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Oral History Transcript — Dr. Rudolf Kippenhahn

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Interview with Dr. Rudolf Kippenhahn
By Owen Gingerich
At Max Planck Institute, Munich
June 18, 1978

 
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Rudolf Kippenhahn; June 18, 1978

ABSTRACT: Brief discussion of early events in Kippenhahn’s career: his first position under Ernst Zinner at Bamburg; contact with Ludwig Biermann at Universitat Gottingen; early work with computers, particularly the impact of the numerical method invented by Louis Henyey at University of California, Berkeley, and early large-scale applications of electronic computers to astrophysics.

Transcript

Gingerich:

Let me ask you a little bit first about your background, about where you worked, whether you would consider your education astronomical or physical, and then we’ll lead up to the papers.

Kippenhahn:

Yes. Well, my story’s a bit influenced by the war and the postwar time. I was born in Czechoslovakia, grew up in Czechoslovakia, and I had to leave Czechoslovakia 1945. I had contact with science during the war, when I still went to school. During my vacation I spent altogether I think three summer periods with Cuno Hofmeister at Sonneberg Observatory, and I learned how to observe variable stars plates …

Gingerich:

… I assumed variable stars …

Kippenhahn:

This is how I started. But then after ‘45, when there was a major problem to find a place where you can find food, because there was the food shortage, and I had to study where I found people where I could stay and could eat, so I started right afterwards to study mathematics, because at that time I was in Halle, which is in East Germany, (it was in the Soviet occupied sector), and so I started mathematics and physics, but the main field was mathematics. My parents meanwhile had also left Czechoslovakia and lived in Bavaria. In ’48 I crossed illegally the borderline and continued my studies in mathematics in Erlangen. I always was interested in physics and took all the courses in physics, but I never had any chance to learn astronomy. After that pre-university period with Hofmeister, I had no contact with astronomy, until I had to get my oral exam for the PhD in mathematics. Then according to the regulations at Erlangen University I had to make an exam in applied mathematics and applied physics or whatever; it was a free choice, and I thought, I told them I would like to have an exam in astronomy, but there was no astronomy at the university. And they found out that Zinner in Bamberg was close, and they asked him whether he would ask me some questions in astronomy. It happened that Zinner at this time was close to retirement, and his was a very small observatory and had no good equipment, and Zinner only worked in history of astronomy. But there was always a problem with the Bamberg Observatory, not a particularly clear legal situation, and so it was never quite clear when his real retirement age was, either 65 or 68. If he would be considered as a real university professor, it would be 68, but as a normal government employee, it would be 65. So he was about 65 at that time, and he wanted to go on, and so for this he needed somebody as an assistant, to make the whole place a little bit more lively. So in the exam, he actually didn’t ask me very much. He offered me a job. And I took it. It was a risk, but I took it, although I had been offered a job in mathematics, but I didn’t feel that I would achieve very much as a mathematician. I never had the drive really for pure research in mathematics. And so I stated, and it took me quite a while before I got contact with Professor Biermann at the Max Planck Institute. And then I went into theory, and after six years, I left Bamberg for this Institute, which at that time was in Gottingen — so that’s my background. I was originally a mathematician. Gingrich: So when you became connected with the Max Planck Institute, it was at the same time that you were in Gottingen, and then you moved here with the Institute?

Kippenhahn:

The whole institute moved from Gottingen in ‘58, and I was here at the Institute until ‘65, then I got the chair in Gottingen. Then I was in Gottingen for ten years, and then I left Gottingen and came here and succeeded Ludwig Biermann.

Gingerich:

Now, you were interested in astronomy as a boy?

Kippenhahn:

Yes. I built my own telescope and all that.

Gingerich:

Did you make variable star observations, or any of these kinds of things?

Kippenhahn:

Not at home. My equipment was never good enough to do any reasonable amateur work, but I once thought I had found a comet, with that small telescope. It turned out, it was right in the Scutum Cloud, and was there at the same place the next day, and it turned out to be the cluster M 11.

Gingerich:

I see. At least there wasn’t a ghost image in your telescope.

Kippenhahn:

No, not that.

Gingerich:

That’s interesting, because as an amateur telescope maker, I also discovered a comet, in about that same region, in Cygnus. And I was very excited and sent a telegram to Harvard Observatory, but it had been found at least six weeks earlier by somebody else, and I was just out of touch. They sent me back a postcard thanking me for my observation, which I thought was rather cruel, considering that I had spent the money for a telegram. Now, when is it that you got involved in the stellar interiors calculations? This must have been after computing machinery was becoming available.

