kosambi Archives - And then...

Shameless Self-Promotion

DDK maintained a charmingly frank notebook diary during his Harvard years. On the 19th of January 1927 he notes: […] Life is good.

After 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 http://tinyurl.com/jgn2djj. 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 Wordsworth, Bliss 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:

jan19

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.

D D Kosambi: Selected Works in Mathematics and Statistics is published by Springer. ISBN: 978-81-322-3676-4

SOMe more on SOM

In my previous post, I wrote about SOM or self-organized mediocrity, the unnecessary but seemingly inevitable fate of many academic departments in the country. Some colleagues wrote in, a few in agreement, but a few to express dissatisfaction with what I had written.

I thought I would take the chance to expand the discussion, with a little help from my friends. On the face of it, there is little to disagree with the idea of SOM. Most cases of institutional decay seem to be nobody’s fault but those of the protagonists. But in writing on issues like higher education and other public matters, one challenge is to go beyond stating the obvious. While the problems are quite apparent, as are some solutions, their resolution seems to require near superhuman effort at least within the constraints imposed by the existing system.

As my friend SR said: Yes! Very nice to read. Then what……? What does one do about this? Accept that this is so? Do we see a change? Do we see a change in theory? In practice?

Many questions, SR, but the post was meant to provoke an individual reaction. What should you do? You too have been in a position of responsibility. If only I had a prescription for what we all should do! I personally don’t believe that one has to accept the inevitability of SOM, but avoiding it will only come with some hard work and harder decisions. Some of it is knowing, like the Red Queen, that one has sometimes to keep running as fast as possible to even just manage to stay in the same place. And as for how to make a palpable change, one that one can see, an answer was to some extent posed by another friend, AD. Of which more below.

Our Departments and Universities are to be seen always as works in progress, projects under construction. I think that point of view gets lost, once some success has been reached. But with the smallest slips – like a bad hire – one is saddled with a liability that does not go away easily. In fact, it propagates easily, as mediocrity breeds much faster than excellence.

AD’s diagnosis is that a major cause for SOM is hiring people who are less than top quality in both technical AND social skills. It is pretty easy to evaluate technical skills and thus to hire only A-level people technically. But, social skills are much harder to evaluate. People who lack the desire and ability to work together to build an organization will ultimately kill it. Such people are interested in building their own careers, groups, fiefdoms, etc., but not the organization.

The desire and ability to work together is an absolute essential when it comes to nurturing an academic institution, or perhaps any large enterprise as AD also wrote, This could also have been written about many academic institutions in the USA as well as businesses around the world. It likely true for almost all large government organizations.

Another friend, MP felt that I had deliberately pulled [my] punches which would have made this a telling piece. I don’t agree with your analogy because the sand pile retains its shape, but mediocrity digs bottomless pits! To which I kind of agree and kind of don’t. The only linen I would have to wash is predictably petty, and actually with the passage of time, I find the details less interesting than the broad brush-strokes. Sure, every department has its politics, and some of it’s denizens are cursed with a long memory for trivia, the griots who keep alive a list of past injustices, of academic and non-academic skirmishes and battles. But my concern was more that this story seems to get played out everywhere, with an occasional change of cast, but the same institutional ecosystem. And MP is absolutely correct that the critical sandpile keeps its shape, but the mechanism of SOM ensures a flat and uneven landscape. The pits, in short.

The crab mentality also makes sure that nobody rises above the low mean. And the most recent instance that prompted my somewhat bitter comments had to do with trying to establish a department to study a major new discipline, only to find opposition on the most flimsy grounds. Each campus also has its Kaikeyis, who remember every past promise, and for whom a personal advantage overwhelms that of the group. But let me not say more on that- each of us has tales that are better told in convivial company. I’m not pulling my punches, MP, but there is just so much one can say. Without naming names, we do know that the landscape is littered with departments that had everything going for them have not stayed anywhere near their peaks.

