D. D. Kosambi

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D. D. Kosambi
Born July 31, 1907
Kosben, Goa
Died June 29, 1966
Pune
Occupation Mathematician and Marxist Historian

Damodar Dharmananda Kosambi (July 31, 1907-June 29, 1966) was an Indian mathematician, statistician, and Sanskritist who contributed in genetics by introducing Kosambi's map function. He was well-known for his work in numismatics and for compiling critical editions of some ancient Sanskrit texts. He was also a Marxist historian of ancient India. He was critical of Nehruvian policies which grounded capitalism in the guise of democratic socialism, and was an enthusiast of the Chinese revolution and its communistic ideals. He was a leading activist in the World Peace Movement.

Contents

[edit] Biography

[edit] Family and Childhood

D.D.Kosambi was born in 1907 at Kosben in Goa, which was then under Portuguese rule. His father was the Buddhist and Pali scholar Dharmananda Damodar Kosambi, who hailed from a Saraswat Brahmin family, but spent many youthful years as a Buddhist bhikshu renouncing home and family, travelling extensively.[1] Kosambi's mother, Balabai came from the Lad family of Goa.

[edit] Education

After a few years of schooling in India, in 1918 D.D. Kosambi and his elder sister, Manik Kosambi, went to Massachusetts with his father, who was assisting Harvard University professors in compiling a critical edition of the Visuddimagga, a book on Buddhist philosophy. There he spent a year in the Grammar school and then was admitted to the Cambridge High and Latin School in 1920. He became a member of the Cambridge Branch of American Boy Scouts.

It was here in Cambridge that he befriended another prodigy of the time, Norbert Wiener, whose father Leo Wiener was Kosambi's father's colleague at Harvard University.

Kosambi did well in his final school examination. He was one of the few candidates who were exempted on their merit from passing an entrance examination essential at the time to enter into Harvard University. He joined the university in 1924, but eventually postponed his studies, and returned to India. He stayed with his father who was now working in the Gujarat University, and was in the close circles of Mahatma Gandhi.

In January 1926, Kosambi returned to the US with his father, who once again worked in Harvard University for a year and half. Kosambi studied mathematics under George David Birkhoff, who wanted him to concentrate on mathematics, but the ambitious Kosambi instead took many diverse courses excelling in each of them. In 1929, Harvard awarded him the Bachelor of Arts degree with a summa cum laude. He was also granted membership to the esteemed Phi Beta Kappa Society, the oldest undergraduate honours organization in the United States. He returned to India soon after.

[edit] Back in India

[edit] Banaras and Aligarh

He obtained the post of professor at the Banaras Hindu University (BHU). He taught German along with Mathematics. He struggled to pursue his research on his own, and published his first research paper, "Precessions of an Elliptic Orbit" in the Indian Journal of Physics in 1930.

In 1931, he got married to Nalini, daughter of a very wealthy and distinguished member of the Madgaonkar family. It was in this year that he also obtained a job at the Aligarh Muslim University and got the opportunity to work with well-known mathematicians like Andre Wile and Vijay Raghavan. During his two years stay in Aligarh, he produced eight research papers in the general area of Differential Geometry and Path Spaces. His fluency in several European languages allowed him to publish some of his early papers in French, Italian and German journals in their respective languages.

[edit] Fergusson College, Pune

In 1933, he joined the Deccan Education Society’s Fergusson College in Pune, where he taught mathematics for the next 12 years. In 1935, his eldest daughter, Maya was born, while in 1939, the youngest, Meera, a well-known sociologist and feminist was born.

In Pune, while teaching mathematics and conducting research in the field, he started his interdisciplinary pursuit. In 1944 he published a small article of 4 pages titled ‘The Estimation of Map Distance from Recombination Values’ in Annals of Eugenics, in which he introduced what later came to be known as Kosambi's Map Function.

