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Interview of Saul Teukolsky by David Zierler on February 4, 2021,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
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Interview with Saul Teukolsky, Hans A. Bethe Professor of Physics and Astrophysics at Cornell and Robinson Professor of Theoretical Astrophysics at Caltech. Teukolsky recounts his childhood born in a Jewish family in South Africa, and he explains the tensions between his parents’ politics, who were accepting of apartheid, and his own views which rejected this as a national injustice. He describes his undergraduate education at the University of Witwatersrand and the impact of the Feynman Lectures on his intellectual development. Teukolsky explains his interest in pursuing general relativity for graduate school, and he discusses the circumstances leading to his enrollment at Caltech, where he studied Newman-Penrose equations and perturbations of the Kerr metric under the direction of Kip Thorne. He discusses his year-long postdoctoral research position at Caltech and his subsequent decision to join the faculty at Cornell, where he developed the gravitational theory program. Teukolsky explains the significance of the Hulse-Taylor discovery at Arecibo on general relativity, and he describes the early impact of computers on advancing GR research and specifically on numerical relativity which he worked on with Bill Press. He discusses the rise of computational astrophysics, and he surveys his interests in pedagogical issues in physics and his early involvement in LIGO and the LISA collaboration. At the end of the interview, Teukolsky explains how he has tried to communicate astrophysical concepts to broad audiences, and he expresses optimism that massive advances in computational abilities will continue to drive forward fundamental advances in the field.
This is David Zierler, oral historian for the American Institute of Physics. It is February 4th, 2021. I am delighted to be here with Professor Saul Teukolsky. Saul, it’s great to see you. Thank you so much for joining me.
To start, would you please tell me your titles and institutional affiliations? And you'll notice I pluralized both, because I know you're in more than one place.
Right. So, I'm the Hans A. Bethe Professor of Physics and Astrophysics at Cornell. But that’s now a half-time position. And for the other half, I'm the Robinson Professor of Theoretical Astrophysics at Caltech. This arrangement has just been for the last four years.
These are both paid positions?
When were you named to the Bethe Chair?
Did you meet Hans?
Oh, yes. I arrived at Cornell in 1974, and Hans retired in 1975. That’s when he started his new career in astrophysics, when he became professor emeritus. My office was two doors down from him, and I became quite friendly with him. But actually, what got me even closer to Hans and his wife Rose was that my wife and I became friendly with their son, Henry Bethe. Henry was an expert bridge player. My wife and I play tournament bridge. [both laugh] So we actually became friendly with Henry, and this was a second connection to Rose and Hans.
That must have been incredibly meaningful to you, when you were named the chair in his honor.
Yes, very much. Very much so.
I want to ask a question sort of in the moment. And that is, in theoretical physics, have you found the past ten months to be an opportune time, in this moment of physical isolation, perhaps to work on equations or papers that you might not otherwise have gotten to? And on the flip side of this, even though you don’t rely on laboratories and physical interaction for experiments, in what ways has the lack of in-person, interpersonal relations been a hindrance to the things that you've been interested in studying lately?
I would say that things have actually been difficult, because a lot of things that you take for granted when you're having in-person interactions just take longer to do online. Everything has to be arranged ahead of time. It’s very difficult to spontaneously interact, although we have some workarounds. So, for example, I had to teach my course online, and even though it was a course I had taught before, just transferring my lectures into a form that I could use for the students online was very time-consuming.
But to put it into perspective, we were already set up in a certain sense for online work. I'm part of a research collaboration that extends beyond Caltech and Cornell, so we were already having online meetings. We’re used to having collaborators in Europe and Asia and dealing with time zones. We're all au fait with Zoom and Google Meet and this kind of thing. And so certainly compared to other businesses that have had to adapt, I would say we've had it a lot easier. And no comparison to the grocery workers and the people who have really been the heroes of what’s been happening.
But as you emphasize, the spontaneity of in-person interactions, the so-called hallway meetings or coffees that you have, that really does yield important scientific work that has been lacking over this past ten months?
Right. And it affects the students. I have a lot of students right now, they're all sitting in their apartments, all over the world, basically isolated. In the past, if they had a question, they could just walk down the hallway and talk to me or one of the more senior graduate students in the group or someone like that. Now, we use an application called Slack, which has become very popular also in the business world. It’s something we've been using for a long time. It attempts to duplicate this kind of interaction—you post something, it’s quicker than email, and more informal. But it’s still not the same as getting that personal interaction. I have a couple of students who seem to me to be quite depressed. Just being stuck inside and not having that social interaction is very difficult.
Saul, in what ways has remote teaching made your dual appointment between Pasadena and Ithaca easier? Or was the arrangement set up so that semester by semester, you would only have responsibilities in each location?
We're set up so I would be one semester in each location, so that’s not been an issue.
Let’s go all the way back to the beginning, Saul. Let’s go back to South Africa. Let’s hear about your parents, first. Tell me about them and where they're from.
My father was born in Poland in 1901, but when he was two years old, his family immigrated to South Africa. And on my mother’s side, my mother was born in South Africa. Her parents were from Lithuania, and they also came in the early 1900s, part of this huge wave of Jewish immigration from Eastern Europe and from Russia. All these families went wherever they could get a visa, basically. So, some relatives ended up coming to the US. Some went to England. Both my parents’ families ended up in South Africa, just because that’s where they could get in.
Is your sense that it was anti-Semitism primarily that was pushing them?
Yes, there were pogroms in the late 1800s and early 1900s. It was not a good time to be Jewish in those areas, and a lot of people left.
How long had your mother’s family been in South Africa by the time she was born?
About 20 years. My mother was part of a big family—there were ten children in a small farming town called Aberdeen, in the middle of nowhere in South Africa. She was one of the middle children. And so, I have a large collection of first cousins on that side of the family.
Did your father have memories of Europe?
No, he was too young when he left.
And where did his family settle?
They wandered around a few places, in Kimberley for some of the time, I believe, where the diamond mines are. But eventually both my mother and my father ended up in Johannesburg, which is the main commercial city, a population of a million people, right in the middle of the gold mining area.
Did your parents come from families who had religious backgrounds?
No, they were not very observant. It was a typical social thing where they all wanted their children to be more observant than they actually were.
And this caused some tensions.
[laugh] And where did your parents meet? In Johannesburg?
In Johannesburg, yes.
Were they set up?
I don’t know the story. My parents didn’t share that kind of stuff, and I never thought to ask.
Saul, is your sense from your parents’ generation that the Jewish community in Johannesburg was pretty tight knit? That there was maybe one degree of separation at most between everybody?
Socially, yes. It was 100,000 people or something, so it’s not a small group of people. But certainly, everybody knew everybody’s business. [laugh]
Observant or not, did your parents belong to a synagogue?
Oh, yes. Yes. Not that they attended. [laugh]
But in South Africa, it’s different than the United States; there aren’t the divisions between Reform and Conservative and Orthodox?
There were two divisions; there was Reform and Orthodox. And the Orthodox was not the ultra-Orthodox. It was sort of more what today would be called I guess Modern Orthodox.
Right, right. Were there Charedi, or however you would say that, in South Africa?
That was a very small community in those days. Remember, I left 50 years ago, so things may have changed-- [both laugh]
And Saul, you were born in Johannesburg?
I was born in Johannesburg, but when I was three months old, my parents moved to a town called East London, which is a coastal town, had a population in those days of about 100,000. They bought a hotel there. So, I actually grew up in East London, a few blocks from the beach.
Was that your parents’ business, real estate?
No, no. Running the hotel. They were in the hotel every day. In those days, most hotels were not part of some corporate chain or anything like that. If you ran a hotel, you did everything. So they were in the office, would greet people when they were checking in. There was a bar, which was open to the public. There was a restaurant. There was a dining room for the guests. They did everything. And I grew up in this environment. We had an apartment next door. And I didn't think much of it at the time, but I mean, in retrospect, it’s pretty strange. Apparently—I don’t remember this, but according to my mother, she once cooked something at home that I didn’t like, and I said to her, “I don’t have to eat this! I'll go to the hotel!” [laugh] And I would go to the dining room in the hotel and order off the menu.
[laugh] Saul, I'm curious, even from an early age-- I understand that the impact of apartheid was not monolithic across South Africa; in other words, in some places, it was worse than others. Growing up for you, what do you remember in terms of how pervasive these divisions were?
It was everywhere. So East London, as you can tell by the name, was settled by whites from Britain. They came in the 1800s, during the colonial era. The government that came into power in 1948 was run by the Afrikaner whites, and they were the ones who implemented and formalized apartheid as the national policy. But the attitudes of the majority of the whites, whether they were English-speaking or Afrikaans-speaking, were pretty monolithic.
There were pockets of opposition. Particularly the Jewish community was very split. My parents were ardent government supporters. They really were into apartheid. But there was a very small South African Communist Party, and there were other small groups that were opposed to apartheid. There were a lot of Jewish members of those organizations. So, there was a split in that way. But in terms of just say, going out into town, apartheid was everywhere. And as a child, you don’t think about these things. It seemed normal—this is what you encountered. It was only when I was about 15 or 16 that these things began to bother me.
Saul, it’s a very historically complex and sensitive question, but given that both of your parents’ families were refugees, where their whiteness was irrelevant to how they were treated in Eastern Europe, did they ever reflect on the irony of their whiteness never being an issue in terms of their success and acceptance in South Africa?
Well, as I said, I became more politically aware when I was a teenager. And like a typical teenager I—let’s say I brought this up in a not very polite way, with my parents. And they got very upset about this. Because, I think, deep down, they did understand the incongruity of their position. But this didn't change their attitudes. Basically, their rationalization was that they both came from relatively poor families, they had worked hard to build up a business, and they felt that whatever they had, had come from their hard work. And I think they really felt that the majority of the Blacks in South Africa were unable to accomplish what they had accomplished. So, they didn’t take kindly to my suggesting that maybe they had been able to accomplish what they accomplished because they had cheap Black labor to work in their hotel. So, this caused a lot of arguments in our family.
Given that you grew up in the hotel environment, did you develop any friendships with any of those Black employees?
Oh, yes, lots. For example, in our own apartment, we had two Black servants. One was a maid and nanny, and one was the cook. Since my parents worked a lot of the time, before I went to school I was essentially brought up by these two women. And the one in particular, the cook, taught me to read. I was very close to her. And I had other friends. There was a mixed-race handyman for the hotel, who did all the repairs. I would hang out in his workshop, with all of the tools, and he would show me how to use a screwdriver and all those kinds of things. I was a curious child. So, despite apartheid, it was quite common for white children to be in contact with non-white adults. It was only when you became an adult that you were expected to stop this.
Did your parents live to see post-apartheid South Africa? Or did they at least live long enough to see that change was coming?
No, my father died in the 1980s. And my mother moved to Ithaca after my father died. So by the time Mandela was elected, she was already living in the States.
How did she feel about those changes? Did you engage her in those kinds of discussions?
It was still fraught. She never really changed her views.
Saul, what kind of school did you go to as a young boy?
I went to a government school.
What does that mean, government school?
Well, unlike England, [laugh] where public means private and private means public—this was a public school, where any white citizen could go. It was government-funded. It was an all-boys school. There weren’t too many co-ed schools in those days. And then there were also some private schools. Some of them were religiously affiliated, convent schools. Some of them were just private schools modeled on the British paradigm, where you actually paid fees to go to. Fortunately, I was not sent to one of those. Those were mainly boarding schools. So my school was a couple of miles from my house, and I would take a city bus to go there. When I was older, I could ride a bike to go to school.
