus define a plane....Equations generated curves; curves embodied equations". To that Newton added the question of motion which embraced the infinite and the infinitesimal together. "To measure curvature was to find rate of change".

In 1665, soon afterNewton graduated, Cambridge was closed due to plague ravaging England. Back in Woolsthorpe Newton worked alone and laid the foundations of calculus, theories on gravitation and light. Newton returned to Cambridge in 1667 and was elected a fellow. He took the oath to "embrace the true religion of Christ with all my soul". "Chastity was expected. Marriage was forbidden". In 1669, at the age of 27, Isaac Newton became the Lucasian Professor of Mathematics. The mathematician's heart was in physics though.

Newton's paper on the nature of white light was read in the Royal Society in 1672. Newton, Gleick says, "declared triumphantly-"that light consists of Rays different refrangible". Hooke objected to Newton's theory that proposed light was "corpuscular" in nature, particles. Newton responded that "that followed from his theory and not the other way round". Dutch scientist Christiaan Huygens also joined the debate on the "wave theory" side. Newton felt insulted and wanted to withdraw from the Royal Society. "He had tried to show how science is grounded in concrete practice rather than grand theories". As these debates raged Newton, in 1675, reached another milestone. In the seventh year of his fellowship Newton was required to take the "holy orders and be ordained to the Anglican clergy". Gaelic notes "England's universities were above all else instruments of Christianity". Newton was spared the ordeal by the King who exempted the "Lucasian professorship, in perpetuity, from the obligation".

Hooke and Newton would clash again when the "Principia Mathematica" was published. Both Hooke and Newton had rejected the Cartesian idea of "vortices" to explain planetary motion. Both were circling around the ideas that "a body orbiting another in an inverse-square gravitational field" would trace an elliptical curve. Conversely, they also realized that a gravitational force law to describe a body tracing an elliptical curve around another body can only be a "inverse-square law". Hooke did not have mathematical proof but Newton did. Edmund Halley and Flamsteed who were calculating data about meteors supplied Newton with theories and data. Newton, Gleick shows in scintillating pages, went where no philosopher or philosophy went. Book III, The System of the World, "gathered together the phenomena of the cosmos. It did this flaunting an exactitude unlike anything in the history of philosophy". Gone are the flights of fancy of a philosopher or dreary sophistries of reasoning and in its place science arrived with exactitude. Hooke wanted credit for the inverse square law, which in reality was nothing more than a guess until Newton supplied the mathematical proof. Newton was irked and he called philosophy a "litigious lady that a man had as good be engaged in law suits". Halley published the Principia out of his funds.

Newton was charged with promoting atheism, a dangerous charge in that era.Will Durant writes "he appended to the second edition a general scholium on the role of God in his system". Though Newton kept up the appearances of a devout Christian in private he was anything but. Gleick says he preferred writing "AC (after Christ) instead of AD". Newton questioned the idea of trinity, a heretical and dangerous sacrilege then. To Newton Christ was less than God the Father. Though celibate Newton confessed to not only sexual thought but charged his friend Locke of having tried to entice him with women.

Hooke died in 1703 and Newton ascended to the power at the Royal Society. In 1704 Newton published his next major work "Opticks" which revolutionized the understanding light. Along with Opticks Newton published  a paper "On the Quadrature of Curves" that laid down the fundamentals of Calculus.  German mathematician Leibniz who had corresponded with Newton on what he called "fluxions" claimed that he too was the inventor of this new mathematics. As president of Royal Society Newton was judge, jury and prosecutor. Newton literally forged documents in his favor. History has now declared both Leibniz and Newton as co-inventors of Calculus.

What did Newton, specifically the Principia, achieve? James Gleick is categorical, "Newton had made claims that could be tested". In 1733 the French Academy of Scoences proved Newton was correct that the earth was "broader at the equator". Gleick is emphatic, "The Principia marked a fork in the road: thenceforth science and philosophy went separate ways". "By mathematizing science science, he made it possible for its facts and claims to be proved wrong". Conceding that Einstein's Relativity shook the world of Newtonian determinism Gleick cites Thomas Kuhn who suggested that "Einstein had turned science to problems and beliefs". However, Gleick cautions, "Einstein did shake space-time loose from pins to which Newton had bound it, but he lived in Newton's space-time nonetheless: absolute in its geometrical rigor", "he happily brandished the tools Newton had forged".

