傳播數學知識．促進數學教育

Interview with Prof. Joel Lebowitz

**Interview Editorial Consultant:** Tai-Ping Liu

**Interviewer:** Tai-Ping Liu(TPL)

**Interviewee:** Joel Lebowitz(JL)

**Date:** July 14th, 2011

**Venue:** Institute of Mathematics, Academia Sinica

Prof. Joel Lebowitz was born May 10, 1930 in Tiachiv, Czech Republic (now Ukraine). He received his B.S. in 1953 from Brooklyn College, and Ph.D. in 1956 from Syracuse University. He has been a faculty at Steven Institute of Technology, Yeshiva University, and now at Rutgers University. He is one of the founders and editors of the Journal of Statistical Physics and also a member of National Academy of Sciences. For his contributions in statistical mechanism and mathematical physics, he has been awarded several honors in mathematics and physics, including Max Planck Medal and Grande Médaille of the French Academy of Sciences. He is also an active member of the human rights community and a long-term co-Chair of the Committee of Concerned Scientists.

TPL: Perhaps, we could start from a traditional question. How did you decide to go in this direction of statistical mechanics and theoretical physics?

JL: When I was an undergraduate student in Brooklyn College, one of my teachers was Professor Melba Phillips . She is a co-author on a famous book on electrodynamics, “Classical Electricity and Magnetism ”, you must have heard it. She was a student of J. Robert Oppenheimer , and a post-doc of his. When I was deciding to go to graduate school, she recommended that I go to Syracuse University where a friend of hers Peter Bergmann was working. Peter’s main interest was in general activity, he was a post-doc of Einstein , worked with Einstein at some point, but just at that time he was also interested in statistical mechanics. Melba Phillips gave a course, a kind of senior course in college which used Peter Bergmann’s book on statistical mechanics. I believe, that was probably the way it came about. I remember reading a book by King Chen on statistical mechanics during the summer between my finishing college and going to graduate school. And then in Syracuse, Peter was interested in statistical mechanics. In one of the people I took the course with was Kai-Lai Chung , who was in the mathematics department at Syracuse University just at that time and he gave a course in probability theory and I guess that was my first course in probability theory because I was really a physics student. I can’t remember whether I was officially registered or I sat in over there. During my first year at Syracuse University, two things happened. One there was a conference in Pittsburgh on statistical mechanics. I was a first year graduate student amongst many of the students of Peter Bergmann, we all drove to Pittsburgh and went to this conference. There also, Onsager was also participating in that conference. And then another thing happened also when I was in my first year. Doob , the probabilist, came to Syracuse and gave a talk and I started reading his books. Also Mark Kac came to Syracuse in first and second year. He was at Cornell at that time so he came. He talked about Onsager’s solution of the Ising Model. I also remember that, particularly from the beginning, it was the same year where Lee and Yang had their theory about zeros of the partition function of the Ising Model and there was a seminar about that as a graduate student. Many things happened in the direction of statistical mechanics.

TPL: Wow, this list of names is overwhelming.

JL: Yeah I haven’t thought about that for ages but you asked this question. Indeed that was what happened.

TPL: Do you have any recollections of what kind of person or scientist, you mentioned Onsager, Doob, Mark Kac? Do you have some impressions of them?

