Lucasian Chair.org

Sir M(ichael) James Lighthill is a pioneer in the field of the aerodynamics of high speed aircraft and missiles. He contributed to the theory of jet noise and to the theory of shock waves. His calculations helped to improve aircraft and missile performance and to limit jet engine and supersonic boom noise. Lighthill applied his aerodynamics knowledge to the problems of the flight of birds, insects, animal locomotion in water, and to the biomechanics of hearing. In 1964, he was awarded the Royal Medal by the Royal Society of London and in 1971 he was knighted. He was born in Paris, France in 1924 and educated in England. He studied mathematics at Cambridge University and graduated in 1943. Sir James was interviewed by Dr. Robert Bruen. Dr. Bruen's thesis explains the history of the Lucasian Chair at Cambridge University, Cambridge, England. The current holder of the Lucasian Chair is Stephen Hawking. Some past Lucasian Professors were Isaac Newton, Isaac Barrow, George G. Stokes, and Paul A.M. Dirac.

Bruen: What subjects were you most interested in as a child?

Lighthill: I was interested in mathematics by the age of three or thereabouts. Like most mathematicians, I was fairly precocious and ahead of my age group. Fortunately, I was able to persuade the schools that I attended to let me learn alongside students who were older than me. I started this at the age of five and at the age of twelve I won a scholarship to Winchester College, where many mathematicians were fostered. When I went to Winchester College, I met Freeman Dyson.

Freeman Dyson is now a professor of physics at the Institute for Advanced Study in Princeton, New Jersey. He and I are the same age. We managed to persuade our teachers to allow us to study together. Both of us won scholarships to Trinity College, Cambridge at the age of fifteen. Of course, we were much younger than the other students, and the university administration felt we had to wait until we were seventeen to go further. This turned out to be rather good for us.

We continued to study mathematics with enthusiasm, but it also gave us time to study many other things. I developed a strong interest in languages. We were able to study the humanities as well as mathematics because we had that extra bit of time before going to the university. When we went to Cambridge, we found that we didn't need to study the undergraduate material at all.

Bruen: Tell me more about your friendship with Freeman Dyson.

Lighthill: Freeman Dyson and I were both seventeen when we went to Cambridge in l94l. We only went to postgraduate lectures. It was during the war and there was a rule that nobody could have more than two years of university education. No matter what stage of our education we were at, we had to go straight into the war effort. Bright students were managing to complete the undergraduate degree in two years. We were all working hard, knowing that we had to go to war. Very few other students, besides Dyson and I, were attending postgraduate lectures. Nobody had time to take a degree and then do postgraduate work. We had some great mathematicians almost to ourselves.

Bruen: Who were some of the mathematicians that you studied with?

Lighthill: We were two out of four or five students in classes given by Godfrey H. Hardy [1] and John E. Littlewood [2]. Hardy and Littlewood were great mathematical analysts. They both believed that their analysis was completely pure mathematics that could never be used. A famous book by Hardy called, A Mathematician's Apology specifically makes this point. During my career in applied mathematics, I found that the training in basic analysis was endlessly valuable. I remember telling Hardy that I found what he taught valuable, but unfortunately, I don't think he ever believed me.

Bruen: Who influenced Dyson the most?

Lighthill: Freeman Dyson was influenced by P.A.M. Dirac's [3] training. Dyson became a theoretical physicist.

Bruen: How about you? Was Dirac an influence?

Lighthill: Yes, he taught me about mathematics. Dirac invented the Dirac delta function, which is the simplest function and is now called either a distribution or a generalized function. They are two alternative words for the identical concept. Later on in my career, I wrote a book on generalized functions which was certainly influenced by Dirac. He is one of the three people to whom I dedicated the book. The book is called Introduction to Fourier Analysis and Generalised Functions (Cambridge 1957).

Bruen: What was it like for you during World War II?

