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.


Sinning by Silence?

Weltenangst. German somehow seems the right language to use in the present context and if this word is not already a part of the general vocabulary its high time it joined weltschmerz  in describing the present global collective and perpetual sense of disquiet that does not seem to let up no matter where or when one looks, home or abroad.  There is, in a way that has not earlier been quite as sharp, a distinct sense of the binary: us/them, right/left, right/wrong, in/out… One yearns for a  world where the distinctions are recognizably blurred, where the blacks and whites give way to more  shades of gray, where one can be more definitely unsure… when one is more willing to learn, and to change.

But since that is not to be, this post is about the need to speak out, inspired by a friend in New York from whom I learned of Ella Wheeler Wilcox‘ poem Protest, written over a century ago. In words that are truly timeless, and as pertinent today as when they were written, she says:


To sin by silence, when we should protest,
Makes cowards out of men. The human race
Has climbed on protest. Had no voice been raised
Against injustice, ignorance, and lust,
The inquisition yet would serve the law,
And guillotines decide our least disputes.
The few who dare, must speak and speak again
To right the wrongs of many.

The poem itself is longer, but this post is about the last two lines from the excerpt above, “The few who dare must speak and speak again”. And it is essential that those who do not speak should at the very least, support those who speak for us, for the values that we hold dear.

The heart of one of the crises we are presently facing, the breakdown of communication between the UGC and the rest of the universe on the matter of admissions to the Ph D, is a matter of perceptions. The UGC believes that a system that works in the US or elsewhere should work here. The here knows that the system that would work elsewhere does not work here, and the proof of the pudding is in its eating… To give complete weightage to an interview would tilt the balance in favour of the more articulate. Who also, typically, have had many of the advantages that make them more articulate in the first place… It is simply not true, as Mr Javadekar asserts, that “UGC regulations on MPhil and PhD admissions are as per the best practices of the world. It is being implemented healthily in all universities. The problem is there in one university.” His statements reflect an imperfect understanding of what the best academic practices are, and what that one university has been trying to do all these years.

To start with, the MPhil is a dying degree that should be allowed to become extinct as per the best practices of the world. And as for healthy implementation, the healthiest implementation of admission to the PhD is through the GRE Examination and applications, with no weightage at all for an oral examination… US university admissions committees know full well that their brightest graduate students (typically those from Asia) may not speak English well enough when they enter, so using performance in an oral entrance examination as a yardstick would serve them badly. They do what works well: Administer a good written examination and choose the best from the written scores. Of course they do it intelligently as well, using a combination of measures, but an interview is typically not one of them.

The UGC would best serve the University community  by restricting itself to be a regulatory body as far as curricula are concerned (if at all) and stay away from prescribing admission rules and procedures. There are mechanisms aplenty to identify those who do not follow fair practices, and instead of finding routes of exempting them from fair play (such as declaring them to be INI‘s or Institutions of National Importance), it would serve us all better if the UGC would step in and insist on an even playing field for all.


To make the point further, the real responsibility is to ensure that all have an equal – or equitable – access to higher education.  And one of the reasons for this is that the workforce, especially for skilled jobs, should have a balanced representation. Gender imbalance, for example,  at the hiring stage reflects to a large extent the gender imbalance at earlier stages, that of admission to the qualifying degree for example. This is what has been termed the leaky pipeline in the context of gender representation in academic careers, but it is clear that the leaky  pipeline idea operates just as well for all other groups, particularly those that have been excluded for one or the other reason.

The human race, Ella Wilcox asserts,  has climbed on protest, and indeed we have. And protest we must, at these ill-argued, poorly considered fiats decreed by a body that has lost its relevance, the UGC which should also heed that students of all persuasions are now are opposing this move …

And not just this. It appears that the idea of a university is lost on the very group that needs it most, the government. In the abstract, the government of the people, by the people and for the people, should use those very people it has invested in to help it think through and devise a better future for the rest of the people. And arguably, that is one of the jobs our universities should undertake – take our country into its future. At least that is what, again in the abstract, each modern nation does. It is 2017 after all, and one of the blindingly obvious truths is that any government needs to use the best minds that it can muster, not just the best brawn. To disregard uncomfortable thought is more than just another mistake… Minds are terrible things to waste.

In the past three years, especially in higher education administration one has seen a relentless and uncompromising policy of choosing complaisant and available mediocrity for purposes of ideological resonance. This is a big mistake, one that we really cannot afford, not least because there is saner counsel available.

In a journal article that is available on the net, David Roy Smith of the Department of Biology, University of Western Ontario (DOI: 10.15252/embr.201643750) points out (passionately, one might add) that by democratically electing a person who openly mocks science and what one has learned from science (in the USA) puts both the basic sciences and our planet in danger. To quote from Smith’s article, “The situation is looking equally dire in other parts of the world, with nationalist, anti-immigration, and big business interests taking precedence over the preservation of our planet, its natural resources, and its ecosystems and species. To be an environmentalist, an academic, or a scientist of any kind in this polarized and pernicious political landscape risks being labeled an elitist, a liar, an ultra-leftist, and someone who is out of touch with the average person.”

