The least difficult part of writing this post has been to decide on a title, and one that would share some of the awkwardness and pain that one feels in writing of this, the belated realization that I have met the (internet) trolls and they are us.

UntitledThis Saturday on the occasion of Eid-ul-Fitr, I shared the following striking painting that was originally posted on FB with the annotation “Reproduction of an 18th century Rajasthan miniature depicting Lord Krishna sighting the Eid moon and pointing it out to a group of Muslim men and women. Shared by our great history teacher Prof. Harbans Mukhia. Let’s resolve on this Eid to win back the Indìa of magic the picture depicts.”  I’m glad I did this – so many of my FB friends have gone on to share it further… And I was pleased that my erstwhile colleague from JNU was responsible in some part for having spread the word, and the message. However, see the Addendum below, as well as an article that has appeared in the Indian Express. [Fact checks at this point: a) The painting is not Rajasthani, probably Kangra. b) it is not the Eid moon. Actually, it is not even the moon per se, it is a solar eclipse that Krishna and Balarama are pointing out, and c) it is not a group of Muslim men and women, it is Krishna’s adoptive family and friends in 18th century poshak.]

Apparently many other people had also sent out the image, so I was a bit surprised when shortly thereafter, someone commented on my FB post and pointed to a tweet from True Indollogy to say “This picture is fake. There is no such 18th century painting. I challenge you to reveal its whereabouts (where is it located?)”. And then, “Secularism is not a one way street.”

Even the straw-man in the argument would be bewildered. The painting is a charming remembrance of times past, when it was possible to keep one’s religious identity distinct from one’s politics, and when, one would like to believe, all these issues were not automatically conflated. I, in particular, had not talked of secularism, and believe it or not, for most of us who have liked or shared the image, it was just a nice way to convey Eid greetings. We may have been mistaken in what the image was about, we may have made our interpolations (mentally at least, if not in writing) but in any case, the image is not “fake”, and while its provenance can be debated, it’s message would be as compelling were it a thousand years old, or three. [Fact check: The image is in the Smithsonian. So much for that. And it is a solar eclipse, giving a sense of wonder. And Krishna and family are clearly enjoying the view of the eclipse, unlike modern day Indians who avoid seeing such natural phenomena for all sorts of superstitious reasons. Which is an equally good and compelling message from the painting.]

Other than to point out that the self-same image had indeed appeared on the pages of Swarajya some years ago, I have not said anything, and neither am I going to add to that debate here, but I have been bewildered (to the extent that age permits) by the ensuing discussion on the two-way streetness of secularism and so on, and the fairly large number of ‘plus’ or people-like-us who can find serious fault with either the picture, its purported image, or its use today. Or that the way in which the term secularism has become to mean something very different from its textbook definition, of the principle of separation of the state from religious institutions.

John-Tenniel-Humpty-DumptyWe are in a wonderland of sorts, so I can quite accept that words mean whatever the user intends them to mean, like this memorable interchange from Through the Looking Glass.

The importance of being master cannot be denied, but it is impossible to carry out a discussion, meaningful or or not, to establish mastery on the pages of FB, as this very helpful video on the science of trolls so carefully explains.  But the post and subsequent comments confirmed the feeling, much like Oliver Perry said, that we have met the trolls and they are us.

A Cave Troll, from:

Of course, the internet being what it is, there is already a FB page for Trolls-r-Us though this is not relevant here. Neither is a similarly named website, “an archive of misinformation and propaganda.” This struck a nerve, given that one had been accused of propagating fake news, so I did a random search of this latter website for the word India, and found this gem: Egyptian pharaohs were of Slavic origin, the true history of Russia is hidden by masons […]. The human species was evolved not in Africa, but on the territories of current Russia. The Russian ancestors were known as Aryans who came to India. These Russian ancestors are mentioned in the Indian Vedas.” The site goes on to say These claims contradict the available anthropological data. So yet another nugget of wisdom is said to be contained in the Vedas. Having heard so many claims these past few years of what all our ancients knew or had known and having been both privately and publicly embarrassed by it, I was mildly surprised that there were not more claims on that site.

And this then brought to mind a paper that I had seen many years ago with the title On the Remarkable Spectrum of a Non-Hermitean Random Matrix Model by Daniel E. Holz, Henri Orland, and A. Zee. What had caught my eye at that time was the abstract, and in particular the last phrase: A non-Hermitean random matrix model proposed a few years ago has a remarkably intricate spectrum. […] The spectrum is complicated because our matrix contains everything that will ever be written in the history of the universe, including this particular paper.

We are indeed living in the matrix. Verb. sap.

Addendum (my notes in blue, others comments in italics)

A friend (and a real one) on FaceBook commented: This was being shared as an example of  ‘secularism’. Later, one of my friends posted a long clarification that showed this was not as it was claimed to be. I will copy it here or refer to it.