JL: Onsager, I got to know very well. I was a post-doc of his for a year. After I finished graduate school in 1956, from ‘56 until 1957 I was his post-doc. He was a very interesting man, besides being a very good scientist. He was very proud of his martinis. He made very good martinis when I was there. And he knows all the things about botany and other things. He was kind of person who managed to get off from being on committees. So when I was a post-doc I was actually living in New York but Onsager was in Yale at New Haven. So once a week I would drive up to New Haven and then I could spend a whole day with Onsager. He would sit in his office. He was marvellous. He could integrate cubes of Bessel functions without looking up the books. When he got some papers, some new papers, he would go to his filing cabinet and take out some of his old notes and check whether the paper that was sent to him was correct or not. So, he was a wonderful, interesting man and he liked to talk in some kind of oracles, oracular things. I remember particularly, already after I was his post-doc, I was working with Oliver Penrose on a problem of meta stability. Onsager at some conference in a lobby of a hotel asking us “What do you think is meta stability, an equilibrium phenomenon or is it something kinetic phenomenon, not equilibrium phenomena?” So I thought for a moment. His answer was that there was a factory in Canada, they made some kind of gel and everything work very well. But one winter the pipes froze, they moved the factory. One was supposed to understand, it took me some time, that meta stability is a kinetic phenomenon. Once the pipe froze, they kept on freezing every winter afterwards because some seeds were left over there. So that was the kind of things that Onsager was like. When I was telling, he also came out one time. I was working with Elliott Leib on Coulomb’s system and we have to think about chi’s theorem. That you can fill a box with balls of different diameters and if you make them smaller and smaller, you can fill it up arbitrary fraction of the volume of the box. So I told Onsager about that. He said, “Ah… I see. That’s what they taught me in engineering school, that graded sand makes the best cement.” Graded sand meaning there is grains of different sizes, and that makes the best cement because it fills up very well. So that’s the way Onsager would talk. I don’t know Doob. I only met him once or twice. Mark Kac I also got to know well later. In fact, at one point we were jointly co-chairs of the committee of concerned scientists, a human rights organisation, so Mark Kac and I were both co-chairs of that committee. So, I got to know him over there and also scientifically when he was working with Uhlenbeck and Hemmer . Those were wonderful people.

TPL: The situation is quite different these days, it seems to me that young people now have a very different environment in regards to what to do, whom they will meet and so on. What would you suggest young people to do now because of the very different situation?

JL: I am not so sure it’s so different. You know, at least I organize conferences on statistical mechanics twice a year and many really senior people like Freeman Dyson , Phil Anderson and Michael Fisher and other people come to these meetings. I do think that young people still have a chance to meet people like that. I guess it’s important not to be shy, so you know, people like Varadhan, he is very accessible to young people, or to other people. I am not so young anymore, so maybe I am not quite the right person to ask the question but I don’t think it’s so different, I think it’s important of course for people not to be too shy.

TPL: That’s an encouraging, positive note to the young people. In 2003 we both attended a meeting at Accademia dei Lincei in Rome. I remember we were trying to cross the street, and I did not know how to cross the street because cars kept coming from both directions. You just walked slowly and deterministically. So I just followed you. I still recall that I asked you after we had crossed the street: “You must have endured some hardship that makes you to be able to confront the present difficulty with such an apparent ease.” Does this make sense?

JL: Yes, it makes sense. It certainly makes sense.

TPL: You have scientifically started a lot of things, this meeting you have just mentioned which happens twice a year, you have an important journal, “Journal of Statistical Physics ”, that you founded, but you also have the Committee of Concerned Scientists which you are co-chairing. So, what drives you to do all of these things?

JL: Well, different motivations in different areas. Conferences are just, I enjoy doing them but I think it’s a Chinese saying about a monkey who went to brought the Buddhist, it says that even a thousand mile journey begins with one step. So you just have to make one step and you keep on going. Well that’s what at least the conferences have been. I started it when I was in Steven’s Institute of Technology in 1961. The first conference was in 1961 and I just kept on doing it. It’s the 106th coming up in December (2011).

TPL: That’s has really created very close knit family in a way.

JL: I think, at least it helped. It made statistical mechanics a friendly subject, much less strong competitive as some other fields in science. I think it has helped that. I have enjoyed doing it. As far as the Committee of Concerned Scientists, well, you mentioned, I certainly have been exposed to human rights violations myself. I think that it’s important for everyone, but I think particularly for scientists in a way. I think scientists have a kind of vision; one has a vision in science of a grand universe and a grand subject of fact. As human beings trying to understand what the universe is about, so it seems that the similarities and qualities which unite people are so much bigger than the things which divide them and therefore scientists ought to be particularly conscious of supporting good things, supporting human rights and supporting freedom. After all, some sense we know or should know what is important and what is not important. One hopes, one can actually achieve a little bit of positive results.

TPL: So we should set example for the race of humanity.

JL: I think so, I think especially those of us who are fortunate of us who live in free countries and actually have good economic conditions should feel sympathy and empathy for others in less well-off situations.

