Oral History Transcript — Dr. S. Chandrasekhar
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S. Chandrasekhar; October 31, 1977
ABSTRACT: A thorough, reflective survey of the life and work of this theoretical astrophysicist. Early life and education in India (1910-1930) and experiences at Trinity College, Cambridge (1930-1937), with comments on E.A. Milne and A.S. Eddington; debate with the latter over collapse of white dwarf stars. Move to U.S. in 1937, with comments on the situation at Harvard and Princeton since the 1930s, and especially on H.N. Russell, J. von Neumann and Martin Schwarzschild. Social context at Chicago University and Yerkes Observatory since 1937, with remarks on G. Kuiper, O. Struve, B. Strömgren, etc. Work as teacher there, and as editor of Astrophysical Journal from 1951 until it was given to the American Astro- nomical Society in 1971. Scientific work resulting in Introduction to the Study of Stellar Structure (1939) and publications on stochastic processes in galaxy and in general, radiative transfer, interstellar polarization, hydrodynamics and hydromagnetics (including experimental checks). Recent work on general relativity and Kerr metric; comments on cosmology. General remarks on the social structure of astronomy and its cultural role. Extended discussion of his way of functioning as a theorist.
Weart:We did discuss a lot of specific examples, but I wanted to ask in general about your working habits. How do ideas, scientific ideas or pro- grams, come to you? I have some specific questions about it but maybe you could just respond to that.
Chandrasekhar:As a rule the sequence of investigations I have undertaken have followed approximately along the following lines: when I find that my interests in the area in which I am currently working are beginning to fade, I look ahead and select a general topic on which I should like to work next. The next stage is to learn the subject by reading a book or more likely a series of review articles. Often I am attracted to a particular aspect of the subject because I feel that what are known in it are incomplete and inco- herent; they do not form a pattern that I find satisfactory to my taste. This dissatisfaction leads to a problem at a modest level; other problems follow, my ideas begin to clarify, and gradually a point of view emerges.
Weart:Have you ever started into an area and found that it wasn't particu larly interesting, that is, read up a bit and decide, No, that was not a fruitful field?
Chandrasekhar:An instance of this kind occured when I started working in the field of turbulence in the late forties and early fifties. I did publish a few papers in the subject for two or three years; but I found that I was not making much progress. Moreover, the area was becoming controver- sial. I therefore left the subject and went on to problems in hydrodynamic and hydromagnetic stability which occupied me all during the fifties. My work on the classical ellipsoids during the sixties started in a similar way. The subject was more susceptible to the kind of treatment which appeals to me. I found that there was a method which I had developed which gave certain of the classical results in a very simple way. therefore started learning the subject ab initio and found that there was a whole lot in the subject which was incomplete; and some of it was plainly wrong. I also found that my method was capable of answering all the ques- tions that one may wish to ask in a very complete manner. I spent several years on the subject. I should add that I collaborated with Norman Lebovitz (a former student of mine) on many of the aspects.
Weart:When you first went into it you might not have seen that it would lead so far?
Chandrasekhar:No. It was an instance where I found that the subject began to grow on its own. And that is the way it often happens to me. For example, some three years ago I got interested in the general relativistic theory of black holes. Some major contributions had been made by others to the subject; but I did not think that the subject was organized in a systematic way: it appeared very incoherent and there seemed to be many strands that were hanging in thin air. So I started working in this area; first, in a very modest way, beginning with the Schwarzschild black hole. Soon I found that I could extend my methods to the Kerr metric. The subject seemed to grow and eventually I was able to obtain a complete solution to the entire set of equations governing the perturbations of the Kerr black holes. My method of work has always been to start at a very modest level, and find out whether I am able to develop methods which will solve known problems in a much simpler way than had been done before; and if I am successful in finding simpler methods of solving problems, which had been considered difficult, then I begin to apply my methods to problems of increasing difficulty and scope.
Weart:I see. So the key point may be in searching for the particular methods that are to be applied?
