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Interview of Fred Hoyle by Alan Lightman on 1989 August 15, Niels Bohr Library & Archives, American Institute of Physics, College Park, MD USA, www.aip.org/history-programs/niels-bohr-library/oral-histories/34366
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In this interview Fred Hoyle discusses his childhood and growing up in Yorkshire; parental background and influences; early reading in science; early experience with literature; influence of Eddington's books; education at Cambridge; interest in mathematics; early interest in exploring cosmology after World War II; history of development of steady state model; influence of Dirac and preference for understanding mathematics first; thesis work with Dirac; personality of Dirac; history of work on nucleosynthesis in stars: the Cavendish Laboratory, nucleosynthesis in supernovae, carbon production in helium burning, the triple alpha reaction and the excited state of carbon, collaboration with William Fowler, important paper by Al Cameron, work with Fowler and Geoffrey and E. Margaret Burbidge; nonstellar production of helium; defense of the steady state model; "little big bangs" in the steady state picture; Hoyle and Taylor work in 1964 on limiting the number of types of neutrinos; motives in doing science; rejection of big bang model from biological considerations; reading in biology; early career as a popularizer of science; role of particle physicists in making cosmology a respectable science; Mach's principle; attitudes toward the horizon problem, the flatness problem, and the inflationary universe model; Hoyle's work on inflationary behavior within the steady state model; reasons why the inflationary universe model has been influential; attitude toward the de Lapparent, Geller, and Huchra work on large-scale inhomogeneity and influence of that work; theory versus observations in cosmology and problems with the big bang model; attitude toward work on the early universe; importance of long-range interactions and boundary conditions in the laws of physics; ideal design of the universe; question of whether the universe has a purpose.
I wanted to start by asking you a few questions about your childhood – nothing too personal. Could you first tell me a little about your parents? Then, I'd like to ask you about any books that may have been influential. Did your parents have any influence on your deciding to become a scientist?
It's quite possible the answer is yes. But I must say that the whole of our valley was an engineering valley. It was connected with the wool trade. So I was brought up with the clatter of machinery from the factories, as I walked to school every day. Now, that has to have some effect, as well as the home background. My father was always interested in scientific things. He had gotten a number of friends [with similar interests], none of whom had a university education, but they tried to understand what was going on at the time. For example, from about 1922 onwards, they built radio equipment. This was a great mystery in our village, and there were 20 or 30 people who were wiring up their own little radio receivers. There was a far greater feeling that it was possible for non-trained people to understand science than there is today. I think I remember that they had the R. W. Woods textbook on optics and were trying to understand that.
"They" being this group including your father?
Yes. My father also had a chemistry set. I don't remember ever seeing him operate it, but it was lying there in a cupboard, so when I was about ten years old I took it down and began to use it. I had very little use for formal education in those days. I didn't want to have anything to do with school.
How did your mother feel about that?
She knew that legally I had to go to school. So the struggle was between the legal requirement and my determination. That lasted about six months, before it was sorted out. During this time, I read the one book in the house on science, a chemistry book. It was after that that I took these things [the chemistry set] out. And I thought, "Well, if I have to go to school, I have to go," but at least I had the concept that I could read books and so forth. Then I became old enough to go to the town library. It was reasonably well stocked with books. It must have been about this time that popular books on relativity, like [Arthur] Eddington's, were beginning to arrive. So, with all these things put together, it wasn't an unlikely proposition that I would be interested in science. My mother was trained as a musician. My father played the violin. I could see that I didn't have the gifts that were necessary for music. That might otherwise have been an alternative, but I quickly rejected it. By age twelve, I had pretty well decided.
That you were interested in science?
Did you get encouragement from your mother as well as from your father?
Yes. My mother was a school teacher, and by the time I was three she had taught me the multiplication tables. So, by the time I was three, I knew what the school kids we’re chanting in class about at eight and nine. See, that's why I was bored in school. The English classes I regarded as absurd - for a reason that one of my colleagues at Cambridge many years later expressed very well when he said that every child of eight has a perfect knowledge of syntax. [Hoyle laughs.] He said, "So why do we teach English?" I very much had that attitude toward the humanities from an early age. I would do them if I had to do them, but only if I had to. The tragedy of my life is that I never had a teacher who pushed me, from the age of six to the age of eighteen. Until I went to Cambridge, I was just allowed to drift, more or less.
It's interesting that you had that experience with the humanities, considering that you later wrote books of fiction and plays.
Well, the teaching was mostly formal, connected with punctuation and that sort of thing. Occasionally, when an English teacher would get out Shakespeare, although it was difficult for someone of my age to understand, it seemed to me that it had a lot more interest. If I had had teachers of imagination, it might have been otherwise. I suppose that what a kid encounters is fairly formative. Actually, my great grandfather was a poet.
Did you read some of his poems at a young age?
Yes, but they were in what we called the Yorkshire dialect. It's a kind of Anglo-Saxon dialect. That's the only form I knew them in. I didn't realize how sound his command of formal English was. Had he been alive, had I visited him — if the age groups had been somewhat different — then I suppose my life might have been different.
I've often wondered myself what would happen if I had overlapped at the same age as one of my great grandparents.
It could make a lot of difference.
Yes. You mentioned the Eddington book in relativity. Did you read that at the age of ten?
Not his technical book, but a more popular book. I was fascinated, but I didn't understand it. By the time I was, say twelve, I had understood the difference between the layman who is interested and a real understanding. Out of this, there grew my strong feeling that before one can be involved in science, one has to have a tremendous sense of craftsmanship. I still get mountains of letters from the lay public, [proposing] various ideas, and you can chuck it all out because you know that the brain isn't properly ordered to understand the problems they aim to solve.
Were there any other particularly influential books in science that you remember from this age?
Not of the Eddington type. But I would often grab hold of encyclopedias that sort of thing, if I wanted information. Not the good stuff — just information. We had nothing like the Encyclopedia Britannica in the house. My problem always, even before the teens, right to the time I went to Cambridge, was to find anybody — local community, school teachers, or otherwise - who could solve problems. I had reached the stage that there were technical things I couldn't solve, and there was nobody I could go to. It's still true. It's still the biggest bugbear in education generally. Whenever I go to Cambridge -– my granddaughter is there in science — the first thing they say is, "How do we do this one?"
At this young age, did you think at all about the universe as a whole, about cosmology?
That would be very much so, because of Eddington's books. He was always on about this. [Cosmology] was a very powerful theme in his writings. What he was really trying to do was to offset the importance of physics by the importance of the universe, trying to match the strength of the Cavendish Laboratory — in the internal struggles of Cambridge University — with astronomy. It was a political struggle that I inherited myself, years later.
