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Interview of Vera Rubin by Alan Lightman on 1989 April 3, Niels Bohr Library & Archives, American Institute of Physics, College Park, MD USA, www.aip.org/history-programs/niels-bohr-library/oral-histories/33963
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Childhood experience looking at the stars; influence and encouragement of parents; early reading in science; influence and importance of Maria Mitchell; education at Vassar; graduate work at Cornell; discouragement from going into science at Cornell; influence of Martha Stahr (now M. S. Carpenter); master’s thesis on large-scale motion of galaxies; motivation in thesis work; problem of coming into science from a nontraditional background; community reception of master’s thesis work; experience of delivering a paper at the AAS meeting in 1951 while nursing a newborn; community resistance to idea of a bulk rotation of galaxies; graduate work at Georgetown; exclusion of wives from the Applied Physics Lab; influence of George Gamow; reasons why Rubin did not continue her work on large-scale motions; Rubin's dislike for work that is controversial; support and influence of Rubin's husband; thesis work on correlation of galaxies; different kinds of geniuses in science; personality and style of Gamow; motivation of work on rotation curves of galaxies; importance of Kent Ford's spectrograph; Rubin's preference for problems that few other people are interested in; history of discovery of flat rotation curves and implications for dark matter; initial reaction (and surprise) to discovery of dark matter; community reaction to discovery of flat rotation curves; attitude toward the horizon problem; attitude toward the progress of science; attitude toward the flatness problem; attitude toward the inflationary universe model; reaction to de Lapparent, Geller, and Huchra's work on large-scale inhomogeneities; Rubin's belief that there are many things we don't know; importance of work to determine what motions of galaxies should be; visualization in science; relation between theory and observation; outstanding problems in cosmology: dark matter; experience of women in science; cultural conditioning of gender differences at an early age; Rubin's own experiences with gender discrimination in science; ideal design of the universe; question of whether the universe has a point.
I wanted to start with your childhood. Could you tell me about any particularly influential experiences you had as a child, particularly anything that got you interested in science?
My father was an electrical engineer. He's presently 92 and still could be holding down a job. He had a very analytical way of looking at things, and I enjoyed that very much. I think that was a very large influence. My childhood bedroom — if childhood could be about ten years old — had a bed which was under windows which faced north. At about age 10, I started watching the stars just move through the night.
Lying in your bed?
Lying in bed. By about age 12, I would prefer to stay up and watch the stars than go to sleep. I started learning. I started going to the library and reading. But it was initially just watching the stars from my bedroom that I really did. There was just nothing as interesting in my life as watching the stars every night.
Did you have siblings?
I have an older sister. She's now a judge. I had the usual friends who pointed out constellations of stars. But it really was watching the stars. It was getting some sense of the motion of the earth. I found it a remarkable thing. You could tell time "by the stars." I could see meteorites. My parents were very, very supportive, except that they didn't like me to stay up all night.
They knew you had an interest in this?
They knew I had an interest in this. A few years ago, I met a friend of my mothers who I do not know at all and hadn't seen for 50 years. She said to me, "The last time I saw you, I was picking your mother up at your house. As your mother went out the door, she yelled up the stairs, 'Vera, don't spend the whole night with your head out the window!' " So yes, they knew I was doing this. But the net result was that when there were meteor showers and things [like that], I would not put the light on. Throughout the night, I would memorize where each one went so that in the morning I could make a map of all their trails. I really don't think [my parents] would have protested as much as I [then] thought they would.
But you did make a map of the meteors?
I really would make maps, yes.
Did you get encouragement from your mother as well as your father?
Yes, from both of them. My father helped me build a telescope, which was really a total flop, but was sort of fun. I ordered a lens from Edmund's and got a cardboard tube that linoleum came rolled on. I took a bus downtown and brought it home on the bus. We were living in Washington, in the city, and you could see the stars during the night in Washington in the early forties. So I went downtown on a bus and got a linoleum tube, which I brought home and turned into a little telescope. I tried to take some pictures, but none of it worked because the telescope didn't track.
Other than this influence from your father, who was an electrical engineer, do you remember any books that you read that had an impact on you at this age?