Kippenhahn:

I got interested immediately after I had come into astronomy from mathematics. I don’t know how it came. In the Bamberg Observatory there was a book on stellar structure, which is only known to German readers, but by the famous Heinrich Vogt from the Vogt-Russell theory and he had written a book, I don’t even know the exact title — AUFBAN AND ENTWICHLUNG DER STERNE — something of this kind. This first edition was published during the war or at the beginning of the war, and I tried to study this book in Bamberg. I had no help and it was very difficult. It was also not too good a book. It is too close to the original literature, so really the content of the book is not consistent within the book. You see parts were taken from Chandrasekhar’s 1938 papers on degenerate configurations, and many parts were just taken from the literature. It was not too good a book, at least not for learning. So I worked with that, and — yes, it was, how do you say in English, autodidact?

Gingerich:

Yes, an autodidact.

Kippenhahn:

I really shouldn’t talk too much about myself. We wanted to talk about astronomy. But one thing, how I really got connected with the Institute, which was not easy after the war. No positions available. I had nobody who could recommend me, nobody knew me at that time — it was in that postwar era time, in 1951. And then I read the literature, and I also first went to Biermann and showed him what I’d done, on novae, which was something which he immediately found out was complete nonsense. And so he suggested to me, I should do plasma physics, so I went back to Bamberg arid read papers on plasma physics. I got an idea about how magnetic variables would work, I made a theory on magnetic variables, and I sent that theory to Biermann, who didn’t answer for months. Meanwhile, I looked into my theory. I found two mistakes in the theory. And then came Biermann’s letter telling me that there were three mistakes in the theory, each of which made the theory completely wrong. And so, it was all just crackpot; I had sent a theory which was nonsense. They are quite experienced with crackpots. But my advantage was that I had already found two of the mistakes, and after Biermann answered me, I understood also the third mistake. So I sent back a letter saying that I’m really very disappointed that I’d made these three mistakes, and I understand these mistakes, and so I see that my theory is completely nonsense, but I still, although that’s not very encouraging, I don’t want to give up theory of astrophysics, and asked him when I could come and talk to him again. They had plenty of crackpots, but they’ve never had crackpot who immediately gave in that he had made mistakes. Then they allowed me to come, and they asked me to give a talk, to give a colloquium on a paper by Cowling which had just appeared in the literature, in MONTHLY NOTICES, and I read that paper and understood it and I gave a colloquium on it. From that point on, I got firm connections with the Institute, and two years later, I got a job there.

Gingerich:

So your connections were, commuting down here occasionally…

Kippenhahn:

Yes to Gottingen, from Bamberg.

Gingerich:

Now, that was working with plasma physics. How did you move from there to — problems of interiors?

Kippenhahn:

Well, the thing was that Lust, who is now president of the Max Planck Institute, had a job in the astrophysics part of the Institute. At that time it was just a group in the Institut fur Physik. He was one of the first who got a fellowship to go to America, and I got offered his position for half a year. Then, at this time, Hoyle and Schwarzschild’s paper in ApJ Supplement, on “Evolution of Stars in Globular Clusters,” on the ascending branch, was just published. And when I came to Gottingen, Biermann suggested that, he had the feeling that this could be done technically better than they had done it. It had a complicated — I don’t know if you have read that paper?

Gingerich:

I know the paper but not in detail.

Kippenhahn:

It was on a fitting method. And there was at the Institute a man named Temesvary who for quite a while was an American. He’s now back in Germany. He was a student of Heinrich Vogt. He was interested in stellar structure, and the two of us started with the new, still home-made computers, to write a program which was supposed to be re-do these Hoyle-Schwarzschild calculations. At the same time, when I was at Gottingen, Schluter stimulated me to work on filaments, and from that half a year, two papers came out, the filament paper, and one in 1958 that was published in 1958 in Zeitschrift on stellar structure. With Temesvary and Biermann. ’58. Volume 46.

Gingerich:

Right, I have that one here.

Kippenhahn:

We got better with the convection theory. I think this was the first time the mixing theory was really applied to stellar models.

Gingerich:

Now, Biermann had been working for some time with convection in stars.

Kippenhahn:

Yes.

Gingerich:

And this was an application of the things that he had done?