Were you always interested in the natural world, even as a young boy?
Yes, I guess so. I was an omnivorous reader. My mother was very good about keeping books in the house, getting me books either from the library, occasionally buying books and so on. But if I look back to what I read—I certainly gravitated towards books about scientific things. And I don’t know whether you want to take this as a sign, but there was a neighborhood boy that I was friendly with, who was about three years older than me, and he had a chemistry set, and I must have expressed some desire to my parents, because for my seventh birthday, they bought me a very small chemistry set. It had about four chemicals in it. You couldn't do much. But I certainly never followed the instruction book about experiments to do. One of the first things I did was put some sulfur on the blade of a pen knife and then set it alight to watch the beautiful purple flame, and smell the pungent odor of the burning sulfur. But, you know, I was seven years old, and when I wanted to put the flame out, I treated it like a match, and shook it.
And a blob of sulfur landed on the curtain and set the curtain alight.
So, in retrospect, my parents were hopelessly naïve. I mean, they had no clue. They hadn’t gone to college. They didn't know anything about science. Giving a 7-year-old, unsupervised, a chemistry set-- [laugh]
When did you start to exhibit real academic talent in math and science?
Well, I don’t know about the talent part. But school was always very easy for me. I was always top of the class. But my schooling was pretty bad. This was the 1960s, but the schooling was still modeled on Victorian England. Even the English had moved on by then, but we had inherited this system from colonial times, and so everything was about following a curriculum that was absolutely laid down. Exams consisted of regurgitating what you had been taught in class. There was no sense of encouraging creativity or trying to apply what you had learned into new situations. So, I found it very easy to regurgitate stuff. I had a good memory. If you showed me once how to do something, I could do it again. I was a good parrot. Do you detect some bitterness in my attitude about this?
And your high school was all boys, straight through?
And would you say, looking back, you had a strong curriculum in math and science?
No, we didn't. For example, we didn’t have calculus in twelfth grade, or anything like that. What can I say? I didn't look forward to school. I wasn’t excited about learning new stuff. I thought most of my teachers were pretty boring. It was not very inspiring at all.
In terms of either your family’s financial ability to pay for school, whatever cultural expectations there might have been to go far or stay near, what opportunities were available to you? What kinds of colleges did you think you were in range to apply and be accepted for?
There were only government-funded colleges, so there was a standard tuition across the whole country. And most whites could afford the fees, which were pretty low.
But going abroad, like an Oxford or a Princeton, that was—?
No, that never entered my mind, to do that. I was becoming a little more savvy, now, about this kind of thing, and I didn't see any reason. I understood that if I was going to have any kind of an academic career, I would have to go abroad for postgraduate work. But there didn't seem to be any compelling reason as an undergraduate. There were a few people I knew who had gone to Oxford or Cambridge or something like that, but that just didn't appeal to me. The best of the South African universities were the University of Cape Town and the University of the Witwatersrand, which was in Johannesburg. So, I was happy to go to Johannesburg, because that’s where my family was from originally—I still had relatives there.
And also like the British system, you declare a focus or a major right away, as a freshman.
That’s correct. So I enrolled for a bachelor of science degree, which meant that I only did science courses, and I had to do one half-course in the humanities. And not only that, it was a selection from a very short list. So, I selected the philosophy of science.
And that was my half-course, and everything else was only science.
So, you were set on science, but were you particularly focused on physics from the beginning?
No, no. [sigh] I didn't know really, what a physicist did! My high school science curriculum involved things like Boyle’s law and Charles’s law, from I don’t know when, the 1700s. And Ohm’s law, and Snell’s law. [laugh] This was all ancient stuff. There was no relativity. There was no quantum mechanics. I mean, I didn't even know what I didn't know. And the thought of—I mean, taking a glass block and measuring angles of refraction—who wanted to make a career out of that? I just didn't know—
—what you would do! It was just that I seemed to have more talent for the sciences, or more interest. I enjoyed doing those things. And I wanted to find some avenue, but I wasn’t quite sure what it was going to be.
So how then did you settle on physics? Was it a professor?
Well, you had to declare two majors, but you took four courses per semester. So in the beginning, I took Math 1, Applied Math 1, Chemistry 1, and Physics 1. It was pretty clear after the first year that chemistry was not my forte. I did not do too well in the labs.
You also burned your mother’s curtains, as a 7-year-old. [laugh]
Well, yeah, so that was probably a sign right there. So I stopped taking chemistry after my first year. The parts of chemistry I enjoyed were actually more the physical chemistry anyway. So for a while, it was between math or applied math or physics. And then I guess the turning point came in my second-year physics class. I had a terrible instructor. It was really deadly dull. We had the Sears and Zemansky book as our textbook, which I found very boring. But the instructor did one very good thing. At the end of the year, he suggested that we might read The Feynman Lectures on Physics. Most of it was material that we had supposedly covered in these first two years of physics. And the stuff I was reading there, the way it was presented bore no resemblance to the way I had seen it. It seemed so fresh and interesting and made all these connections. I got very excited.
I actually remember, for me there was a precise turning point. It was when I read the part where Feynman talks about an electron moving parallel to a wire that has an electric current. The current generates a magnetic field, which exerts a magnetic force on the electron. And so the electron moves closer to the wire. Then he says, “Now imagine you're riding on the electron. So, you're at rest, and the wire is moving. Now, because you're at rest, there’s no magnetic force. It requires you to be moving, to feel the magnetic force. So how come you get closer to the wire?”
And then he goes on to explain how, with relativity, you can understand it. I was completely bowled over by this. It introduced me to a whole wonderful new feeling that there was all this exciting stuff out there. I can pinpoint it to my reading that section in that book. That was when I really got excited about doing physics.
Were there any professors, as an undergraduate, where you were able to connect your personal excitement with their knowledge and expertise?
I'm asking because as you tell it now, you're not exactly on a path to become Kip Thorne’s graduate student at Caltech. There’s something missing here.
Well, so the other part that’s missing was, back in high school, when I was interested in science, I got fascinated by Einstein. I wanted to understand what the fuss was all about. So, I read some books—popular books about relativity, including some written by Einstein. And I found them very frustrating because I couldn't understand them. They would explain these things, and some of them even had a little bit of algebra, which I could reproduce, but I just didn't get it! And in particular, I read Einstein’s description of general relativity and I understood the “general” was because you could use general coordinate systems—suddenly, you didn't have to have the nice x, y, and z that we learned in geometry, but you could have any coordinates! And then I said to myself, “How the heck do you measure anything? If x, y and z can be any coordinates, what does it mean to measure something?” They wouldn't explain it!
Then when I was an undergraduate, there was no relativity course offered, so I got one of the textbooks—Adler, Bazin, and Schiffer. It was one of the well-known, upper-level books. Many hundreds of pages. And by then, I had enough mathematical skills. I worked through the book, I derived all the equations, I could do all of the mathematics. They still never explained to me how you make measurements! [laugh] So I was frustrated, in a way. I wanted to understand relativity, and nobody would explain it to me [laugh] or could explain it.
But you put that frustration to good academic effect. It was a motivator to continue to study.
Yes, I understood from this little taste I got from The Feynman Lectures that there was this interesting field out there that I wanted to know more about. And so, I think that that’s where my motivation came from.
When you made the decision that you would pursue a graduate degree, what kind of advice did you get? How did you know Caltech from Oxford from Princeton to wherever? How did you make these decisions?
That’s a very good question. The head of the department was Frank Nabarro, who was a serious academic, an internationally known condensed matter physicist. He was a Fellow of the Royal Society. So, I got advice from him. And there was another lecturer, Eddie Price, who I was quite close to, because he was the South African chess champion at one time, and I played a little chess, and sometimes he would get me to substitute on the university team when one of their players didn't show up. He was one of my lecturers, and I was a little close to him. So, they both talked to me.
I certainly understood some of the mechanics of applying to these places. You know, this was pre-internet, so the way you found out about places was you had to get the catalogs of the universities, which were in our university library. Many of the catalogs were ten years old. [laugh] So I could go to the library and look at the Princeton catalog, and I could look at the list of faculty. I learned about John Wheeler as the person who worked on relativity, and they offered a course in the subject. And I found one or two other places. So, I got it in my head that Princeton was my top choice, because then I could work on relativity with John Wheeler. And I applied to Caltech because of The Feynman Lectures, but according to my Caltech catalog, there was nobody there doing relativity.
Kip Thorne was probably a graduate student ten years earlier.
Yes. In the catalog I had, he wasn’t mentioned. I can’t remember where else I applied. I applied to maybe five or six schools.
Saul, do you remember who was listed for relativity at Caltech?
There was no relativity.
And yet you still applied.
I applied because-- Well, I had to have backup. I understood that you couldn't just apply to one place, right? I wasn’t completely naïve!
[laugh] But you knew that you wanted to focus broadly on theory and specifically on GR?
Yes. My undergraduate training was good enough to tell me that it was theory and not experiment. I don’t know if you've heard of the bubble raft experiment? It’s supposed to teach you about dislocations in crystal structures. You use a bell jar with soapy water in, and you pump air into it, to generate pressure. You blow soap bubbles—you make a two-dimensional raft of these bubbles that’s supposed to represent molecules in a crystal. And then you can study dislocations. And in the middle of this experiment, in a big lab filled with tables of students, I applied too much pressure to the bell jar, and the rubber stopper flew out and sprayed the whole class with soap solution.
So yeah, I was not cut out, I think, to be an experimentalist.
Saul, I'm curious if you applied to Texas, which at the time probably had the largest relativity group.
I think I must have. I'm sure I knew about the University of Texas, and I'm sure I applied there.
So what was the decision-making process?
Well, so the decision-process was first of all, I was rejected by Princeton. And I was crushed. I mean, it was extremely upsetting to me.
Did you know if Wheeler was still taking students, ten years later?
Oh yes. Wheeler was still active. But very early on, I heard from Caltech. I got a nice acceptance letter from Carl Anderson, who had won the Nobel Prize for discovering the positron. But I sat on this application, I didn't accept, because I waited to hear from Princeton. Then I was rejected. And I can’t remember where else. But in the end, I decided-- I can’t remember all the details of why, but I decided to go to Caltech, and I thought, “Well, maybe I'll get a chance to work with Feynman, to work on particle theory” is what I thought I would do.
Meaning that the chance to work with Feynman was well worth it, even if you wouldn't be working on GR?
And I understood that it was a good institution, and that there would be other good graduate students there. I can’t remember all the people who advised me, but it seemed to me a good place to go. I arrived in August of 1970. I had to choose courses, so I went to the library at Caltech to get an up-to-date catalog. I opened the catalog, and looked at the course roster, and there was a relativity course! And it was taught by this guy, Thorne, who I’d never heard of. And so I decided, “Well, I wonder who this is. I better look him up.”
In those days, you looked up this kind of thing in Science Abstracts. Today, of course, everything’s online and you’d use Web of Science. But in those days, it was a thick book, which had the abstracts of all papers published over a period of time. You could look up somebody’s publications this way. So I'm busy looking through this, and standing at this raised desk where these things were, and—remember, this is the summer time now, in Pasadena—and next to me, there’s-- I can only describe it as a caricature of a hippie. This young guy with long hair down to his shoulders, and a beard, and an open-neck shirt with a kind of string tie with some kind of medallion. And sandals. And I see he’s also looking in the general relativity section of Science Abstracts. So I say to myself, “Oh, maybe this one of Thorne’s graduate students.” So I said, “Oh, I see you're also looking in the general relativity section.” And he stuck out his hand and he said, “Hi, I'm Kip Thorne. Who are you?”