I read a lot of books, such as [James] Jeans's book, The Universe Around Us[1] and Eddington's early books.[2] But I was already hooked. It really came from the sky. In the late 1930's, I remember, there was an alignment of five planets. That impressed me. I didn't realize at that time how likely such a thing was. Then there were several auroral displays. It was those things that really [captured my interest]. It was the visual experience more than what I read in books.
Did you read anything about cosmology or the universe as a whole at this time?
Well, the Jeans's books. His books had these wonderful things — some things that I still remember. In retrospect, the things that impressed me most were the very, very far-out things — you know, ideas about whether, when you look in one direction, you can see light from stars in other directions.
That's going around universe?
Going around, that's right. It was those kinds of concepts that really fascinated me more than the everyday, conventional astronomy. In retrospect, that's very far from the way most cosmologists work, but they were the ideas that really intrigued me.
Did you come across the concept of the big bang or the birth of the universe in your reading?
That's hard for me to remember. I probably did, although it may have been a little later. George Gamow was in Washington. Ralph Alpher was writing his thesis under him. I remember going to a talk by Ralph Alpher on his thesis work.[3] That was probably in high school or very early in college. So I knew those ideas [at that time].
It was probably early college because that must have been in the late 1940s.
That's right. I entered college in 1945. In fact, it turns out that Ralph Alpher worked in this building in the late 1930's as a secretary. They would not hire women here until during the war. Even the secretaries were male. I have since learned that he got out of high school very young and wanted to work for a year before going to college, so he worked here as a secretary.
Vera Rubin on Maria Mitchell and why she became an astronomer.
Did you know when you were in high school that you wanted to go into astronomy, or was that later on?
Yes, by high school I knew I wanted to study astronomy. I knew I wanted to be an astronomer. I didn't know a single astronomer, but I just knew that was what I wanted to do.
Did you know that it was a career possibility or have some sense of that?
Yes, I knew about Maria Mitchell, probably from some children's book. I knew that she had taught at Vassar. So I knew there was a school where women could study astronomy. So, yes, it never occurred to me that I couldn't be an astronomer.
Is that why you went to Vassar?
Yes.
Because of Maria Mitchell?
Yes. That and a lot of other reasons. I needed a scholarship and they gave me one. I didn't apply to many colleges. There were not an enormous number of colleges where a woman could study astronomy. But I knew about Vassar because of her.
When you went to Vassar, was she there?
No, shame on you. She died in 1889. This is off the subject, but one of the things that I have attempted to do in my life, and I clearly haven't succeeded, is to make the story of Maria Mitchell as well known as the story of Benjamin Franklin. She really is a great heritage of the American scientific scene. When Vassar was founded in 1865, she was the first professor of astronomy. She was already well known from doing astronomy.
Who was influential for you when you were at Vassar?
Well, Maud Makemson was the director of the observatory. I learned a lot of important, fundamental astronomy, but even there the idea of being an astronomer [was not especially encouraged]. I don't think I got enormous support for it. The feeling was that there were very few observatories and very few astronomers needed. I wasn't discouraged at all, but I can't say that I was overwhelmingly encouraged. There was a lot of encouragement there for science in general. [There was] a lot of physics and a lot of mathematics. But astronomy, even there, was a very tiny department. It was not a major department on the scientific scene.
In addition to taking courses in astronomy, did you study cosmology at all at that time?
No. I studied fundamental physics and mathematics — no cosmology whatsoever.
Did you take some astronomy courses?
Yes. I got my degree in astronomy.
Tell me a little bit about your stay at Cornell. Did you get your master's at Cornell?