Lighthill: All my life, all I wanted to do was pure mathematics, and then I had this interruption for two years. I was awfully frustrated about going into the war effort. It did prove to be much more stimulating and interesting than I had expected. I went to the aerodynamics division of the National Physical Laboratory.

I was assigned to Sydney Goldstein, an applied mathematician, who told me that it was a good job for someone 19 years old. Goldstein was typical of the applied mathematicians that I would have studied with at Cambridge had there not been a war. All the applied mathematicians were working in the war effort. With the exception of Dirac, I had never worked with a first rate applied mathematician. Goldstein thought the war might go on for a long time and he wanted England to have supersonic aircraft to fight the Germans. It was my job to find out everything known about supersonic aerodynamics, work done mostly by German scientists like Prandtl [5], and take it from there.

The first year I read a lot of papers on supersonic aerodynamics. One can see a tenuous link between the sorts of ideas that were coming out then and the ultimate shape of something like the Concorde. Incidentally, I was deeply involved with the Concorde, because at the time of its development, I was director of the Royal Aircraft Establishment. The war ended sooner than anticipated and the question was what to do next.

I applied for a fellowship and received one for Cambridge to do what I was meant to do -- pure mathematics. But I only spent a short time doing pure mathematical research when I found people were inquiring about papers I had written while at the National Physical Laboratory. I wrote 12 papers in all. For example, G.I. Taylor, a mechanical scientist, had questions about what I wrote and so did Goldstein. I found myself getting sucked back into fluid dynamics. Fluids are liquids and gases, and aerodynamics is part of fluid dynamics.

I started some new work. I did that because on the one hand there was incompressible aerodynamics or low Mach number aerodynamics, and then there was supersonic aerodynamics. I had done a lot of both of these, and I wanted to do something in between like transonic aerodynamics. I started some pioneering work in transonic aerodynamics, an interesting and more difficult field. Transonic aerodynamics is governed by equations of a mixed type. It was difficult to find ways of solving these equations, but I invented a new method which was based on certain hodograph transformations and mapped out problems in ways which could help them to be solved. I also worked on extensions of supersonic theory to more complicated problems like delta wings.

Bruen: Then what happened?

Lighthill: I received the biggest challenge of my life. In 1949 someone came from the Ministry of Aviation and said that they had jet aircraft that had been used for military purposes. The question was, can these jets be used for civilian purposes. The problem was whether or not the noise levels could be made tolerable to communities living near airports. It was a good question to be asking in l949, because they were absolutely miles away from having an actual jet that was a civil aircraft. This was to become one of the abiding influences on my life; the question of how jets can be made quieter and more powerful at the same time.

The paper that I published in 1952 is one of the most cited papers in aerodynamics. The law that it produces is a rather amusing one. It is called, Lighthill's Eighth Power Law of Jet Noise. The law says that there is a tendency for the acoustic energy that is emitted from the jet to vary as the eighth power of the jet exit velocity. For various reasons, which I will not go into, the actual power delivered by the jet goes as the cube of the jet velocity. It means there is a sort of efficiency of noise production which goes as the fifth power of velocity which is ratio of acoustics energy to jet power. The acoustic efficiency or the ratio of noise energy emitted to the jet power delivered therefore varies as the fifth power of the jet Mach number. So this efficiency increases if you can bring down the jet Mach number, which is the ratio of the jet velocity to the atmospheric speed of sound.

You can have engines that will be more powerful and quieter at the same time. Because this efficiency varies as the fifth power of the Mach number, you produce big changes in efficiency with small changes in Mach number. The consequence is that you need to go to wide-bodied engines, so you can have lower jet speeds with the delivery of much bigger thrust. That trend is what made jet aircraft possible, for it would never have been environmentally possible without a reduction in noise. Originally the noise was really horrifying and severe from military aircraft. Jet aircraft have become increasingly quieter and this has made the whole development of jet transportation possible. I am still involved in this area of work.