Chandrasekhar:It is difficult to know which comes first. But in all cases, it begins with my dissatisfaction with the work that had been in an area. Then I try to reorganize the subject in a coherent way; and in doing so I quite often find that I am able to develop techniques of solving problems in the area which go much further than what had been accomplished before.
Weart:I was interested in your Ryenson Lecture*. You made some comments on Newton, and one couldn't help wondering to what extent they might apply to theoretical physicists in general. For example the famous statement that Newton was "always thinking on things". Do you "always thing on things", do you keep a problem in your mind day after day?
Chandrasekhar:When I am working in a certain area, and I have been blocked by some difficulty, then I am constantly aware of the problem and explore means of overcoming the difficulty. Sometimes the difficulties are of a technical nature requiring a novel approach; and often such technical problems keep me at bay, sometimes for weeks at a stretch. My thoughts concerning a subject are generally at two levels; a relaxed contemplation of what the subject is about, its arrangement and its coherence; and a strenuous effort to solve particular technical problems. For example, in the last piece of work I have done on the complete integra- tion of a set of 76 equations of Newman and Penrose which replace the conventional Einstein equations, the technical problems of reductions of the equations to a manageable set is already massive.
Weart:This general relativity stuff is amazing, yes.
Chandrasekhar:I found that after some months of effort, I got to a dead end. I simply did not know how to proceed. I was completely blocked for three months. Then I started afresh and gradually the problem untangled itself, and the final solution was found six months later. But during those six months, I was constantly worrying over overcoming the sequence of stumbling blocks that constantly appeared on the way.
Weart:When you say you went at it fresh, do you mean you went back to first principals, to the original problems?
Chandrasekhar:Well, I was going along a certain direction; but since that way of proceeding was checkmated, I had to go back to the beginning and start along a different direction. The different point of view from which I started led to many alternative routes all along the way; and I always had to select one. Retrospectively, I am somewhat astonished that when there were so many alternative paths that I might have taken, the ones I did take seemed to have been the right ones. I can see that they are right now; but I did know this at that time.
Weart:I see. Although you said sometimes you did get into a blind alley and then you'd have to back up.
Chandrasekhar:Back up! I had proceeded cheerfully along one line; and found that at the end of three months it led to a a dead end. I had no choice but to go back to the beginning and start afresh.
Weart:I see. To what extent do you keep the physical idea in mind while you're doing this and to what extent is it a matter of mathematical formalism?
Chandrasekhar:Well, in the particular instance that I was talking about, the problem was one of solving a large number of equations; and the choice of the sequence is a most important one. In other instances, the problems are physical; and the principal questions concern the best way of formulating them as mathematical problems.
Weart:Do you sometimes find yourself sort of going back to the physical problem for guidance in making your way through the mathematics?
Chandrasekhar:My concern has always been one of formulating well defined physical problems in mathematical terms. Once I have selected a physical problem for a solution, then the principal questions revolve around how best one may formulate it.
Chandrasekhar:And then the problem of solving it. For example, I became interested in the polarization of the sunlit sky. The first question was how to take account of polarization in formulating the equations of transfer. In other words, the question concerns polarization itself: it is not adequate to describe it in the conventional terms of total intensity and the degree and the nature of the polarization, quantities of different dimensions. None of the extant books gave me any help. But then I found in Stokes' Collected Papers, a paper (written in 1852) which was exactly the right one for my purposes: polarized light can be represented by a vector - the Stokes' vector, as I called it. The equation of transfer becomes a matrix equation; and the problem of solving it is a major one.
Weart:I see. So it takes place in phases.
Weart:An then, tell me -- this is something that's hard to talk about -- do you visualize things? That is, do things come to your head as words or as pictures, as pictures of mathematical symbols?