Yes, I got my master's[4] at Cornell. I got married when I graduated from Vassar and entered Cornell. Actually, I had been accepted by Harvard. I have a letter somewhere from [Donald] Menzel saying "Damn you women," handwritten across the bottom. [This was in response to] a letter I wrote saying that I wished to withdraw because I was getting married and going to Cornell. He scribbled across this very formal letter, thanking me for letting him know, something like "Damn you women. Every time I get a good one ready, she goes off and gets married," or something like that. My husband was already in graduate school. My husband was getting his degree under Peter Debye, and I think it's fair to say that, although he has probably been my strongest supporter, we never even considered doing anything else but my joining him at Cornell. So I entered the Cornell graduate school in 1948 and got a master's while he was completing his Ph.D. That was even less of a department than Vassar. It almost didn't exist. There was one man — this is for publication so I'll have to speak cautiously. He had been a navy navigator during the war, and he was not a very sympathetic person.
In what way?
Oh, toward anyone learning [about] or being in astronomy. He actually called me in when I arrived and told me to go find something else to study. [He said] that they didn't need astronomers, and I wouldn't get a job and so forth. There was a second person in the department, Martha Stahr [now M.S. Carpenter]. She may have been the only woman faculty member at Cornell at that time. The place was almost exclusively male. I have since read in Margaret Rossiter's book[5] that at that time there was one assistant professor, so I presume it was she.
[Thomas] Gold and [Edwin] Salpeter came somewhat later?
That whole development in astronomy came later. Cornell was a very exciting place because of the physics. [Philip] Morrison, [Richard] Feynman, and [Hans] Bethe were there and I studied under all of them. Feynman was on my committee. He took off for Caltech about a week before my master's orals, and I added Morrison to my committee. During the time I was there, Morrison once gave a talk in the physics department on Baade's work on the two stellar populations. That was 4 or 5 years later, but he thought it was an important enough development to bring to the attention of physicists. The astronomy department really was an undergraduate teaching department. But Martha Stahr had come from Berkeley and knew galaxy dynamics. I learned a lot of galaxy dynamics from her. It was in picking a master's thesis that I chose to work on the question of whether there were really large-scale motions of galaxies as distinct from the conventional Hubble expansion.
I wanted to ask you about that in a few minutes. Well, maybe I should ask you about your Ph.D. work at Georgetown.
It's very much related to the master's work, because when my husband finished at Cornell, he took a job with the Applied Physics Lab in Washington. He actually shared an office with Ralph Alpher. It was through that contact that [George] Gamow, who was then a professor at [George Washington University], heard about my master's work and called me and talked to me about it. It was through those discussions that I ultimately wrote my thesis under him.
Okay, maybe I should go back and ask you some questions about your master's work. You worked on the rotations of nearby galaxies and on a search for a universal rotation?
No, I did not do the internal rotations of galaxies.
That was not part of your master's?
No. At the time, there were something like 108 or 109 galaxies with known radial velocities. That's a number that seems incredibly small to us today. I just asked the question whether, once the expansion had been taken out for those 108 galaxies; there was a large-scale systematic residual motion. The only large-scale motions I knew about were rotations, because I knew the galactic dynamics. So I just attempted to take that whole formalism and apply it to the motions of the galaxies. But at that time, I had done no work on internal motions.
What I meant to say was the bulk rotation of systems of galaxies.
That's right.
Did you have any cosmological motivations for working on that? What really got you into that?
The only motivation that I can point to is just plain old curiosity. That really has motivated an enormous amount of my work. In retrospect, because I have been asked this question before, I think part of it was [that since I came] from such a non-traditional background, I didn't know what everyone would have said, [such as], there weren't enough galaxies and the velocities probably weren't good enough. I used magnitudes to get distances. The magnitudes probably weren't good enough, but I think that because my background had been so non-traditional, it was just a question that seemed worth answering.
Why do you say that your background was non-traditional?
Well, I went through Vassar in three years, so I had three years of Vassar, a couple years at Cornell, and I probably had not met a single person that you would call an astronomer.
So your background was more in physics?
No. By non-traditional, I mean it wasn't Harvard and it wasn't Princeton and it wasn't California, where working astronomers and really great people did their work and taught their students, and therefore, the students probably tended to come out in a more traditional mode.
They knew what the set of great questions were.
That's probably right. Even if it hadn't been taught in that way, they had absorbed certain attitudes. They knew what people were working on. I just hadn't been through that. So I call it, in that sense, a non-traditional background. And truly, even to the present day, I really don't consider myself a cosmologist. I'm just curious about these things and try to find answers.