When Goldstein became a professor of applied mathematics at Manchester University I went to work with him. He built a splendid team. But he was suddenly bitten by the call to Zionism and in 1950 he went to Israel where he became the top academic at the Technion, the technical university at Haifa.

I succeeded Goldstein as a professor of applied mathematics and for the next nine years I ran this group of applied mathematicians. It was great fun.

Bruen: When did you become director of the Royal Aircraft Establishment at Farnborough?

Lighthill: At the end of the 1950's Farnborough had about 8000 employees. Its mission, like that of NASA Langley, was aeronautical research. It had out-stations with an airfield at Bedford. I threw myself into administrating the place.

It had departments covering everything from chemistry to electronics, but was centered on aerodynamics and structures. We were just developing what was to become the Harrier, the vertical take-off aircraft. We were also developing the Concorde, and trying to move Britain forward as fast as possible into space science. While I was there, I could not actually do research myself. It was, however, perfectly feasible for me to write long review articles. These review articles were not just summing up what other people had done, but taking my own point of view. I really enjoyed working there, but after about five years I decided to move on. It was a turning point for me, because I wanted to change the direction of my research. I enjoyed enormously the 21 years that I worked with aviation and aeronautics, but I felt that I did not want to spend the next 21 years of my life on that kind of research. Aeronautics has altered the human condition completely and made the world a neighborhood. All that was well underway. I did not feel that the big advances were going to come in aeronautics after that and perhaps it would be more interesting to do something different.

I decided to move into other subjects like oceanography, which has gradually expanded to become the sciences of the earth's fluid envelope. I rather like the phrase, the earth's fluid envelope, because it includes the atmosphere, the oceans, the ground water, the rivers, and lakes. This has been my primary interest since 1964. I also became more interested in biological applications of fluid dynamics. I had only touched upon it earlier in my career. I became interested in the whole animal kingdom from the point of view of aquatic locomotion and how they generate the thrust to move through water.

When I was at the Royal Aircraft Establishment, what fascinated me most, was that right next door was the Institute of Aviation Medicine. Superb doctors worked on breathing apparatus for pilots. I found that one of the hardest problems was having the two institutions collaborate effectively. The engineers were also working on breathing apparatus for pilots, but the doctors said it was much too complicated for anyone but the doctors to understand. I thought it was a challenge to establish cooperation between engineers and doctors.

In 1966 I set up a physiological flow studies unit at Imperial College. Physiological flow studies are concerned with the cardiovascular system and the respiratory system. Doctors, physiologists, engineers and mathematicians worked together in this unit. It was a success story, in fact they celebrated their silver jubilee last year. The secret of interdisciplinary studies is to set up a team of people who have the expertise in the component disciplines and then each must learn the others language. It is too complicated to learn the discipline of the other person, but one can learn the language and then communicate it. Jargon consists of technical terms which describe important ideas for which there are no ordinary words. We had to learn biological jargon and they had to learn the mathematical jargon.

Bruen: When did you decide that you wanted to become a Lucasian Professor?

Lighthill: Out of the blue the idea came to me that I ought to be a candidate for the Lucasian Chair when Dirac retired. I think my colleagues in fluid dynamics at Cambridge felt they would like me to be a candidate because there had not been anyone in fluid dynamics since Stokes had been a Lucasian Professor. Dirac had been a professor for almost forty years. Stokes had been a Lucasian professor even longer and so there was a tradition in fluid dynamics. It turned out that the majority of the faculty favored my appointment. The appointment actually happened in April 1968, although Dirac was not due to retire until October of 1969. I went to Cambridge in October of 1969. It was a splendid ten years. I concentrated entirely on fluid dynamics research. I wrote books. My big bookWaves and Fluids includes work on acoustics, oceanography, water waves, atmospheric science, internal waves in the atmosphere, and so on. I also have a book on mathematical biofluid dynamics. But my best seller is an eighty paged book called, Introduction to Fourier Analysis and Generalized Functions, published in 1957.

