KB: I think it is best to start with the name “Mathematical Reality.” What would you say is the reason for it?

Dr. BSR: I was looking for a suitable name to capture the fact that I was going to write about truth and beauty in theoretical physics. During the earlier years when I was doing my Ph. D in theoretical physics, I was motivated more by the sense of mathematical beauty than the truth a particular theory contained or gave rise to. It is not that I was not concerned with “truth.” In fact, that was the main reason for my choosing theoretical physics over pure mathematics. I say pure mathematics in a quite serious sense, for I had been involved in studying pure mathematics for nearly four years exclusively, I mean, to the near exclusion of theoretical physics, two years before I began my Ph. D program. 

I worked through several volumes of J Dieudonne’s “Treatise on Analysis,” and many of Serge Lang’s books and of course, Abraham and Marsden’s “Foundations of Mechanics,” to name a few. But after that brief period of immersion in pure mathematics, I returned to theoretical physics being forcefully carried away by a sense of profound mathematical beauty. So when a year ago, when I thought of writing about my insights and perspectives, I thought of fusing truth and beauty with serenity and insight and naturally the term “Hilbert’s Pace” popped up in my mind.

KB: Now that you mentioned it, could you go over a little about how you came to theoretical physics? I think this will give a much needed perspective into the term, “quest,” that you talk of quite often.

Dr. BSR: Sure. I came across the term “theoretical physics,” apparently by accident but really by a half-conscious stumbling upon it led by my deep quest. As many may not be aware, till my 7th grade, I was a conventionally bright student, at the top of my class. But during my 8th and 9th grades, I had an appalling fall in academics and I plummeted to the bottom of the academic ladder, in fact securing the 33rd rank in my class and dubbed the worst student in the school! In my 10th grade, however, I realized the danger I had fallen into, of the abyss I was heading into, from which there could be no climbing back. I put in a prodigious amount of effort and jumped back onto the higher rungs of the academic ladder. 

So after my 12th grade, I found myself joining an engineering college for the Bachelors degree program in Mechanical Engineering. Now there were around five months before the engineering college started. I had gotten interested in physics and mathematics in my 11th and 12th grades and so I continued to study mathematics and physics independently. I went to bookshops and got hold of advanced books on mathematics and physics. I think it was during this period that the word “theoretical physics,” struck me. I think it was in the Feynman Lectures on Physics. But initially I did not give that much importance to it, though it no doubt intrigued me. 

After the five month period was over, I was filled with a profound sense of quest and eagerly went to the engineering college, more so at the prospect of getting access to the library than for the classes. You must remember that in those pre-internet times, libraries were the only source of books, especially on advanced mathematics and physics. So I went to the college library and looked around. Two books caught my attention. One was a beautiful silver colored book by Morse and Feshbach, “Methods of Theoretical Physics.” The other was by Bjorken and Drell, “Relativistic Quantum Mechanics.” That was my first conscious encounter with theoretical physics. I plunged into Morse and Feshbach’s book and in around two month’s time, was into the thick of it. By the time I was through reading the book, I knew that I was not born to be a mechanical engineer but a theoretical physicist.

KB: When you say “I was not born to be a mechanical engineer but a theoretical physicist,” are you saying that you were aware that you wanted to be a scientist right from your early years?

Dr. BSR: In a sense, yes, though the word scientist had not particularly drawn my attention. In India, when people talk of a scientist, they mean more in the sense of technology, of invention or innovation. They have the idea of Edison who was an inventor, to represent the image of a scientist. I have no problem with that except that I think it distorts the meaning of the term scientist. A scientist is one who seeks the unknown and is more into discovery than invention. Well, I was more interested in discovery, though I did engage myself in many a hands-on tinkering with gadgets and minor inventions, that most kids are into.But I was more interested in the philosophical quest for what is behind phenomena and did not then realize that being a scientist could lead to that. But yes, even then, I was aware that I was going to be someone who discovered things. 

KB: It was during your engineering program that you actually got into theoretical physics. It would be really interesting to know more about that, and keeping the theme of the website, “Hilbert’s Pace,” you could talk about your pursuit of mathematical beauty in theoretical physics.

Dr.BSR: I think it is quite natural for me to be motivated by mathematical beauty because of the unconventional and novel way I entered theoretical physics. Normally one would do so starting out with Classical Mechanics, Classical Electrodynamics, Quantum Mechanics along with Mathematical Methods. I, on the contrary, started out with General Relativity!

KB: General Relativity? How could you manage that? Without the background that the branches you mentioned, especially as General Relativity is one of the more difficult branches of theoretical physics and is not accessible before the doctoral level. 

Dr. BSR: I agree, it is very unusual and in my case it is one of the power of ignorance triumphing over knowledge. With my present understanding of cognitive neuroscience and positive psychology, I would say it was a case of me not having picked up “learned helplessness,” that most students do. I mean, I was not “taught” that it was not possible to do fields like General Relativity and so I went ahead and did it. The how does not matter, as once you have a sufficiently strong “why,” the how gets figured out by the subconscious. But I think I am digressing a bit too much from our main theme. 