If I am correct, I remember reading that you presented this master's thesis work at a meeting of the American Astronomical Society in 1951.
In 1950. December, 1950.
Can you tell me how that was received?
I could write a book. [There's] more than you want to know.
Tell me a little bit.
I had a child, our first son, who was born the 28th of November. Is all this going to be published? I shouldn't say anything I don't want published.
You will have a choice to remove some things for the public and leave other things for the archives.
Okay, let me say this for the archives. I had these two professors at Cornell, the two people in the department who knew what I was doing. Probably late in the fall, the department chairman said that in as much as I was going to have a child and therefore couldn't go to the meeting to give this talk, he would give it, and in as much as I wasn't a member of the AAS [American Astronomical Society], a member's name would have to be on the paper. He really had nothing to do with what I had done. Therefore, I spoke up and I said, "Oh, I can go."
Being nine months pregnant?
That's correct. We didn't have a car. December in Ithaca is very snowy. My parents came up from Washington and drove us [to the meeting]. This was their first grandchild. [My parents both] came from Philadelphia and had lived in Philadelphia most of their lives. My mother was born there, so there was family there. They drove us to Philadelphia. My father has since said that he aged twenty years on that drive through the snow with his first grandchild. I think it's a correct statement that I did not know one person at the meeting. I was nursing a child. I was not a member of the AAS. I walked in that morning, gave my talk and left. That was the extent of it. So that's sort of the background of giving this paper. I put this in as non-traditional. I didn't really even know what I was getting into. I gave the talk. It was a ten minute talk, which was not an awful lot.
What was the title of your talk? Was it "The Universal Rotation of the Universe" or something?
It had two titles. I submitted it under the title "Rotation of the Universe." Well, I know what I would do now if a 21 or 22 year old, someone who you had never heard from, submitted a paper called "Rotation of the Universe." I've [re-read that paper] in the last couple of years. The abstract[6] appeared in Astronomical Journal. [In it], I say what I did and it's perfectly respectable.
This was based on your own observations?
No. I did no observing.
This was just data analysis?
Oh, it was impossible for a normal person to get observations. Let me back up a minute and say that while I was working on this, it was known that [Milton] Humason had a whole set of radial velocities, and Martha Stahr wrote to him asking if these could be made available. I think the letter came back saying that they would be published very soon and I would have them. They were published in the Humason, Mayall, and Sandage[7] [paper] in 1955 or 1956, so that was six years later. There also was [another] letter. I really have forgotten from whom. There was talk from Princeton that Kurt Godel was working on rotating universes, and therefore I should wait. So from both the observers and the theorists that were in contact, there were reasons why I shouldn't do this. No, you had to have [access to] one of the largest telescopes to get radial velocities. They were hard. So this was just data analysis. But to get back to this abstract. At the end of the abstract, I actually evaluated terms like the radius of the universe, the shear, the energy — things that are only a mild embarrassment now. But the thesis itself, I think, is a respectable piece of work. Once a year or so someone like Jim Peebles asks for a copy. I have xeroxed it half a dozen times. It's totally out of date, because the data were not really good enough to do it. So I came in and gave this talk. Then a variety of people got up and made their comments, none of whom I could identify because I didn't know who they were.
What were the comments like, do you recall?
[All but one] of the comments were of the form that you just couldn't do this for a variety of reasons, comments which I think I have probably hidden in the back of my mind. [Martin] Schwarzschild got up, as he does; he's so nice to very young students. He said all of the things that one would like said — that this is an interesting thing to do, that the data probably are not good enough, but that it was an interesting idea for a first step. So he made me feel somewhat less than mashed to the ground. Then when it was over — there must have been a break right after it — [Dirk] Brouwer, who was the editor of the Astronomical Journal, came up to me and said, "We can't publish a paper that's called the 'Rotation of the Universe.' " He changed the title to the "Rotation of the Metagalaxy." I think that's what it is. I would really have to look. But I think that was an acceptable term.
But he was interested in publishing it?