With the Institute of Theoretical Astronomy?
Yes. It's ironic that when I was a graduate student just learning to solve problems, there was this tiny astronomy group, just a minute drop in the ocean compared to the Cavendish Laboratory. In my own Cambridge days, say up to 1970, I suffered quite a bit because of the rivalry between the two. Now, astronomy has overwhelmed [the Cavendish].
Let me ask you a little about your education at Cambridge. You got both your degrees there? I don't know exactly how they translate to American degrees. You were both an undergraduate and a research student at Cambridge?
Who had the biggest influence on you at Cambridge?
Nobody had much influence on me in my first two years. I packed what are four years’ work into three, which was foolish for a person from a small, remote part of the country, not coming from one of the big, public schools. The first two years were formal, learning things like mathematical analysis. The third year was preparation for research. Then, our lecturers were world class figures, and they had very considerable influence. People like [Paul] Dirac and Eddington would have had a huge influence. At the end of my second year, I made an effort to read Dirac's Quantum Mechanics during the summer, and Eddington's Relativity.
You were reading it again at this point?
Yes, at last I was tackling relativity properly. I had dropped the mathematical technique pretty well stone dead by then, which is a pity because there was a lot still to learn.
When you say you "dropped" it, do you mean you stopped taking further courses in mathematics?
I had completed the normal courses. Of those that were advanced, it wasn't really obvious what one should take. Mathematics is like a huge ocean. You feel like if you are thrown into it, there is an infinite distance to swim and you still get nowhere. Whereas, if I had known what to do, it would have been fine.
When you say "what to do," do you mean what mathematics would have been appropriate for the science that you wanted to do?
So, you already knew that science is what you wanted to go into?
Yes. I knew a fair amount of nineteenth century mathematics. But I didn't know any twentieth century mathematics. I used to puzzle about what later became distribution theory. I still remember in the summer of 1935, when I read Dirac's book, coming onto a certain page and finding it very mysterious. But I had to pass on. Time was of the essence, so I couldn't do more than maybe spend an hour on that page. And that was the page [Richard] Feynman subsequently built "his path integrals out of. [Hoyle laughs.] Feynman, of course, was already a research student, so he could really think about it. But I was still an undergraduate, and it is the essence of being an undergraduate that you learn a lot of things only superficially.
But you realized there was something missing there.
Something missing, yes. But also, we students were rather badly served, in the sense that most theoretical physicists had a strong down on group theory. Indeed, had I even been told that group theory was highly important, it's not very clear what could have done about it in the 1930s. There were no suitable books on group representations. There was a book by [Eugene] Wigner, but it was in German. It's a difficult book even in English. It's an excellent book if you already understand [the subject]. If you want to look up a huge amount of fine detail, then it's very good from that point of view. But it would be very difficult to learn from. All these special courses that students go to nowadays were not available.
You explained how you were interested in science from an early age, but what got you interested in cosmology in particular?
Eddington's books, when I was a child.
When you read Eddington's book, and other books that presented cosmology, and you encountered the big bang theory, did you have any preference for open versus closed universes? Any preferences for the different possibilities within the big bang?
No, I don't think so. I think, if I go back to my student days, I simply learned relativity unemotionally. I didn't have any feelings. I just wanted to know what had been done. In those days, there still was not the Robert son-Walker metric. That was not available. It might have been available in the Avant garde literature at that time, but I didn't encounter it. From 1936, I was doing research in nuclear physics, so cosmology was only a side issue to me. But had I been doing research in cosmology, I would have paid a lot of heed to H.P. Robertson's famous article on cosmology in Reviews of Modern Physics. When I did read it, it happened in a rather strange way. After the war, I began to learn technique again because I had to teach undergraduates — that's when you really have to understand, when you have to teach. I used to work quite a bit with [Hermann] Bondi in those days. Bondi was not sure what he should do. His expertise was in partial differential equations, fluid motions, things of that sort. So it was a big step when I suggested to him one day that maybe he should look at cosmology. I think he had been asked by the Royal Astronomical Society to write what was then called a Note, and we were discussing what he should write.
Why did you suggest cosmology?
Because, to my mind, the subject had been in abeyance for a long time. The Note was supposed to bring together a body of knowledge, if it seemed timely that that body of knowledge should be described. It was like a review article. Bondi thought this was a good idea so he began to read in relativity and cosmology, and then he came across Robertson's article. At that stage, I also went through it in some detail. It was only then that I began to have technical feelings about cosmology. If you remember Robertson's article, it's fairly encyclopedic in its structure. He doesn't express himself emotionally in favor of this or that. He just covers the possibilities. And so we naturally thought, "Has he really thrown his net wide enough? Are there any other possibilities?" That's when we began our own cosmological speculations — from the point of view of getting the range of possibilities as wide as we could. Was there anything that had been missed?
And was that seed to your later thinking about the steady state?
Yes, I think so. We had a strong hunch that there must be something [else], because there was no creation of matter in it, and we felt that that had to [be given] expression at some point.
Why did you feel that creation of matter was an element that should be incorporated [in a cosmological theory]?
The actual historic sequence of events was this: It was [Thomas] Gold who had the notion that perhaps one might have a steady universe. Bondi and I quickly pointed out that you couldn't have a steady universe unless you had creation of matter. Bondi, in particular, rejected it for a while. I accepted Hermann's rejection temporarily, but certain events in the next eight months returned my ideas to it, and in early 1948 I discovered how to deal with creation mathematically. Then Bondi returned to it. That was the sequence of events. Gold had the idea. I was very interested that when I got the mathematical way of doing this — it was a crude way of coupling a scalar field to gravity — I found that the Gold steady [state] idea came as a consequence. Then they [Bondi and Gold] returned to it, and tried to use the steady idea as a philosophical principle, which to me has always been the cart before the horse. I've always felt that one must get the physical equations [first], and then one sees that the steady state is an asymptotic solution to the equations. Everywhere I've ever seen the coupling of a scalar field that creates matter to gravity, it leads to the steady state theory as an asymptotic solution.
Does the Brans-Dicke theory do that?
It doesn't create matter.
It has a scalar field, but it doesn't create matter.
That's the key thing. So, we've gone from various stages. I had a very crude system to do it. Then, in the 1950s, Maurice Pryce produced an action formulation that allowed one to create matter, and it led to the same ultimate conclusion. But the Pryce action has the difficulty that it is not invariant with respect to changes in length scale, the so-called conformal invariance. Narlikar and I found the way to do this in 1972-1973. Our theory is conformably invariant, and, again, it has the steady state as an asymptotic solution.