That is something that those of us who teach at this one University are quite familiar with. Being at JNU is equated in the public (post-truth coloured!) eye as being ultra-leftist and all of the other things Smith says.  We see this again and again: To be an academic of any kind in a polarized and pernicious landscape is a major risk. To whit, the following:

copy-2-of-southasian-map-by-himalWe are taught – those of us who have learned of the physical world – that there is no special place in space from which one should derive all our coordinates. There really is no preferred sense of direction other than by convention and by legacy.  For many years now, I have had the Himal South Asia magazine’s unusual map hanging in my office and have had innumerable discussions (of a non-political kind) about how it helps to change one’s point of view about our country, whats up south and down north and so on. I must say that learning to see this map every working day (and learning to refer to it in as normal a fashion as possible) has also been instructive in its own way, and it seems more natural now to draw a line from Kanyakumari down to Kashmir rather than the other way around. To have any sense of nationalism hinge on a completely arbitrary definition of up or down is to have a somewhat unhinged sense of nationalism.

cheAnd speaking of ultra-leftist, another thing that hangs in my office is (what I consider) a superb poster, a telescopic image of Ché Guevara on the South American continent… something I picked up forty years ago when it was fresh and new, and another thing I have had to explain to any number of visitors who eventually all come down to “Ah… JNU, what else can one expect?” But this is just one poster, and it is more about the kind of aesthetic I cared about at some point in time rather than some ideology that is indelibly tattooed onto my soul.

By discrediting academic values, one discredits a rational approach to governance that might see dissent and protests as part of a process that is, in the end, enriching because of its argumentative nature. And we must therefore support the few who speak and speak again.

Talking about Science

Several strands of discussion came together in my mind recently, sparked first by an email from the Vikram Sarabhai Community Science Centre, asking for Science Communicators, and then by two op-ed articles in the Hindu, on whether or not scientists should be responsible for communicating their science to the general public, apart from some ongoing discussions in FB and on Twitter on the same issues.

image7There is no gainsaying that this is an important matter, and a difficult one to address in a wholly satisfactory manner, especially in a multilingual country like ours, one where the general level of education is not as high as one would like. Nevertheless, one must laud efforts that have a non-negligible impact, and the Science Express is a brilliant example of how things can be done right. This is a unique collaboration of the Department of Science and Technology, the Science Museums and the Indian Railways who have come together to make a science exhibition train that travels across the country, and has been doing so since 2007, and by now it has traveled over 142,000 km and welcomed more than 1.56 crore visitors. It has become the largest, longest running and most visited mobile science exhibition in the world. Now the DST wants people to man this remarkable science museum. They would like

Young science postgraduates/graduates or equivalent. Education or experience in science communication, science education, environmental science, environment education, life sciences or related disciplines will be given preference. Excellent communication skills and knowledge of multiple Indian languages is desirable. Candidates should be self-motivated and medically fit for the long and continuous exhibition tour.

Self-motivation is indeed required, and the ad spares no punches:  The job involves work without off days and continuous travel on the train.This being a mobile exhibition, changing location frequently, the candidates should have ability to quickly adapt to different and challenging local conditions. Consolidated salary in the range of Rs. 20,000 to 24,000/- per month…

As the photo above (taken from the SE website) shows there are people who will bite, though one does wish that the job would be more remunerative- what the train does seems so valuable, and in a country like ours, so severely necessary.

Coincidentally, and somewhat ironically, one of the op-eds in the Hindu pointed out the lack of science communicators or more accurately, the lack of a critical mass of science communicators in the country. That of course is neither here nor there, since there is the glaring lack of a critical mass of persons from almost any discipline (or of persons of discipline for that matter) in the country. But Gautam Desiraju makes other points when he asks “Are scientists responsible for communicating their work to the general public?” Both his write-up as well as the counterpoint by R. Prasad, whose rejoinder simply  points out that  ‘There is a huge price to pay when scientists remain in a cocoon’ are charmingly illustrated with images of scientists communicating with non-specialists!

This morning I had occasion to talk with a younger colleague about these viewpoints, and both of us recalled how influential (in our own lives) some popular books by well-known scientists had been: What is Life? by Erwin Schrödinger, Stephen Hawking’s Brief History of Time, or James  Watson’s Double Helix, not to mention some truly popular books (in their times) by some of the greatest scientists, The Origin of Species by Darwin and Cybernetics by Norbert Wiener. I only learned very recently that Wiener was persuaded to write up his ideas in order to communicate them to the public by a French publisher – and given the prolixity of the language used, it is a wonder that the book reached as far and wide as it did. Nevertheless, as we use cyberspace to communicate our ideas today, our debt to him is obvious. And the very readable What is life? resulted from a set of lectures to the general ‘lay’ public in Dublin in the war years.