That’s great! [laugh]
You can’t make that up.
No. And I'm now picturing Kip Thorne with hair.
Yes, in those days, he had long hair down to his shoulders! So that was my first meeting with him. And I signed up for his course. And I finally learned how you make measurements—
[laugh] —in general relativity!
Kip was able to explain this to you.
Absolutely he understood that. And not only that, I didn't have to ask him to please explain it. He understood that this was an important part of understanding the theory, and he explained it.
Saul, aside from the general research interests that would have connected you with Kip, on a personal level, did you connect with him right away?
Yes, pretty much. Another factor was—remember, this was 1970. This was perhaps the lowest point for particle theory, in a certain sense. It’s right before the renaissance that took place in the seventies. And I remember there was some talk that Feynman gave to the graduate students, where he essentially told us, “Don’t go into particle theory. It’s dead. All these bright people have been working on it and not getting anywhere. Nobody understands it.” Basically, he told us “do something else.”
This is before he would go up to SLAC all the time.
No, he was already going to SLAC. Every year, I took Feynman’s course; it didn't matter what he was teaching. So I took the course where he taught us all about partons, which was the big experimental activity at SLAC. But I didn't get a sense during that course that he felt that everyone was on the brink of a breakthrough. It was more that they were groping to try to understand some phenomenological aspect of all these complicated experimental results.
What was Kip’s style like, as a lecturer?
Marvelous! I think he modeled some of it on what he learned from Wheeler. Because later I had some lectures from Wheeler. Both of them were masters of what you put on the blackboard, of using different colors, just of being very clear about what were the main points and what were side issues that were not the main points. And also in their expectations of you as a student.
One of the big changes for me from what I had had before was this idea that a student was expected to be able to apply what you've learned in a lecture to a problem that you hadn’t seen before. I mean, it seems strange to say it, but it was a novel experience for me. I found that compared with my US-trained fellow students, I was better prepared in mathematics. I knew more than them. But they were better than me at solving new problems. And so, I really had to work hard. It’s a little bit like doing crossword puzzles; after a while, you get better at it. And I went through, in my first year, a lot of the equivalent of crossword puzzles.
Saul, of course, you also had to be de-Victorianized, going back to the curriculum from—
Yes, that's what it was. It was a skill that you had to develop, and I had to work hard at it. So, I learned a lot from Kip’s problem sets and expectations. He was in the middle of writing the famous textbook—Misner, Thorne, and Wheeler. And so, we were taught out of Xerox copies of that book, and there was a reward if you found typos.
[laugh] And as you mentioned, of course, particle theory went through ebbs and flows historically. Your understanding of GR obviously would have been through the lens that Kip provided.
But more broadly speaking than that, where was GR generally, academically, at that point? Was it an exciting field to be in? Was it still a backwater? What was your sense at the time?
No, it was an exciting field. Before the sixties, it was a complete backwater, as far as physics was concerned. It was mainly mathematical types who were interested, since it was just so divorced from the rest of physics. But then starting in the sixties, there were a number of things that turned things around. One of them was the technological breakthroughs that made new experiments possible. Weber got interested in building gravitational wave detectors. There were other precision tests of relativity going on. There were new observations in astronomy, quasars in particular, which seemed to require relativity. There was the microwave background radiation in the 1960s. Pulsars were also in the 1960s. These were all discoveries that suddenly seemed to require relativity for their understanding in one way or another. And so, when I started out in the early 1970s, I was coming into this exciting background. Certainly, within Kip’s group, we all had a feeling that we were right at the cutting edge. That at any moment there were preprints coming in that could change what we were doing.
And who was in that group? Who was the core of people in that group with you?
Well, it was a marvelous group to be in! When I was a first-year student, there were students I guess up to their fourth or fifth year. There was Jim Ipser, Richard Price, Clifford Will. Bill Press was a year ahead of me. Alan Lightman was my contemporary. Don Page came soon after me. These people became lifelong friends, most of them, and many of them stayed in the field.
And there was really a spirit of cooperation? Everyone was helping each other? It was not more competitive? I mean, competitive in a good way.
A very good example of what the spirit in the group was like is the story of the physics problem books. We all had to take qualifying exams at the end of our first year, and one way to prepare for them was to work through some of these problem books. Most of them were by Russian authors, and because of Kip’s visits to Moscow we knew how high the standards were for physics students there. It turned out that there was no problem book in general relativity. So, we decided to write one before the Russians did. Four of us, Alan Lightman, Bill Press, Richard Price and I, spent a summer collecting all the problems we could find from existing books and courses, and also just making new problems up. We then had a lot of fun the next year trying to solve them. Those that we could solve, we put in a book that Princeton University Press published. The book has been in print ever since, and the Russians never did bring out a competitor. And I still have a folder somewhere of the problems we couldn’t solve!
Coming back to cooperation in our research, though, Kip was absent a lot of the time. He would hole himself up in his cabin on Mount Palomar to try to finish MTW. So if you wanted to talk to Kip, you often couldn't just wander down the hallway, so you talked to the other graduate students. And Kip I think actually explicitly encouraged us. I don’t know how much his experience at Princeton had been like this, but this idea of having a cohort that you can talk to is very important. And certainly, for me, when I became an advisor of students, I was influenced by my own experience and I've always tried to have students talk to each other. I think you learn a lot just by explaining what you're doing to somebody else.
Saul, this yields very important insight into Kip’s style as a mentor on an interpersonal level. But academically, what was the process like in terms of you going about putting a thesis topic together? Did Kip essentially hand them out to the entire cohort, or did you more or less come up with your ideas on your own?
No, so what happened was Kip gave me a problem. Towards the end of the first year sometime, we had a one-on-one meeting where he discussed a problem. A lot of the work in the group was focused around black hole perturbation theory. There were lots of motivations for this—there had just been some breakthroughs. Some students of Misner, who was a close collaborator of Kip’s, had worked on perturbation theory for spherical black holes, Schwarzschild black holes. So, a lot of the projects that people were working on were related to this. And he gave me a problem, which was to figure out what happens to the horizon—the surface of the black hole—when the black hole is perturbed. How does the surface actually change, how does it move, and so on? And that was my official thesis project. But I never solved the problem! That was not my thesis, in the end. And in fact [laugh], it wasn’t solved until more than 20 years later.
Which might indicate how difficult it is?
Well, or how poorly equipped I was to tackle it. [both laugh]
So the story of how I got to my thesis project was that Jim Bardeen visited Caltech on sabbatical in the Spring of 1971, which was toward the end of my first year. So I was still taking courses, but I now had an office in Kip’s group, and I was the new kid in the group, trying not to stick my head above water too much. Jim and Bill Press were collaborating on a project, which involved studying perturbations for Schwarzschild black holes. They were using an approach called the Newman-Penrose formalism that Richard Price, who was a senior graduate student at the time, had introduced into the group. This was a different way of treating the mathematics of relativity. It had been developed in the sixties by Newman and Penrose.
By the way, I left out that one of the big influences in the renaissance in general relativity in the 60s was the influx of these new mathematical methods—including obviously the work of Penrose, who recently won the Nobel Prize for this work. But also of course the work of Hawking had a big impact. Anyway, Richard had introduced this technique to our group, and then Bardeen and Press applied it to perturbation theory of spherical black holes.
One day, we were walking back from the cafeteria after lunch and Bill was telling me that Bardeen had applied this Newman-Penrose formalism to the Schwarzschild perturbation problem and had come up with some useful equations. I didn't know what I didn't know, and I said to him, “Well, if it works for Schwarzschild black holes, I'm sure it works for rotating Kerr black holes.” And Bill said to me, “No” or probably something a bit more sarcastic than that.
So, I went back to my office and sat down and looked at what Bardeen had done. This was all formalism that was floating around in our group. Ipser had worked on doing these things. Price had used it. I had read all their stuff. So, I knew enough to apply Bardeen’s approach to rotating black holes—as I said, I was a very good parrot. [laugh]
You were also relying on your mathematical abilities as well.
Well, somewhat. But really it was more pattern recognition. I understood enough about the similarities. When you use this formalism, rotating black holes have certain similarities to non-rotating black holes. I was convinced that this would be enough to do the same thing that Bardeen had done. And so, I tried it. There were actually two stages to the problem. The first one was, you have all these complicated equations, and you manipulate them to get a single equation that describes how the gravitational waves propagate. So that’s called decoupling the equations. You want to decouple them and get a single equation for this variable that you're interested in. And within a few hours, I could do that.
So the next day, I came into Bill’s office, and I said, “You see? Look!” So he said, “Oh, well, but now you have to separate the variables.” Because at this stage I had an equation, a partial differential equation that mixes up all the coordinates. You now have to get simple ordinary differential equations, one for how the wave depends on each coordinate, to be able to solve this. In the case of a spherically symmetric black hole, because of the symmetry, we knew how to do that. You know, the black hole is sitting there. It’s not moving in time. So, nothing depends on time, until you perturb it. And also, it’s spherically symmetric, so nothing depends on the angles. So you can separate out that dependence, and leave yourself with just an equation that depends on the radial variable. And that’s much easier to solve.
Now for a rotating black hole, the rotation is at a uniform speed. Nothing changes in time. So the time variable would still separate out. And also the angle about the axis, everything was axially symmetric. You could separate that dependence out. But the radial variable and the other angle—the latitude variable—they would be coupled together. You could have this oblate-shaped black hole, with a non-spherical geometry, and you'd have a partial differential equation, which especially in the 1970s, would be a bear to solve. And so, the goal became to try to see if you could separate those variables, even though there was no obvious symmetry.
There had been earlier work by Brandon Carter in the late sixties for a simpler problem, but also with rotating black holes. He had found an unexpected result that you could separate the variables for this simpler problem. So the question was, could you do it for these gravitational perturbations? And so that’s what I tried to do. I worked very hard on that, but I got nowhere. Part of this was motivated by Weber’s claims to have discovered gravitational waves. If it were true, how could you explain it? Misner had a model that it was somehow gravitational synchrotron radiation. And Penrose had discovered you could extract energy from rotating black holes, and maybe you could tap into that.
So, there were all these ideas in the air that would require you to be able to figure out what would happen if you perturbed a rotating black hole. There would be lots of potential applications. I would go to the library to look up math books on separating variables. And in those days, when you checked a book out, there would be this little sheet stuck in the front, where the librarian would write in your name, and then a rubber stamp of the date you had to return the book by. So, I could see who else had checked the book out, and it was all my predecessors… I would see Ipser’s name, and Price’s name—[both laugh] Everybody had been there before me reading these books! And I was getting nowhere. Kip even paid for me to go for a month to Maryland, to work with Misner. The idea was to see if Misner, who was an expert on many of these things, could give me ideas. But I got nowhere, and I came back feeling ashamed. You know, like I had let Kip down. He had paid for me to have this experience with Misner, and I had nothing to show for it.
But is this to say that Kip sent you to Misner because he wasn’t equipped to handle this himself?
Well, I don’t know if he wasn’t equipped, but Misner knew a lot about partial differential equations, and the hope was he would give me some suggestions for things to try, and so on. And I still got nowhere.
You needed a Plan B.
