The one that got away

I thought I had made a complete bibliography of D D Kosambi‘s published works in mathematics, statistics, as well as in other areas of science, but there was one paper that was hiding in plain view. 

The October 1, 1932 issue of Nature has a letter by Kosambi, titled “The Expanding Universe” on pages 507 and 508 of volume 130 (the image on this page is from the Internet Archive). The letter is dated 28 July with the byline Malleswaram, Bangalore. 

In the 2 July issue of Nature that year, the cosmologist E A Milne, Rouse Ball Professor in Mathematics at the University of Oxford, had published a note, which was, as I learned from the Stanford Encyclopaedia of Philosophy, the start of a debate and a major ideological conflict in the field of cosmology. Milne opposed Eddington and others’ relativistic cosmology and instead put forward another cosmological model, that of  kinematic relativity. The details of the ideological conflict and the evolution of the ideas themselves make for interesting reading, and while I can’t claim to understand most of the arguments, Milne’s subsequent statement, that “a theory cannot be accepted as satisfactory unless it is philosophically satisfying” does strike a chord.

Finding a theory “philosophically satisfying”  seems like a somewhat restrained way of saying that one finds it beautiful. Many physicists have made similar remarks linking truth and beauty, some very directly, as for instance Paul Dirac who said that it was “more important to have beauty in one’s equations than to have them fit experiment” or Steven Weinberg,  “time and again physicists have been guided by their sense of beauty not only in developing new theories but even in judging the validity of physical theories once they are developed”. (It is good, though, to keep in mind that the pursuit of elegance and beauty can be misleading in science; see the cautionary essay by Phillip Ball.)

What is quite remarkable is that the first comment on Milne’s paper was the note by Kosambi, who although not participating in the ideological debate, pointed out that an assumption made by Milne was not essential, and that Milne’s results would hold more generally. The note is short but reveals much – Kosambi’s familiarity with the n-body problem, the work of Birkhoff on ergodicity, and with cosmology.  It had been just about three years since he returned to India from Harvard.

Following Kosambi’s note is a longer comment,  dated 19 August, by Milne who says

“It is very satisfactory to find that the explanation I have. given of the phenomena of the expanding universe can be freed from some of the restrictions which were introduced. […] Mr. Kosambi points out that the expansion and recession to infinity may also occur under more general conditions. But Mr. Kosambi is scarcely correct in saying that in my explanation “the material particles that form the universe are taken initially to have been enclosed in some finite space “.

Milne then goes on to derive some extensions of his ideas which  he feels “remove many of the traditional philosophical difficulties concerning time and space as a means of description of matter and motion.”

This post is, of course, not about Milne’s theory (which had its ups and downs) or even about Kosambi’s note itself. In the summer of 1932, Kosambi had already decided to resign from the Aligarh Muslim University (AMU) where he was a lecturer in Mathematics. The briefly vibrant department of mathematics at AMU was crumbling, with André Weil returning to France and Vijayaraghavan moving to Dacca. DDK would then join the Fergusson College in Poona  and would spend the next dozen years or so there before moving to the Tata Institute of Fundamental Research in Bombay in 1945. The visit to Bangalore was a summer vacation – the 25 year old Kosambi was visiting his sister Manik and her husband, Dr Ram Prasad and staying with them at their home in Malleswaram. 

The timeline is, quite frankly, astonishing. The issue of Nature in which Milne’s first article is published is dated 2 July. Kosambi’s note has the date 28 July, a gap of just a little over three weeks, in which time he had to read the paper, realise that he had something to say and say it bluntly: 

IN NATURE of July 2, Prof. Milne has published a very simple and attractive explanation of the phenomenon that has given rise to so much speculation among recent cosmogonists. The sole defect in his clear analysis is that the material particles that form the universe are taken initially to have been enclosed in some finite space, but without mutual action, or even collisions. I should like to bring to the notice of those interested that the last restriction may be easily removed.

Even by today’s standards, this is impressively quick. There was airmail of course and the Indian Institute of Science in Bangalore (where Kosambi could probably have accessed the journal) would have had a subscription to Nature. In three weeks therefore, DDK must have read and reconstructed the argument of Milne’s work, added his observations, written up his note and mailed it out to the Editors.

In less than a month Nature had received the note, sent it to Milne who had reviewed, and responded in detail, by August 19. It then took the journal another month to publish both the notes, on October 1 – three months to the day from 2 July. And that too in 1932.