TPL: That makes sense to me. It’s not very accurate to say this, but we should make this as a religion. It’s our responsibility, our duty. You have worked on so many subjects and touch upon directly many scientists through collaborations, as mentors, as friends so forth. But could I ask a very narrow question, are there some particular moments in your scientific career in your own research that you have a vivid memory of it and you feel good about it?

JL: Yes, well, various occasions, I remember particularly once, taking a shower and finally realizing something about long range Kac potentials about asymptotic.

TPL: How old were you then?

JL: Oh, That must have been in middle 60s, so I was 35 year all.

TPL: of course, showers are always enjoyable; in whatever it is you are thinking.

JL: Of course it is, exactly. I remember thinking about Coulomb systems in trying to prove existence of several dynamic limits for Coulomb systems and long-range potentials, which Elliott Lieb and I worked on later, a proof of this thing. Being driven in a car, I was going up to the country. My wife was driving me and I was able to sit and think. Yes, so there were particular ones. It’s one of the great joys, as you know, of doing science, of doing mathematics, one gets those Eureka moments. It’s some award for the many lonesome days one spends not getting anywhere.

TPL: Those are the moments although very small, but provide good feelings for a long time. You work with Elliott Lieb, he’s quite a different kind of person from you.

JL: Different, yes, but we get along very well. We are good friends for a very long time, since we were colleagues for a very short while at Yeshiva University. We did our first paper was about heat conduction in harmonic crystals. That was 60s also. We have worked on and off together for a long time. We both live in Princeton, he is at Princeton University but I am at Rutgers but both live in Princeton, and we still do some work together. In particularly, we have a tradition now, I guess four times a year, at Elliott’s birthday, his wife’s birthday, my wife’s birthday and my birthday we get together for a birthday celebration, a celebration for a birthday dinner. Yes, I have worked with some very good collaborators and people. I have Eric Carlen as a colleague.

TPL: He moved there a few years ago.

JL: Yeah and so we have been working together. Also a little bit from kinetic theory, I have established some work with Clément Mouhot .

TPL: I see, that I didn’t know.

JL: We have just started; we just started having some correspondence.

TPL: Smart young guy, I know both of these young collaborators of yours well. It’s very nice that good young people keep coming up.

JL: That’s wonderful. They seem to get younger and younger.

TPL: I like your perspective, life is getting better and better as one gets older. That’s true, because in your case this is very true because you are still full of energy and that is a phenomenon. We know there are people who continue to doing research for many years but you probably have set an almost L∞ norm. So since your first paper and now, for how many years you have been continuing to do research?

JL: 1954 that was the first paper, so it has been 57 years. People have done much longer. Phil Anderson, he is now 88 and Freeman Dyson is 88 too. They are both still working. Joe Keller is 87. So I still got something to look up to.

TPL: So you are still a young guy. What’s your interest lately, what is your recent interest?

JL: Well it’s still non-equilibrium statistical mechanics.

TPL: How do you define non-equilibrium statistical mechanics? What is it?

JL: Well, it’s if you wish, kinetic theory but on a more microscopic level. I mean it’s just what happens, it’s a time evolution of systems but also a stationary state, non-equilibrium. It’s the kind of problems that is from kinetic theory but actually not starting with Boltzmann equation or Navier-Stokes equation but starting with more microscopic dynamics. Also I am interested in the quantum mechanical aspects of these phenomena. But in general, I guess non-equilibrium is like non-linear. It’s everything except the very small piece, which is equilibrium. Everything else is non-equilibrium.

TPL: Equilibrium is a particular case.

JL: Yes, that’s like the linear case which is very special.

TPL: Yet most of the action has been to this very particular case.

JL: You know, that’s like looking for the keys where there is light. You know that story.

TPL: Now, I have a general question put on you. I am asking this question because I remember I asked another question of how did Boltzmann come up with his H-theorem and why logarithmic function. I asked that question to the audience a few times and people give me various answers. Peter Lax said that in information theory there is the entropy. But that was much later after Boltzmann initial idea, so I told people more than once that Joel Lebowitz has the best answer which is that, Boltzmann must have tried a number of functions.