I think I've pushed you ahead too much in time. Let me go back for a moment. In the late 1930s, when you were at Cambridge as a student and you became aware of the Robertson paper, what was the general attitude about the big bang theory? Was the interpretation of Hubble's discovery accepted?
Oh yes. There was never any question at all about that. British astronomers were never plagued very much by the Shapley-Curtis controversy.
Let me go back to something you just mentioned, that in developing your own version of the steady state theory, you felt that the equations and the physics should come first and the philosophy should come second. Could you elaborate slightly on that? I was already going to ask you why you felt that your version of the steady state needed to be derived more closely from the equations [than the version of Bondi and Gold]. Is that something that is just basic in your approach to science?
Yes. That might have been Dirac's influence. Dirac always said, "Find the mathematics first, and think what it means afterwards." That was probably a canonization of his own experience with negative energy states. He originally thought they were electrons and protons, that positrons were protons. But later, he found vacuum states. I was one of his few students. He always said, "Don't go at it like an engineer, in a mechanistic way. Learn the mathematics first." There was a great introduction to one of his papers — I think it was the paper in which he infers the magnetic monopole — in which he says that the nature of physics is that one must have the answer in mathematics first. Using previous ideas, bits and pieces of previous physics is not the way to make real advances in physics. The better way is to study abstract mathematics. It was almost impossible to be the student of a man who held that extreme view arid for it not to rub off a little.
Was Dirac your thesis advisor?
Yes. Well actually, I had a strange business. I got an appointment [as a fellow of St. John's] before my thesis was due. So it was all turned around. Normally, you go through your thesis and then you look for a job. But with me, it was the other way around. So I never bothered very much about the thesis. But I did discover that when I began to get a salary, as long as I could claim to be a student, I was free of income tax.
So it was convenient.
It was convenient indeed. That is why Dirac agreed to be my research advisor. He thought it amusing. He didn't want students, but here was a student who didn't want a research director. That was the typical Dirac sense of humor. But he had a conscience, because he used to invite me to tea once a term. I very quickly divined that the German style of discussing physics, hammering away at it and discussing it, is what Dirac hated. What he liked to do was to think quietly about a problem, work out the solutions, and then present the solutions. He didn't want a lot of talk at the blackboard. I realized this, and so I would talk to him about other things, like mowing the grass — mundane matters. And I discovered that he had a keen interest in practical problems. He's always given out as a person who was impractical. That's just wrong. The nearest I ever came to having a serious row with him was when we were building a house in Cambridge, and we didn't fit a heat pump. He said that was ridiculous [Hoyle laughs.] This was typical of Dirac. If he ever built a house, it would have to have a heat pump, but to my knowledge he never did.
That's interesting in light of the earlier thing you said about him, that you shouldn't approach physics like an engineer, but in terms of abstract mathematics.
He reserved all his engineering for the everyday world.
So he was able to compartmentalize these two different approaches.
Was he interested in philosophical matters at all? Did any of that rub off on you?
No, nothing that I ever came across — except possibly this from a seminar in 1938. I sat on the fourth row, as befitted my status. It was Bernal who was giving the seminar. He was explaining some complicated thing in chemistry. I think it was a theory of Ising's. Bernal made some remark like, "It's not the right theory, but it gives the right answers." And Dirac drew him up straight away and said, "That isn't right. If it gives the correct answers, it's the correct theory." That was absolutely Dirac's attitude. It didn't matter what the theory was, if it fitted the observations, it was the right theory. The only question was, "Did it fit?"
That sounds like Richard Feynman's attitude toward physics.
Let me move closer to the present. Can you recollect at all your motivations in your work with Fowler and the Burbidges in 1957 on the synthesis of elements in stars?
I started in 1945 with equilibrium calculations. I'd been started on it basically by a visit to Mount Wilson, in which I met Walter Baade. Baade brought the phenomenon of supernovae to my notice. I'd actually studied the case of novae, and I had what were then heterodox ideas about novae. I felt that they were stars at an advanced stage of evolution, not at an early stage. The current theory was that novae were giants. And a nova was like a flare on the surface of the sun. I happened to be able to pay a visit to Mount Wilson, just over a weekend in 1944, and I met Walter, and he agreed about novae, but he said to me, "I don't understand why you should be interested in novae when supernovae are far more interesting." He gave me some papers, and we talked about it. Within a matter of a week or so, I realized that this supernova business might take the temperature environment [in the star] into regions that I had not previously contemplated. There had to be an ultimate temperature environment at which one would run into statistical equilibrium. And that was something I knew I could calculate. But I knew I would need the energies of nuclei, their masses. I didn't have them in the radio station where I was. I managed a month or two later to find some excuse to come to Cambridge, and I ran into Otto Frisch. I should explain that I actually knew the senior physicists at the Cavendish quite well, because when my first research director, Rudolph Peierls, left Cambridge in 1937, he suggested to people like [John D.] Cockcroft that they ought to have a theoretician. He'd been the theoretician on their little management committee. Amazingly, they put me -– a second year graduate student — on this committee. So although I was only a second year student, I knew a fair bit about the Cavendish. That's what made my subsequent almost ejection from the Cavendish rather bitter. The nuclear physicists were essentially kicked out of the Cavendish. But in those days — [Ernest] Rutherford was dead only months -– the nuclear physicists were trying to do things by committee. They didn't have a director. I happened to know Frisch in this way. I ran into him, and I explained that I wanted nuclear masses. He said, "There's something I can give you," and he gave me a table of nuclear masses in German, by a chap called Mattauch. I abstracted from this the nuclei I wanted. And so I was then able to make a calculation, to raise the temperature and see what happened as one ran into statistical equilibrium. I found to my great interest — we are now coming to the summer of 1945 — that I got the iron peak. There was enough known from the work of [Victor] Goldschmidt, a Norwegian chemist — this was before Harrison-Brown — that there really was a peak there. So although I had only crude masses, there was a general match. I was quite excited. Then, in the late summer of 1945, I said, "Well, what happens if I keep the temperature rising." Then I found that the nuclei broke up into alpha particles, and then ultimately into nucleons. I realized suddenly that if you put the temperature up, as the star evolved, that there had to come a time when nuclear reactions were energy absorbing rather than yielding energy. When the university started, and I gave my first seminar — Dirac was there and Maurice Pryce and a crowd of people — I talked about this and how ultimately, if you had a star that reached this point, it would have to draw on gravitation to supply the energy, and therefore it would be in a state of dynamic collapse. Then, it all came together in the idea that if the center of the star collapsed, the outside might blow off. That was my first paper, on nucleosynthesis, published in 1946. By this time, I was a young lecturer. I was learning a lot about the mathematics I should have learned better as an undergraduate. We had then a much heavier teaching load than they have today. [Of course], they have a lot of committee work today, so that about evens out, I suppose.