The importance of communicating one’s ideas to whatever audience that shows an interest cannot be overstated. I’m not sure I want to get into whether it is a scientist’s moral obligation or duty to do so, but it does seem to me that the value of most things we do is enhanced when the communal nature of our activities is explicitly recognized. And the effectiveness of the work is directly related to the size and width of the community that is aware of or is made aware of it.

Investment in research or in scientific activity is ultimately a  community decision –  and given our political system, it is reflected in the way in which the budget for science is decided. Which in turn is determined by the party (or parties) we vote into power. The bulk of research in the country is therefore publicly supported, and one of the issues at hand is whether the results of publicly funded research need to be shared with the public that funded it. [The argument has been made very forcefully in the west, where research is funded both publicly and privately. When private companies fund research, the results are guarded zealously for possible patents, but many have argued for full public access to publicly funded research – and this has formed the vanguard of the Open Access movement. But of that later.] One can take the point of view that the public in question do not have the required sophistication to appreciate the nuances, the finer details of most areas of research, and there is some truth in that. But the same argument would hold for, say, music, or cuisine, or poetry or any number of things that we enjoy as a community and appreciate as individuals. Each of us may hear the notes we wish to hear – or can hear, for that matter – and make of it what we will. We may get a sense of the larger scheme of things, whether the finer points of raga Anandabhairavi or the crucial role played by the p53 gene in each of our cells, or any number of the other wonders that we have created or discovered, and there will be those among us for whom even this vague sense will provide the catalyst for other avenues of exploration and discovery.

71hz53cqn-lThere is a sense in which the privilege of being invested in to pursue publicly funded research is very much an expression of the trust of a society. By acknowledging this as part of a social contract, almost the very least one can do is to pay back to society by talking openly (and clearly) about what one does and the results one has obtained. If one doesn’t, there is always the danger that someone else, less able and less articulate might well do so, and other than writing bitterly about X’s misrepresentations, one will not be able to do much else. Science communicators (as a tribe) play a different role. At their best, their function is to integrate many approaches in an analytical manner, and present this in a format that is sometimes easier on the eye. (In this genre, and from my own area of interest, there are few books that compare with James Gleick’s Chaos: Making a New Science, a hugely popular and hugely influential description of chaos theory and nonlinear science. And accurate as well.)

awThe friendship and the intense discussions between Goethe and Humboldt, for instance, as Andrea Wulf discusses in her brilliant The Invention of Nature, were mutually very influential, with Humboldt’s detailed reports being inspirational not just to Goethe, but also to Darwin, Wordsworth and John Muir among others. One can argue that the state of science, and the state of the world, was very different two centuries ago, as it surely was. Card-carrying scientists were fewer and the language that scientists used was not as forbiddingly jargon-filled as it can seem today, but there is good evidence that the lay public flocked to hear Humboldt and his descriptions of South America, much as today’s audience might well be glad to hear from a specialist, of the unexplored vistas of string theory or human behaviour or the brain.

Hearing about a subject from someone who has contributed greatly to it can be much more than just inspirational: the authenticity of experience transmits itself in a very unique manner. It is quite another thing to have someone else talk about it, though there are exceptions, of course- some science journalists are very effective communicators of the big picture, in a way that a practitioner who is focused on some small portion of the puzzle may not be. And of course, this is their forte, putting together a narrative that can grip a reader in a way in which an individual’s very personal story might not. But authenticity has a separate value and cannot be substituted…

Which is why it might be good to occasionally worry about communicating just what it is that one does – science, poetry, or philosophy – to a wider and larger audience. The process might well be beneficial to the quality of what one does in the first place! And today there are many different ways in which this might be done. Through a blog, for instance, or a YouTube channel, through books and articles, or by public lectures, the tradition for which is sadly absent in most of our cities.

Does this, namely taking the time to communicate one’s work to others – even if one doesn’t have to – take away from the presumably more important task at hand, of doing the science in the first place? To which one might well ask why do science at all then. And in any case, it is an unrepeatable exercise. What other work would Gamow have done if he had not written 1, 2, 3… infinity? Or what other vistas might Richard Dawkins have explored, had he not spent his time writing The Selfish Genome or The Extended Phenotype. I prefer to think that this, in itself, was the essential task, to write the books that would go on to influence others.

newsfeynmanOne can go on talking about talking about science… but in the end the basic points are few. There needs to be much more about scientific matters in public discourse, particularly in this day and age, when almost any aspect of our daily life is so influenced by the scientific advances of the past few centuries. It has always needed science communicators (who may or may not be practicing scientists) to do their bit, to bring out the significance of the work, and to see where value can be added. But hearing about any field directly from the ones who have contributed to its advance – in whatever way – has a charm and value all of its own.