Kippenhahn:

In principle, yes. I’m not sure now at the moment whether we had used the mixing length theory in Biermann’s form as it was published by Biermann, or whether we had already the improvement by Bohm-Vitense. This I don’t know at the moment. But actually, they don’t differ too much.

Gingerich:

I understand that she wrote hers from the ideas that he had announced, but obviously her paper was worked out well enough that it became the one that was cited over and over again.

Kippenhahn:

Yes. But I think Bohm-Vitense had published a paper on the sun with the new method, earlier, but we used Biermann’s method, and later when Baker and I did the Cepheid work, then we used the formulas by Bohm-Vitense.

Gingerich:

Now, you say they were home-made computers. What size and scope?

Kippenhahn:

Oh, we used the G-2. I forgot completely the storage and all that. But we could find out about that…

Gingerich:

It was something made here?

Kippenhahn:

Made here by Billings’ group. And —

Gingerich:

So it was a unique model available in Munich?

Kippenhahn:

It was in Gottingen. It was still — and this is one of the great experiences of my life, that it took us five hours to integrate from the surface to the center core, from the stellar surface to the degenerate core. It was still a fitting method. You establish the initial conditions, and see what you can fit with the partially degenerate core, and it took us five hours to compute from the surface to that central region, and to find out how bad the fit is. Then you re-do this. So you could sit in front of the computer, and many lights flashed, and after a while we understood these flashes. We knew when it was in convection just from the lights, and then when there were integration procedures and all that, and you could really see the printout which came after each step. We always made a journey from the surface to the star: hydrogen neutral, then hydrogen partly ionized, … and opacity governed by H minus, neutral hydrogen and so on. We learned this over these five hours. This was quite an experience, to us, in 1957. And at this time, we missed a great discovery, which, two years later, became public — namely the existence of the Hayashi line.

Gingerich:

I thought you were going to say the Hayashi line, because I know at Harvard, when Hayashi’s paper came out, and Chuck Whitney looked at it, he said, “Oh, why didn’t we think of that? It’s rather obvious.”

Kippenhahn:

In these integrations inward to the core, we started for a given masse — the mass was always fixed, 1.3 solar masses — we started at a point in the H-R diagram and integrated inwards, and the fit told us where the point was in the H-R diagram, and we got a new quantity, which was a measurement for the quality of the fit. There were four different equations one had to solve, or actually only three because the luminosity was to remain constant. The luminosity came from the surface of the degenerate core, from the shell burning, so there were three calculations to integrate. The difference between MR and the total mass had to go to zero at center. And it sometimes happened that long before we reached the core, the mass was already zero. So they were just wrong fits; we threw them away. And if we would have been clever, as Hayashi was, we would have understood that these are the models you get on the right hand side, and that there is no way of getting models in that area in hydrostatic equilibrium. This is what Hayashi found. We had these models, but had not been aware of their fundamental importance. We had not his models, but we had the integrations which didn’t give us models. But we were not aware of the general —

Gingerich:

So obviously there were other people computing around this time, Hayashi and Schwarzschild for example.

Kippenhahn:

Yes.

Gingerich:

To what extent were you aware of other people applying computers to this kind of project at this time?

Kippenhahn:

As far as I know, only these two. And then later came Richard Sears with his solar models. In ‘58 when the Institute was at Munich already, Marshall Wrubel came in, and we had him here for one year. We discussed with him. He had just published his Handbuch der Physik article on stellar interiors. But I didn’t do any stellar evolution after ‘57, actually. I did stellar rotation and things like that. And then I did with Norman Baker the Cepheids. We started ‘59 with the Cepheids. This was when Shevakin (USSR) had published a paper on the He-II ionization, but this was just based on a two layer model, and Baker and I used the outer layer, modified outer layer program, modified compared to the Temesvary program, by Temesvary and myself, and Baker and I used the same computer, the Gitswite G2, and did a paper which was I think published, it must have come out in —?

Gingerich:

That means Baker came to Gottingen?

Kippenhahn:

Oh no, to Munich, but no, Baker had just got his PhD with Morrison and wanted to go into astrophysics, and Munich was the place he started astrophysics. Norm Baker from Columbia University.

Gingerich:

I see. With Philip Morrison?