No administrative duties, or for that matter, no duties were attached to the post at all. The only stipulation was to generally reside during full term within five miles of St. Mary's Church. In Newton's day, he was required to give lectures. During the eighteenth century those requirements were suppressed.

While I was at Cambridge I met a marvelous zoologist named Torkel Weis-Fogh, a Dane, who succeeded Sir James Grey as professor of zoology. He was an expert on insect flight. Great discoveries were made in insect flight. For example, the bigger insects fly like a smaller version of a bird. Smaller insects fly quite differently. They use what is now known as the Weis-Fogh mechanism of flight generation. Insects clap their wings. It is also known as the clap and fling mechanism. They clap their wings behind their back, once per wing beat, then fling the two wings open about the common trailing edge. Air rushes into the open gap. This produces a circulation around each wing. It is a marvelous mechanism that works instantaneously because Nature abhors a vacuum.

The fruit fly drosophila uses this method 200 times a second. It turns the wings over at the end so the fly always has the leading edge forward. The angle of attack is always positive. This is just one of the many works that Weis-Fogh and I did on insect flight. It was an interdisciplinary team, zoologists working with mathematicians. We also brought in a good engineer and did some good experiments.

Bruen: How have other Lucasian professors influenced you?

Lighthill: I have taken a strong interest in Newton and Barrow because they interacted. Saunderson was interesting because he was blind and was a good mathematician in spite of his blindness. During the l8th century there was a stagnation in scholarship. A great pity. Airy was very good. He was an interesting man who did interesting analytical work, the Airy Functions. Stokes was a grand genius. I want to emphasize my almost boundless enthusiasm for Stokes. Stokes' papers are an absolute joy to read. They are brilliant. What he did for viscous flow theory, for compressible flow theory, and for water waves was unsurpassed.

You have to somehow keep the collective memory of science alive. I think, for an elderly professor like myself, that it is of one of our jobs to keep reminding people of the wonderful things that were discovered by some of these people.

The professorship has an excellent reputation. That's why I took it. Even though I was nicely installed in London, it was a great opportunity for me. I thoroughly enjoyed Cambridge until Weis- Fogh died suddenly in 1974. After that I did not find it quite so interesting. When I was invited to become the provost of University College London (UCL), I thought it would be fun to run something again like I did at the Royal Aircraft Establishment.

It was a challenge to keep a good place good in difficult times and make it even better by making good appointments. When I retired, I looked back over a 110 full professors for whom I chaired the committees that had selected them. I realized the college had really been changed quite a lot as a result of bringing these people into leading positions. We made some excellent appointments. We are feeling quite good because University College London has come in just behind Cambridge and Oxford in the list of research ratings for the country. UCL has a strong medical school, great science, engineering, humanities and social studies. It has done extremely well in all those areas, as it did on two successive occasions when I was provost.

During the time that I was provost, the total amount of research support from external sources exceeded that of Cambridge, though it was still less than that of Oxford, but we are pleased. When I took over, they were just beginning to merge with University College Medical School. I realized that the clinical side of the university was not nearly as strong as the scientific side, but I managed to have a merger between our medical school and neighboring Middlesex Hospital Medical School.

When I retired a superb man took my place who had a lot of experience with industry. I was terribly keen that the college have the closest possible industrial relations. It seems frightfully important for applied science. I was able to get industry to endow a number of chairs in the college. When they appointed a first rate industrial scientist as my successor it was a compliment to me. It meant they had actually been listening to my message.

My move to a little office on the eighth floor of the mathematics department was no problem to me. The new provost and I see eye to eye. He is not in any way embarrassed by my being around. It's nice for me, because although I don't do anything administrative within the college, I go to lots of social functions and keep in touch with my friends. It works well.

Bruen: Who is the other Lighthill listed on the door?