It was published with all the other abstracts. [The paper itself was rejected for publication by both the Astrophysical Journal and the Astronomical Journal.] Last April, at the de Vaucouleurs's Symposium in Paris, I gave a talk[8] on large-scale motions — just a review paper — and some of this history was in it. When it was over, several people got up and said things that I had never known. One of the most interesting [comments] was by Frank Kerr, who I think said that for reasons he can't even remember, at the council meeting of that meeting, [there was a] debate about whether they were even going to permit this paper to be given or not. In those days, you had to submit an abstract, and they really decided whether they would permit the papers to go or not.
Let me ask you a question. When you said that [all but one] of the comments were of the sort that you can't do this — and this may be asking you to make a judgment — do you think that people were saying that you can't do this because the data is not good, or do you think they were saying you can't do this because the whole concept of a bulk rotation is ridiculous?
I can't remember. I'm sure that even if they were saying the first, what they really meant was the second — that the whole concept of these very large-scale motions was just ridiculous. Yes, I think that's fair. I think that was the general belief.
Why do you think they felt that was ridiculous?
Well, let me see. The Hubble constant then was five times larger, so the universe would have been smaller. I think ideas of systematic effects extending over those large ranges would just have been considered outlandish.
Outlandish compared to the standard model?
Yes. It's just too long ago for me to really remember what was in people's minds.
Let me ask one other question. At this time, when you were doing your master's work, were you familiar with the different types of cosmological models? I guess the steady state had just come out, but let's say steady-state versus big bang, or within the big bang, the different types of models such as closed versus open? Did you think about that at all?
I certainly knew of that. I certainly knew of the big bang model. No, I really didn't do the work in the framework of any cosmological model.
Did you have any preference for any particular model?
No, probably not. Well, certainly probably for the big bang over the steady-state, but that was really just prejudice more than anything else.
Let me ask you about your work at Georgetown a little bit.
That was an interesting place, and it probably deserves more credit than it's gotten. Because it was in Washington, there really were a lot of interesting people around who taught there. Radio astronomy was just getting started. I studied radio astronomy under Hagen, who was at NRL and had just done some early radio astronomy work. He was the man who ultimately headed the very early space program to get up the first U.S. satellite. I studied spectroscopy under Kiess from the Bureau of Standards. Kiess and Meggars are the people who had done most of the spectroscopic table work in the handbooks, the really classic spectroscopists. I did some work with Charlotte Moore Sitterly on spectra. It was a very interesting place to be.
That was all at Georgetown?
Yes, that was all at Georgetown. As I said, I had heard from Gamow because of my master's work.
Did he contact you or vice versa?
He contacted me.
At Cornell?
No, when I got to Washington, after my husband started working at the Applied Physics Lab. He contacted me because he was to give a talk at the Applied Physics Lab.
He was at George Washington?
Yes, he was at George Washington, Actually, [he had been] brought there by Merle Tuve, director of this department, but I really knew none of that. He contacted me and wanted some details of my master's work, which I gave to him. Then I asked him if I could come hear this talk, and he said 'No' because wives were not allowed in the Applied Physics Lab.
Wives were not allowed in the Applied Physics Lab?
That's correct. It was a classified place, and there was security. So it was very easy to keep people out.
Did you think that he was just saying that non...
No, he meant wives. Wives were not allowed. It was through that contact that she [started] talking. I spent about one day at Georgetown on a thesis problem that Carl Kiess had given me. It had to do with faint lines on the solar spectrum. They had a Roland grating at Georgetown, and they did some solar spectroscopy. By the end of the day, I decided that wasn't the thesis problem that I wanted to work on. Gamow had an interesting question. He wanted to know whether there was a scale length in the distribution of the galaxies. He just posed this question to me, and I decided to work on that.
The spatial distribution?
Yes, the spatial distribution of galaxies. So he posed that question, and that's what I took for my Ph.D.[9]
So it was fairly vague...
Yes, it was very vague. He wanted one number. He wanted the scale length.
That doesn't direct you much on how to obtain that number?
No, it doesn't direct you at all. But that's the kind of person he was. I knew what I was getting into. He just threw out lots of interesting questions. I ultimately performed a two-point correlation function on the Harvard galaxy counts to do this.