Kippenhahn:

He wrote his PhD thesis under Morrison, in Ithaca [Cornell], and after he received his PhD at Ithaca, he got a job here or a visitor’s fellowship for two years, and during this time we wrote that Cepheid program, and made non-adiabatic pulsations, the linear theory, the paper which then came out in ZEITSCHRIFT FUR ASTROPHYSIK, I think it came out in ’62. But it was submitted ’60 or ’61. And this was parallel to work by John Cox. Gingerich Yes.

Kippenhahn:

So at the IAU in Berkeley [1961], John Cox and we — was there somebody else? — I think, John Cox and we presented our thoughts.

Gingerich:

Ledoux and Whitney had worked, to some extent, without making such elaborate computer models, at some point in there.

Kippenhahn:

I don’t know exactly, but it was somehow a different line. I mean, when you are working, you are, always looking who is the most dangerous person, who might come out with the results? You have to be aware of this. And I remember only John Cox. Christie came later, with his non-linear pulsations came much later. And then, I was in America, ‘61 to ‘62, first Princeton, then Pasadena. Now, in the time before I went to America, there was an uneasy feeling about stellar evolution. The computers were failing, and Schwarzschild had just got to the Helium flash, but he couldn’t go through the helium flash if I am correct. I think so. Hoyle and — I don’t know his co-author — had published models. There was always a problem to get off the main sequence. It was fairly easy for low luminosity stars because you can do this with a sequence of models which are in thermal and hydrostatic equilibrium. But if you go into the region where you have to cross the Hertzsprung gap, where you have an evolution governed by the thermal time scale, all the numerical methods didn’t work then. And there’s a paper by Hoyle, who claimed to have got into the Cepheid zone, he came close, — he came further, but you have to fiddle around with your solution, make some assumptions. So, there was no honest way to go into the red giants, from the main sequence. All of the computers were there. And there was already a paper by Henyey and Levy and somebody else, two co-authors, Levine(?) I don’t know now, on the method, which nobody understood. Nobody, so far as I know, really used this method. And then, in 1961, at the IAU in Berkeley, when Cox and Baker and I presented our results, Henyey gave a talk on the Henyey method.

Now, Henyey, you probably remember him, was not very fast in publishing things. So one knew that there was a method but he wouldn’t publish it. So he gave a talk on that. And I made notes, Schwarzschild made notes; I don’t know who else. And I couldn’t understand the whole things I had just my notes — It was a complicated method. Then I started my time, it was September, ‘61, in Princeton, and after a few weeks, Schwarzschild came and said that he had written a program with Harm, a program using the Henyey method. So Schwarzschild, from the notes he had taken from Henyey’s talk, had written a program with Harm, and it worked so that Schwarzschild was full of enthusiasm, that he now can go through the helium flash, where he had failed with the old methods. Or at least he could do it faster. So I looked up my notes, and made an outline of the Henyey method. It was four pages, where I described in detail the Henyey method for the people here in Munich. We had a programmer here, Abbie Hofmeister, she had published with us for quite a while. She started as a programmer. She was a mathematician. And I wrote up for her about four or six pages of the Henyey method, and I took a copy of that to Pasadena, where I started then at the beginning of ‘62. There I met Iko Iben and a Japanese fellow, Minoru Nishida. Iben had been working with Richard Sears on main sequence models and all that, the kind of work they did before they knew the Henyey method worked, and we once in a while met. Nishida asked for a copy of my Henyey notes, and he translated it into English. It was in German. He translated it and then there was also an English version. Long before Henyey published it, several copies of that method were around. I don’t know where they went. I don’t know whether Iben, for his code, used a copy of that paper. I don’t know.

During that IAU meeting, Weigert, who lived in East Germany, happened to be in West Berlin, and one morning he woke up and learned that they are building a wall. So he sent a telegram to Munich, “Shall I go back to East Germany, or can I get a job in West Germany?” Everybody was in Berkeley. This telegram was transferred to Berkeley, and Biermann offered him a job from Berkeley. So then, three people who then worked on stellar evolution here were together, Emmi Hofmeister as a programmer, Weigert from East Germany, and I was still in America. And when I left Pasadena, I remember before I left Pasadena I met Icko Iben again, and he was trying to invent, a new method for integration. That’s what I remember. And I said, “Why do you try to put effort into a new method? Why don’t you take Henyey’s method, which is working now in Princeton?” And it was working in Berkeley. I must have visited Berkeley again, in 1965, because I remember Henyey in front of the computer, with a man whose name I’ve forgotten, who published on mass loss of red giants later. I forget his name but I probably could reconstruct this. They were sitting in front of the computer, and once in a while the computer printed numbers, and they had an H-R diagram and plotted a dot. This I really would like to have — sitting in front of a computer, just draws an evolutionary track — compared to all that we had done before, in my experience, five hours to integrate inwards and see how the fit is. In October, ‘62, I went back and we immediately started to write a Henyey program here, with IBM 17 — I don’t know the number or what kind of computer it was, but an IBM computer.