Were you interested in making elements in stars at this point?
I was interested in all sorts of things. There were many directions. If you look at my papers over the period of 1945-1950, you find they go in all sorts of directions. My head was exploding. Astronomy was at a stage that if you knew any physics at all, there were a hundred things you could do. But I did get a research student, a chap called Dresel. I remembered a point in Bethe's paper of 1939, on the carbon-nitrogen cycle, where he hints at how you would proceed to keep going after the carbon-nitrogen cycle. So I thought to myself, "I've done the end and Bethe did the beginning. What happens if we try to close the gap?" I gave this as a research problem to this student. He was the only chap I ever had as a research student who got dissatisfied and left. Everybody else finished their Ph.D. thank goodness. Our ethic was that if you gave a problem to a research student, it belonged to the student, not to the director. So although we had gone quite a long way in the business of making carbon from helium — I'm talking now about 1948 and 1949 — there wasn't anything I could do about it, under our system. Every student is given, say, six years in which he can [finish]. So if after two years, he seems to pack things in, you still have to give him another four years. There was nothing I could do. So when Ed Salpeter published carbon production by helium burning, in 1950 or 1951, I was mad, because I felt we'd missed out on it. Then I had an invitation to Caltech in the winter of 1952-1953. I determined to talk on this. I had to give some lectures. I thought this would be an opportunity to review this first step that I'd missed out on. Of course, I was heavily motivated to see if there was anything in addition that Ed hadn't got. What he hadn't put in was what happened to the carbon that is made from the helium if there is still helium around. I realized that the carbon would go very quickly to oxygen. So it didn't look like a very good way to explain the carbon in the world. But then I said, "Well, there is carbon in the world, obviously, so how are we going to deal with that?" I realized that the only way was to make the reaction rate of the triple alpha reaction much quicker. There is just one way to do that, and that is to have a resonance level in the carbon nucleus. One could calculate what this optimum energy level would be. I did the calculation and found a level where no level was supposed to be. Then I went to see [William] Fowler. Now he gives a story, which isn't true, that he told me I was crazy, to get out. He didn't. He was very polite. He called his research students, and they discussed whether they could check it. I have to be right [about the story], because they checked the situation within two weeks, and if he'd told me to get out, they wouldn't have done that. In fact, Fowler, on the blackboard, explained to his students that if [my predicted energy state] was a spin 0 [nuclear state], with a certain parity, it would have escaped previous experiments. So they should design the experiment on the basis that [the state] had that spin and parity.
So Fowler knew where to look.
When you realized that you couldn't make enough helium in ordinary stars, did that shake your faith at all in the steady state theory?
I never had any faith. I don't take much stock in faith. I'll explain that to you later. Anyway, when they found this state, I redoubled my efforts in my Caltech course of lectures. Then I found the further processes of carbon-burning and the oxygen-burning. I wrote all this up. It was delayed about a year. It appeared in 1954. I called it the origin of nuclei from carbon to nickel, paper I, because I deliberately left out all neutron reactions — not because I hadn't studied them in some detail, but I realized the subject was too vast, so I kept to charged-particle reactions. My intention in a further paper II was to include neutron reactions. Two things prevented me from writing paper II. When I got home, I had a paper from Chandrasekhar to referee [for The Astrophysical Journal]. A couple of referees had recommended rejection, but Chandra was uneasy about it. So he sent the paper to me just to take a look. The paper was by Al Cameron, who was then a young research worker at Chalk River, and it had the carbon 13 alpha-n reaction. I thought, "Oh my God, I've missed that!" Then I knew why it had been rejected. Chandra didn't give me the names, but I could guess who the referees were, and I knew why they had given bad reports — because Al had made an important discovery. So I wrote back to Chandra and said, "Of course, you must publish it."
That was in 1954?
Somewhere around there. Then, Willie Fowler came on sabbatical to Cambridge, and the Burbidges were both in Cambridge. The only house my wife and I could get was ten miles south of Cambridge, so communication was difficult. I always had the agreement with Cambridge — they were very generous at giving me leave — that when I was back, I would do my full stint as a university lecturer. So I didn't have much time. And as well as logistical difficulties, I had some reservations about their project. It involved slow neutrons, so I would otherwise have been interested. But I knew that the cross sections of slow neutrons on various elements can be immensely dependent on which isotope you're using. And all the cross sections we had in 1953 and 1954 were just total cross sections for each element. So I was very dubious as to whether the aim of Fowler and the Burbidges would be any good. Actually, they dealt with the difficulties in a rather ingenious way. They avoided the heavier elements and for the lighter elements Fowler felt that he could calculate neutron absorption cross sections from known energy-level diagrams. I think Burbidge did the calculations of the resulting multiple simultaneous equations. What they got was interesting. They started at something like neon and went up to scandium or thereabouts, calculating production abundances, particularly for odd nuclei that were quiet good. Then we all came together at Caltech in 1955-1956. Willie had arranged to get the Burbidges fellowships at Caltech. I had an invitation. Several other things had happened that were favorable. Suess and Urey had produced a new table of abundances, which was an update of Harrison-Brown. That was a tremendous piece of data. Technetium had been discovered by Paul Merrill. That really showed that nucleosynthesis had to be important in stars. To me, it was perhaps still more important — more important than to my colleagues I think — that Barbara and Martin Schwarzschild had done a survey of stars in the solar neighborhood and had found a variation in the ratio of metals to hydrogen of the order of three. Not the big ratios of a hundred that came along a year or two later. That really stamped out the possibility of the synthesis of the heavy elements being primordial. So we had all these things. My contributions to BBFH [Burbidge, Burbidge, Fowler, and Hoyle] were concerned mostly with neutrons. Because if you look at the r-process, in particular, it's really an equilibrium calculation. I agreed with Fowler about what beta decay rates I should put in. So there we were and it was done. Actually, we made some terrible mistakes, which are not usually emphasized!
If you wanted to talk about that, that's fine. I wasn't planning to ask you about any mistakes.
I'll just mention the worst mistake. I think it came from Walter Baade's insistence that the decay of a supernova was 55 days, plus or minus half a day. That meant that you could not make any case at all for the production of nickel 56. You really had to go into the iron peak rather slowly to avoid nickel 56. And that led us into the californium mistake. We were just blocked off from the correct dynamics for that process.
I started to ask you another question before. When you realized that helium could not be made in stars, how did you fit that into your cosmological views?