Of course, the worry is always one’s own. The School of Physical Sciences at JNU started off in 1986, and now 30 years later, one keeps worrying about how it is doing… I had tangentially suggested (appealing to a comment of D D Kosambi) that some of our difficulties come from the challenges of trying to build alien structures without the requisite resources- the sad consequences of growing an expensive research enterprise in an under-developed country. But when I said “from the inside one cannot easily tell if the half-life has been crossed or not“, my friend KK pointed out that the job had to be done by oneself.

In a thoughtful note, he went on to say that measures of half-life can be gauged internally by asking some difficult questions. I’ve edited his note to share (here is a recipe, SR),

Rate of change: Lifespan of faculty, and how has the faculty strength changed over time. Is this competitive? Sustainable?
Average age of faculty retained for 5 years, 10 years, 20 years since inception. Many departments don’t have the freedom to hire as they choose, but it is possible to plan on keeping a desirable age profile.
Students: Are they generally getting better or worse in grades/skills/capability/employment? Are teaching laboratories keeping up with the times, given the resources.
Process time: Is the university a faster or slower place to implement a decision compared to what happens in society? (Agility in making a purchase etc.).
Infrastructure: Are the basic facilities outside the university better than that inside? Why?
External connections: Are connections getting built with targets outside the University? University departments should eventually benefit some group, especially in industry or in different sections of society.

There may be more ways, but the basic point is clear: Look within. If you want to know how to avoid self-organized mediocrity, most of the answers are there.

Self-organized Mediocrity

In the late 1990’s Per Bak, a vastly talented theoretical physicist, wrote a book titled How Nature Works: the science of self-organized criticality. The title of this blogpost is more than a little inspired by him, and could well be How Universities Work: the process of Self-organized Mediocrity.

Sadly, there is really no attempt on my part to be tongue-in-cheek. The process of self-organized mediocrity is all too evident in department after department in institution after institution in the country, especially the less endowed ones.

As for self-organized mediocrity, or SOM, once one has give the phenomenon a name, what more is there to say? But like T S Eliot might have said, giving it a name is a difficult matter, it isn’t just a holiday game… And like the wonderful idea of Gross National Happiness one might equally well say that there is not much more to the concept than the name, but indeed there is… It makes sense to draw attention to the fact that a country benefits more from the happiness of its people than what it produces for others.

Nevertheless, SOM will bear some elaboration even though the “effanineffable” name itself conveys much of the basic concept. There is a long-standing in-joke among academics, that academic politics are so vicious because the stakes are so small. Variously attributed to Henry Kissinger, Woodrow Wilson, Wallace Sayre and others, the basic sentiment apparently goes back to Samuel Johnson, in whose times, the universities had very different structures. But in some sense the joke rings somewhat hollow these days, particularly for the Indian university. The stakes are not really all that small at all, and the internal politics at most academic institutions can be vicious. Regrettably, its also not just the internal politics- the world outside the campus walls has a way of sneaking into academic affairs and in many of our institutions, the (external) political positions inform and guide the internal.

This is a particularly difficult time for higher education in India. There is not enough money, the resources are stretched almost to breaking point, and there is little appreciation of what higher education truly entails. In some sense, the old model has exhausted itself: it is simply not possible to educate the large numbers of students (at present and in the future) with the tools and techniques of the 1970’s and 1980’s, which is what is extant at most institutions at present. And the style of the 1980’s differs too little from that of the 1950’s, while the youth of today are light-years apart from those of the 1980’s or the 1950’s, in mentality, in preparedness, and in motivation. Apart, not ahead.

Universities tend to succumb to inertia, and public universities inevitably succumb to an inertia fueled by public cynicism and low expectations. The demand for high quality higher education at negligible cost is a hangover from colonial times, regardless of how it might be dressed up as a state responsibility to provide good education to its people. This has resulted in our country creating small enclaves of privilege where a few can indulge, at state expense, in scholarship without having to pay for these privileges by having to teach others. Some find asylum in such enclaves (and then proceed to educate others on the need to respect “merit”) while others who gravitate to universities find the environment plagued by excessive political interference and few resources.