We immediately started to write the program. We did it in the spring, ’63. We started with a seven solar mass star. The star was in the red giant region and had started helium burning. It had crossed the Cepheid strip first, and then we got the loops and all that. Baker and I immediately applied our Cepheid code to the models obtained, and in order to check if it gets right the models and the period luminosity relations. Baker was in America at that time already, so we did this joint work at Columbia and here. Then, yes — in summer ‘63, we had this seven solar mass evolutionary track, and I think we had already started with the five solar mass evolution, and in fall of ‘63, there was this first Texas conference. The quasars were just found. There I met Iben and Schwarzschild and showed them the first results. At this time, Iben still did not have his code going. He was working on pre-main sequence evolution, and for quite a while, he was leading in the pre-main sequence evolution, evolution toward the main sequence, still following the old Henyey idea, Hayashi-Henyey idea, not the later (???) type dynamical phase. They were all hydrostatic equilibrium, yes. And then, to be honest, then we got a bit into difficulties with Iko Iben. We had mailed preprints throughout the world in the summer, ‘64, there was the IAU in Hamburg, and in Hamburg it turned out that Iben had suddenly presented a whole set of evolutionary tracks, from the main sequence to helium burning, and although we had contacted him, and he had information from us, he didn’t tell us anything. He came out with this, his results, as so to say, as a surprise for everybody. Biermann had met Iben, who said he wouldn’t believe ours until he had got done with his program. And after he had got done with his program, he published them. We always had the difficulty, in our country, that Unsold didn’t allow us to publish in English… So most, practically all the papers published in ZEITSCHRIFT DER ASTROPHYSIK had to be published in German.

Gingerich:

I had heard that before. I perhaps should have asked him about it when I interviewed him [Unsold].

Kippenhahn:

Now, he doesn’t remember so well, how the whole thing was. I’m on very good terms with him, but when I tell him about that, he doesn’t remember how it was. We both have different memories of the thing, see. But I think it’s a whole strategy what we did, we computed the five-solar-mass star, from carbon burning to the most advanced phase, while Iben, — and I think this was wise to do — applied the simpler phases of the evolution to different masses, and this is more important for observation. You know, this is the story of the single star evolution — we published a series of papers — but, the seven and five-solar-mass evolution, or at least the seven-solar-mass evolution, was done first here; as you see it is not quoted very much. Because there Iben came out with his whole set of computations, really one paper after the other. Then, Weigert and I went to Gottingen; and at that time, we didn’t have computing facilities in Gottingen, but it helped us to think about problems. And during the university break, the time when there were no lectures, I visited Munich regularly to use the computer. And Weigert and I thought, if we had some Munich computer, what should we do? And what we had on our minds all the time was the problem of binary evolution. I came here. Weigert wrote a program, the first version, and I went to Munich and tried to get this program running, and had to improve it to get it running. And then we wrote these two papers, which you saw were quoted quite often. This was the evolution of close binary systems, two papers, that came out in 1967. So, this is stellar evolution.

Gingerich:

I remember last spring, you made some remarks to the effect that the era of computing interior models was sort of over. That somehow, given that computer power and that mathematical method, a great deal of model building was done, which in effect creamed off the easy problems.

Kippenhahn:

I think so. Yes. The physics was known, more or less; in general, you knew what kind of equations had to be solved. The computers came. This was not sufficient. The Henyey method came. And then, this was a time to cream off all of it, and it turned out that even binary evolution, you can do many things in binary evolution with spherically symmetric models, just because the very deep interior of even a closed binary system is spherically symmetric. And there was a time, I did some work with these — papers which are not so often quoted — on rotating stars.

Gingerich:

Now, you said you had some papers which were rarely quoted?