My reaction when I first saw it in a WhatsApp group was somewhat like this: It is so anachronistic! Eid in the time of Krishna? Lord Krishna with Muslims? Islam arose around 7 CE. And, this is supposed to be shared “via Harbans Mukhia”? Really? What did Prof Mukhia say about this? A joke or fabrication? Or, something else? Need to know a lot more. I don’t know what to make of this. It is really problematic to say Islam existed in that period. Secularism shouldn’t attribute symbolism where it may not exist in that form. The interpretation associating it with Eid is puzzling. “

Well, it was indeed shared via Harbans Mukhia, although he does not say that it was  an example of secularism (see my post above) but he did identify the others in the picture as muslims and went on to say: Is this the India we have lost?

There are allegorical references in many paintings and this is something that all of us are used to, so anachronism may not be such an issue. If one were looking at the painting as a record of some incident or a depiction of some event, clearly more research is needed. He then went on to quote his friend on FB:

Since many people shared the of us shared the image, here’s a clarification: For all those who are interested, here is Prof. B N Goswamy’s response to Prof. Gulam Sheikh’s query about the “Krishna sighting Eid moon” image. Please also forward it to other friends who may be sharing the image with wrong details. Also, those of you who are Prof. Mukhia’s FB friends, could you please check if the post in his name with the wrong attribution for the image is “genuine” — and alert him to this?

B. N. Goswamy: “I must confess that I had not seen this image before, despite being quite familiar with the Bhagavata Purana and this series of paintings from the Tehri-Garhwal collection (painted by one of the members of the first generation after Manaku and Nainsukh). However the present ‘reading’ of it is completely meaningless based as it is, chiefly I think, on the appearance of Nanda who is dressed like a Mughal courtier: with that kind of beard, and wearing a long jama and a sloping turban. The anachronistic impossibility of a Muslim figure to be seen in the Bhagavata Purana or this series apart, this is the way Nanda appears in every single folio of this series whenever we see him! Even in this regard, if one notices from close the jama Nanda wears is clearly a Hindu style jama, tied as it is, in Hindu-fashion, under the left armpit. There is not the slightest doubt about this.

Topped by that is the silly statement that it is a Rajasthani painting! Of course it is not. It is a Pahari painting from the series to which I have referred above. […]

The pointing towards the moon in the sky by Krishna and Balarama seems to be from an obscure passage, possibly in chapter 28 of the tenth skandha, where Krishna, after rescuing Nanda from Varuna who had seized him and taken him to his dominions, leads him and other kinsmen, using his powers of illusion, to a vision of his domains. There, after the rescue, the text says, Krishna “manifested to the cowherds his own realm” which is beyond the range of tamas … One cannot be certain, however; it is not unlikely that the episode occurs more fully in some other rescension of the Purana and not the one generally in circulation.

I have no idea where the present folio is. If it can be located, surely one will find a text on verso, like on other folios of the same series.

Long answer? But hopefully of some use.

Indeed, very useful, but also see the article in the Express. To be honest, I had also thought the image was more Kangra than Rajput, but that was just a superficial impression. The interpretation above, replete as it is with references and with caveats is more along the lines of a collegial note of correction on an over-interpretation of the image. Many of us who shared the image did so without any reference to either the identities of the persons there and without scholarly interpretations. As I said above, we are used to allegories in all our religious texts, and therefore to take everything so literally and to find fault, in of all things, the coexistence of different religions seems extreme. Many people found that the image evoked a memory of the way things were (or we imagine they were, or hoped they were). And I am willing to let it be.

We may well be in a matrix where all pasts and all futures are possible.


Death by Infantilization

The American poet bell hooks might have been speaking about the situation in JNU today: “Sometimes people try to destroy you, precisely because they recognize your power — not because they don’t see it, but because they see it and they don’t want it to exist.”

In my thirty plus years at JNU, I have rarely spoken in a public meeting, but when asked to do so on “What JNU has contributed in the Sciences” on 28 February this year, I felt I must. Partly because it is getting increasingly difficult to fight the losing battle of public perception versus ground reality, and also, because I was provoked by a recent public discussion on Lok Sabha TV, where blatant lies were broadcast, and the participants congratulated each other on their moral positions, each ever so smug and self-righteous.

Day after day there is an article in one or the other medium, with JNU faculty trying their best to explain just what the issues are to those who are not at JNU. This is not a case of “us” explaining to “them”, but there is more than a little schadenfreude in the point of view that cannot see what the fuss is all about. Not to mention a number of articles devolving around what-about-when-X-did-Y-to-Z

jnuNone of which can account for the slow and painful killing of an excellent university. And what lies at the heart of this heinous action is the basic incomprehension of what a modern university is, or indeed what a modern Indian university should be.