One of the most important contributions of Kosambi to statistics is the widely known technique called Proper Orthogonal Decomposition (POD). Although it was originally developed by Kosambi in 1943, it is now referred to as the Karhunen-Loeve expansion. In the 1943 paper entitled 'Statistics in Function Space' presented in the Journal of the Indian Mathematical Society, Kosambi presented the Proper Orthogonal Decomposition some years before Karhunen (1945) and Loeve (1948). This tool has found application to such diverse field as image processing, signal processing, data compression, oceanography, chemical engineering and fluid mechanics. Unfortunately this most important contribution of his is barely acknowledged in most papers that utilize the POD method. In recent years though, it is heartening to note that some authors have indeed referred to it as the Kosambi-Karhunen-Loeve decomposition.[2]

It was his studies in numismatics that initiated him in the field of historical research. He made a thorough study of Sanskrit and ancient literature, and he started his classic work on the ancient poet Bhartrihari. He published his critical editions of Bhartrihari's Shatakatrayee and Subhashitas during 1945-1948. It was during this period that he started his political activism, coming close to the radical streams in the ongoing Independence movement, especially the Communist Party of India. He became an outspoken Marxist and wrote some political articles.

[edit] TIFR days

In 1945, Homi J. Bhabha invited Kosambi to join the Tata Institute of Fundamental Research (TIFR) as Professor of Mathematics, which he accepted. After independence, in 1948-49 he was sent to England and the US as a UNESCO Fellow to study the theoretical and technical aspects of the computer. During this time, he was a guest professor of geometry at the Chicago University. He spent some time at the Institute of Advanced Studies, Princeton. In London, he started his long-lasting friendship with indologist and historian A.L. Basham.

After his return to India, in the Cold War circumstances, he was increasingly drawn into the World Peace Movement and served in his capacity as Member of the World Peace Council. He became a tireless crusader of peace, campaigning against the nuclearisation of the world. Kosambi's solution to India's energy needs was in sharp conflict with the ambitions of the Indian ruling class. He stressed on alternative energy sources, like solar power. His activism in the peace movement took him to Beijing, Helsinki and Moscow. However, during this period he relentlessly pursued his diverse research interests, too. Most importantly,he worked on his Marxist rewriting of ancient Indian history, which culminated in his book, Introduction to the Study of Indian History (1956).

He visited China many times during 1952-62 and was able to watch the Chinese revolution very closely, making him critical of the way modernisation and development were envisaged and pursued by the Indian ruling classes. All these contributed in straining his relationship with the Indian government and Bhabha, eventually leading to Kosambi's exit from the Tata Institute of Fundamental Research in 1962.

[edit] Post-TIFR days

His exit from the TIFR gave Kosambi the opportunity to concentrate on his research in ancient Indian history culminating into his book, The Culture and Civilisation of Ancient India, which was published in 1965 by Routledge. The book was translated in German, French and Japanese and was widely acclaimed. He also utilised his time in archaeological studies, and contributed in the field of statistics and number theory. His article on numismatics was published in February 1965 in Scientific American.

Due to the efforts of his friends and colleagues, in June 1964, Kosambi was appointed as a Scientist Emeritus of the Council of Scientific and Industrial Research (CSIR) affiliated to the Maharashtra Vidnyanvardhini in Pune. He got involved in many historical, scientific and archaeological projects (even writing stories for children). But most of his works that he produced in this period could not be published during his lifetime. On June 29, 1966, he died in Pune. He was posthumously decorated with the Hari Om Ashram Award by the government of India's University Grant Commission in 1980.

His friend A.L. Basham, a well-known indologist, wrote in his tribute to Kosambi:

At first it seemed that he had only three interests, which filled his life to the exclusion of all others- ancient India, in all its aspects, mathematics and the preservation of peace. For the last, as well as for his two intellectual interests, he worked hard and with devotion, according to his deep convictions. Yet as one grew to know him better one realized that the range of his heart and mind was very wide...In the later years of his life, when his attention turned increasingly to anthropology as a means of reconstructing the past, it became more than ever clear that he had a very deep feeling for the lives of the simple people of Maharashtra.[3]

[edit] Kosambi's Historiography

As a historian, Kosambi is revolutionised Indian history writing with his Marxist approach, crucially diverting from the mainstream nationalist and imperialist schools. He understood history in terms of the dynamics of socio-economic formations rather than just a chronological narration of "episodes" or the feats of a few great men - kings, warriors or saints. In the very first paragraph of his classic work, An Introduction to the Study of Indian History, he gives an insight into his methodology as a prelude to his life work on ancient Indian history:

"THE light-hearted sneer “India has had some episodes, but no history“ is used to justify lack of study, grasp, intelligence on the part of foreign writers about India’s past. The considerations that follow will prove that it is precisely the episodes — lists of dynasties and kings, tales of war and battle spiced with anecdote, which fill school texts — that are missing from Indian records. Here, for the first time, we have to reconstruct a history without episodes, which means that it cannot be the same type of history as in the European tradition."[4]

According to A. L. Basham, "An Introduction to the Study of Indian History is in many respects an epoch making work, containing brilliantly original ideas on almost every page; if it contains errors and misrepresentations, if now and then its author attempts to force his data into a rather doctrinaire pattern, this does not appreciably lessen the significance of this very exciting book, which has stimulated the thought of thousands of students throughout the world."[5]

[edit] Books by D.D. Kosambi

[edit] Works on History and Society

  • 1956 An Introduction to the Study of Indian History (Popular Book Depot, Bombay)
  • 1957 Exasperating Essays: Exercise in the Dialectical Method (People's Book House, Poona)
  • 1962 Myth and Reality: Studies in the Formation of Indian Culture (Popular Prakashail, Bombay)
  • 1965 The Culture and Civilisation of Ancient India in Historical Outline (Routledge & Kegan Paul, London)
  • 2002 D.D. Kosambi: Combined Methods in Indology and Other Writings - Compiled, edited and introduced by Brajadulal Chattopadhyaya (Oxford University Press, New Delhi)

[edit] Edited Works

  • 1945 The Satakatrayam of Bhartrhari with the Comm. of Ramarsi, edited in collaboration with Pt. K. V. Krishnamoorthi Sharma (Anandasrama Sanskrit Series, No.127, Poona)
  • 1946 The Southern Archetype of Epigrams Ascribed to Bhartrhari (Bharatiya Vidya Series 9, Bombay) (First critical edition of a Bhartrhari recension.)
  • 1948 The Epigrams Attributed to Bhartrhari (Singhi Jain Series 23, Bombay) (Comprehensive edition of the poet's work remarkable for rigorous standards of text criticism.)
  • 1952 The Cintamani-saranika of Dasabala; Supplement to Journal of Oriental Research, xix, pt, II (Madras) (A Sanskrit astronomical work which shows that King Bhoja of Dhara died in 1055-56.)
  • 1957 The Subhasitaratnakosa of Vidyakara, edited in collaboration with V.V. Gokhale (Harvard Oriental Series 42)