It had always been with us. Actually, Bondi, Gold, and I wrote a short paper called "Black Giant Stars" in 1955 in which we said that you had to have more helium than you could make in stars, in visible stars. We had it made in clouds, which subsequently became the giant molecular clouds. So we were well aware that helium could not be explained in ordinary stellar nucleosynthesis, already in 1955. But I said before that I don't really work in terms of belief. I didn't go beyond saying that the steady state theory is a possibility. When I have defended it, I always defended it on the grounds that what were claimed as disproofs were things that a mathematician would not regard as disproofs. They were full of holes.
That's right. I asked Bob Wagoner to do a lot of calculations on that to see if we could get the abundances right in what we called a little big bang. The one interesting thing in that particular part of the' paper is that there is some case for the occurrence of the r-process in little big bangs. That is, the ratio of neutrons to heavier elements is right for the r-process. I have not at any time since seen anybody who has suggested what I would call an alternative, plausible r-process, once californium-254 was out of the picture. There is another interesting point where we went wrong. You can take a local object, and you can ask what its mass would have to be in order to produce the standard ratio of photons to baryons — something like 3 x 109 — that you get from the primordial synthesis of deuterium and lithium. If you do it, as we knew physics at that time, the mass is about 1020 suns. But we didn't do that case in our paper because it would have seemed almost too ridiculous to consider a mass of 1020 suns for a little big bang. That's practically the whole [observable] universe.
And the photons just come from the amount of radiation in thermal equilibrium that you would expect in a star of that size?
Yes. There is a standard formula for it, going back to Eddington. But the point that has emerged now, in the 1980s, is that there may be nonbaryonic matter — a hundred times more than baryonic matter, perhaps. Then you can calculate what is the total mass of such a little big bang, still sticking to the same ratio of 3 x 109 for photons to baryons. And the answer is 1016 [suns]. That's just a nice big cluster [of galaxies]. That original calculation that I was trying with Bob Wagoner and Willy Fowler has now gotten more interesting. If we say that the bangs are cluster sized, then we are not in a bind about primordial deuterium, helium, and lithium.
And this could all be done within a picture of a global steady state?
Yes. But I have had a problem with the steady state in the following sense. If you work from the mathematics to the universe, there's nothing I can see in the mathematics that would require anything more than average values to be maintained. That's to say, if I average over a certain time span, which should be at least a few Hubble periods, the situation is steady. Whereas, Bondi and Gold, with their "perfect" theory, require things to be steady on a timescale of, say, a hundredth of a Hubble period. Now that is a much more rigorous theory. To defend it against observational attack is much harder than to defend my version. This has always been a problem. I think if I had to give an opinion on the attack that was made against the Bondi-Gold restricted form of the [steady-state] theory, I would have to say today that it is a lot weaker than most people think, but it is probably strong enough. But it isn't strong enough to rule out the version of the theory averaged over a whole Hubble period or longer.
I have some questions about another one of your papers. In the last decade, there has been a lot made of the ability to limit the number of neutrino species from big bang nucleosynthesis calculations and the observed helium abundance. My understanding is that you and Tayler were maybe the first to have pointed this out, in your paper of 1964. Did you take that seriously at the time?
Well, we knew, of course, of the muon neutrino, and I suppose we realized that this would make a difference. I remember Steve Weinberg asked me why didn't I use the abundances to argue back to the temperature. It wasn't doable, unfortunately, because a slight variation in the temperature makes a big change in the abundances. And we didn't know the abundances accurately enough to do the calculation in reverse.
Would that have been the same calculation that would have allowed you to give a specific number of neutrino species, [as constrained by the helium abundance]?
I think we could not have seen it as anything like the importance it is given today. If I were to claim that we saw its ultimate importance that would surely be wrong. We weren't working with that level of accuracy.
But you did have the idea.
Did it occur to you in that work with Tayler that the blackbody radiation might survive to the present, appropriately redshifted?
Of course. This was unavoidable. We did not invert the problem, in the sense of going from the helium abundance to the background, because this would have been meaningful only if we'd had an exceedingly accurate helium value — which we didn't.
Let me return to your paper with Tayler in 1964. After calculating that the ratio of helium to hydrogen should be greater than 0.14, you say that if it could be "established empirically that the ratio is less than this in any astronomical object, we can assert that the universe did not have a singular origin." Was a possible disproof of the big bang theory one of your motives in this work? If not, what were your motives? 
No. My motive, as always in every piece of work I do, is to find out. The truth is more important than one's own predilections; a maxim which I feel is largely ignored at the present day.
I have a related question. Although you have been one of the advocates of the steady state theory — and I understand the sense in which you consider it just one possible theory — many of your theoretical calculations have been used by others as strong support for the big bang theory. Does that present any conflict to you?
Well, it does today. It wouldn't have done when Wagoner and Fowler and I were writing our paper in 1967. In those days, I didn't have any strong feelings about it. But today, I do have rather strong feelings that I don't think the big bang is right. I happen to get those views from something that hardly anybody else believes, but I just don't think that the huge complexities of biology could have evolved in a mere 1018 grams of material on the earth. (The biosphere of the earth is 1018 grams.) I don't think that chemical evolution [on the earth] could possibly have produced the biological system. I think this has to be considered as a cosmological issue.
You discussed this a little in your recent paper in Comments on Astrophysics.
Something like that, yes.
So you think it requires more than the Hubble time to produce the biology we see?
Yes, that's right.
So we need more time than the big bang gives us.
Yes. Now, I'm feeding in ideas that most people wouldn't accept at all. But to me, they have a strong force.
When did you develop this idea? Isn't this an idea you could have had many years ago?
Most of the last ten years I've spent reading technical biology. It's come as a result of understanding the complexity of enzymes and all the rest of the biochemistry that is involved. I've never learned biology the way a student learns it, with all the funny names and classifications. To me, that doesn't mean anything. But what the various molecules do is very striking. Physicists set no store at all by the words they use. Whereas, all biology students at university tell me that unless you use the right nomenclature — even if your ideas are right — you get heavily marked down. They make a huge performance out of all the names.
I think it may be even worse in medical school.
It may be. I just say, "The enzyme that does that," whereas they have all sorts of names for things. I suppose that if you are talking among yourselves, it makes useful shorthand. But it has no consequence at all.
But you said that up until your reading in biology…
I didn't know enough about it.
You weren't thinking of your new argument and the use of your calculations to support the big bang was perfectly agreeable to you.
Let me ask one more question about your work at this time before I move to the present. Your radio talks in the late 1940s and some of your popular books have been very influential. I was wondering what motivated you in this kind of popularization of science.