When I moved to JNU in 1986, one of the main things that attracted me to the university was that it was a graduate school. The School of Physical Sciences was started that year by then Vice Chancellor P N Srivastava with the idea that it would be a school of studies that recognized no disciplinary boundaries within the physical sciences. Having been at places where (in today’s language) the silos were impenetrable, it seemed like more than a breath of fresh air. For mainly professional reasons and some personal ones, I was happy to move to JNU from the institute I was at in Mumbai.


Some things about JNU seemed wonderful. The size, for one- it seemed to have so many more possibilities with four times the number of teachers and fifty times the number of students, not to mention the acreage, which was about fifty times as large as well. The number of disciplines – there were 8 Schools in JNU then (SIS, SLLCS, SSS, SES, SLS, SCSS, the old ones) and SPS and SAA, the new ones. There were some special Centres as well (some of which are now Schools in their own right), but the academic environment was rich compared to the smaller and more specialist campus I had been a part of in the preceding few years. It was a small matter that many people thought that we were a School of Physical Education, formed along with a School of Arts and Athletics… those were the initial days and we hardly cared.

The atmosphere was even more wonderful. This was a short enough time after 1983, and the memories of the earlier times were strong. The campus was politically alive, and the Ph D students who trickled into the School of Physical Sciences – 4 in 1987, 5 in 1988, maybe 6 or 7 in 1989, and so on – brought in the culture of the rest of the campus into our growing School. Our Ph D students of the early days were mostly all resident in the hostels, so we indirectly got to hear of what was discussed, the issues that were debated, and above all, we got to see first hand what an enabling campus the JNU was. Our students came from a very different demographic than the students at most institutes, and we could see first hand the change that JNU brought about in their lives, as indeed it did in ours.

kk1There were also some not so pleasant aspects of being at JNU. One was the two culture divide, caused in part by the huge disparity in size between the science Schools and the much larger Schools of International Studies, Language, and Social Sciences. The SPS was very small, even after we started the MSc in Physics, in 1991 or 1992. The students were younger and there were more of them, but still we were a mere ripple in the JNU, and some of the rules and regulations that were needed for a small cohort were not always in consonance with what the larger body had decided. But we went along, for the most part happy to be part of a public university, and adapting to the changes that were needed.

One of the most remarkable aspects of JNU was the position of students vis-a-vis the faculty. From the earliest times, the sense of participation of all students in university matters has been complete, be it at the level of governance or at the level of pedagogy- students have been able to participate in decision making, and indeed their opinions have been sought and respected. Most students (other than in the languages, that is) at JNU entered the university after a Bachelor’s degree elsewhere at the very least- and were therefore also adults for the most part. And they were treated as such, in terms of their responsibilities, in terms of our expectations of them, and in the way in which we dealt with them and their various issues.

images.jpegWhich is why, when in 2017 or 2018, the University administration does not condescend to talk to students let alone treat them as sentient beings capable of making their own choices, it seems an aberration. To be fair to the Administration (with the capital A) they do not talk to teachers either – unless one conforms to an archaic mode of conduct- but in the process, the entire University, teachers and students alike, is given the “Daddy knows best” line, and it is up to us to conform.

This process of infantilization is simply unacceptable.

It is tiresome to repeat the arguments of why the attendance issue is being misrepresented, and why it could and should have been done better, so I shall not. But as one who has taught at JNU for the past thirty or so years, I know that the real issue is of learning. Over time, the nature of pedagogy has changed, not just in JNU but also all across the world. The internet, the availability of online material, YouTube, Wikipedia, more books and better libraries- all of this has democratized the classroom as never before. To be sure, teachers are still needed, but our roles have evolved in a fundamental and significant way, something that the purveyors of attendance sheets cannot realize. The focus has to shift to evaluating outcomes fairly, to know what students have acquired and to ensure that they have learned the skills they need and not to ensure that they have 75% attendance. That is simply not the point, and in short, they.just.don’


And regrettably, they cannot realize it because, at a deep and fundamental level, the real reason that they just don’t get it is because they simply are not very capable. It can indeed be difficult to have to cope with not being very good… being  fairly mediocre and knowing it can be a difficult cross to bear. The knowledge also that come what may, try as one might, one is never going to quite make the cut: When mediocrity is coupled with authority, the combination is toxic.