Chandrasekhar:As a rule I find that I think concretely. There is a book by Hadamard, "The Psychology of Mathematical Invention", in which he points out that most great mathematicians think in vague and general terms, not concretely, and not in terms of formulas. I recall reading Hadamard's book in a plane; and as I was reading it, I told my wife, "I am rapidly developing an inferiority complex: I do not seem to think in the way that Hadamard says he thinks, and in the way he says that other great mathematicians also think". I think concretely in the sense that I concentrate on particular aspects of the problem; and quite often I think in terms of symbols.
Weart:You visualize them?
Chandrasekhar:In some ways yes. My thoughts often concern the sequence of steps I must take towards the solution of a problem.
Weart:Is this a sort of spoken commentary that goes through your mind?
Weart:I see. But with the symbols mix d into it.
Weart:I see. Would this vary to some extent on what problems you're working on? For example when you're working on stellar interiors or fluids might you actually visualize the interior or the fluid, or does it still take place in this more mathematical form?
Chandrasekhar:I think on the whole I think mathematically.
Weart:I see. Is there any sort of a tactile sense, that is any feeling of picking up these things and moving them about with your hands, that sort of an idea? Or is it more through a verbal stream?
Chandrasekhar:It's more like a verbal stream.
Weart:I see. That's very interesting. You know different people have very different approaches to these things.
Weart:Have you ever been guided, for example in your work on general rela- tivity, by any more general, almost philosophical ideas or general ideas about how such things should work?
Chandrasekhar:I do not believe that I think "philosophically". I am most often concerned with the structure of a subject and the inner relationships among its component parts. And by and large I try to formulate problems whose solutions may have some degree of permanence: their lasting interest is one which I aim at. For example, my present interest in the Kerr metric derives from the fact that it represents an exact solution for the black holes that occur in nature. Consequently, any fact about the Kerr metric can in some sense never get out of date. Both the object and what one may say about it (so long as it is relevant and it is correct) have some degree of permanence. It is the degree of permanence, and not the current fashion, that holds the greatest attraction for me.
Weart:I was thinking also in terms of the way you work your way through to a solution -- when you're faced with a very complex mathematical problem, whether there is anything you have to go on, other than pure mathematics itself, in order to find which of these may have the best way through. Is it simply intuition?
Chandrasekhar:Very often it is conviction and faith that sustain me. found for example, that what was true for the Schwarzschild black hole appeared in some sense to be also true of the Kerr black hole: there were many parallels. It then became a matter of conviction with me that every problem which is solvable in the Schwarzschild geometry must also r e solvable in the Kerr geometry. And to a very large extent this conviction has been substantiated. A young man who was working with me, Steve Detweiler, did not fully share my convictions; and he left collaborating with me and went on to other things which interested him. But kept on and now he tells me that he is surprised that my initial ideas turned out to be largely true. Of course to some extent one's convictions derive from one's experience; and I am not blaming Detweiler.
Weart:It may go by analogy with some earlier problems you worked on.
Weart:I see. In any of this has your way of thinking changed over your career? Can you think of ways that you may approach a problem now with more experience and so forth than you used to?
Chandrasekhar:I think that on the whole I have progressively tried to work on increasingly difficult problems. At the present time it does not make much difference to me whether I am successful. As it has been stated, it is the quest, and not the arrival, that matters. Perhaps, to some extent, can afford the luxury of this approach. At an earlier time, the solvability of a problem was rather more in my mind. I would say that the only difference, as time has gone along, is a certain degree of confidence in pursuing more difficult problems. My attitude is, "If I don't solve the problem, well!, I don't solve the problem!"
Weart:You separated it.
Chandrasekhar:Well, Brian Carter told me that he did not know I was in the audience when he made this bet, you see. So I didn't get the five pounds.
Weart:If he had known you were there he might not have....
Chandrasekhar:That is what he said when I met him afterwards and when he knew of my separations. Well, solving problems and meeting challenges Constitute some of the pleasures in doing science: someone poses a problem, and one is pleased if one can solve it. I don't think that I have become so staid that I cannot, on occasions, get the kind of vicarious pleasure that one can sometimes find in the pursuit of science. But by and large I am generally more serious than solving a problem because someone has issued a challenge.