It was really very simple. They started because Herbert Butterfield, I think, was asked by the BBC to give a course of five lectures. The idea had been started by a fellow of my college [St. John's], Peter Laslett, who had persuaded the BBC to implement the idea that there might be a high level market for university-style lectures. Laslett was a historian, and Herbert Butterfield was a fellow historian. Now, at a rather late moment, Butterfield contracted out, saying he just didn't have time to prepare the necessary material. So Peter came to me after dinner one evening at St. John's, and said, "Look, are you in need of earning some money?" I replied, parrot like, "My God Peter, am I in need of earning some money!" To which he said, "I can get you a contract to give five talks on astronomy, at something like 50 pounds a time. Are you interested?" So that's why I did it.
He must have thought that you were up to it.
I suppose so. We were together at the college, he knew me quite well, and I’d often talked to him about general subjects like history, and he knew I had fairly wide interests.
So he must have thought you could tell a good story.
Back to the money as a perspective, I think my whole salary for the year was 400 pounds at the time. So 250 pounds was quite a lot. You know what Dr. Johnson said. "Sir!" he said, "There are few more innocent ways in which 'a man can be occupied than in the getting of money." [Hoyle and Lightman laugh.] That's the answer to your question.
I've heard that you originated the name "big bang." Is that correct?
Well, I don't know whether that's correct, but nobody has challenged it, and I would have thought that if it were incorrect somebody would have said so. I was constantly striving over the radio — where I had no visual aids, nothing except the spoken word -– for visual images. And that seemed to be one way of distinguishing between the steady-state and the explosive big bang. And so that was the language I used.
Are visual images important to you in your actual research, besides the pedagogical use?
No. I was never a very good geometer. I had to do all my geometry algebraically. I'm not very good at visual imagery.
I want to ask you some questions about recent developments, but first, from your perspective now, what would you say are some of the critical events that led to cosmology's becoming a respectable subject of study?
I think it really dates from the particle physicists seeing cosmology as a vehicle, a convenient laboratory, for the execution of their ideas.
That would be fairly recent.
Yes, that's fairly recent.
Mid 1970s or something.
So you think it was the particle physicists who helped give cosmology respectability?
I think so. I think if cosmology had had to depend on astronomers, it would be in a much weaker state. A great deal of sound and fury hasn't really led to any improved understanding of astrophysics that I can see. I think if you asked the young kids taking a course in cosmology today what are the reasons for believing in the correctness of the big bang, their first two reasons, probably their only good reasons, would be the reasons that we already had in 1965 — the deuterium, helium, and lithium [abundances] and the microwave background. The microwave background now is in awkward shape because of the recent Japanese sub millimeter measurements. If those [measurements] hold up, there is potential trouble there.
But you think it is the interest of the particle physicists, rather than those two observations you just mentioned, that gave the subject its respectability?
Yes. I sometimes ask myself, "If I had to attack this popular view [of cosmology], who are the hardest people I'm going to have to push against. And I feel it is the particle physicists, not the astronomers. The big guards on the front line of the scrimmage are the particle physicists. [Laughter.]
That's a wonderful way to look at it. Do you remember when you first heard about the horizon problem? I realize that in the steady state, there is no horizon problem.
Actually, we did have a problem even in the steady state, because, by the 1960s, Narlikar and I began to see the steady state as an asymptotic solution. Basically, just as in any other expanding material system, random motions disappear with adiabatic expansion. But you aren't sure that random variations in the metric are going to adiabatically expand away. So we did a lot of work on that. Because it's really a question of Mach's principle, which is another way of putting it. There have been a lot of considerations of Mach's principle in relation to general relativity. And it took a long time, from the 1940s, to the 1960s, before people were generally convinced that Mach's principle was outside general relativity. You have to add cosmological boundary conditions to general relativity.
So you were thinking of that in terms of boundary conditions?
We were thinking of that, which is another way of putting the horizon problem.
I guess one could also think of it in terms of initial conditions, which is another boundary. I guess you must have considered it to be a serious problem, since you were concerned about it within the steady state.
Yes, we did, but it was from Mach's principle.
The way to institute Mach's principle.
Yes. Because you always have to remember that Gödel had produced a model, a rotating universe, in which one would be in trouble with Mach's principle. It was important to us, because we had the universe driven by the creation [of matter] for an infinite number of expansion periods, that we were not getting into a Gödel situation where the boundary conditions were wrong.
Within the big bang model, did you think that the horizon problem was serious?
Well, I don't think it is solved, no. I have to have my own… Frankly, I have a lot of trouble following…
I have to do it my way. That's what I'm trying to say. And I think the way I do the inflation models must be the same, because I find it in terms of what you might call a cosmological constant. The way I do it, it doesn't create matter. It's just the old de Sitter solution.
I want to ask you about the inflationary model in a moment, but I was first just interested in how you thought the horizon problem might be solved, whether you ever considered appropriate initial conditions as a legitimate solution to the problem.
You mean specialized initial conditions?
Yes, specialized initial conditions.
I never did, no. If you had asked me in the early 1960s what would be my objections to the big bang [model], specialized initial conditions would have been one [of my objections].
Would you feel the same way about the flatness problem? Or do you consider that [to be a problem] — the statement that the gravitational energy exactly balances the kinetic energy?
That's the closure problem, isn't it? I think the observations would vote for an open universe. Except if one makes an ad hoc addition of missing mass.
I was thinking of the statement that it seems to be unlikely that the ratio of gravitational to kinetic energy would be so close to unity today, so many Planck times after the beginning [of the universe]. Do you put any stock in that problem?
Well, I sort of feel that it's not really my problem. It's a problem of the people who want to argue for the big bang scenario. It's their problem. But I should tell you that in any of these arguments, I never overweight the arguments against my opponents. I think that [the flatness problem] is a strong argument against the big bang, but I always discount arguments against the other side because I feel you want to keep a balance. For instance, if a person has a theory that I am attacking, and the form in which they present the theory can be knocked down, but there is another form that evades my objections, I never just concentrate on knocking out the published version. I look at the other one. I like to overweight the opponent's position, because otherwise you can go terribly wrong. I believe that this [the flatness problem] is serious. If I were arguing for the big bang, it would worry me very much. But, as I said before, it's their problem, not mine.
Let me ask you a couple of questions about the inflationary universe model now. I realize that inflation is just a different form of the steady state, but when you first heard about the work of Alan Guth and other people, how did you react to it?