There are many things that need to change in JNU, and those that have lived with it for the past so many years are best placed to advise on what is needed and how best to make the change. The hostels need better administration, for sure. The fees need to be rationalised to a less embarrassing level: the JNU annual tuition fees have not changed in years, the hostel charges are unrealistic, and this is against a backdrop where salaries and scholarships have been growing, keeping pace with the growth of the economy in fair measure. One can list more, indeed several more things that need change, but this should, in the best spirit of the campus, be done through discussion, through debate. Not via edicts, and certainly not under the pretence of having had decisions passed in the Academic Council when they were not. Or by the fabrication, the fraudulent claim that letters of support were strongly endorsed when the eminent alleged signatories simply deny ever having done so.  A shame that it has come down to this.

There is a peculiar stillness in the University today – a disquiet and a lack of enthusiasm that does not bode well. Dialogue is out, and in some sections, so is hope. Many of the things that the old JNU fought for and implemented have been done away with, and the price to be paid is that the campus demographic will change significantly in these few years. And then, there will be no one left to care.

Sunset in Cubatão

cubataoShortly after I moved to New Delhi in 1986, I got to spend six weeks in Campinas, Brazil. On the way to the beach at Guarujá one weekend I drove with some friends through the not so picturesque town of Cubatão, which, as Wikipedia will gladly tell you, was one of the most polluted cities in the world, nicknamed “Valley of Death”, due to births of brainless children and respiratory, hepatic and blood illnesses. High air pollution was killing forest over hills around the city.


It was a dull and soulless city abutting Santos in the state of São Paulo, but the high pollution also threw up so much particulate matter into the atmosphere that it helped to create some really spectacular sunrises and sunsets. My colleague at the University of Campinas, Alfredo, had this idea for his perfect movie noir – Sunset in Cubatão – along the lines of Blade Runner and to my possibly caipirinha fueled imagination it seemed like a great idea. It was the 1980’s after all.

Most of the cities here were not as polluted then, and environmental caution was not a matter of any concern. In the ’90s, when winter fogs became more common in north India, it was more a nuisance with flight schedule disruptions than any matter of serious concern. But the last ten days in Delhi have been a nightmare.

tenorBreathing hurts. The eyes smart, one can feel the acidity (or so I imagine) of the air as it passes through one’s nostrils. It does not smell particularly bad always, but the air is not fresh by any stretch of the imagination.  It is just impossible to take a deep breath and that has ruled out any exercise, even the most modest exertion. Schools were shut last week for a few days, but they have reopened, and there is little indication that serious political intervention is going to take place. The long term effects on us all, and on the environment is worth thinking about, else it may not be long before our city’s Wiki entry includes the epitaph “high air pollution killed Delhi’s urban forests”.

Photo on 13-11-17 at 11.55 AMYesterday, in particular, was very difficult- even in my office in JNU, arguably one of the greener parts of Delhi, wearing a mask made it somewhat easier to breathe. I posted this picture on Facebook and was inundated with invitations to move to Kashmir, Hyderabad, Manipur, Melbourne, and ironically, São Paulo! I hear that things have improved there since the 1980’s so maybe its a good option. Cubatão, here I come!

Pushpa Bhargava, Mentor and Friend

152When I came to the University of Hyderabad in 2011, one of the first people I called upon was PMB, Pushpa Mittra Bhargava. Someone I had known in one or the other capacity since 1983, my most recent interaction with him then had been at a book release at the IIC, when my colleague at JNU, Prof. Bipan Chandra had asked me to be one of the speakers at the NBT release of PMB’s book Angels, Devils, and Science. I’ve forgotten now precisely what I said, but given my preoccupations at that time, I would have spoken of Kosambi, and Bernal, both rationalists who would have appreciated the argumentative Bhargava.

PMB was nothing if he was not complex. Fiercely loved by some of my friends, he was also as disliked by some others. He was outspoken, unapologetic, opinionated, he could be dismissive of others and very full of himself, but he was also always knowledgeable, erudite, and above all, genuine. By the time I got to know him, when he had more time to spend, it must also be admitted, he was already in his late 70’s. In 1983, though, he had invited me to CCMB to give a seminar, and I remember his interest at that time was on Manfred Eigen’s hypothesis on the origin of life, and whether something like life might have just happened by chance in the chaos of early Earth. From that early interaction, a scientific collaboration grew between Somdatta Sinha, staff member at CCMB and myself, resulting in three journal articles, and more importantly, a lifelong friendship (it helps also that we share a birthdate) that has outlived spouses and geographical dislocations. We wrote an article that has appeared today in The Wire, and I quote from it below, with permission.

Pushpa Mittra Bhargava – a.k.a. PMB – was larger than life. His flamboyance was multidimensional, from the striking printed bush-shirts he was very often seen wearing, to the scientific friends and colleagues he cultivated, to the remarkable institution that he built and causes he espoused. Never one to shy away from controversy, he was one of the most outspoken public scientists in the country, and one who stood his ground on political as well as scientific fronts. There have been few like him in terms of his personal courage, and fewer still who were as unafraid to be vocal on issues that challenged his personal convictions.