Isaac Newton was celebrated in prose by Alexander Pope and Wordsworth, William Blake drew a portrait of him, Voltaire studied him and literally proselytized for him in France, he was knighted and when he died nobles were his pall bearers and he was interred in the Westminster Abbey.

Portrait of Newton by William Blake (Image courtesy Wikipedia)

"Nature and Nature's laws lay hid in the night
God said, "Let Newton be!", and all was light" --- Alexander Pope

"Newton with his prism and silent face
The marble index of a mind for ever
Voyaging through strange seas of thought alone" --- William Wordsworth

Science has decisively outpaced philosophy and America, the land of pragmatism, which became the leader of science, had little use for European style sophistry. No one embodied the American spirit of science better than Richard Feynman. In Feynman was a spirit of irreverence and absence of philosophy unlike Einstein who read Kant as a child. Philosophy does not even provide the questions anymore let alone answers. Schrodinger owed to illicit sex as much as he owed to Vedanta for inspiring his theories.

The questions that the authors of the Tamil book failed to ask where: Why is it that it took an Austrian scientist to find the ideas in Vedanta that could inspire a scientist and not any Indian scientist? What in the Austrian scientist's Viennese education enabled him to see in Vedanta what no Indian scientist did? How many Indian exponents of Indian philosophy arrive at the same conclusions? Above all what paradigms of the Vedic era are relevant for science today? I'll write a detailed review and rebuttal of the book later.

The traffic of knowledge across the European continent is staggering in scope and requires a meditated appreciation for the scope at which it occurred. Ideas, amidst turmoils of wars, flowed in all directions. Ideas from Frances, Netherlands, Germany and England all collided and created a new world. That books written in France, Germany and England were translated, shipped to other countries and debated in scientific circles providing a magnificent intellectual stirring is a fact that should astound us, those who live in this modern social media age, on a grand scale. What is even more important is how they were eager to learn from others and not mired in petty nationalist chauvinisms. That too, given the kind of era it was, passes comprehension.

This was to be a book review of James Gleick's "Isaac Newton" but morphed into a different tone. Gleick's book is very mediocre. The narrative is uneven and his extensive quotes in the English of that era are irritating to read. What is really a letdown is Gleick's inability to explain science in a more lucid manner. This is shocking considering that Gleick's biography of Richard Feynman, "Genius", was critically acclaimed both for the sensitive portrayal of Feynman and for the lucidity of explaining esoteric concepts like Quantum Dynamics. I read portions of Will Durant's magisterial 11 volume "Story of civilization", specifically, volumes "The age of Reason" and "The age of Louis XIV" after I finished Gleick's book. Durant, who wrote nearly 40 years ago and was no scientist, covered all the material that Gleick, writing in 2003, covers. Durant's explanations of the theories and their significances are spot on. And, as only Durant can do, he provides a panoramic perspective of that era. Gleick's book should be read only because Durant's 11 volume series is out of print.

Science has marched forth from the shadows of philosophy and education has been liberated from the clutches of Church and State paving the way for what we call today 'secular education'. Both of those achievements are now under siege from the Hindutva camp.


References:

1. Isaac Newton - James Gleick
2. The Age of Reason -- Will and Ariel Durant
3. The Age of Louis XIV -- Will and Ariel Durant
4. Isaac Newton https://en.wikipedia.org/wiki/Isaac_Newton
5. The Royal Society https://en.wikipedia.org/wiki/Royal_Society
6. Francis Bacon https://en.wikipedia.org/wiki/Francis_Bacon
7. New York Times Book Review of "Schrodinger: Life and Thought" by Walter Moore -- This addresses briefly the role of Vedanta in Schrodinger's life - http://www.nytimes.com/1990/01/07/books/the-lone-ranger-of-quantum-mechanics.html?pagewanted=all