I was strongly caught up in biological studies at that time, so I didn't react very strongly. I've returned to cosmology only in the last two years, and so I've begun to construct what I think is the equivalent of the Guth inflationary model. In a sense, I wish I had studied it in 1980, when he produced it, because to me it is only a way of explaining why we should have a cosmological constant. And that doesn’t seem to me to connect to the particle physics in a way that I would find interesting. I know that they go into the inflationary state, for something like 65 orders of magnitude of the expansion factor, but they mysteriously come out with the radiation and the particles, and I don't see where the particles and the radiation have come from.
So you think the theory is not complete at the moment. Are you willing to accept the cosmological constant in your own work?
Yes. It turns out that in the mass propagator that Narlikar and I used in our work around 1970, you cannot change the wave equation if it is the solution of a delta function in space time, that is to say, a point source. But if you take a line source, you can add a term and still maintain scale invariance.
And that extra term corresponds to the cosmological constant?
That extra term is the inflationary term, yes. We got it around 1970, but we didn't employ it.
Does it come in naturally? Does it have a natural value, or does its value have to be put in from the outside?
It's a cube term in the wave equation, for the mass propagator. There's a constant multiplying that cube term, and that's the cosmological constant. There's no way of finding out what the constant should be.
Would you think that [term] would be motivated by some of these cosmological problems?
You mean to find out what it should be?
Or to find out that it should exist at all, that there should be this term instead of zero. You said that you were working out the inflationary models in your own terms.
Well, when I found out that it led to the de Sitter metric, which is empty, and then I wasn't very interested. The steady-state equations lead to the de Sitter metric, but it [the model] is not empty. So that's a difference. So I feel it's probably a mathematical fiction, not the real physical thing.
So you would prefer then, in order to get out the so-called benefits of inflation, to stick to the steady state?
If I am going to get something that looks like inflation, but that really does create matter, then I find that the steady state is more attractive.
Why do you think that the inflationary universe model has been so influential?
Because it obtains some of the advantages of the steady-state theory (e.g. isotropy, flatness…) while still adhering, at least formally, to the big bang.
Let me ask you about an observational discovery. Do you recall when you first heard about the work at the Center for Astrophysics by de Lapparent, Geller, and Huchra on the distribution of galaxies on spherical-like surfaces. That was around 1986.
Did that alter your picture of cosmology at all?
Yes, it altered my picture, in the sense that it suggested to me that if I am going to have a model in which there are many creation centers, what we used to call little big bangs, and not just one big bang, I had better make them related to that picture. That sets the scale. And that automatically told me it was going to be 1016 or 1017 solar masses.
And that's why that number that you had derived in a different way was interesting to you. In this recent paper of yours in Comments on Astrophysics, you wrote that the big bang theory, in its relation to observations, hasn't progressed one inch since 1965. Do you consider that to be a problem with the theory or with the observations?
No, it [the problem] is not with the observations, surely. The observations have been an avalanche compared to what had gone before. I think it's a problem with the theory. It may be unique in the history of science that a correct theory doesn't lead to profitable correspondences to observations. It would be the first time in science…
…that a correct theory has gone for that long a period without good contact with observations.
Let me ask you a broader question along the same theme. In the last 20 years, how do you think theory and observation have worked together in cosmology? Have they worked together successfully or poorly?
I think you could say that there has been some development in the primordial nucleosynthesis — this group of three or four key nuclei. I think they have done some pretty hard work trying to relate the cosmological values to the observed values, as a function of the photon to baryon ratio. How good this is, is another question, about which one might be optimistic or cynical according to one's point of view. I'll just present the cynical view. The helium value of 24% seems to me to be based on a trace sample of material, namely the dwarf galaxies. It would seem to me quite clear that if there are samples around in the universe running all the way from 20% to 30% — and there are quite a few observational astronomers who will show you evidence for that being true — then if you work hard enough and confine your attention to a particular kind of object, you can get the value you want [for the helium abundance]. Now the lithium 7 to hydrogen value. Is it 10-9 or is it 10-10? And what does it mean? Well, 10-10 is a pretty good value from carbon spallation by cosmic rays. So what does that mean? It looks to me that there is a case from the population I stars that 10-9 would be a primordial value — from the point of view of the disk of our galaxy, at any rate. So, I am not altogether sold that these are very good numbers. I have a feeling that the astronomers who claim these as good results [in support of the big bang theory] wouldn't be so assertive if they didn't feel that they had a strong theory behind them. If the observers were leading and had to stand on a value, it wouldn't be anything like as precise as they claim. That's my feeling. That, I would have thought, was almost the strongest piece of observational correspondence [to theory]. What else is there? Yes, there is the microwave background. A lot has been done at shorter and shorter wavelengths.
Let me ask you about something on the extreme theoretical side — the extrapolations way back into the early universe in the big bang theory, done mainly by the particle, physicists in the last decade. Do you think that kind work of theoretical work is valuable at this time?
I can only answer that by saying that if I was back in 1970 and was adjudicating on the award of money to research grants, I wouldn't root very strongly for giving a lot of money to that research. I have a strong feeling that progress comes out of relating mathematical analysis that doesn't have many parameters in it to observations. For this [new work in particle physics applied to the early universe], the theoretical parameters are almost infinite, it seems to me. Of course, there are no observations. I find it very difficult to think it's worth spending any time at all on problems that relate to the early universe. It's quite different with your point about the distribution of galaxies. I take it we're talking about a distance scale of about 5000 kilometers per second. I think that's very interesting.
Did it surprise you when you heard about that discovery?
Not entirely. I remember Donald Shane counting galaxies out to about 18th magnitude — just a straight count on the sky. And he got a large-scale pattern. He discussed with me whether there were clusters of clusters. So that is rather what I expected.
So you knew about the idea.
Shane didn't have redshifts. He just had the counts [positions] against the background. But it was already clear that if you counted say, between· 17.5 and 18.5, you could see a possible hierarchy. So my mind had been prepared for it. I wasn't shocked.
What do you think are the outstanding problems in cosmology today?
My attitude is unorthodox. I don't know whether it is useful or not.
I would very much like to hear it.
I take the view that the laws of physics are not what people think they are. What we count as the laws is a combination of the true laws together with a cosmological influence. There are long range interactions. When you look at a book on particle physics and look at the masses of the various octets, nonets, deciplets and so on, if you believe in the canonical view of physics, then all that is a part of basic physics. I don't believe it is. I think that those numbers
…are determined by long range forces.
Yes. There is a basic physics. But in my way of looking at things, I don't have to assume that the various peculiar aspects of physics — particular masses etc. –- depend wholly on the basic laws. They are also a product of the way the universe actually is. What we actually see in the laboratory is a product of two things: long-range cosmological influence and the laws, which are very very much more elegant and symmetrical than particle physicists believe. None of this awkward left-handedness — it's just a cosmological influence that is producing that. The various masses, and so on, are not as ugly as they seem to be. To give an example, I feel that modern cosmologists are the way astronomers were for almost two thousand years, in thinking that the elements of the planetary orbits had a basic physical significance. We know [now] that the basic laws don't have any particular relation to those numbers. The elements [e.g. orbital radii] just depend on where things are.