Let me get back to that, of mathematical reality. So, having started out with General Relativity, it was natural for me to be struck by its profound mathematical beauty of what Hawking and Israel capture so beautifully in the book they are editors of, “General Relativity, An Einstein Centenary Survey,”

“No-one can recall without a thrill his first encounter with this Carollian world where space is curved, time a fourth dimension and honest witnesses blithely disagree on the most elementary questions of what happened when and where.” 

I had first came across the term “tensors,” in the book by Jeremy Bernstein, “Einstein,” that I read in my 7^th grade, and later, during the five month period before my engineering, I read the absolutely wonderful book, “Space, Time, Gravitation,” by Minrosky et al, a Mir Publishers book. That book really gave a glimpse and opened my eyes to the magical beauty of not only tensors but of Elie Cartan’s exterior calculus, Riemannian Geometry, Finsler spaces, Weyl’s gauge invariant geometry, Kaluza-Klein theory and so on. But this was at a semi-technical level. I soon got hold of the beautiful Landau and Lifshitz course of theoretical physics, Vols 1 and 2, “Mechanics” and “The Classical Theory of Fields,” respectively, and that was the beginning of my serious learning in General Relativity. I followed this up with the older book by Peter Bergmann, “Relativity,” and then another older book by C Moller, “General Relativity.” These were the only books I could get hold of during those times when libraries and that also, the libraries at the research institutes, were the only source of such books.

Around this time, things happened quite fast and cutting a long and involved story short, I began to meet Prof. J Pasupathy, at the Centre for Theoretical Studies, Indian Institute of Science, Bangalore, India, from time to time. He gave me Steven Weinberg’s book, “General Relativity,” that I mastered in one month’s time and moved on to the bewitchingly beautiful book by Hawking and Ellis, “The Large Scale Structure fo Spacetime,” and of course, Misner, Thorne, Wheeler’s “Gravitation.” That was the point of no return for me. I could never, ever live an ordinary life. It lifted me to heights I could not imagine. I was lost in ecstasy for weeks and months working through that book. It led me to master Topology and Differential Geometry from the books by J Kelly, “General Topology,” Hocking and Young, “Topology,” Sigurdur Helgason, “Differential Geometry, Lie Groups and Symmetric Spaces,” and Kobayashi and Nomizu, “Foundations of Differential Geometry,” Vols 1 and 2, V I Arnold’s “Mathematical Methods of Classical Mechanics,” T J Willmore’s “Total Curvature in Riemannian Geometry,” and a host of other wonderful books. 

And in all these, the most beautiful experience I had was mastering Elie Cartan’s calculus of differential forms and working out the Schwarzschild and Kerr solutions of the Einstein field equations, maximally symmetric spaces, the Penrose 2-spinor formalism and classification of the gravitational field, Twistor cohomology etc. In a sense, mathematical beauty came to me most evocatively in the works of Elie Cartan. Nothing else quite equals that and even today, I am into pursuing the deeper ramifications of Elie Cartan’s work through the framework of multisymplectic geometry, especially from the works of G Sardanashvily and his collaborators, Jerrold E Marsden, Mark Gotay (The GIMMSY articles) and of course, Robert Hermann’s wonderful books on Cartan’s work.

KB: That really was a sweeping view of your entry into theoretical physics. I have myself mastered Elie Cartan’s methods and cannot but agree on what you said. In my own work, I am applying symplectic geometry to quantum mechanics and truly, the mathematical beauty is really striking. 

Dr. BSR: And added to the pursuit of Elie Cartan’s methods, I soon encountered Gauge theories…and…my breath almost fails to utter this…it was the most enthralling, magical experience of my life…to realise that the structures behind Gauge theories and Fibre bundles were the same. I can only describe this by quoting Keats in his Endymion,

“Wherein lies happiness? In that which becks 

Our ready minds to fellowship divine, 

A fellowship with essence; till we shine, 

Full alchemiz’d, and free of space.” 

I lost sense of day and night in working through these realisations and understanding upon understanding crowded upon me. I worked on theoretical physics so much that often I was awake for two days at a stretch and slept only the next day, missing my classes at the engineering college. I would get up in the midst of a dream and rapidly transcribe my insights that I had received in a metaphorical form, into words. I could no longer identify with what I had been just a few years earlier. I was a transformed person, the quest had captured me completely and I felt truly blessed, for want of a better phrase, to have been vouchsafed this path into theoretical physics. Theoretical Physics, to me, therefore, is the deepest calling of the soul, the hero’s journey, an adventure to the promised land. Shelly’s Alastor or Spirit of Solitude, best captures my feelings, in the infancy of my entry into the world of theoretical physics.

“By solemn vision, and bright silver dream,

His infancy was nurtured. Every sight

And sound from the vast earth and ambient air,

Sent to his heart its choicest impulses.

The fountains of divine philosophy

Fled not his thirsting lips, and all of great,

Or good, or lovely, which the sacred past

In truth or fable consecrates, he felt

And knew.”   