Well, yes. So now I needed a Plan B. So I wrote a small paper with Bardeen and Press on other aspects of the Kerr metric. And that has actually turned out to be one of my most highly-cited [laugh] papers, because it had some simple properties of Kerr black holes, and my main contribution was some relatively simple formulas for circular orbits, which are now widely used in textbooks, and I feel very proud of that. But again, it was not much—it’s just, you know, doing it first, and you get cited. The trick was, you got some complicated things, but if you factored them using the square root of r instead of r, you got much simpler expressions. [laugh]
And Bill Press and I wrote another little paper, but I wasn’t really getting a thesis done. So, I went back to trying my official thesis, and I was getting nowhere with that. Every two weeks or so, I would take out my notes on trying to separate variables for the Kerr metric, and I would try something new. But I still kept getting nowhere. And then finally, after maybe six months had passed, I tried one more manipulation, and it worked!
What was it? What did you do this time that you didn't before?
Well, instead of taking the fundamental variable to be this Newman-Penrose quantity, if you multiplied the Newman-Penrose quantity by another quantity that appeared in the Newman-Penrose equations, and treated that as your fundamental variable, then the equation you got separated the r dependence and the theta dependence. Why I did that, I don’t know.
And the irritating thing was these Newman-Penrose quantities came in pairs. The one I was focused on was called Ψ4 (“psi-4”). The reason I focused on that quantity was it’s the thing that describes the outgoing gravitational waves, which was what you would be interested in, from an observational point of view. There was another Newman-Penrose quantity called Ψ0, which describes incoming radiation. Who’s interested in that? You’re going to set that to zero. Well, it turned out that when I looked at the equation for Ψ0, its variables separated without having to do any fiddling. Had I only looked at that quantity first—
—I would have had immediate success.
Ultimately, though, the intellectual torture was probably beneficial to you.
Yes, it was beneficial, because it turned out there were relationships where you could relate the Ψ4 to the Ψ0 and all kinds of interesting stuff did come out of that. So now I had the result, which Kip helped me to write up. Kip was very big on writing clearly. So typically for a graduate student, you would write a first draft. This you typed, with the math handwritten. Then he would write in red pen his corrections. I remember getting the paper back, and I thought-- I was pretty good at English, you know? I was Victorian-trained, [laugh] or whatever.
And I got back this paper, and there was more red than black. He had rewritten everything! I was shocked. But fortunately, my ego wasn’t too big. I swallowed hard and looked at his suggestions, and realized that my writing was very formal, and very terse. I had a sequence of equations, with very few words in between.
It was not descriptive.
Not nearly enough. And when I did have descriptions, they were very terse. What I learned from Kip was to help the reader and to try to tell a story. And that was actually very good for me. So that’s another thing that I've tried to pass on when I became an advisor. Students will always write the first draft, and then we go through iterations. I also have my pet peeves. It’s become a bit of a joke, where the older ones tell the younger ones what to avoid, and things that I'm going to pick out in their writing. I don’t let anyone use “due to the fact that”—
[laugh] Saul, when it was time for you to defend, was this a mutual decision between you and Kip that you were ready?
No. What happened was, Kip called me in one day toward the end of my third year and said to me, “I think you've done enough to graduate. Write up your thesis and schedule an exam.” And writing up your thesis meant you stapled together your papers that you'd already written, and then you had to write an introduction, which tied them together. That was the model for the thesis. I think all his previous students had done the same thing. I was actually shocked. I thought a thesis had to be a magnum opus. [laugh] Anyway, I was going to be kicked out of this nice cocoon and was horrified at the thought of having to fend for myself. Also, there were visa issues for me. I got married at the end of my first year, so my wife’s visa was tied to mine, and she was working as a high school teacher. It was all kind of complicated.
Your wife was South African as well?
Yes, I met her in my first year of my bachelor of science degree in Johannesburg. She was also doing a bachelor of science degree. And in the South African system, there was no distinction made for teachers—she took all the same science and math courses that I did. We got married at the end of my first year at Caltech. Then she got a job at a Catholic high school in San Gabriel, a few miles from Pasadena. Every year we had to make a trip to the immigration headquarters in downtown Los Angeles, where she would be interviewed. Part of the interview was to make sure you weren’t taking a job away from an American. Based on some of our experiences there, I think actually part of the job interview was just to look at you—I think there was a racist element to this process. But anyway, we were dependent on the system. And I expressed some desire to Kip to stick around, and he just said, “Okay, we'll make you a postdoc.” So basically, I was told to get my PhD, and then Kip would keep me on for a year as a postdoc, which meant a higher salary, so I was happy with that arrangement.
Saul, the process of writing an introduction forces you to think about all of these different papers and their connections.
So both scientifically and intellectually, what were those through-lines, as you had to come up with them?
Well, besides Kip on my committee, there would be other people who were not in general relativity, but who were physicists. And the idea was that by reading the introduction alone, they could understand what the setting was for the problems that I had worked on, why they were important, and for me to summarize what I had found. And to make it intelligible to them. Again, that’s a model I follow to this day. I ask my students when they write up their theses—you staple together your papers, but then this introduction is not for me; it’s for the other committee members. How good are you at communicating with them?
Saul, I wonder if the process of writing the introduction made you think more strategically for a career, what kind of a niche you might fill on a faculty ultimately?
I don’t think the writing of that helped me formulate things. I think it was more that I did understand that if I was going to have an academic career—then as a junior faculty member—it was important to demonstrate that I could do something else, that I wasn’t stuck working on the same stuff as was in my thesis. And if we remember, we should come back to this. This turned out actually to come back to bite me. I had worked on these perturbations of the Kerr metric. I had solved a particular problem that a lot of people had tried to solve. But I couldn't make a lifelong career of doing this. I had to move on and do something else.
Not necessarily move fields, but broaden your sensibilities?
Yes. Not just keep doing Kerr perturbation theory. I could work on black holes. And that was a big enough area, but I had to move on.
Who else was on your thesis committee?
Feynman was on my committee, and I remember him very clearly, but I have no memory who the third person was! Having Feynman just blotted everything else out.
Feynman is memorable all the time, but was there something specifically memorable during the defense?
Yes. Kip would ask leading questions. Like a lawyer leading the witness. The idea was to make the student shine in front of the other members of the committee. So, he wanted me to explain why it wasn’t obvious a priori that you could separate the variables in this problem, that there wasn’t any underlying symmetry, and why this was different from using the axial symmetry or the time symmetry. There’s a technical way of explaining this, where if you've had a relativity course, I could use the words “a Killing vector,” where Killing is actually the name of a person. But I was nervous to use this term, because after all, I was supposed to be able to communicate to non-relativists. And I was getting myself all tangled up [laugh] trying to explain what a Killing vector was, without using the phrase “Killing vector.” And I could see that Kip was twisting in his chair, getting more and more agitated. Finally, he interrupted, and he said, “I'm sure if you use the word Killing vector, Professor Feynman would understand.”
[laugh] That’s great. What was the dynamic like between Feynman and Kip? Were they equals? Could you tell, in terms of their dynamic, that Kip was junior to Feynman?
No. Everyone knew that Feynman was special, had a special way of thinking about things. I had many, many experiences of that myself. But I never saw him be condescending or treat someone else as being inferior to him. The only thing that really got Feynman upset was, for example, if there was a physics colloquium where he felt the speaker was not being honest. I think he felt it was his duty to make sure the graduate students weren’t taken in. He would interrupt and ask a question or make it clear that he felt that the speaker was sweeping something under the rug. There was one occasion I saw where Heisenberg came to Caltech and gave a seminar in Beckman Auditorium. The place was packed. It seemed like the whole of Caltech was there. Heisenberg proceeded to put forth a theory that even to my novice ears sounded far-fetched. Heisenberg was one of Feynman’s heroes, so at least he waited till the end of the talk to show his skepticism, instead of interrupting in the middle.
Saul, besides delaying your visa running out, I wonder if at this point you were thinking that the postdoc was really your ticket to making a life for yourself in the United States, and not going back home?
Oh, I was never going back. I mean, part of it was political. I felt that even though growing up as a white person in South Africa I was in a very privileged position—just in terms of living standards, having servants, all of that kind of thing—it was a very authoritarian society. So even for whites, there was this very rigid way where you were expected to conform. And if you didn't conform, there were social repercussions. I just felt I didn't want to be part of that. So that was very clear to me. But then also scientifically, it was very clear that there were very few post-graduate opportunities in South Africa.
Was the decision to stay at Caltech simply the quickest and simplest means of extending your stay in the United States? Did you think about postdocs in other institutions?
Well, what I wanted to do was have this extra year at Caltech, where I would be able to start a job search. I didn't feel that I was ready to suddenly be thrown on the job market.
But you could have done that with a postdoc elsewhere. That’s partly what a postdoc is.
Yes, but by the time Kip sprung this on me, it was already toward the end of the third year.
Aha, I see.
And I was kind of-- it was late.
So that’s an important point. Really you weren’t-- what this really is about is you weren’t ready to defend when he said, “Let’s go.”
That’s correct. Yes, I hadn’t written up a thesis, and I hadn’t applied for positions. It was that kind of a thing. So, he said, “All right, well, I'll make you a postdoc for a year, but defend now.” [laugh]
To go back to the academic and intellectual side of things, to the extent that you did understand that you would need to broaden out your sensibilities in GR, was that postdoc at Caltech useful in that regard as well?
Not particularly. I spent the postdoc year doing more applications of my thesis work, really. There was a lot to be done. I was picking the low-hanging fruit, if you like.
And were you focusing on both second postdocs, which in your case would in some way be really a first postdoc, or were you focusing on faculty positions at that point?
More on faculty positions. The point is, there were some positions open. I think there were three positions open in the year that I was applying.
These were positions specifically in GR, you're talking about?
That’s correct. There was one at Yale, where Bardeen was at that time. There was one at Texas at Austin, which had the DeWitts and Matzner and a few other people. And then there was a position at Cornell, where, as I found out later, two tenured people had left, and they created three junior positions out of those positions—one of which was going to be in general relativity. So, the two people who left were Bob Wagoner—who worked in cosmology and some relativity and more astrophysical kinds of things—and also a particle theorist. So out of those two senior positions, they made a particle theory position, a relativity position, and a theoretical astrophysics position. So, I applied for the general relativity position.
Saul, do you know-- I mean, you're about the same age-- were you applying to the same jobs as Bob Wald?
Bob graduated a year ahead of me. I knew him already, because he was a graduate student at Princeton and Kip’s group was in touch with Wheeler’s group. We may have applied for some of the same positions, I just don’t know.
Right. I'm asking because I'm curious that Chicago was not one of the places that was offering a position in GR the year you applied.
No, they were not offering a position there. I think Bob was a postdoc at Chicago from 1974 to 76, after being postdoc at Maryland, and then took a faculty position at Chicago after that.
What was most compelling to you among the places that accepted you?
I accepted the Cornell job as soon as it was offered to me. I didn’t even wait to see the outcome of my other applications. It was largely because of Ed Salpeter, who was the head of the theoretical astrophysics group—I mean, he was theoretical astrophysics at Cornell. He had started out as Bethe’s postdoc in particle theory, and then decided he didn't like particle theory, and moved into theoretical astrophysics. And he used to visit Caltech, originally to talk with Willie Fowler in nuclear astrophysics. But he had become friendly with Kip, and it was a small, clubby group. Ed was visiting Caltech in the spring of this year when I was applying. There was a party for Ed, I think it was at Marshall Cohen’s house. So, Ed came, he gave a talk, and then there was a party where all the faculty were invited. And Kip arranged for me and my wife to be invited to this party so that I could meet Ed. And what can I say? [laugh] It was the start of a friendship. Even though he was very senior to me and much more eminent, we really just hit it off.
