Selected Writings by
Sachi Sri Kantha
[see also One
Hundred Tamils of 20th Century - Professor C.J.Eliezer]
Professor Eliezer, the pride of Eelam,
excelled in numbers. Thus it is apt to cite what the chapter named 'Numbers' in
the Holy Bible says:
"And Eleazar the son of Aaron the
priest was to be chief over the leaders of the Levites, and to have oversight
of those who had charge of the sanctuary." [Old Testament, Numbers -
Like what is said in the holy book, our
Eliezer of Eelam, born on June 12, 1918 at Navatkuli, Jaffna, also became the
chief of the Tamil diaspora at a critical period. Here is another passage.
"After the plague the LORD said to
Moses and to Eleazar the son of Aaron, the priest, 'Take a census of all the
congregtion of the people of Israel, from twenty years old and upward, by
their fathers' houses, all in Israel who are able to go forth to war." [Old
Testament, Numbers - 26: 1-2]
Like what the holy book says, our Eliezer, the
son of Jacob Richard Eliezer and Elizabeth Ponnamah, also took a census of all
the congregation of Tamil diaspora and polished them for the pre-eminent
campaign of their lives.
While Eelam Tamils bid farewell to Professor
Eliezer's mortal remains today, his accomplishments in the academic arena and
human rights activism will continue to glitter for a long time to come. In the
21st century and hence, excellence and elegance among Tamil intellectuals and
scientists will be measured by the now established 'Eliezer yardstick'. How one
stands up in comparison with Eliezer? - this will be the ultimate measure of
achievement for any Tamil kid growing up in this newly-minted century.
Professor Eliezer's mentor in Cambridge
University was Paul Adrien Maurice Dirac (1902-1984), one of the giants of 20th
century physics. Dirac established his reputation among his illustrious
contemporaries such as Einstein, Bohr, Raman, Rutherford, Curies and Pauling by
being awarded the Nobel prize in physics at the age of 31 for the discovery of
new productive forms of atomic theory.
Dirac was also renowned as an unpretentious
gem of a man with minimal words. There is a humorous anecdote about an American
journalist who visited Dirac and found out that his initial words of greetings 'Come
in' was the longest sentence Dirac uttered in the entire interview.
Precision of thoughts and words was Paul Dirac's forte, and presumably Professor
Eliezer also absorbed this talent under Dirac's tutelage.
An example of this is evident in the
transcript of the now-infamous SBS Television (October 4, 2000) program shown in
Australia. Excerpts follow:
"Reporter: Are you an agent for
Prof. C.J.Eliezer: Certainly not.
Reporter: How would you describe, then, your relationship with the
Prof.C.J.Eliezer: As an admirer, as an emotional admirer of the LTTE.
Reporter: A sympathizer?
Prof.C.J.Eliezer: Sympathiser, yes.
Reporter: Somebody who gives the LTTE advice?
Prof.C.J.Eliezer: I have not given them any advice.
Reporter: Somebody who provides the LTTE with support when asked?
Prof.C.J.Eliezer: Well, they haven't asked me for anything, but
irrespective of that, they'll find my pronouncements at meetings and things,
they'll find them useful.
Reporter: Useful in terms of furthering their cause?
Prof.C.J.Eliezer: Yes, because they're all committed to the idea of
liberation, and as they are, I am, and we
do it in different ways."
In this exchange of opinion, I found Dirac's
influence on Prof. Eliezer: just stating specifically and precisely where he
stood in his relationship with LTTE. To savor, I provide Prof. Eliezer's
reminiscences of his Cambridge days in 1940s, about how he came to write his
first scientific paper. This first appeared in the book, Tributes to Paul
Dirac, edited by J.G.Taylor [Adam Hilger, Bristol, 1987, pp.58-60].
Excerpts are given below.
|"My supervision by
It was by a chance circumstance that
Professor Dirac agreed to supervise me for the PhD. He usually did not
take on students. In June 1941, after completing Part III of the Tripos,
I was intending to stay on for research, and Dr.A.H.Wilson had agreed to
supervise me. During that long vacation, however Dr.Wilson was called
away on war work. In early October I had a letter from Professor Dirac,
in his very neat handwriting, which went something like this: 'As
I am appointed your supervisor, come up and see me sometime. I lecture
Tuesdays, Thursday, Saturdays at 10, and the best time to catch me is
after a lecture.'