PMB, born in Ajmer in 1928, was educated in Lucknow. He obtained his PhD from Lucknow University in 1949 and shortly thereafter moved to Hyderabad, to work at the CSIR’s Regional Research Laboratory (RRL) as an organic chemist. Although he spent a few years in the US and in England, he remained a Hyderabadi for the rest of his life, and Hyderabad is where both of us got to know him more closely, although at different stages of our lives.

Like few other chemists in the country in the 1950s and 1960s, PMB was greatly taken up by the ‘molecular’ approach to biology. He was an evangelist, and as students we recall his efforts in the early 1970s in persuading the faculty and students of leading chemistry departments in the country to look into the then-nascent field of molecular biology. He campaigned with great energy for setting up the Centre for Cellular and Molecular Biology (CCMB), first within RRL Hyderabad (now called the Indian Institute of Chemical Technology) in 1977.

Although a separate campus was not established for the institute until the mid 1980s, he was able to attract some outstanding talent to CCMB as well as some stellar visitors – James Watson and Francis Crick among them. From its inception, the CCMB had a distinctive character, marked by a fresh and distinctly innovative approach. It was always a very special type of laboratory within the CSIR. PMB’s vision was evident on all scales, from the type of building to the art in the corridors, the groups that were formed and the problems that were studied.

In turn, two very distinctive features of PMB and his approach to institution building are worth noting. The first is the sense of aesthetics, his ability to integrate artistic sensibility into the work environment, something he shared with Homi Bhabha and C.V. Raman. Indeed, he paid close attention to the details of design and he prioritised aesthetics and functionality over all else, be it the CCMB or his own residential quarters.

The second was his belief in the need for scientists to speak up for the cause of science, and the need for public intellectuals to engage on contemporary issues in forums that were appropriate. He ensured that CCMB would have occasions to invite the common people to come see what science was being done there, but he would also make the lectures by leading scientists available to the public at large. He believed that it was the duty of scientists to fellow citizens to explain and encourage them to get excited by science, and think scientifically.

From the early 1980s to this day, thousands of school and college students and their parents, and countless others, would visit CCMB and learn from the faculty and students there as to what work was going on. Another of his passions was MARCH (Medically Aware and Responsible Citizens of Hyderabad), an organisation that he cofounded and which would meet every month to discuss some issue or other pertaining to public health. Given his sensibilities, these would be current and he would also get some of the leading experts to come and talk.

Of course, the cause of public engagement could take extreme forms. In 2015, he returned his Padma Bhushan (awarded to him in 1986) to the Government of India as a protest against the government’s attack on rationalism, reasoning and science. Years earlier, in 1994, he had resigned from the fellowship of the science academies of India for their lack of opposition to governmental plans to introduce astrology into university curricula. He spoke out against many issues, such as homoeopathy, GM crops, irrational beliefs and superstitions, pseudoscience and the lack of scientific temper, and about which there are numerous reports in the media. He responded to national issues with conviction and inevitably made enemies for his strong views and actions.

But what remain are indelible impressions of PMB the man. Both of us were associated with and influenced, in different ways, by him over a long period of time. Oddly enough, it was his intellectual curiosity that stimulated our academic collaboration, starting with an invitation to RRL to speak at the CCMB in 1983. At that time, SS had just joined CCMB as a young faculty member: fresh from JNU and working in an area of biology most people were unfamiliar with, and always ready to question the ‘administration’s decisions’.

PMB would listen patiently. Faculty meetings encouraged long discussions, dissent, arguments over institutional issues – and all this came largely from the sense of belonging that he instilled in the staff. Hugely nationalistic, in a way that was appropriate at that period of time, PMB would ask, “Why can we not do this work here?” of one or the other scientific problem. Keenly aware of trends in world science, he encouraged faculty to think of difficult and completely new problems that could have applications to society. He had the ability to find excellence and innovative ideas in people, independent of their rank or academic pedigree.

Regular group meetings with scientific literature reviews, a steady stream of national and international visitors whom the young faculty and PhD students always met, implementing a full technical group to support biologists with instrumentation issues, setting up a fully participatory and shared work atmosphere, and, most importantly, making young students and faculty feel the aura of basic science and giving the confidence of wanting to do interesting and difficult work, was PMB’s seminal contribution to the next generation of students and faculty.