JL: He certainly did. Actually, I don’t know exactly, in Boltzmann’s writing he realized that if you add the thing about entropy being equal to the log of the phase space value, I mean that $S = k \log W$ is on his grave stone. If you consider a system where you can neglect potential energy and you ask the given one particle distribution, what is the corresponding volume in the 6th nth dimensional phase space, then you get essentially $f \log f$ and $-f \log f$. You get just for the log of the volume and the phase space, and if you are on the energy surface you specify. I think both one expresses that. So this is just really exactly equal to log of the phase space one is given by $f \log f$. so you should think of $f$ as an empirical distribution and ask which $f$, what does phase space volume correspond to different $f$ and you find that it is given by $f \log f$ and therefore you want to maximize that, if it’s a minus sign you want to maximize that. At least the way I like to think of $f \log f$.

TPL: Of course, this is the after his initial H-theorem.

JL: No, I am sure you are right about that he tried many things. I guess he must have had that eureka moment also, where he discovered that he could do so.

TPL: My question actually was the following, in the 19th century; mathematics was very much central to this scientific technological development, there were people like Laplace , Faraday and so on. Mathematics of course is essential to science but mathematics department on the other hand may be doing activity within mathematics department. In teaching we still teach the basic courses, calculus, linear algebra and that are any civilized person should know. On the other hand, research we have done in most department of mathematics is it correct to say that it is not as essential to scientific development as in the 19th century?

JL: I am not sure I understood your question. You’re asking present day mathematics.

TPL: Present day mathematic research within department mathematics is it as weaved into scientific development technology as we see computer, biology and so on. Do you think we are still in a central position?

JL: I think mathematics is, not necessarily all the research done. You know mathematics has become some branches very abstract. But surprisingly of course it turns out many times even most abstract mathematics does find its way to applications.

TPL: Like number theory.

JL: Yeah, it finds out. So, I think many mathematicians, certainly do not work on problems related to natural sciences, the way they did in the 19th century. There’s an interesting article, long time ago by Freedman Dyson at some point who were saying how mathematicians have missed out on not spending more time essentially on Maxwell equations. He thought that was one of the things we as mathematicians should have come into much earlier over there. But I think, mathematics has its own internal dynamics. But it is still true; Wigner has a famous saying that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it. It really is surprising and keeps on going for all time.

TPL: Mathematics has its own dynamics and the beauty of this is that we should let our human curiosity carry wherever we are.

JL: Exactly. I mean, I have read again, a little bit recently, an essay by Wigner of course and it really is remarkable. Did you ever read the essay? He starts out with a story, there were these two college roommates, one of them did something in business, and the other one became a statistician. They met and he asked what he is doing and he said he was doing statistics about the distribution of heights of some other people. They show a graph and here is a formula. This other guy, there was a simple $\pi$ in there and asked what is $\pi$. Well the circumference of a circle. The guy says: “Surely you must be joking. How does the circumference of a circle have anything to do with the distribution of heights? You must be pulling my leg.” It’s there. So it is surprising, it is there.

TPL: But what do you do when you are not involved with science or concerned with science activity. What is you hobby?

JL: Good question. If I have too much time I like to swim, I have a swimming pool. I like to go to the movies; don’t have too much time for that. When I was young, I used to do ceramics at one time. But that was a long time ago. But tone of these days maybe I will get back to it.

TPL: Ceramics, I see, that involves a lot of things right? There’s a sculpture part of it there is a chemical part.

JL: No I wasn’t involved with the chemical part, just the making part and decorating and glazing. Yesterday we went to the National Palace Museum and I enjoyed looking at the wonderful ceramics from a long time ago.

TPL: Which periods, there are several periods, first, just one colour and then several colours and so on. Which period do you like?

JL: I don’t know enough about periods. I like the simple kind of stuff, the ones which are not over decorated. The ones which are just some of the single coloured sculpture vases. I like particularly there was one pot, I don’t know form which period which had grayish blue glaze with some spots of heavier blue, kind of informal, not very done. Mostly I like the ones which are not so controlled, things which look as if they were freer. I like that and I like very much the calligraphy also over there. There were two parts of the museum that I liked the best. Most of them are really beautiful, I like that. Of course, the ceramics sculptures are also interesting also, I mean the horses.

TPL: Right, that’s earlier one, that’s Tang Dynasty. The one color ones are from Song Dynasty.