Like the eccentricities of the orbits.
Yes. So that's what I am working on in cosmology. I've gotten quite a long way. I've got some of the masses — octet masses and so on. But I am stuck all the time with a problem that Narlikar and I had. It occurs to me about once every five years, and I sweat about it for about a month and I don't get anywhere. It's basically the old business of why the ratio of the gravitational force to the electrical force is related to the square root of the number of particles [in the observable universe].
The Dirac large number hypothesis.
Yes. Or to put it another way, if you calculated in a sensible way you should wind up with all particles having the Planck mass. I feel something is hidden in there.
And you don't like Dicke's anthropic explanation for that?
No, I'm afraid not…
And you are working on that right now?
Yes. I'm not entirely happy though. I am reminded in the whole of this problem by a remark of Feynman's. He thought that what we see as gravity really has to be a statistical theory. The details he thought must be the innermost physics of all. Unless we really see the bottom of it, we can't understand it. I have that feeling all the time. But the coincidence of the numbers is so striking, that even if one can't understand the fine details, one ought to understand the principle of the thing. But you know, [the relation between the gravitational and electrical force] has been an [issue] since Einstein in the 1920s. Einstein already had the idea. So it's survived now for 70 years without anybody having an idea [about how to solve it] — rather like the Riemann hypothesis.
What is the Riemann hypothesis?
About the zeroes of the zeta function lying on a straight line.
Let me end with a couple of even more speculative questions. You may have to put some of your natural scientific caution aside. If you could design the universe any way that you wanted to, how would you do it?
If the physicists are right, I wouldn't do it their way. I sort of feel that if my way of looking at it turns out to be right, then probably one wouldn’t want to do it any better.
With Mach's principle and the long-range influence?
Yes. After all, you say to yourself, Schrodinger’s equation admits the existence of enzymes that will promote chemical reactions involving only the minutest energy differences, in such a way that physical systems — bacteria and so on — will find the bottom of the thermodynamic potential well to an incredibly high degree of accuracy. Now who is going to design a world that's better than that? I grant you that there will be a day when physics and astronomy and biology are sufficiently well understood that we will be able to begin to argue about what other games could be played. I think Feynman said it's like someone discovering the rules of chess. Until you've found the rules, you can't play the game. We don't [now] know enough about the rules to play the game. There will be a stage when we do eventually know enough about the rules to ask whether we could play a better game.
I'm not a particle physicist myself, but it seems to me that some of the particle physicists are now asking whether the universe could have been designed any differently, and asking if there is a unique set of laws, like the so-called theory of everything.
Oh yes. Are there groups that would have all the properties? Yes. Once one knew what the groups were and how everything interacted, then it would be possible. But if you say, "As soon as I've written down the groups, then I know everything," if that is your attitude, then such a game is only the easier part of it. My view is that you have to put in all the interactions that go on in a many-particle system. Then, it's a hard question to answer. At the moment, it may not be a profitable one. I just want to find out how to understand the system.
Let me ask one final question. There's a place in Steve Weinberg's popular book The First Three Minutes where he says the more the universe seems comprehensible, the more it also seems pointless. Have you ever thought about this question?
Well, I think Feynman was nearer the point when he said that you have to know the rules before you can understand the game that's being played. Feynman's example was a child who watches two grandmasters. First, the child has to figure out how the pieces move. But it's a long step from there to understanding the game, and a still vaster step to being able to play a better game.
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 e. g. A. S. Eddington The Expanding Universe (New York: McMillan, 1933).
 P. A. M. Dirac, The Principles of Quantum Mechanics (Oxford: Clarendon Press, 1935).
 E. Wigner, Gruppentheorie Und Ihre Anwendung (Ann Arbor MI: J. W. Edwards, 1931).
 Editor’s Note: This question and Hoyle’s answer, were communicated in written form after the interview.
 H. R. Robertson, “Relativistic Cosmology,” Reviews of Modern Physics, vol. 5, pg. 62 (1933).
 C. Brans and R. H. Dicke, Physical Review, vol. 124, pg. 925 (1961).
 Private communication to Hoyle.
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 H. Bondi, T. Gold, and F. Hoyle, “Black Giant Stars,” The Observatory, vol. 75, pg. 80 (1955); Editor’s Note: To be exact, this paper proposes giant molecular clouds to explain recently observed infrared emission and notes that if such clouds were powered by conversion of hydrogen to helium, the resulting helium would roughly agree with observed cosmic ratios of hydrogen to helium; the paper does not explicitly state that the cosmic helium abundance cannot be made in ordinary stars.
 F. Hoyle and R. Tayler, “The Mystery of the Cosmic Helium Abundance,” Nature, vol. 203, pg. 1108 (1964).
 R. A. Wagoner, W. A. Fowler, and F. Hoyle, “On the Synthesis of Elements at Very High Temperatures,” The Astrophysical Journal, vol. 148, pg. 3 (1967).
 See Ref. 20.
 Editor’s Note: This question, and Hoyle’s response, were communicated in writing, after the interview.
 Editor’s Note: This question, and Hoyle’s response, were communicated in writing, after the interview.
 F. Hoyle, “The Steady-State Theory Revived?” Comments on Astrophysics, vol. 13, pg. 81 (1989).
 F. Hoyle and J. V. Narlikar, Proceedings of the Royal Society, vol. A270, pg. 334 (1962); Proceedings of the Royal Society, vol. A277, pg. 1 (1964); Proceedings of the Royal Society, vol. A282, pg. 178 (1964); Proceedings of the Royal Society, vol. A282, pg. 184 (1964).
 K. Gödel, Reviews of Modern Physics, vol. 21, pg. 447 (1949).
 A. Guth, “Inflationary Universe: A possible solution to the horizon and flatness problems,” Physical Review D, vol. 23, pg. 347 (1981).
 See Ref. 9.
 Editor’s Note: This question, and Hoyle’s answer, were communicated in writing, after the interview.
 V. de Lapparent, M. J. Geller, and J. P. Huchra, “A Slice of the Universe,” Astrophysical Journal Letters, vol. 302, pg. L1 (1986).
 See Ref. 25.
 R. H. Dicke “Dirac’s Cosmology and Mach’s Principle,” Nature, vol. 192, pg. 440 (1961).
 S. Weinberg, The First Three Minutes (Basic Books: New York, 1977), pg. 154.