[edit] Mathematical Publications by D.D. Kosambi

  • 1930 Precessions of an elliptical orbit, Indian J. Phys., 5(3), 359-364.
  • 1931 On a generalization of the second theorem of Bourbaki, Proc. Acad. Sciences UP, 1
  • 1932 Modern differential geometries, Indian J. Phys., 7(2), 159-164.
  • 1932 On the existence of a metric and the inverse variational problem, Proc. Acad. Sciences UP, 2, 17-28.
  • 1932 Geometric differentiale et calcul des variations, Rendiconti della Reale Accademia Nazionale dei Linceit, 16(6), 410-415.
  • 1932 On differential equations with the group property, J. Indian Math. Soc., 19(1), 215-219.
  • 1932 Affin-geometrische grundlagen der einheitlichen feld-theorie, Sitzungsberichten der Preuss B. Akademic der Wissenschaften, Physikalisch-mathematische klasse, 28, 342-345.
  • 1933 The classification of integers, J. Univ. Bombay, 2(2), 18-20.
  • 1933 The problem of differential invariants, J. Indian Math. Soc., 20, 185-188.
  • 1933 Parallelism and path-spaces, Mathematische Zeitschrift, 37, 608-622.
  • 1934 Collineations in path-space, J. Indian Math. Soc., 1(2), 68-72.
  • 1934 Continuous groups and two theorems of Euler, Math. Student, 2(3), 94-100.
  • 1934 The maximum modulus theorem, J. Univ. Bombay, 3(2), 11-12.
  • 1935 Systems of differential equations of the second order, Quarterly J. Math. (Oxford Series), 6(21), 1-12.
  • 1935 Homogeneous metrics, Proc. Indian Acad. Sciences, 1(A:12), 952-954.
  • 1935 An affine calculus of variations, Proc. Indian Acad. Sciences, 2, 333-335.
  • 1936 Differential geometry of the Laplace equation, J. Indian Math. Soc., 2, 141-143.
  • 1936 Path-spaces of higher order, Quarterly J. Math. (Oxford Series), 7(26), 97-104.
  • 1936 Path-geometry and cosmogony, Quarterly J. Math. (Oxford Series), 7(28), 290-293.
  • 1938 Les metriques homogenes dans les espaces cosmogoniques, Comptes rendus, 206, 1086-1088.
  • 1938 Les espaces des paths generalises qu'on peut associer avec un espace de Finsler, Comptes rendus, 206, 1538-1541.
  • 1939 The tensor analysis of partial differential equations, J. Indian Math. Soc., 3, 249-253.
  • 1940 Path-equations admitting the Lorenz group, J. London Math. Soc., 15(2:58), 86-91.
  • 1940 The concept of isotropy in generalized path-spaces, J. Indian Math. Soc., 4, 80-88.
  • 1940 A note on frequency distribution in series, Math. Student, 8, 151-155.
  • 1941 A bivariate extension of Fisher's Z test, Current Science, 10, 191-192.
  • 1941 Correlation and time series,Current Science, 10, 372-774.
  • 1941 Path-equations admitting the Lorenz group - II, J. Indian Math. Soc., 5(2), 62-72.
  • 1942 On the zeros and closure of orthgonal functions, J. Indian Math. Soc., 6(1), 16-24.
  • 1943 Statistics in function space, J. Indian Math. Soc., 7, 76-88.
  • 1944 The estimation of map distance from recombination values, Annals of Eugenics, 12(3), 172-175.
  • 1944 Direct derivation of series spectra, Current Science, 13, 71.
  • 1944 The geometric method in mathematical statistics, Amer. Math. Monthly, 51(7), 382-389.
  • 1945 Parallelism in the tensor analysis of partial differential equations, Bull. Amer. Math. Soc., 51, 293-296.
  • 1946 The law of large numbers, Mathematics Student, 14, 14-19.
  • 1946 Sur la differentiation covariante, Comptes rendus, 222, 211-213.
  • 1947 An extension of the least-squares method for statistical estimation, Annals of Eugenics, 18, 257-261.
  • 1947 Les invariants differentials d'un tenseur covariant a deux indices, Comptes rendus, 225, 790-792.
  • 1948 Systems of partial differential equations of the second order, Quarterly J. Math. (Oxford Series), 19(76), 204-219.
  • 1949 Characteristic properties of series distributions, Proc. Nat. Inst. Science of India, 15(3), 109-113.
  • 1949 The differential invariants of a two-index tensor, Bull. Amer. Math. Soc., 55(1:2), 90-94.
  • 1951 Seasonal variation in the Indian birth rate, (co-authored with S. Raghavachari), Annals of Eugenics, 16(2), 165-192.
  • 1951 Series expansions of continuous groups, Quarterly J. Math. (Oxford Series 2), 2(8), 244-257.
  • 1952 Path-spaces admitting collineations, Quarterly J. Math. (Oxford Series 2), 3(9), 1-11.
  • 1952 Path-geometry and continuous groups, Quarterly J. Math. (Oxford Series 2), 3(19), 307-320.
  • 1954 The metric in path-space, Tensor (New Series), 3, 67-74.
  • 1954 Seasonal variation in the Indian death rate, (co-authored with S. Raghavachari), Annals of Human Genetics, 19(2), 100-119.
  • 1958 Classical Tauberian theorems, J. Indian Soc. Agricultural Statistics, 10, 141-149.
  • 1958 The efficiency of randomization by card shuffling (co-authored with U.V. Ramamohana Rao), J. Royal Stat. Soc., Series A (General), 121(2), 223-233.
  • 1959 The method of least squares, J. Indian Soc. Agricultural Statistics, 12, 49-57.
  • 1959 An application of stochastic convergence, J. Indian Soc. Agricultural Statistics, 12, 58-72.
  • 1963 The sampling distribution of primes, Proc. Nat. Acad. Sciences U.S.A., 49, 20-23.
  • 1966 Scientific numismatics, Scientific American, February, 102-111.

[edit] Notes

  1. ^ Citation needed
  2. ^ Citation needed
  3. ^ A.L. Basham, "Baba: A Personal Tribute"
  4. ^ An Introduction to the Study of Indian History, pp.1
  5. ^ A.L. Basham, op cit

[edit] External links

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