I saw him at the earliest opportunity,
and showed him some papers I had been reading about mesons, which were
new particles then. Dirac looked at them carefully and said: 'These are
interesting particles - our theories for all particles have some serious
difficulties when we consider how they interact with each other. It is
better to try to solve the difficulty for the simplest of all particles
- the electron - before dealing with some complicated ones'. He said he
had recently completed a theory of radiating electrons. He gave me a
thick reprint and suggested that if I read it and found it of interest,
we could then think of a specific problem.
My first paper
After months of my preliminary
reading, Dirac suggested that I look into the hydrogen atom problem,
with radiation taken into account. From the family of mathematical
solutions, one had to select a physically acceptable solution.
I first tried the three-dimensional
case, then the two-dimensional and finally the straight line case where
an electron is projected towards a stationary proton. I had expected
(and so had Dirac) that one would get different solutions with the
electron hitting the proton in different ways.....
Methods of solving non-linear
differential equations were not well known in those days. I was foolish
enough to think that an exact solution could exist, but I could not find
one. I wrote off to Miss.M.L.Cartwright and Professor J.E.Littlewood for
advice. Both of them very kindly helped. It turned out that the electron
got stopped before it could reach the proton.
I told this to Dirac, and he seemed
surprised. Then he asked the obvious question which foolishly I had not
asked myself. What does the electron do after it gets stopped? At the
spur of the moment, I said: 'The electron would start moving outwards,
then come to a halt, and move back towards the proton and get stopped,
probably closer to the proton, and continue this oscillating motion till
it falls into the proton'. Dirac's face lit up with pleasure. That is a
very beautiful solution, he said.
I left the room in high spirits. But
my elation was short lived. When I worked out the equation, I found that
the electron, after its first stop, would move away from the proton in a
run-away type solution. At the earliest opportunity, I met Dirac again
and told him. He said he too had worked it out and come to the same
conclusion. Write up what you have in a paper, he said. That paper was
published in the Proceedings of the Cambridge Philosophical Society
When Prof. Eliezer published this paper, he
was 25. Until last year, even after reaching 80, he continued to publish
research papers in physics and mathematics solely or in collaboration with other
colleagues. For record, here is a select list
of Prof. Eliezer's technical papers which had appeared in the international
journals. For journal papers, annotations are in the order of year, volume
number and page numbers.
A Personal Note
On a personal note, I like to add that
I have been unlucky in not meeting Prof. Eliezer in person. But his was the
first name of scientist I heard when I was 10 and learning the first steps in
science. My father, who is 5 years younger than Prof. Eliezer [and a junior
contemporary to him at Hartley College, Point Pedro] used to talk about him
quite often at home, to inspire me.
During my Colombo University days in the
1970s, one of Prof. Eliezer's nephews, Dr. Kumar Eliezer (who was senior to me
by five years) became a friend of mine, when we jointly traversed the Eelam zone
of the island in a van to conduct science quiz contests in Tamil for the Sri
Lankan Association for the Advancement of Science between 1978 and 1980.
My link to immediate Eliezer household was
through gracious Mrs. Ranee Eliezer, with whom I have exchanged annual New
Year-Easter greeting letters during the past 10 years. When I read in her last
year's letter where she had quipped humorously and cryptically, "We have
become doctor's pets", I had a premonition that the illustrious life of
Prof. Eliezer is nearing its end. It did end on March 10, 2001. What a wonderful
life it has been, spanning three generations and influencing minds in Ceylon,
Britain, Malaysia and lastly Australia.
Prof. Eliezer's scientific
publications (select list)
1. The hydrogen atom and the classical
theory of radiation. Proceedings of Cambridge Philosophical Society,
1943; 39: 173-180.
2. On the classical theory of radiating
electrons. Proceedings of Cambridge Philosophical Society, 1945; 41:
184-186 (with A.W.Mailvaganam)
3. A discussion on the exactness of the
Lorentz-Dirac classical equations. Bulletin of Calcutta Mathematical
Society, 1945; 37: 125-130.