And what little is available is bitterly fought over. The crab mentality in academic institutions is well known the world over – one does not mind not having something so long as one’s colleague also does not have it, and one can do a fair amount by way of machination and petty politics to ensure that nobody does better than oneself. Except that in pulling others down, the only denouement that is ensured is that all are at a uniform low level: this is the self-organized mediocrity. And Departments will do the same to other Departments when it comes to space, students, or any other resources, gradually driving institutions into mediocrity…

[I should here acknowledge the inspiration behind this nomenclature. The theory of self-organized criticality or SOC has been around and quite influential for almost three decades now. It deals with systems whose dynamics – without external impetus – drives itself to a critical state and maintains it there. The archetypical example is a sandpile depicted in the charming illustration above: adding more and more sand beyond a point leads to a sandpile that maintains it’s shape by letting off sand in avalanches. The picture is, of course, incomplete without another denizen of the beach, the crab.]

I recently found that one of my heroes, D D Kosambi said something to the same effect in an autobiographical piece he wrote towards the end of his life. In the early 1960’s, K. Satchidananda Murthy and K. Ramakrishna Rao of the Department of Philosophy at Andhra University in Waltair invited a number of thinkers to contribute articles on their personal philosophy as researchers. This collection eventually appeared as Current Trends in Indian Philosophy, a book that was published in 1972 by Andhra University Press. One of the articles therein is by DDK, titled Adventures into the Unknown. This essay runs to some twenty pages and has been excerpted, bowdlerized and re-published as Steps in Science in the DDK commemoration volume, Science and Human Progress.

DDK-pic2 — D D Kosambi in his mid-twenties

Both versions of the essay were published posthumously (Kosambi died in 1966) and they largely overlap, except that the more widely circulated commemoration volume, Science and Human Progress, has been somewhat sanitized. The wit of Kosambi is largely missing in this autobiographical piece, and given that the original is very articulate on some of the more difficult aspects of Kosambi’s life, it is a pity that the editors of the latter felt the need to remove these bits. (I hope to discuss the articles and the changes in a subsequent post on this blog; I have my theories…)

One bit that was not excised in the second essay was on Kosambi’s perceptions of the working conditions for the scientist in India: The greatest obstacles to research in any backward, under-developed country are often those needlessly created by the scientist’s or scholar’s fellow citizens. The passage of time has not done much to change the appositeness of this observation even if it was deeply coloured by the personal tribulations that Kosambi had faced towards the end of his life.

One of the sadder aspects of self-organized mediocrity is that it is both not inevitable and is really quite unnecessary. And at the same time, the academic landscape is littered with universities that were great, departments that had seen better days, all described with more than a tinge of “what might have been”, and regrets for what was not achieved.

I have been mulling over the present post for some time now. In part it is occasioned by responses to an earlier post on the Department of Chemistry at IIT Kanpur. A comment made by more than one of my friends was that successful examples of institutions in India were uncommon enough that one needed to analyze just why they were successful while others were not. But that would require the efforts of a gifted analyst of the sociology of institutions, or maybe an institutional historian and archivist.

When the School of Physical Sciences was just established at JNU, well-wishers told those of us who were there at the time that twenty-five years was the half-life of most departments in the country. Its been nearly 30 years now, but from the inside one cannot easily tell if the half-life has been crossed or not. But one thing that has become obvious in recent years is that the present funding pattern of the UGC makes it very difficult for universities to achieve any kind of excellence. In fact, carrying out the routine tasks of teaching and research (at whatever level) can take all one’s effort-

But to get back to Chemistry at IIT-K, one of the things it seems to have done was to evolve with the times. As an IIT, the institution was also insulated, by and large, from the sickness of poor funding. And regardless of what the internal dynamics might have been, the Department has always stood as one. Regrettably, this does not happen in most other academic departments, and the consequences are out there in plain view for all to see…