This must have been one of the earliest ones.
Yes. Like the large-scale motions, this also pre-dated the current interest in the problem by about twenty years. In this case, at least I could say I entered it in total ignorance of how to proceed. I had to learn from scratch how one could go about doing this.
I am curious why you chose not to continue your work on the large-scale motions, on the universal rotation? Can I ask that question?
Surely. That is an interesting question. I don't think anyone has ever asked me that question. I think there are two answers, and they both contribute. First of all, the only real contribution would have been observational. What would have been required would have been more galaxies, and better velocities and better magnitudes. I had two children by then. I think the honest answer is' I knew that I just couldn't do things like that. There was no way I could get myself to an observatory and gather data. It was totally out of the question. So there was never any thought of doing that. The second [answer] is that although several times in my career I have found myself in relatively controversial positions, I really don't enjoy it. For me, doing astronomy is incredibly great fun. It's just an incredible joy to get up every morning and come to work and, in some very much larger framework, not even really quite know what it is I'm going to be doing. In a sense, [the heated controversy] really spoiled the fun. I mean people were really very harsh. Maybe one learns to take this. I'm not sure you do. My way of handling that, in every case, has just been to go off and do something very different.
Change fields?
Yes. It never occurred to me to continue on that work. Probably 10 or 15 years later, I started thinking about ways in which I could return to this earlier problem.
After sort of dropping this great problem in your lap, did George Gamow interact with you very much?
Very much is probably the wrong word. My husband really has been an enormous support, especially in the early days when I knew no [other] astronomers. He listened to everything I had to say. He's a very high-powered, very skillful mathematical physicist. Although I have no idea of how I came to the formalism [I used in my thesis], I'm sure talking to him was one of the main ways. Then, ultimately, I did get much of my direction from Francois Frenkiel, who was a hydrodynamicist.
When you talk about formalism, do you mean the two-point correlation function?
Yes, I mean applying that. That's right.
That's something that most people don't learn in graduate school.
That's correct. [Frenkiel] was a very interesting man. He was a refugee. He also worked at the Applied Physics Lab. All my contacts really were through my husband. Frenkiel had done some very interesting work in Kolmogorov theorems in hydrodynamics. I think it was really through him that the actual formalism came, but I'm not even certain of that. How I got on to the Harvard galaxy counts is probably through Georgetown, through Father Heyden. He was the chairman of the Georgetown department, and he had earned his Ph.D from Harvard during the war. I think in rather short order, it became clear that one way of doing this problem was to take these counts of galaxies along the sky and apply the two-point correlation procedure. My whole thesis consisted, virtually, of this one calculation, which people would now make on a computer in minutes. I had a desk calculator, and I did virtually all of my work at home at night because I had two.
Calculating the distance of pairs?
That's correct. Products of pairs at different separations. The Harvard galaxy counts, even in those days, had a sort of mediocre reputation. There were all kinds of rumors that the "Harvard" women had counted flyspecks and so forth. I think [the reputation was] truly undeserved.
These rumors came from Harvard?
I don't know where they came from. I couldn't tell. I think these women were doing an incredible service for 50 years of astronomy and deserved better.
These were all angular separations, is that right?
That's correct. All I had were counts within — I don't even remember — three minutes [of arc] or nine minutes or something. There were essentially plots of the sky with a number every so often, and the number told you how many galaxies had been counted in that square. It was fun. I enjoyed it.
Do you think that you absorbed any of the style of doing science that George Gamow had?
No, I wasn't smart enough. You know, Mark Kac, in his autobiography,[10] says that there are two kinds of geniuses. There are the kind of geniuses we would all be if we were very, very smart and knew what we were doing. Then there is the kind of genius in which there is no way your mind would think that way. I would put Gamow in that class. He had an incredible mind. He was very curious about how the universe worked. But he had a lot of good ideas about how the universe worked. And he had no interest in how you got the answer. In fact, in most cases, I think he would be totally incapable of getting the answer.
Oh, really? So he was not technically [proficient]?