JL: That’s beautiful things, I mean when I was in China in 1986; I visited the Academy in Beijing. I don’t know if you know Hou Be Lin. He was my host at that time and we went around and rode back on little horses, contemporaries one. It was wonderful.

TPL: I have heard some physicists try to work on biology and try to apply ideas from statistical mechanics to biological studies. Of course in social science that has been done. Now have you ever thought about the role of mathematics in biological studies?

JL: Well, I have thought about it yes, and I am very interested personally in it. Unfortunately, for myself, I found that it requires too much knowledge of biology. It’s not so easy to get in to doing that. But, I have strongly encouraged my students, some of them to try to go in that direction and some of them have done very well in fact. I had a graduate student named Peisen Zhang, he was from Beijing, and he has made quite a good name for himself in biology, more in the computer aspects of analysing DNA and other kind of things. He is just moved from Cold Spring Harbour, one of the top places in biology, he has moved to Texas, A&M University. He got some big professorship.

TPL: In which department?

JL: In biology, I don’t know which department of biology.

TPL: Right now? So he is a biologist now? That’s nice

JL: He has switched over. I think he is one of the really success stories, I mean he is recognized as a biologists. I don’t think he thinks of himself anymore as a physicist. He was a student, a physics student at Rutgers. I have had a post-doc from Germany who now has got his own lab of 25 people in Berlin doing purely biology. So there have been transitions but apparently, it’s still just on the verge, so to speak, of combining biology which really deals, biologists in general think of very specific, specific functions, specific organs, in mathematics which tries to make general theories it still needs some time to get them together. But I think it’s undoubtedly, I think going to be a part of mathematics; I mean mathematics is going to become a part of biology. I don’t know whether it is to the same extent that mathematics and physics became. It is such a fascinating field and I do think that mathematics has something, has a lot to contribute, but it has to find the right niche and the right place. It takes biologists a long time also, but they don’t understand the mathematics.

TPL: But the couple of success stories you just mentioned also, having mathematics training was useful to them.

JL: Yes, I think it was useful but maybe more as a background. Though maybe for Michael Jiang it was more than that because maybe I think he is doing some kind of computational biology and there is a background for more. For the other person, there is certainly more a way of thinking about it and trying to find general features, asking the right questions and things like that. The Institute for Advanced Study in Princeton has got a biology group over there and it is not clearly how it is going to work out. But they have been convinced that this is the right direction to go at least.

TPL: Yeah, so you will encourage mathematics talented students given the opportunity should at least give himself a chance in biology.

JL: Exactly, I have one student at the present time and we have made contact. These people come from statistical mechanics but work in biology, they kind of ask different questions but different ways than biologists would ask, in particular, you have data from firing of neurons in the eye and then you try to infer some effective interaction between them by using maximum entropy way of taking the data and putting in the form of a statistical mechanics problem. Then see, because you measured two body correlations, two points, and see if you can get higher order correlations using this method of constructing effective interactions.

TPL: I see, so there are different ways one can enter into biology. One is to try to see where the ideas in statistical physics can be applied. Another is to simply use mathematical training as a cultural background.

JL: Exactly, but it is important part is that one really has to be in contact with biologists, with people like that. Otherwise, many times, it is like doing theorems of both a spherical code, which doesn’t really work that way.

TPL: That’s good. It’s very nice to hear what you have thought about these things.

JL: I am very interested in that myself. I keep on hoping I will find some problem for myself to do. Actually a long time ago, somebody who worked with Joe Keller also, Sol Rubinow , he died some time ago. But before that, he went to Cornell medical school and he was doing biological type of work and I worked with him actually and we did something. Well we tried to do something medical but it didn’t work, trying to see optimal phase of giving chemical therapy for cancer patients. It seemed to be too complicated to really work.

TPL: So you have always been keeping a keen interest.

JL: Yeah, I think it is fascinating.

TPL: What you think the reason for your abundance of energy.

JL: I think genetic.

TPL: I guess that’s the most important. You have abundant energy. Also, you are not afraid of doing things in a new way. I would look forward to get together with you in the near future. Thank you very much.

- Tai-Ping Liu is a faculty member at the Institute of Mathematics, Academia Sinica.