There were also aspects of PMB that were difficult to deal with. Views that diverged widely from his were unsustainable. Those who could not convince him of their viewpoint either had to concur or leave. He could be arrogant, on many issues he was mistaken or inconsistent, and he could often seem autocratic and dogmatic. He had his blind spots. But for all his strong opinions, he had a commitment to quality, and in the end this is essential to build anything that will last.eminent-scientist-pm-bhargava

And PMB was much more than even this. To people around him – students, young faculty, the lab-boys, gardeners, drivers, people who managed the instruments, air-conditioning, guesthouse and canteen, and others – he was intensely personal. Cutting across hierarchies, he was one of them, their own PMB. He made everybody feel that working together towards excellence in all spheres is the way to excel. CCMB was not only known for its science but also its cleanliness, beauty, reliably excellent facilities and the ability to have the scientific faculty, administration, engineering, stores and purchase, gardening and hospitality services work together smoothly, like a well-oiled machine.

It would not be an exaggeration to say that all this happened largely due to the contagious enthusiasm that PMB radiated. He was always there. This was a new approach to the directorial style, one that was uncommon in those days (and even now). He knew everybody by name and made it his job to know each person’s concerns. He made lab rules such that anybody could work at any time of day and night, but in a way that safety was never compromised. Support to all employees to be dropped back home at night after work, or if they were stuck in any emergency condition anywhere in India, and interactions allowing free discussions – these were all hallmarks of making one feel ‘at home’ in the workplace.

UntitledHe was one of the finest institution-builders in India as he could integrate the Indian culture of togetherness with the western culture of hard work. Several people who went on from CCMB to other institutions have tried to replicate such an ethos. So have several others who have seen it work so effectively at the CCMB. Beyond the flamboyance and everything else, PMB was a great inspiration. A friend and guide to many, his direct and indirect influence on Indian science and scientific culture will be lasting.

1917. It was a Very Good Year.

thWhat Einstein said of Mahatma Gandhi, that generations to come will scarcely believe that such a one as this ever, in flesh and blood, walked upon this earth, is more than applicable to Einstein himself. From 2005 – declared by the United Nations as the World Year of Physics, to celebrate the centenary of Einstein’s annus mirabilis – onward, there have been many occasions to mark one hundred years of one or the other incredible contribution of his.  For Einstein, many years were very good indeed.

UntitledWhat makes 1917 special in some ways is the appearance of three other papers, each unrelated to the other (as the three of 1905) and which altered the fields that they touched upon. It would well have been called another annus mirabilis, had not 1905 already happened.

Early on in Volume 6 of the Collected Papers of Albert Einstein titled The Berlin Years: Writings, 1914-1917, his “Inaugural Lecture”, delivered upon his election to the Prussian Academy of Sciences, he alludes to the soon-to-be-presented papers on his General Theory of Relativity, saying “We have determined that inductive physics has questions for deductive physics and vice versa; and eliciting the answers will require the application of our utmost efforts. May we, by means of united efforts, soon succeed in advancing toward conclusive progress.” That conclusive progress was to appear in the journal Annalen der Physik in May 1916, entitled “Die Grundlage der Relativitätstheorie” (On the Theory of General Relativity). But that was 1916.

The first of 1917’s three gems was On the Quantum Theory of Radiation, wherein he  came up with stimulated emission and laid the foundations of laser physics. The second was Cosmological Considerations in the General Theory of Relativity, in which he set the foundations of modern cosmology.

UntitledAnd the third. On May 11, 1917, Einstein presented a paper to the German Physical Society,  and this was published on the 30th of the same month, in the journal Deutsche Physikalische Gesellschaft. Verhandlungen,  19, 82-92 (1917). Titled On the Quantum Theorem of Sommerfeld and Epstein, this paper essentially anticipated Hamiltonian chaos and its implications for quantum mechanics, the field of Quantum Chaos. Considering that it was written before wave mechanics and the Schrödinger equation, this paper is remarkable, also because Einstein seems to have explicitly understood the quantum implications of classical nonintegrability.


As he puts it, if one examines any volume element in configuration space, any given orbit can pass through that region infinitely many times, either (a) with a (few) well defined values of the momentum – as on a torus – or (b) “there are infinitely many [values of the momentum] at the location under consideration“. In other words, small changes in the positions can correspond to very different momenta. Another way of saying something similar had to wait for Ed Lorenz in the 1960’s, who termed this as sensitive dependence on initial conditions, or what we term today as classical chaos.

The quantum condition he derives (and which now goes by the name of Einstein-Brilloiun-Keller-Maslov or EBKM quantization) uses the classical invariants identified by Poincaré, and Einstein goes on to give, in his view, the proper quantum conditions (11) that correspond to integrals along independent paths on n-dimensional tori (as in the figure above).


But being Einstein, he “notices immediately that type b) excludes the quantum  condition we formulated” earlier in the paper: this is the insight that was to lead half a century later, to the beginnings of the field of quantum chaos, the knowledge that there were classical motions for which quantum conditions could be stated, and those for which it was not possible, at least not in the same way. More can be read about “Einstein’s Unknown Insight and the Problem of Quantizing Chaos” in Douglas Stone’s article in Physics Today in 2005.