4. On Dirac's theory of quantum
electrodynamics: the interaction of an electron and radiation field. Proceedings
of Royal Society London, 1946; A187: 197-210.
5. The application of quantum
electrodynamics to multiple processes. Proceedings of Royal Society London,
1946; 187: 210-219.
6. Radiating electron in a magnetic field. Proceedings
of Cambridge Philosophical Society, 1946; 42: 40-44.
7. The classical equations of motion of an
electron. Proceedings of Cambridge Philosophical Society, 1946; 42:
8. The hydrogen atom in a generalized
classical electrodynamics. Physical Review, 1947; 71(2): 49-53.
9. Quantum electrodynamics and the
interaction of the hydrogen-like atoms with a radiation field. Bulletin of
Calcutta Mathematical Society, 1946; 38: 145-160.
10. The interaction of electrons and an
electromagnetic field. Reviews of Modern Physics, 1947; 19: 147-184.
11. Quantum electrodynamics and low energy
photons. Proceedings of Royal Society London, 1947; A191: 133-136.
12. Relativistic wave equations. Nature,
1947; 159: 60.
13. On the classical theory of particles. Proceedings
of Royal Society London, 1948; A194: 543-555.
14. Generalizations of the A.M. and G.M.
inequality. Mathematical Magazine, 1967; 40: 247-250 (with D.E.Daykin)
15. Generalizations and applications of
Cauchy-Schwarz inequalities. Quarterly Journal of Mathematics, Oxford
Series, 1967; 18(2): 357-360 (with D.E.Daykin)
16. On some convex functions and related
inequalities. Symposia on Theoretical Physics and Mathematics, vol.8
(Symposium, Madras, 1967), Plenum Press, New York, 1968, pp.129-132.
17. Generalization of Holder's and
Minkowski's inequalities. Proceedings of Cambridge Philosophical Society,
1968; 64: 1023-1027 (with D.E.Daykin)
18. Elementary inequalities for integrals. Mathematical
Magazine, 1972; 45: 89-91.
19. Generalizations of the Cauchy-Schwarz
and Holder inequalities. Inequalities, III (Proceedings of Third
Symposium, University of California, Los Angeles, 1969; dedicated to the
memory of Theodore S.Motzkin), Academy Press, New York, 1972, pp.97-101 (with
20. A note on time-dependent
harmonic-oscillator. Siam Journal of Applied Mathematics, 1976; 30(3):
464-468 (with A.Gray)
21. Equivalence principle and quantum
mechanics - note. American Journal of Physics, 1977; 45(12): 1218-1221
22. Symmetries and first integrals of some
differential equations of dynamics. Hadronic Journal, 1979; 2(5):
23. The Lie and Lie-admissible symmetries of
dynamical systems. Hadronic Journal, 1979/80; 3(1): 390-439 (with
G.E.Prince, P.G.L.Leach, T.M.Kalotas and R.M.Santilli)
24. Symmetries of the time-independent
N-dimensional oscillator. Journal of Physics, A 1980; 13(3): 815-823
25. On the Lie symmetries of the classical
Kepler problem. Journal of Physics, A 1981; 14(3): 587-596 (with
26. The equivalence principle and quantum
mechanics. In: Proceedings of the Conference on Particle Interactions and
Astrophysics, Mysore 1981 Feb.4-8, edited by T.S.Santhanam,
R.Parthasarathy, Math Science Report 108, Institute of Mathematical Sciences,
Madras, 1982, pp.22-27.
27. Introduction to selected topics of
Lie symmetries. Math Science Report 109, Institute of Mathematical
Sciences, Madras, 1982, 78 pp. [a set of lecture notes]
28. Some reminiscences of Prof.P.A.M.Dirac.
In: Tributes to Paul Dirac, Memorial Meeting held at the Cambridge
University, 1985 April 19; edited by J.G.Taylor, Hilger, Bristol, 1987,
29. On pursuit curves. Journal of
Australian Mathematical Society, B 2000; 41: 358-371 (with J.C.Barton).