What clicked immediately?
I just hit it off with him.
And you were talking about an appointment right from there?
Well, yes. He was telling me about Cornell, and about his experiences at Caltech. But he was very down to Earth. So I felt that if I were offered a job there, I would like to be with this person. It was that kind of an interaction.
To come back to the ebb and flow of theoretical particle physics at this point, you're coming to Cornell at an incredibly exciting time. I wonder if-- It’s not your field, but just being in the faculty, what that felt like, just to be around all of the excitement.
Well, it was exciting. Besides Hans and Ed, I got to meet Ken Wilson. Ken always wore a white shirt with no jacket and tie, and wandered the hallways deep in thought with his shirt hanging out, looking very disheveled. I got quite close to Ken, because of his interest in large-scale computing—which I was starting to get into later. I also arrived right in the midst of all the excitement with charmonium. There were people working on that at Cornell. But I was enjoying what I was doing. I never felt the temptation to try to switch into particle theory.
And in fact, what happened was that more and more of the particle theorists went into astrophysics.
To some extent, yes. But of course, there was a renaissance in particle theory right around that time, with QCD.
What was your impression of the Cornell physics department when you first arrived? Did it feel culturally like a very different place from Caltech?
It was very similar to Caltech, I felt. As a contrast, I knew a bit about the Princeton physics department at that time, because as I said, Kip had a close connection to Wheeler, so we were close to the graduate students there. And I was friendly with Bill Press, who had gotten a job a year ahead of me, at Princeton. We visited there. So, I got a sense of the Princeton physics department, and it was very different, much more hierarchical than, say, the Caltech or the Cornell departments at that time.
And as a junior faculty member, this was probably good for you, that it was not so hierarchical?
Exactly, yes. The Cornell department was very welcoming. In those days, faculty socialized to a much bigger extent than we do today. Part of it was the whole sociology of the faculty wives. Today, most wives of junior faculty have their own careers, not to mention faculty husbands of the women on the faculty. There’s just a whole different way of life now. But in those days, it was very common for faculty wives to arrange faculty dinners and things like that. And they always made a point of inviting the new people. We were made to feel very welcome. We developed a lot of friendships with people through what started out as structured gatherings.
Did you take on graduate students right away?
Yes, but there was a kind of birth control that was driven by finances. How many graduate students could you support? And so the typical thing for a new faculty member then was you supported one graduate student.
And where in GR would you get funding? NSF?
Initially, the students were funded by TAs. My startup package was, “Here’s a pencil. Here’s your chalk.” [both laugh] “Be grateful we've given you an office [laugh] of your own.”
So, Ed helped me write an NSF proposal for the gravitational theory program. I had no clue how to write a proposal. Ed wrote the introductory part, and then I had to write what I proposed to do. But the budget wouldn't cover a graduate student. It covered some summer salary and some travel money for me. The idea was that if I was successful, maybe at my renewal they would increase the level, and maybe I’d get some funding for a graduate student. But theory students TA’d a lot. And it’s still true, to a large extent.
Saul, what was your understanding of the culture of promoting from within? In other words, at a place like Harvard or Stanford, junior faculty basically understood that they would not get promoted. What was your understanding of Cornell and their culture?
Their culture at that time, and still true, was that they tried to be careful about who they hired—and if you lived up to their expectations, you were quite likely to be promoted. So, it was very different. And that certainly was a factor in people accepting job offers there.
Were you made to understand, or did you understand enough on your own, that your ability to secure funding and get graduate students was very important to tenure considerations?
I think we understood that it was important, but it was not the overriding factor. The overriding factor was I had to publish research that the outside letter writers could say was of high quality and important. This work should be work that I had done since my graduate student and postdoc days. It was understood that the opinions in these letters were probably the main criterion. The other things were important—being a successful mentor of graduate students, securing outside funding, getting good teaching evaluations. These were all important things, but if they were all in place but the outside letters were damning, I would not get promoted.
In terms of the publishing, both in terms of your own inclinations and because of tenure considerations, when was it important for you to have collaborators and when was it important to publish on your own?
I don’t think that that was something we actively thought about. In those days, theorists did not have big collaborations. If you had a collaboration, it was one or two people that you worked with. And the idea was that if you had a senior person you collaborated with, they would be asked for a letter, and they would be expected to describe your contributions. So that was not an issue, really.
In terms of the topics, and as you emphasized, since your dissertation—meaning this is new stuff you're coming up with—what was that? Was Numerical Recipes or numerical relativity, was that part of it at this point, or did that come later?
That wasn’t part of the tenure thing. The most important new piece of work I did as an assistant professor followed from the discovery of the Hulse-Taylor binary pulsar. Cornell ran the giant Arecibo radio telescope in those days. My primary appointment was in physics, but I had a joint appointment in astronomy, so I became friendly with all the astronomy people. The Hulse-Taylor discovery was made at Arecibo, and so we knew about it before any publications. Taylor came to visit Cornell and I got to talk to him.
Meanwhile, the word was out. There were already preprints. The relativity community jumped all over the discovery. Everybody understood that the pulsar in its orbit was a very accurate clock moving in the strong gravitational field of its companion neutron star. Also, it’s moving at some fraction of the speed of light, so there must be relativistic effects from the speed and the strong gravity. You should be able to measure them. And so the relativists were pouring out these papers—“Oh, look for the second-order gravitational redshift. Look for the second-order Doppler shift. Look for the effect of gravitational waves.” And so on. And poor Joe was a [laugh] radio astronomer. You know, he measured arrival times of radio signals from pulsars at Arecibo. How was he supposed to relate what he was measuring to these effects that the relativists were saying he should be able to see?
And so, here’s where we come full circle. How do you make measurements [laugh] in general relativity? So, I started working out how you would see these relativistic effects in the arrival times of the pulsars. How would they be detectable? How would they change the arrival times? And for me, by this point, this was a relatively straightforward calculation in the sense that I knew what to do. I actually ended up collaborating with Roger Blandford on this, because he had also been thinking about some of these things, more in terms of what you could measure in terms of changes in the frequency domain. But that’s a technical issue.
We ended up writing two papers together. One was how this would show up in frequencies, and the other how it would show up in the arrival times. I'm very proud of the arrival time paper, because all of my frustration with how you make measurements in this theory bore fruit in this very practical application. Later on, as the detection accuracy improved, other people added smaller effects that became measurable. But ours was the first paper that showed how the arrival times are modified by the relativistic effects in the binary system.
And so that was an accomplishment that was nothing to do with my thesis work, but was apparently enough to [laugh] justify my promotion. Then what happened was around this time, Chicago advertised a position, and I was asked if I would be interested in this. And I think this came about through Chandrasekhar, who I had become friendly with while I was still a graduate student at Caltech.
This interest was before or after you were tenured?
This was before, when I was a beginning assistant professor at Cornell. And so, I didn't know if I was interested or not, but apparently-- I'm not sure whether I said something, or whether somehow Cornell found out about this. But anyway, they decided to consider me early for tenure. So, I was very grateful for this attention, and so I got promoted early, and that was very nice.
Maybe this is a good place to come back to something I mentioned earlier, about having to demonstrate that you could do work beyond your thesis research in order to get promoted. This turned out to cause some tension between Chandrasekhar and me later on.
I met Chandra at Caltech during his sabbatical in the Fall of ‘71, the beginning of my second year. He didn’t use a first name, and he had a rule we could call him Chandra once we had our PhD. We’d heard all about him from Kip, who was a great fan. During Chandra’s stay, he was virtually ignored by the rest of the Caltech faculty. He speculated to us this was because he had been the editor of the Astrophysical Journal and had been harsh with many of their papers. But of course, we knew that it was because they were all intimidated by him intellectually!
Anyway, he was alone in his office in Kip’s group most of the time, so when we graduate students went to lunch, we invited him to join us. He would tell us great stories about Eddington, and meeting Einstein, and knowing all these famous physicists who were just names in our textbooks. Chandra’s goal for his visit was to start working on black holes. So Kip arranged for me to show him the Newman-Penrose formalism. Much later, I found out that for the first half of his sabbatical, he’d been with Penrose for the same purpose. I’m not sure I would have been so confident instructing him on the subject if I’d known this at the time!
Anyway, we became quite friendly after that. He visited Cornell after I’d been there for a few years, and he asked me why I had stopped working on black hole perturbations. While I’d found some important results, I hadn’t found the solution for the complete gravitational field, only the part that would propagate out as gravitational waves. I told him that I’d tried to find the complete solution, but it seemed like it was a very difficult problem, and I didn’t see how to get anywhere with it. I also told him that I needed to move on and do something else to demonstrate breadth in my research to get tenure. He got quite upset when I said this. He felt that one should ignore extraneous pressures like this and pursue the research until the problem was completely solved. I didn’t argue with him, but I felt this was an unrealistic view of how the world works for us mere mortals. The way this story ended was that Chandra spent 12 years working to complete the solution of the perturbation problem. The calculations were so involved that he couldn’t fit them all in his book. Nobody has actually used his results because they’re so complicated. An alternative procedure has been developed, which is still being refined 40 years later. But even though I feel vindicated in my decision, I know that Chandra felt disappointed in me for not being a true idealist.
Who was your first graduate student?
My first graduate student was Peter Vitello. He had already been given a thesis project by Ed Salpeter, and basically I inherited him from Ed. He was very sharp, and finished the problem, and went off and did well.
Saul, when did you first start to realize that computers would be very useful for understanding relativity? Was this later on, or earlier during your time in Ithaca?
Well, earlier on. I think Bill Press was a big influence while I was a graduate student. Already as an undergraduate in South Africa, I had learned how to program. Our university had a machine that was available to researchers. It was an IBM with FORTRAN. I even had a summer project with Nabarro, the department head. I wasn’t very successful, but it involved some computer programming. So, I wasn’t a complete novice. But still, certainly Bill raised the level for me. We wrote a paper together that was very computer-oriented in getting the results.
What year was this, when you wrote this paper?
This was in ‘73. It involved solving some slightly tricky ordinary differential equations. By today’s standards, it wasn’t very sophisticated. But by the standards of what other people were doing in theoretical physics, it was considered—
But there’s also, Saul, perhaps a duality there—where even in its primitive stage, computers at that point were capable of being useful? But perhaps also, you, or more so Bill, understood where computers were headed.
Yes, that’s true. But there was a bigger thing that we understood. Even though, for example, I had had some success doing analytic pencil-and-paper work for my thesis, I think we all understood that if you wanted to make advances in this theory that standard mathematical techniques were unlikely to be useful. Just because the theory is non-linear, and all of our mathematics is geared towards solving linear problems. There are very few techniques for solving non-linear problems. So the idea that you'd have to, in the end, resort to computers, was certainly appreciated.
So, there were two branches of research in relativity. There were the people on the more mathematical side who didn't want to touch computers. And there were people in the astrophysical camp, who wanted to apply the theory to astrophysics or to cosmology. And here I was influenced by Kip, whose inclinations were more towards the astrophysical group. I think we all understood you were going to have to use computers if you wanted to make advances there.
Were you able to start conceiving of numerical relatively before supercomputing is really available to you? How do these dual processes work? Intellectually and technologically.
So at that time, the biggest computers were in the weapons labs. Which is still true. [laugh] Anyway, if you needed a supercomputer, you had to get access to one of those machines.