Kippenhahn:

This was more or less a joke. Certainly there was a paper that was printed by Lindsay Smith and myself, on the period-age relation of Cepheids, — I think nobody ever cared about that paper in which I have the feeling that there’s something in it, but I might be quite wrong. I don’t know now when it was [finding paper in list] on the ages of Delta Cepheid stars, ‘69, A&A in Volume I [Astronomy and Astrophysics] –-

Gingerich:

Yes. There is a paper there which has been quoted 11 times. I suppose that’s it page 42?

Kippenhahn:

No, this certainly was another one. Page 142? How was it?

Gingerich:

Yes. 11 times.

Kippenhahn:

I must have missed it. I wasn’t aware of that. 1 thought it was completely ignored.

Gingerich:

No. But there’s another one that was on page 3 of the same volume, that’s only cited once.

Kippenhahn:

Page 3 of the same volume? I’d guess that this is a mistake.

Gingerich:

Maybe somebody incorrectly cited the paper, and created a ghost reference in the Citation Index.

Kippenhahn:

This one on stellar chromospheres is just a conference paper.

Gingerich:

Yes, similarly the low luminosity stars is a conference paper too. That’s the conference in Charlottesville?

Kippenhahn:

Yes, yes.

Gingerich:

Were you there?

Kippenhahn:

Yes. Gingerich I don’t even remember that. I was remembering all the excitement, of course, because Hewish had come over with just mentioning the pulsar positions. Let me go back to the time when you were just coming down here from Bamberg.

Kippenhahn:

I went to Gottingen, then I went to Munich.

Gingerich:

I keep getting it mixed up because Biermann is here now, but he was in Gottingen at that time.

Kippenhahn:

Yes.

Gingerich:

Did you work with him collaboratively on any paper?

Kippenhahn:

Not really that way, that for a certain period, we sat together every day and worked together. In that the first stellar evolution paper with Temesvary he suggested that we should do this, and then he also made some suggestions about the method. Then we just talked to him in regular inters, I think there were only two papers were his and my names are among the authors. We really never worked together in the sense, like, as I do with Thomas here.

Gingerich:

I wanted to ask another question. You weren’t sure what IBM computer it was. Would it have been a 704 or a 709?

Kippenhahn:

We started with a 704, and then we got… 7040 is this right?

Gingerich:

7040 sounds right. I never used one, and I think that’s a possibility.

Kippenhahn:

Well, I would guess that we have mentioned it in the papers.

Gingerich:

When you were working on it, you called it a G-2?

Kippenhahn:

G-2, Gitswite(?)…

Gingerich:

When you were doing the work on the G-2, you didn’t have Fortran?

Kippenhahn:

No, no. There wasn’t — it was a computer in language, rather complicated.

Gingerich:

Did you have to go directly into an octal, or some kind of number system, or did you have a complier?

Kippenhahn:

There was a compiler. We worked on the decimal system. But the storage, the memory cells were counted in octal system. We fed in the program, on paper tape, with paper tape, and we got out the information printed with a normal typewriter, a Telex typewriter.

Gingerich:

It seems amazing, looking back; one got nice results with such primitive computing power, compared to what one has now.

Kippenhahn:

Oh yes. Even before that G-2, the Institute had some GI, which had something like 36 memory cells only, and in addition, the program was stored on punched tape, and they had a reader for punched tapes from the post office, and there were four of these readers, and one could call the other, and The subroutines were small loops on punched tape, and with that machine, which filled the whole room like this room here [about 8 meters square], with that computer, people solved ordinary systems of ordinary differential equations. It’s now compared I would say with a Hewlett—Packard 65 or so. And it used an enormous amount of electricity.

Gingerich:

When you were using five hours per iteration, were you using a substantial block of all the time that was available?

Kippenhahn:

Yes. It was a substantial block. We had, for two or three days in the week, we had the full nights.

Gingerich:

Did you feel pressed that you didn’t have enough computing time?

Kippenhahn:

No. No. It was a complete different way of working with a computer. If you are standing in front of the computer, and if you make a mistake and you have to repair your mistake, the computer is always waiting for you. It’s idling and you have to do something. And so we had some basic rules about computing. One was, if you are in front of the running computer, you are completely stupid, just because you’re getting nervous. And we felt pressed by the computer, if somehow a program didn’t work and we had to change something in the program, in front of the computer. It was a big step forward and we were relieved when, with the modern computers, you go get your program running, and after the first mistake, you are thrown out. You go home, correct your mistake, and go back. We had the full night, and had to use it. And if we failed, we had to wait until we got the next time.