KB: The way you say it, I feel the stirrings of the spirit. Yes, it is so true that as one goes deeper and deeper into the heart of theoretical physics, it becomes impossible to turn back to the ordinary life and I think that is the reason you say it is the hero’s journey. For, as I recall Joseph Campbell’s book, “The Hero with the Thousand Faces,” the hero leaves the ordinary world and embarks on his journey. And as he proceeds, he hesitates and many a time, feels like giving up. And there intervenes a stage after which he knows that the return to the ordinary world before completing the hero’s journey is impossible.

Dr. BSR: Yes, you put it accurately. And in me that departure from the ordinary world and into the world of theoretical physics was also accompanied with a growing sense of what I can best call, austerity, a sense of purity, as if all my physical, emotional, mental and psychic energies were getting concentrated towards the quest and providing the rocket-propulsion necessary to escape the pull of the ordinary world. 

To me, theoretical physics symbolised a mystical journey into the realm of pure thought and spirit and I felt the deep transmutation taking place in me day and night. The mathematical beauty soon fused into truth and then the sense of immaculate serenity settled upon me making my quest for the laws of Nature utterly intrinsic. All these feelings began to bring forth insights too numerous to express and too profound to communicate. That is why, I still have  notebooks and sheets filled with my writings and papers, finished and unfinished, that I have chosen to just let them stack up and stand by. What you are going to see in the website, “Mathematical Reality,” is just drawn forth partly from these insights.

KB: I think it would clarify a lot if you could outline in your own words the famous CFRCE Theoretical & Mathematical Paradigm that was an outgrowth of your vision during your engineering times.

Dr. BSR: Sure, and for that I would have to talk something about the Beginner’s Brain-Mind. The beginner’s brain-mind comes with unlimited possibilities for learning teeming as it is with potential skills that naturally require a worthy challenge. Lacking this challenge, the beginner becomes disillusioned and the psychic energies get scattered in fruitless efforts. It is, therefore, indispensable to provide a roadmap that accommodates the tremendous firing of the BDNF. 

As a young beginner during the heyday of my own strivings in theoretical physics I myself faced this necessity of providing myself a challenge that I could devote all my energies to. As I could not find any guidance from wither the literature nor from the community of researchers, I tried several paths that appealed too me. For a time I even went over entirely into Pure Mathematics thinking that it would best provide the resources I was looking for to take on Theoretical Physics in earnest. After three to four years of Pure Mathematics, I came to agree with what Einstein writes in his autobiographical notes, 

“I saw that mathematics was split up into numerous specialties, each of which could easily absorb the short lifetime granted to us. Consequently, I saw myself in the position of Buridan’s ass, unable to decide upon any bundle of hay.”

Thus disillusioned though not disappointed, by Pure Mathematics I returned to Theoretical Physics. But my immersion in mathematics was not a fruitless exercise. For, when I returned to physics, I found that an entirely new perspective had emerged. Suddenly, theoretical physics seemed to be running through several threads all starting from the Calculus of Variations. I looked to formulate a unifying scheme that would give me the organising principles for my research. As I began to sketch it out, the picture formed on the canvas of my mind and emerged into a full-blown roadmap. So enthralled I was as I put it down on paper that I could not sleep well for a few weeks and lost my appetite. I moved about in a daze and in the classes at my engineering college, I sat like a deaf and dumb person absorbed in my own world and with my eyes abstracted on an inner vision. 

I spend the next few months in the library at the Indian Institute of Science and the TIFR Centre that was in its campus, putting together source books and references and hunting down review articles from Physics Reports, Rivista del Nuovo Cimento, Reviews of Modern Physics, Journal of Mathematical Physics, and several other journals, proceedings of summer schools and conferences etc. And next, it was not enough to list these, I needed to get hold of them in order not to interrupt my studies. Over the ensuing months I managed to get hold of all these and those that were not available I procured them by writing directly to the mathematicians and physicists. 

One of the most memorable of the articles I received was from Marcel Berger, from Paris, “Riemannian Geometry During the Second Half of the  Twentieth Century.” After gathering all these, rather as I was gathering them, I embarked on my grand vision of mastering all the essential branches of Theoretical and Mathematical Physics in a unified manner, mapping out the varied interconnections, inter-dependencies and logical independence of the topics. The more I worked out these sources, the more my notes grew. My engineering studies dwindled away and I began to play truant with my college. 

This pattern carried over through my entry into the Indian Institute of Astrophysics and though my formal thesis work was in Classical General Relativity and Black Holes, I continued to work away on my vision towards Loop Quantum Gravity. I soon saw that the other students began to notice the strange things I was involved in and to prevent interruption I rapidly switched to night mode. I appeared at the institute later and later in the day till there came a stage when I reached the institute as others were leaving for the day. I would go to the library and sit through the whole night with my pile of books and papers that I used to carry in my trekking backpack. Those times I had my motorcycle to the front of which I had devised a special mechanism to attach and tie my backpack as it was generally quite heavy at any given time containing over twenty to twenty five books and papers.

My roadmap also became extremely clear and concrete to me around this time. Here is an updated version as we use it at CFRCE.