But the term supercomputer, this was in your purview already at this point?
Oh yes. I think the term was already in use in the 60s to mean a machine with much higher performance than a typical one. The Cray-I came out around 1976. One of the pioneers in the field was Jim Wilson. His day job was he was a weapons designer at Livermore Lab, but his real passion was to do astrophysics using his expertise in things that exploded or had high densities, high pressures, radiation, and so on. He did supernova explosions and also some of the first work on gravitational collapse of stars. So, certainly we knew about his papers. By the way, he also collaborated closely with Hans Bethe on supernovae.
I was also friendly with Larry Smarr, who was a graduate student with Bryce DeWitt. Bryce had a connection to Livermore. So even though Bryce was very much in the mathematical relativity mold, he also knew about numerical techniques and inspired some of the early work in the 60s in numerical relativity. And so through this connection, Larry’s thesis involved doing numerical relativity, trying to do the head-on collision black hole problem. The first work on that had been the 1964 paper of Hahn and Lindquist, which also originated through the weapons lab connection, I believe. So, certainly numerical relativity was in the air, if that’s the right expression.
When did you first meet Jim?
I'm not sure. There was a summer workshop sponsored by the Battelle Institute in Seattle in ‘78 where he was one of the lecturers. By then I already knew him well. A typical Jim computer code would start out with “A1 equals this, A2 equals this, A3 equals that.” There was no explanation or comment what A1, A2, A3, were. He would never think of naming them density, pressure, or whatever, because that was more typing and consumed more computer memory. Larry had spent a summer at Livermore working with Jim. We used to tease Larry that his biggest contribution to science was commenting Jim’s Wilson’s code so the rest of us could use it. [laugh]
[laugh] Are you in touch with Bill Press during this early time?
Oh, yes, I was in touch since our graduate student days.
No, but I mean specifically as the field of numerical relativity was developing. Basically, it’s the origin story of Numerical Recipes, where that comes from.
No. Numerical Recipes and numerical relativity had separate origin stories for me. My numerical relativity work came about at Cornell because I started collaborating with Stu Shapiro. You remember I told you that Cornell created three positions out of the two senior people who left. So, the theoretical astrophysics hire was Stu Shapiro, who had been a graduate student of Lyman Spitzer’s at Princeton. He had done some numerical work in relativistic astrophysics as part of his thesis. I started collaborating quite closely with Stu.
Our first numerical relativity paper was in 1979. It was on the gravitational collapse of a spherical star. By then, Stu and I were alternating teaching a graduate course on numerical methods in astrophysics. It started because we used to get these second or third-year graduate students coming to work on a thesis, and they had taken all these fancy mathematical courses and stuff like that, and then they would come in to the office and say, “I've been doing such-and-such, but I'm stuck.” And we’d say, “Well, why are you stuck?” And they'd say, “Well, I got this integral. I can’t do the integral.” And then we would say, “Well, do it numerically.” And they would kind of give us this blank store. You know, “What does that mean?” They didn't even understand what we were telling them to do. [laugh]
And so we started teaching this seminar course, a crash course. It was restricted; you had to be a third-year student or above so it wouldn’t interfere with the bread-and-butter graduate courses. It was aimed at the students doing their thesis who needed to quickly learn something about numerical methods. Just jumping ahead a little bit, a few years later, the chairman of the department asked, could we have an undergraduate course like this? I thought about it for a while, and decided, well, why not? So when the course was given, it was the same course, but it was listed under two different numbers in the Cornell catalog—it was a 400-level course, which was open to undergraduates, and a 600-level course, which was open to third-year graduate students and above. And then eventually, it was open to anybody. But in the beginning, it was a Cornell-based thing, focused somewhat on astrophysics.
At the same time, Stu and I had also been alternating teaching a course that was called Compact Objects, which meant black holes, white dwarfs, and neutron stars. There was no good textbook. So based on this course, we started writing a textbook together. It came out in ’83. But in the meantime, I had a sabbatical, where I went to Harvard, where Bill was.
Specifically to work with Bill? That was the motivation?
Yes, and also there were other people there, like Phil Marcus, but Bill was the main attraction for me. During that time, Bill had already started on what turned into Numerical Recipes. He had had a similar experience of none of the graduate students knowing anything about numerical methods. He started a course in self-defense, and wouldn't it be great to have a book. He asked if I was interested, and I basically said, “Well, maybe, but I'm busy on this book with Stu, and I can’t take on another book now, and talk to me later.”
Saul, it’s always such an interesting intellectual decision to know when you have something that’s an article, and when you have something that was a book. So from your vantage point, because you weren’t the driver of that particular decision, but obviously it needed your buy-in, what were the factors in deciding to go with a book? Is it that it’s so complex? Is it that you need a lot of description to convey the ideas? Why a book?
I think that most faculty in the sciences write a book out of frustration with what’s there. You have this feeling that there’s nothing that meets your needs, as a teacher.
Pedagogically, you're saying?
Yes, it’s pedagogical. Or maybe as a monograph for your field. If you have a new student coming into your field, and you want them to get up to speed, you'd like to give them stuff and say “Read this. Bring me questions. And then you can start on this problem.” And I think that’s the motivation for academic books in the sciences—it’s either for a course, or as a monograph.
Yeah, but Saul, in this field, if I may, it’s not as if there was a whole bunch out there to improve upon. It’s a bit of a unique circumstance. You're creating a field, in a way.
Well, yes. So, there’s a distinction in the two books I was involved in at that time. There was first the Black Holes, White Dwarfs book. The existing books weren’t adequate. They were out of date, and they didn't have the right perspective on the field, which was to us, the important thing. They were mainly astronomy books; we wanted more of a physics book. We felt that this was a new area for physics to pay attention to, that physics could both inform the astronomical discoveries that were going on, but that the astronomical observations could teach us about nuclear physics and things like that. We were going to discover what the nuclear force was, not by solving QCD, but by measuring properties of neutron stars. Things like that. And so, this had to be taught in a way that emphasized the fundamental physics. There had to be just enough about the observations so the students wouldn't be lost. We understood that the observational part of the book would become obsolete, which it did, but that the fundamental physics would still be useful. And you know, it’s almost 40 years later, and people still use that book, because the physics hasn’t changed that much.
Right. That’s foresight. That’s a good game plan.
Well, it’s not that we made a lot of money out of that book or anything like that. It was more about intellectual pride, if you like. There’s a gap, and you can fill the gap. And I think that everybody that I've spoken to who has written a physics book, if you try to get to the motivation, there’s this idea that you can express something or bring together something—even in a well-trodden field—that’s just better than the way it has been done before. Or in a not so well-trodden field where there’s a need for that thing.
I think for the book with Stu, there was a need for a book that was more physics-based. There had been an earlier book by Zel'dovich and Novikov in the 60s that had a physics perspective. But that was out of date by the time we were doing this. In the case of Numerical Recipes, that was one where there was a need for a book, and there was no competing book. Because the books--
There was a need for the book because generally the topic was being taught, but it did not have a book? Or where were you detecting the need?
No, not at all—it was not being taught to physicists. So numerical methods, or numerical analysis as a discipline, was typically either in the math department—or if the place had a computer science department, it might be in the computer science department. Or, if there was an applied math department, they might teach a numerical analysis course. But definitely the people who practiced numerical analysis were typically doing a branch of mathematics. They proved theorems. And so, if you read the papers or read the books on numerical analysis, they were full of proving theorems. Here is a method, and we will prove that it is stable if you take time steps no bigger than epsilon—you know what I mean? This was the mindset.
And I don’t want to knock this; this was a perfectly valid and useful enterprise. But from the point of view of a graduate student or a professional physicist who has a particular equation that they need to solve on a computer—and have never been trained in how to do this—you couldn't give them a numerical analysis book and say, “Read this book and everything will be fine, and you'll know exactly what to do.” A lot of the interest for the numerical analysts was just in analyzing every method that was known. Well, a graduate student wants to be told, “Use this method. It’s good enough for what you want to do.” [laugh] Or, “Here’s how to get started.” Since that’s what we were teaching our students, we felt there was a need for a book like this. So when I first said no to Bill, it wasn’t because I didn't see the need for this. It was because I didn't have time.
The first edition was just you and Bill, or you had coauthors also?
No, we had coauthors from the beginning.
What was the division of labor? Who brought what, and how did you divide up who would write what?
Basically, most of the topics were based on our own personal experience at that time. In other words, what had we mastered, either through teaching a course or in our own personal research? So, the topics were a bit idiosyncratic. There were some basic things about working with matrices, or ODEs or stuff like that, that you would expect to see. But there were a few topics that an average user might not have expected to find there, and they were just because for whatever reason, one of us had to learn this, and knew how to do this thing, and so it ended up as a section in the book. And some of those things actually were useful.
What was the reception, after it was published?
Depended on who you asked. The tone of the book was a bit irreverent. We had some snide remarks about computer scientists and computer science, expressing our viewpoint that if you wanted to solve the problem, here’s what you needed to do. And then we would make some jab about what a computer scientist would do. And I think that by and large the computer scientists took this in good spirits, but I think there were a few who were irritated with us.
Some of the reviews were very negative, from the computer scientists. For example, because we didn't discuss such-and-such a method which was known to be better, and so on. From our point of view, they missed the point. Our point of view was that any improvement in what physicists were doing was worthwhile, even if it wasn’t the best ultimately known method. If the best ultimately known method was extremely complicated, and something that the average physicist wouldn't be able to do easily, there was no point in telling them to do that. And I think that there were a number of reviewers who didn't get that. But we collected all of these reviews—we had a certain glee in getting one of these reviews. We took it as a sign of our success. But there were also some very positive reviews from people like Arieh Iserles, who were serious numerical analysts and who did get the point.
Within physics, how parochial were your sensibilities, in terms of the value of computers to GR specifically? Or were you making the broader case, which is—everybody understands this today, of course—is that computational power is fundamentally important to all branches of physics?
You made that point explicitly. You felt like this was the big message behind the book.
Absolutely, yes. That this was something that had to be part of the skill set of every scientist.
Yeah. And is this a controversial statement, to be made among physicists at this point? Did people understand this? What were the reactions within the physics community?
I think it’s one of these generational things. There’s one of these quotes-- I don’t know if it’s true or not; it may be apocryphal—supposedly it was ascribed to Max Planck. We used it in Numerical Recipes. Basically, that physics makes progress one funeral at a time.
That you have to wait for the—
—older generation to die off, before the new ideas come in. In a serious vein, that’s certainly true in the teaching of physics. The best thing would be to have computational physics integrated into the curriculum. You know, that people should give homework sets that require the students to solve a problem using a computer—it shouldn't be a separate course. The problem with that was that a typical physics professor in the 80s couldn't do that! Couldn't make up a problem and solve it themselves, because they hadn’t been trained in that way. It was a real blockage to computational physics spreading into the curriculum.
Saul, you obviously have very strong, naturally inclined towards pedagogical questions. I'm curious if you ever got involved with AAPT, or you ever wondered about how they might think about the pedagogical implications of essentially forcing computers into a physics curriculum.