I first came across this paper of Einstein’s in 1978 or 1979 as a postdoc when I was struggling through Arnold’s text on Classical Mechanics and working on semiclassical mechanics. It may (OK, does) not count among Einstein’s greatest works, but arguably it is the one that has had the greatest impact on my own research. Other works of Einstein have had a much bigger impact on all our lives, of course, but this one is a paper whose centenary I’d like to mark.

Untitled 2And the other two as well. 2017 is the centenary of another annus mirabilis, a smaller one than 2005 perhaps, but enormous by any other standards.

Shameless Self-Promotion

DDKCover.pngAfter what seems an agonizingly long time since the first ideas of the book took root, I got the following letter from my publishers (how sweet that sounds!) last week,

“We are very pleased to inform you that your book has been published and it is available on Customers can order it […] etc.”

D D Kosambi: Selected Works in Mathematics and Statistics is finally done, and is now available in both e and paper formats. The cover on the right shows DDK at three stages of his life, at Harvard, in Aligarh, and finally, in his TIFR years.

To quote from the blurb: This book fills an important gap in studies on D. D. Kosambi. For the first time, the mathematical work of Kosambi is described, collected and presented in a manner that is accessible to non-mathematicians as well. A number of his papers that are difficult to obtain in these areas are made available here. In addition, there are essays by Kosambi that have not been published earlier as well as some of his lesser known works. Each of the twenty four papers is prefaced by a commentary on the significance of the work, and where possible, extracts from technical reviews by other mathematicians.

My personal contribution to the book, other than to edit is, is fairly minimal. Apart from a preface, I have basically tried to describe the academic milieu in which Kosambi found himself at different points in his life, and have also tried to infer what others thought of him in another prefatory essay, “A Scholar in His Time”.

Kosambi gave his academic manifesto in the essay, “Adventure into the Unknown” which also is one of the places where he wrote that Science is the cognition of necessity. (It is quite another matter that the phrase is not one that can be understood in a straightforward manner. Anyhow, as a quote its famous enough.) Reprinting that essay in its entirety seemed appropriate, as also another note “On Statistics” that gives a flavour of DDK’s interdisciplinarity, mixing statistics, erudition, Marxism, etc. The last of the non-mathematical writings is a project completion report submitted by DDK to the Tata Trust in 1945 and it permits, among other things, an inner view of a vastly gifted and somewhat frugal scholar who, in parallel, and for Rs 1800, carried out  6 research projects on issues as diverse as writing a mathematical monograph on Path Spaces, editing a concordance of Bratrihari’s epigrams, and constructing an electromechanical computational device (the Kosmagraph),  among others.

The remainder of the book is a set of reprints. Of his 67 or so papers in mathematics and statistics, about a third are presented, starting with some of his first papers, Precessions of an Elliptical Orbit and  On a Generalization of the Second Theorem of Bourbaki, and ending with one of the papers he wrote under the peculiar alias of S. Ducray,  Probability and Prime Numbers.

An attempt was made to include all the important papers, in particular the ones that made his reputation such as Parallelism and Path-Spaces that along with two other notes by Cartan and Chern are the basic of the Kosambi-Cartan-Chern theory,  the various papers that laid the foundations of scientific numismatics, as well as the papers that he should have followed up but didn’t, such as Statistics in Function Space that foreshadowed the K-L decomposition. The Kosambi distance in genetics was elaborated in  The Estimation of Map Distances from Recombination Values, and this is also reprinted.

Kosambi’s obsession with a statistical approach to the proof of the Riemann hypothesis resulted in several papers of which An Application of Stochastic Convergence, Statistical Methods in Number Theory, and The Sampling Distribution of Primes are reprinted here.  These, as is well-known, effectively ruined his reputation as a serious mathematician.

Chinese. Japanese. French. German. English. DDK published papers in all these languages, sometimes exclusively, and twice the same article in translation. Also reprinted in this volume are three of the foreign language papers, the ones in German, French, and Chinese. The last is of particular interest since it was written during an exchange visit to China in the late 1950’s and only later published in English.