Weart:I understand. Do you ever feel a certain combativeness with the problem itself? If I had worked on some problem for there months for six months I would almost take these equations as being in personal competition with me.
Chandrasekhar:Oh yes! It is only natural that if one has already expended considerable effort on a problem, then one is reluctant to leave it unsolved. In some sense it becomes a personal struggle: the problem against yourself. And if the ultimate goals is to complete one's understanding, then one is very reluctant to accept defeat. And this feeling of personal antagonism towards a problem is a natural tendency. At least it has remained with me all my life.
Weart:I see. It raises a questi how you got that way. Can you think of anything in your training or upbringing that might have contributed to your particular approach to scientific problem?
Chandrasekhar:With regard to what motivates one in one's scientific work, it depends upon the stage in one's career. It is natural that when one is young and ambitious, one hopes that one can achieve some reputation by making a contribution that may be comparable, perhaps, with what some of the great men of science have accomplished. But there was a point in my life, during my early years in Cambridge, when I definitely turned away from that attitude, with the resolve that, in the long run, it would be better for me to try and pursue science with the intent of contributing to it in ways which will have some abiding interest and some value. But I did not formulate this to myself as clearly in those days; but this attitude matured with the years. And it is only with this maturity, that I am able to formulate it in the way I have.
Weart:also curious about your approach to mathematics, your ability to do this sort of very difficult problem. While you were growing up was your scientific ability recognized and encouraged in any way? Specifically scientific or mathematical ability?
Chandrasekhar:It is difficult to say. Actually, as far as the more co on scientific recognitions go, many of them came to me relatively early and rather unexpectedly in the first instance. But I cannot recall that any of these recognitions was a source of encouragement for me in any particular sense. For example, I was awarded the two astronomical medals (the Bruce Medal of the Astronomical Society of the Pacific and the Gold Medal of the Royal Astronomical Society) when I was 42; and I have been told that that was the earliest age at which anybody had received both of these medals. But the citations for neither of these medals referred to my work on the white dwarfs, I suppose because of the reluctance of the two societies in citing something which they considered controversial. So I cannot particularly associate these early recognitions as encouraging me in the kind of work that I considered most relevant.
Weart:I was thinking even earlier, back in India when you were first beginning. Because clearly even by the time you had left India you already had a mind which was very capable of attacking difficult scientific mathema- tical problems. You already had that at that point, and I curious about how they came about. For example did your Uncle Raman play any role in this?
Weart:Did he encourage you to go into science?
Weart:Not particularly. I see.
Chandrasekhar:I have written a piece, which is rather controversial, You know Raman was a very controversial person.
Chandrasekhar:I do not share the popular view of Raman. It should be stated, however, that I did not know him very well. After I left India in 1930 (at the age of 19), I have had the occasion of meeting Raman on only five different occasions (in 1936, in 1951, in 1961, and in 1971); and only for a few hours each time. On the other hand, I was present at his laboratory in Calcutta, in the summer of 1928, some two months after the Raman Effect had been discovered, Also, I recall meeting him in Madras at my home (in March 1928) prior to his going to Bangalore where he announced his discovery. Much of Raman's work relating to the discovery of the Raman Effect was carried out in collaboration with K.S. Krishnan. But unfortunately, Raman and Krishnan fell out in the late forties and they became estranged. It is a very unpleasant and unfortunate story.
Weart:But as for why you became a scientist, a mathematical scientist rather than an English literature person or whatever -- that's something that's just mysterious?
Chandrasekhar:From the earliest time that I can recall, my interest was always in the deductive and and the mathematical aspects of the physical sciences. In a larger sense, however, I have never taken myself very seriously in the sense of having any special gifts. I never found it possible to think of my own accomplishments in science in a flattering way. I have always believed that my strength consists in making the maximum of rather modest abilities by applying myself as best as I am able. That is the way I perceive myself.
I think that's fair enough.