Yes. I was a subscriber to the American Journal of Physics from way back in the days where I actually got the paper thing in the mail. I’ve even published a pedagogical paper in it. Through lack of time, though, I've never seriously contributed. I'm officially on phased retirement from Cornell right now, meaning I will stop teaching courses there. But I want to keep taking graduate students and keep having a research group. When I finally do stop doing that, if that ever happens, I have this dream of writing a series of articles for American Journal of Physics. I keep a folder of notes from my teaching. The first set of articles will be a series on, “Why Do We Keep Teaching Quantum Mechanics So Badly?” And the first article will be “The Vector Model.” The second one will be “The WKB Method.” I have a whole list of things that, if you look at the standard books, are taught horribly, and there’s no reason for it. Because to teach them correctly is not any more difficult. So, I'm not going to write a new textbook on quantum mechanics, but at least maybe I'll write some American Journal of Physics articles on these pet peeves.
Saul, this jumps the narrative, but given what we're talking about now, I'm curious if you see something like the Flatiron Institute, what David Spergel is doing, where computation is central to the whole enterprise—do you see that as the natural progression of the first intellectual kernel of this collaboration?
I think it’s one feature. David is certainly someone who has understood the power of computational things for a long time. And so, the Flatiron Institute is a wonderful accomplishment in terms of bringing such tremendous resources to bear on using computational tools in these various branches of science. But I don’t think an institute addresses the pedagogical side. The pedagogical side is still driven by what’s in the curriculum at university X for physics majors, by who’s teaching the courses and what’s the content, and have they integrated computational expectations into the quantum mechanics course, the classical mechanics course, the mathematical methods for physicists course.
All of these bread-and-butter courses that are traditionally considered part of the curriculum, are they still being taught the way they were 50 years ago? Or has Max Planck’s aphorism borne fruit? Are enough younger people teaching those courses with a more modern approach in terms of bringing computational methods into those courses? That to me is the real question. In research, it’s self-driven. Everybody understands now that you have to use numerical methods. We've seen a huge growth in the use of Mathematica and all of these other tools. But the pedagogy is different.
Saul, when the book really started to catch on, to what extent did you put your money where your mouth was, in terms of your own research agenda and using computers to good effect?
For me, it was in parallel. What has happened is things that I've used in my research have ended up as new sections in new editions of Numerical Recipes. And the same thing for Bill, as well.
When did you start to really look at Einstein’s equations of general relativity as being solvable, or more towards being solvable, with computers? When did that happen?
Well, that was very early. People like Jim Wilson and Larry Smarr had done some pioneering work, as I mentioned. And certainly, when I started working with Stu, we were aware of this long-term vision in the community—it wasn’t something I came up with—it was understood that to solve these equations, we were going to have to do it numerically.
And what about the ways in which computers and ultimately supercomputers would serve as a merge point between GR and astrophysics? Relativistic astrophysics.
Well, yes, this was also kind of obvious. So even in Jim Wilson’s stuff, he would run his supernova code, but instead of using Newtonian gravity, he would put in some of the GR gravity. It was there right very from the beginning. It was understood that you needed to be able to do this.
To the extent that these titles are meaningful, you're probably known as much as an astrophysicist as a general relativist. Would you credit computers with your stature in astrophysics?
Yes, probably. In other words, I would say that many astrophysicists have actually done some observations. [both laugh] I actually do have one observational paper. I instigated a proposal to try to confirm some of the Hulse-Taylor observations. I didn't take the observations, but I persuaded some real radio astronomers that this was worth doing. That’s my one observational contribution. Also, a lot of astrophysicists have worked with real data, analyzing it and so on. And I haven't done that.
So whatever influence I've had has been in trying to show that there are phenomena where it’s important to use relativity to understand them, and that it’s not much more difficult. That if you're going to the trouble of making a supernova code that has the neutrino transport, and it has the hydrodynamics, and it has magnetic fields, and it has convection, then adding GR is actually not that much more difficult. The field is now at the stage where you might as well put in the GR, because it makes a difference.
I had long discussions with Hans Bethe, trying to get this viewpoint across. That he should pay attention to this in trying to understand supernovae. That these apparently small effects make a difference in whether the darn star explodes or not.
Did computers and eventually supercomputers raise hopes that gravity would be unified in the standard model?
No, I don’t think so. With computers, the goal has been to be able to do astrophysical modeling, whether it was cosmology or the supernova problem, or merging neutron stars or black holes—to do these calculations, which are a marriage of astrophysics and GR. And that has been the holy grail of numerical relativity.
What are the origins of your work with LIGO? In other words, from early on, were you aware of what Rai Weiss was doing, essentially all by himself?
Yes. And that was, again, in Kip’s group. It started with Joe Weber. Weber’s claims to have discovered gravitational waves, which turned out not to be true, provoked huge interest. It was pervasive in the relativity community to think, “If it were true, what could these sources be?” Because it required very large amounts of rest mass being converted into gravitational wave energy. And what kind of mechanism could be doing that? A lot of the motivation for research on rotating black holes and energy extraction was driven by trying to come up with any model that could explain Weber’s observations.
And then after Weber, the focus shifted to building interferometers like LIGO. We were all aware of that effort, and there was a lot of work on what kind of sources LIGO might see. We understood that if we were working on the merger of neutron stars with the hope of being able to predict waveforms, then there were these other people who were trying to build detectors that one day would be able to see these things. So yes, it was part of the community in that sense.
So for you, from watching from far afield to having this idea that your work would be useful, how did that progress? What was the point of contact? Was it through Kip?
For me personally, Kip only entered the picture later. In the early 1990s, the LIGO experimentalists (and here I include Kip, of course) got to the point where they were submitting a construction proposal to the NSF. They were asking for hundreds of millions of dollars of taxpayer money. By that point, there had been some workshops in the community, where white papers were written and things like that, with the goal of educating reviewers and the community and the NSF about how ready the field was. That technically these detectors had a chance, and theoretically, enough was understood to make it plausible they might actually see some sources.
I participated in one of these review panels for the NSF. The real people on the panel were people like Dick Garwin and Barry Barish and Boyce McDaniel. You know, people who knew how to build big experiments and understood what a big scientific collaboration was, and actually had built stuff. I was the house theorist. I felt like the lap dog [laugh] who was there to nod my head at appropriate times and say, “Oh yes, we'll be able to calculate this” and “Oh yes, there’s every reason to expect that you'll see such and such” and this kind of thing. Anyway, LIGO progressed in a very public way, and we all understood the possibilities. Of course, nobody could foresee how things would actually turn out! There had been some heated opposition by some eminent astronomers, who had to eat crow when the spectacular discoveries rolled in.
LIGO has a 40 plus-year history, so I'm curious for you, what year or years were your most intense in terms of collaborating?
Well, at this point, I was not part of the LIGO Science Collaboration, which was the official organization of scientists working on being ready for LIGO detections and getting the analysis pipelines up to speed and things like that. They felt a lot of pressure to develop things and to be ready for discoveries, and not to repeat the Weber experience, which had soured gravitational waves as a field. In particular, they didn’t want to be in the position of making detection claims that they couldn't justify. And so they were a little paranoid, but they also felt pressure to be ready, to really focus their goals on making a detection to justify the expense of the experiment.
I would meet with some of the LIGO scientists when I would visit Caltech. I would find out that they were focused 100% on detecting the inspiral and collision of two neutron stars. And I would say to them, “Well, what happens if it’s two black holes?” Now, partly it’s because of what I was working on [laugh] but partly it’s because I understood that just because theorists said that the event rate for neutron stars was such and such, and the event rate for black holes was lower, that experimenters shouldn’t take this kind of prediction too seriously. There are always uncertainties in theoretical predictions. They needed to be keeping an open mind about possible sources. But I was very unsuccessful in communicating or having any impact on this.
I know other people, including Kip, had similar experiences. Kip, you would think, would be more influential than people like me. Their response was that they were under time pressure and they had limited resources—they couldn’t do everything. They had to focus on getting that first detection, and the first detection was most likely to be a relatively weak signal that they would get from neutron stars. To divert their resources to be looking at black holes—who can blame them? Yes, I blame them. [laugh] But not seriously. I mean, I might well have done a similar thing if I had been a manager responsible for the goal of getting a detection with LIGO.
So the result was that all of the work on what the waveform would look like if you actually had black hole collisions and not neutron star collisions, that was done outside the LIGO collaboration. And Kip was very instrumental in this. He was very worried that the first detections would be from black holes and that theorists wouldn’t be able to say whether the signals agreed with those predicted by GR or not. This came to a head 2005. He set up a collaboration between my group at Cornell and the Caltech group, which had been seeded by some of my previous graduate students. Then he went out and raised private money from the Sherman Fairchild Foundation specifically with the goal of helping LIGO to be ready for black hole detections.
I remember saying to Kip at the time that if you were going to spend hundreds of millions on the detector, you needed to also spend a few million on theorists, because they're relatively cheap. We did get some funding out of NSF for this work, but the NSF is always stretched very thin. Kip was able to persuade the private foundation that this was a good place for them to have an impact. Being able to have a bigger group of students and postdocs is what made a big difference to our effort. The key early contributors to our collaboration’s success, people like Larry Kidder, Mark Scheel, Harald Pfeiffer, they were all supported by the Fairchild Foundation.
Where were you on the day of the detection in September 2015?
Completely unaware. I was not part of the collaboration. But very quickly I got embroiled. If you look at the discovery paper that ultimately came out in Phys Rev Letters, it has the detector signal, and superimposed on that, there’s a curve that’s labeled “Numerical relativity.” And that numerical waveform was one of our collaboration waveforms! There was some tension over that whole effort, because they wanted to use our stuff without proper acknowledgement. And this did not go over well.
Now you might ask, “How did they have access to our work?” Well, we had members of our numerical relativity collaboration who were also members of the LIGO collaboration but not officially to do numerical relativity work. It was to do other stuff, such as outreach or data analysis. So, when they became aware of the discovery, the first thing they did was check if it agreed with our waveforms. And then everybody inside LIGO got very excited and wanted to put it in the paper. But there wasn’t a proper procedure to give academic acknowledgement for this, partly because they hadn’t considered the possibility that the first discovery might be black holes and not neutron stars.
So, there were some tensions—I don’t need to go into personalities and details, but let me just say that it involved some letter-writing by Kip to the senior management of the LIGO Science Collaboration, of which Kip was a part, to ultimately resolve that. And in the end, things did get resolved satisfactorily. And now, certain parts of numerical relativity are a recognized contribution to the LIGO Science Collaboration, so you can actually sign up to do numerical relativity to produce waveforms and so on. We're very much involved in doing that. But it didn’t start out very well.
To some extent, a related question—when did you first get involved with LISA?
Well, for black hole simulations, it turns out that the total mass scales out of the calculation. So if we can produce LIGO waveforms, we can just rescale all the frequencies by the bigger masses that LISA will detect and produce LISA waveforms. No need to do any new simulations. The most important issue for LISA is we expect LISA to have a higher signal-to-noise ratio. The signals will be much stronger relative to the noise. LISA will be detecting these supermassive black holes spiraling together, and have the waveforms in band for years, see thousands and thousands of cycles. So, the accuracy that you will ultimately need for the theoretical predictions is much greater. It’s beyond what you can do today. If you take our current numerical algorithms, and you extrapolate to what you could do on a supercomputer five or ten years from now, you still won’t be able to achieve LISA accuracy. The reason is the algorithms that we're using now can’t take advantage of the next generation of computers. The architecture of the new machines is changing. There’s a revolution going on there that many people doing numerical work have their heads in the sand about. So, the focus of our research is to be able to be ready for LISA by coming up with completely new algorithms.
What are the goals-- What’s optimistic with regard to LISA?