A number of people have helped me along the way and it is my pleasure to thank them all here. For the initial suggestion that the book be done, and for sustained and general encouragement, I am very grateful to Romila Thapar. I’ve written about this before.  Meera Kosambi was keen to see her father’s mathematical legacy appreciated and was very enthusiastic about bringing out this collection and helped greatly in more ways than I can describe. She passed away in January 2015, when she knew the project was afoot, but not in any way certain as to how it would all come out. Michael Berry, S. G. Dani, and Andrew Odlyzko discussed and advised on various  points of the mathematics.  Indira Chowdhury and  Oindrila Raychaudhuri helped vis-à-vis archival matters.  Rajaram Nityananda had had many of DDK’s papers digitized, a great boon, and one that made the reproduction of some material much easier! Kapilanjan Krishan,  Rahim Rajan, and Mudit Trivedi  helped me locate some of the more obscure of DDK’s papers. K. Srinivas retyped almost all the papers, and Cicilia Edwin painstakingly proofread most of them.  Toshio Yamazaki and Divyabhanusinh Chavda  told me of their interactions with DDK, helping to flesh out the personality. Finally, Aban Mukherji was gracious with permissions, as were all the journal editors who kindly permitted the several articles to be reprinted.

DDK maintained a charmingly frank notebook diary during his Harvard years. On the 19th of January 1927 he notes: A most restless day. I have forgotten to mention Monday the 17th and an important conference with Birkhoff thereon […] Problems: Fermat’s Last Theorem, the Four color map, the functional equation […] Today was unusually restless with a great deal of time spent, possibly wasted in the Widener. Looked up old issues of Outing, Shakespear’s Hindi Readers, most of Burton’s works [of him more later], Roosevelt on African and Brazilian ‘sporting’ – worthless – Stefansson’s excellent and much remembered Friendly Arctic

All this variety in a single day! To recall WordsworthBliss indeed it was in that dawn to be alive! Kosambi, just out of his teens, was just bursting with energy, both intellectual and physical (for which one must read the diaries in some detail). The earnestness that only comes at that age shines through on the pages quite unselfconsciously:


Exuberance indeed, but also some simplicity: Deep interest, well sustained, is essential in the acquisition of knowledge upon any subject. And the third realization of the day: Life is good.  Yes indeed, to be young was very heaven.


ram1My mother, Malathi Ramaswamy, who passed away in Chennai last month, was a little over eighteen when I was born. This photo on the left, of the two of us, was taken some time in 1954 in Madras, a short while before we left to join my father who was then posted in Srinagar.

Sometime last year she completed a memoir of her childhood and wrote about the Madras that has all but vanished. This was mostly to tell us, our children, and her sisters’ children and grandchildren what little she remembered of her childhood and of those times. Ironically, she went a few days before the final printed copies of the book could be delivered to her, but she knew it was in the making.

The book, titled ALLATHUR VILLA: Nathamoony Chetty and the story of our family is available to read online, and it tells of how my grandmother, Seethalakshmi, was adopted by Allathur Nathamoony Chetty across caste and linguistic boundaries and a huge economic gradient. My mother and my four aunts grew up speaking Telugu at home, Tamil outside, and compared to the rest of their family, were much better off. When any of the five of them would talk about those days, it was always a magical world that they conjured up: the contrasts, the improbability, the role of chance…


Their home, the Allathur Villa of the title, is gone now; sold, torn down, and in its place on Poonamallee High Road, stands a hotel. A few days ago, S Muthiah who does The Hindu’s Metroplus column talked about the book: The tales a house tells.

Many tales indeed. Married at sixteen, my mother entered a very different world as an Army-officer’s wife. She must have imbibed much from her Chetty grandfather during her growing years though, since I can scarcely recall a time when she was not working. First as a school-teacher, shifting from one school to the other around the country as and when my father was posted, and then, after a longer stay in Delhi, as a tourist guide.

And eventually, as an entrepreneur. She found her métier as a tour operator when in the mid 1970’s she and my father founded a travel company in Delhi. Over the next thirty or so years, they promoted tours and accompanied them. From Kashmir to Nagaland, there were few parts of India that she had not traveled through. And as it happened, many parts of the world as well.


The picture above, of her sitting in a truck on the India-Bhutan border shows her at her happiest: traveling, taking people around the country, and being appreciated for it. Her enthusiasm was infectious, as was her optimism – she was the introduction to India for many people, particularly those who came here to explore handicrafts. Some years ago, she and those who had traveled with her described these various journeys on her website, Speaking with Hands. One of these friends of hers wrote to us recently to say that “Malathi has been an inspiration to many with her fierce love, intense interest and devotion to her beloved India. She was a woman of great integrity and conviction fused with love and compassion… She will be missed, by so many.

Like many women who were moving into the business world on their own in the 1970’s and 1980’s she had to write her own rules, and that was not always easy. Not for her, and frequently, also not for those around her… And she always had a project or two, was ever exploring, a characteristic that was admirable (and I did tell her that occasionally, even though it was often not easy to take). She did not shy away from trying to learn, whether it was trying out a new cellphone or laptop, or even reading difficult essays on the nature of modern physics.

UntitledNever at rest, till the end she was always looking forward to that next bit of travel, that next journey, and that next step.  These words from Eliot, I suspect would have resonated quite strongly with her:

We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.