Lighthill: My wife. She is a lecturer in the department. We met at Cambridge as undergraduates. We were married in 1945, and we have five children. My wife has always taught mathematics as well as raising our five children. She has taught mathematics often on the high school level. When she retired as a school teacher, University College London asked her to prepare students in mathematics, because students are not as well-prepared as they once were. She has high standards and the students really understand the university courses after she works with them.

My wife and I are very close. The fact that we are both mathematicians means we are close in an extra way beyond most married couples. She also has a great gift as a hostess, which was marvelous for me when I was the provost at University College London because there was a great deal of entertaining. She is still popular at the college and is invited to many of the social functions.
Bruen: Are any of your children mathematicians?

Lighthill: The youngest is a mathematician, actually a high school teacher of mathematics. She has done a lot of good meteorological research too with the MET office, all on these enormous supercomputers. In the end she became bored working with machines and would rather work with people. Of course the schools want math teachers who have experience with how mathematics is applied in the real world. She is doing that now and thoroughly enjoying it. It is rather nice for us because we keep in touch with high school mathematics teaching through her.

Bruen: What are you working on now?

Lighthill: I have been working with NASA, because although, we made the Concorde a success technically, it has not done everything it promised. For various reasons there are not many Concordes flying. We anticipated that the first generation of supersonic transport would not be economical. You never get economy with the first generation aircraft. We anticipated that the second generation would begin to show good economics. I concentrated on helping NASA on their high speed transport project, HST. This is specifically designed to minimize the level of supersonic boom noise.

I am rather proud of my aero-acoustical contributions because they have clearly influenced the whole development of civil aviation. It has made it possible for jets to be more powerful and quieter. It was quite a difficult mathematical problem to solve. I am fond of my work in biofluid dynamics. It is important to me. I gave a lecture to the American Society of Mechanical Engineers on the biomechanics of hearing sensitivity. It is my latest biofluid dynamics work, about the inner ear and the fluid mechanics of it.

The other area is geophysical fluid dynamics. I have been doing that particularly with relation to problems that really matter to people in tropical countries -- Monsoon Dynamics. Recently I have become involved in understanding tropical cyclones -- that is hurricanes and typhoons. Ten years ago we started organizing an international effort in the field of Intense Atmospheric Vortices. In October of 1993 I chaired a symposium on tropical cyclone disasters. Everyone knows that supercomputers have made improvements in forecasting the weather, and so have satellites, but actually they do not work well together. Supercomputers for the initial data need three dimensional data, the satellites only give two dimensional data. So there is a question of bridging the gap.

There are a fair number of good weather stations on land, radio sonde stations, but there aren't any at sea. Most of the weather ships have been decommissioned. The satellites do not make up for it. The radio sonde stations give the vertical distribution of wind and the satellites do not.

Bruen: What do you think of the work of the current holder of the Lucasian Chair, Stephen Hawking?

I like practical applications in mathematics, rather than speculating about the first ten to the minus something seconds of the universe. Cosmology seems to be almost too close to theology to be interesting. To me, it is not quite science, but more like creation myth.

NOTES

1. Godfrey Harold Hardy was born in Carnleigh, England in 1877 and died in 1947. He was a leading English pure mathematician of his time.
2. John Edensor Littlewood was best known for his work in analysis with G.H. Hardy. He did valuable work in complex analysis, function theory, number theory, trigonometric series and differential equations.
3. Paul A.M. Dirac was a physicist and winner of the Nobel Prize for Physics in 1933. In 1927 he united quantum mechanics and relativity by deriving a relativistically invariant form of Schrodinger's wave equation, predicting positively charged electrons.
4. Arthur S. Eddington was born in England and educated at Cambridge University. He wrote the first complete account of general relativity written in English. The early part of his career he spent as chief assistant to the Royal Astronomer and then he accepted a position as professor of Astronomy at Cambridge University. He held that position until his death in 1944.
5. Ludwig Prandtl was born in Germany in 1875. He was the founder of the German School of aerodynamics.