Well, if you improve your signal-to-noise ratio by a factor of 100, you need roughly a factor of 100 better accuracy in your theoretical prediction. And that’s what we're talking about for LISA. So roughly a factor of 100 better than you would need at the best LIGO sensitivity, which will be reached in a few years. And we have no way of using current algorithms. You can’t just say, “Oh, I'll put the code on a bigger computer with more processors and be able to get 100 factor better accuracy.” It’s just not going to work.
One of the pieces of advice that I've gotten, and I'm not sure whether it was through Kip or how it came about, is in choosing a research area or in working on a research problem, it always helps to ask, why should you be the one to be doing this, and not someone else? What is it that you can bring to bear here? Do you have any advantage? If you're doing observations, do you have access to some telescope? Do you have access to some computer? Do you know some field of physics that will help? Things like that. That’s a very useful part of doing science—people call that scientific judgment. Choosing what problems to do, or how to approach them.
Part of our success—I’m talking about our collaboration being successful in producing these waveforms that LIGO uses—part of it is that we use a different algorithm than other groups were using. Now our algorithm is harder to implement, harder to get working in the beginning, so there’s kind of a barrier. The groups using traditional methods had great initial success starting around 2005. We were a year or two behind them before we could calculate black hole waveforms. But when we could finally do them, our codes were more efficient and more accurate. We could produce more waveforms and with higher accuracy because they were cheaper to run. And this was all related to the choice of algorithm.
Now the reason that I was pushing to use this algorithm was because of what I’d picked up through just being interested in numerical work. I wasn’t the inventor of this algorithm or anything like that, but just being aware of it, through reading papers of other people who were pushing it, and knowing the work in the applied math community, I understood from a conceptual point of view that this was the right way to do it.
And so, in a similar way, today, I have a visceral knowledge that our current algorithms will not work. I know why they won’t work on the giant machines that are coming. And I've interacted with applied mathematicians who are aware of this and gotten advice on what kind of algorithms we should be using. And so, a focus of our group’s research is developing a new method that will do this. It will be good not just for the black hole problems, but also the neutron star problems, any problem that has complicated physics. The fluid dynamics, the magnetic fields, the neutrinos, where a lot of stuff is going on simultaneously and you need the computers to be able to do all those computations at the same time. The point is that it’s not that the individual tiny processors on each chip are going to be faster, but that there are going to be many more of them. So, we'll see. Ten years from now, either I'll be hanging my head in shame and have all my NSF proposals being rejected—but you know, maybe ten years from now I'll be proved right.
A similar question to the where were you on the detection of the gravitational waves—particularly because of your work coming from a theoretical perspective where you understood black holes to be real for 40 years—when the Event Horizon Telescope did have that first picture, what did that mean for you, and what did that mean for your field?
For me, there was a big distinction. The LIGO event was the eureka moment. When I saw that waveform that we had calculated-- I mean, if you think about it, you take 50 coupled non-linear partial differential equations, coming from a theory written down 100 years ago by this wild-haired genius, with all kinds of theoretical work in between about how to get the equations solved on a computer, and then you get these crazy people building this detector—which was so sensitive that you could measure this infinitesimal change in the arm length of these two-and-a-half-mile-long interferometers—a change coming from some collision of these supposed black holes hundreds of millions of light years away—and I saw the signal lined up so well with our waveform. I was-- I teared up, actually. It was just so emotional for me.
It made gravitational waves more real.
Yes. Because for my whole career, I had worked in this vacuum where the thought that any of my work would have any connection to something that was real—it just seemed so remote.
And you mention this now to illustrate the distinction from how you felt with the photograph of the black hole. That was different.
Yes. That was different. Because by the time that the Event Horizon Telescope was successful, I was more focused on looking for the flaws [laugh] in what was being presented than in the eureka—I had had my eureka moment. It was very important, I think, for the impact on the rest of the field, being able to produce those spectacular images, but for me personally, it was the LIGO detection and how well things matched up with our waveforms that was my personal eureka moment.
Saul, to bring the narrative up to the current date administratively, what was the decision behind joining Caltech?
How could I say no? [laugh] I got this opportunity right within a few months of the big discovery. Caltech was the headquarters of the discovery. And the opportunity to interact both with the theorists and the people responsible for the LIGO detector and the detection, it was just a confluence of things. In terms of having a research group, it just was-- You know, I just couldn't say no.
Did you take graduate students with you, or you didn't need to make that choice, because you now have a dual appointment?
I didn’t need to take students with me. I could supervise new students at Caltech, but I still had the students at Cornell. And as I said, we were already doing online meetings before we were forced to do so by the pandemic.
Saul, for the last part of our talk, I’d like to ask one really broad retrospective question about your career, and then one looking forward. So, I'm not sure if you've done much of this, but in the way that you found opportunity to communicate to broad audiences who have fundamental questions for people like you. “How does the universe work? What is a black hole? What is time? What is space-time?” Right? If you look over the course of your career—all of the collaborations that you've been involved in, all of the ways that you have innovated things—what are the most efficacious ways of encapsulating all of these ideas into the broader audience out there that fundamentally has the same questions that you do but doesn't have the tools or experience to know what to ask?
One question is, what can people do in general? That’s a very difficult thing. It requires very talented people if you're going to be giving lectures. With YouTube and all of that, there’s actually a lot of quite good stuff that’s available. If you ask what have I personally done, what has been the most wide-reaching connective thing, I would say it’s through the computer visualizations that I've been able to produce with my students and postdocs.
Starting from the very early work on numerical relativity, there’s always been a sense of the importance of producing visualizations. Because the computer just outputs a whole bunch of numbers, values of the gravitational field, say, and looking at a file of numbers doesn't help. You need pictures, something you can see. My first serious attempt at this was when Stu and I made a trip in the 1980s funded by the NSF to make a movie. We used to joke that we went to Hollywood. We actually went to Culver City, about ten miles away, but Hollywood sounds better. [both laugh]
We went to a company called Digital Productions, which made most of its money doing animations for TV commercials. The NSF paid them to do scientific visualizations with their Cray supercomputer. We made a movie showing the implosion of a cluster of stars to make a black hole. This was used in some PBS things and similar shows. This was all very expensive. Luckily, we were saved by the video game industry. The spectacular growth of gaming drove down the cost of graphics hardware and software so that now you can do on a laptop what used to take a Cray supercomputer.
The visualization that had the biggest impact came out of a thesis project by Andy Bohn, one of my graduate students. The project involved taking a numerical simulation and calculating the precise location of the surfaces of the black holes. That’s actually quite difficult to do, because you don’t know precisely where the black holes are during the calculation. That’s because a black hole is defined by saying it’s a region where, if you're in there, you can’t get out. So in order to know that, you have to finish the calculation to know that if you tried to get out, you couldn't. [Both laugh]
So, it was quite complicated, and he wrote a thesis on some new ideas for how to do it. And as part of that, he made a movie of two black holes spiraling in, and how they would look as they merged. Then he and some of the other graduate students, instead of working on their theses—they got a little carried away, and so they made this visualization more realistic—they put it against a background of stars that they got from a catalog. Real stars, but not the real background for the actual LIGO event because we have no idea what that is, just something to make it look good. If you look carefully, you can see how the images of the stars get distorted when the light rays travel close to the merging black holes on their way to you.
Then when the press release came out about the LIGO discovery, we provided this movie. So when the big announcement was made at the NSF, if you ever watch that on YouTube, you'll see that the director of LIGO showed our movie. You can also find it on websites like CNN, the New York Times, and so on. It was downloaded more than a million times, and it’s still available on YouTube. I get a warm feeling because it’s not a Hollywood movie; it’s an actual calculation, in detail, of what the image looks like according to Einstein’s equations, both for the merging black holes and for the light paths. This kind of thing has an impact. If you read the comments on YouTube of the lay people who watch it, it’s very inspiring. They actually get the point of it.
And implicitly, you're making the case that this is publicly supported science that makes this possible.
Absolutely. And people understand that it’s the real thing. It’s not some artist’s sketch of it.
Saul, last question, looking forward, both in terms of what you want to accomplish personally—you're clearly living up to the dictum that physicists never retire.
That’s not in the cards. What do you want to accomplish personally? And looking at all of the excitement around where computational physics is going—quantum computing—what are you most excited about beyond however long you're defining your career? Long-term, the big things that you think are possible, that fill in what are obviously major, major gaps in our knowledge of how the universe works today?
So, what’s driving my current research is this realization that five or so years from now, when one of my graduate students logs on to one of the national supercomputer facilities that are supported by the NSF, they will routinely have a million CPUs for their personal project. Not a thousand, not ten thousand, but a million. And they will hopefully, through the work we're doing now, have the ability to use those million processors to do important physics with—not just in numerical relativity but in other areas. These techniques are going to be generic. I think that’s a breakthrough that’s going to take place in many areas of physics, including theoretical astrophysics and numerical relativity. Any theorist who wants to have an impact needs to be thinking about that now.
Quantum computing, I think, is too far in the future. And quantum computing is not likely to have an impact on solving partial differential equations, which is what you need for numerical relativity and a lot of astrophysics. It will have an impact on certain parts of physics and certain algorithms, but not PDEs.
Saul, let me wedge in just a question here briefly. To go back to when you were a graduate student, and as you narrate the importance of you learning how to be innovative—how you had to break out of a Victorian mold, and you needed to struggle with a problem and see for yourself the value of figuring it out—as you look to the future, as computers get more powerful, as they become more integral to the endeavor of physics, are you concerned that any of that that you gained without having computers, might be lost? In other words, are we no longer going to live in a world where we're outsourcing all of our problems to computers? What’s your concern in that regard?
You’re right, it’s a very difficult problem. Because it’s gotten to the stage now where many physicists can be successful by running other people’s codes. For example, you can use Mathematica to solve problems that are very sophisticated, because it encodes a lot of expertise. Or you can run our code for numerical relativity to produce waveforms and do physics with those waveforms without understanding the nitty gritty of how the computer was programmed to do that.
The difficulty for an advisor of graduate students is, if you get a new graduate student, and you get them to code up new computer algorithms, and they spend all their time doing that before they can get science output, how do they get academic recognition for that? A lot of the job opportunities require you to have solved some scientific problem. And if what you've done is produce a new computer code that enables people to solve a problem that hasn’t been solved before, but when you're up for your postdoc position or your junior faculty position you haven't actually done that yet, you don’t get job offers. That’s what I'm worried about. It’s an intractable problem, balancing the desire for these things.
The analog for that is in an experimental group, where a fresh graduate student builds some new equipment, but that new equipment is only ready at the end of their time as a student. So what they do is they take data with the previous graduate student’s equipment, so they can have some science output to try and get an academic position. And there’s this analog now with computational stuff, and it’s a very difficult problem. I don’t have a good solution for it.
But in terms of what you want to do versus where the field is going long term, is there a rough idea where you draw those boundaries? Where you see what your greatest contributions are going to continue to be?
What I'm trying to do with current graduate students is make sure that as well as working on the innovative aspects—really getting their hands dirty—they, if possible, have the analog of the student who uses the previous student’s equipment. So, they can actually do some science as well, with the existing state of the art. They can’t spend all their time only writing code that is not going to have payoff when they need to be getting postdoc offers and things like that. It’s a very interesting dynamic, and it’s not ideal, but that’s the way I see it.
We'll see how it plays out.
Saul, it has been a great pleasure spending this time with you. Thank you so much for doing this, and what a historical treasure this is. So I really appreciate it.
I hope so. Thank you. I appreciate your questions.