He was not technically competent at all. He couldn't spell; he couldn't do arithmetic — I may be exaggerating a little bit. But he could pose the questions that no one else could really have thought of asking. I should back up and tell you that at about the time I was working on my master's thesis, he actually published a letter in Nature,[11] which I have not gone back to, in which he asked about a rotating universe. I have been asked whether I even knew of this, and that's also a question I really can't answer. I'm willing to say that I probably did, but I don't even know the exact dates and so forth. [I think my husband pointed out the article to me]. He was incredible when it came to giving ideas. He did this throughout his whole lifetime. He wrote a postcard to [Walter] Baade, after a meeting that I had been to, saying, "Tell me where the stars leave the main sequence, and I will tell you the age of the cluster." He seemed to be the first person who understood what that meant. But I had been at that meeting with him, as a graduate student, and he embarrassed me no end because he would fall asleep and wake up and ask questions that I considered stupid questions. His behavior was unconventional. And then he would just understand things that no one else had understood. So it was fun, but I'm not smart enough to do science that way.
I don't think many of us are. Personally, I think that I have more admiration for people who are intuitive than people who arrive there by...
I think we all do. Especially those of us that really do the work to get the answers because we're not intuitive enough to understand. I think asking important questions is really quite a role to play. I think he played a very large role. He was so unconventional that he probably didn't play as large a role as he might have, both in physics and astronomy.
Let me ask you about your work on the rotation of individual galaxies. What motivated you to start doing that work?
Oh, that I remember. That I know. That's current enough, because that's really the early 1970s. Again, there were two reasons. One was that I had come to work here, and Kent Ford had built a very exceptional spectrograph. He probably had the best spectrograph anywhere. He had a spectrograph that could do things that no other spectrographs could do, and what you need for a program like that is a good spectrograph. Then, of course, the other side of the question is what you are going to look at. In the late 1960s, when I came here, we did what everybody else did who had their hands on a good spectrograph, and that is, we looked at quasars.[12] Kent and I would go out to Lowell Observatory or Kitt Peak a couple of times a year, and we would get spectra of a few quasars. Like everyone else's, they were sort of crummy spectra. It was hard to see what you had. By this time, I knew [other] astronomers. I would get calls from friends, Margaret Burbidge and Martin Schmidt, saying, "Have you observed thus and so? Do you have a redshift? If you don't, I'll go get one." It was all done in a very friendly manner. But, again, it just wasn't the way I wanted to do astronomy, because by and large, these people had much more telescope time than I did. If I had a spectrum and wasn't sure what the redshift was, I was either put in the position of having to tell them what I thought it might be or giving up on that spectrum. After about a year or two, it was very, very clear to me that that was not the way I wanted to work. I decided to pick a problem that I could go observing and make headway on, hopefully a problem that people would be interested in, but not so interested [in] that anyone would bother me before I was done. I chose to study the rotation of M31,[13] and that was what really started that work.
You told me a negative reason why you did that. Is there a positive reason why you chose to do that particular kind of work?
Surely. Yes, I did tell you the negative reasons. It was my old interest in galaxy dynamics. Before the 1970s, [since] large telescopes were so few — although, by the early 1970s, good image tube spectrographs could make small telescopes behave like large telescopes — much of astronomy operated, and had to, in a realm in which much was inferred. You observed a few facts. Astronomers have been incredibly clever, throughout the history of astronomy, of inferring what they would see if they had a slightly bigger telescope. I really think that's almost the history of big telescopes. Then you get the big telescope, and you go back and you see that what you thought you'd get is, in fact, correct. But then you take the next step, and you make another inference. So people had inferred what galaxy rotations must be like, but no one had really made a detailed study to show that that was so. Inner parts of a few galaxies were pretty well known from the work of Margaret and Geoff Burbidge, but outer parts were not. So, partly, it was my old interest in galaxy dynamics, and then also the realization that with the instrumentation I had available to me, I could really do this. And truly, it was this other aspect of picking a program which I thought was a very valuable one to do, but one that was not so in the forefront of astronomy that everyone was doing it.
And breathing down your neck.
That's right. It's only fairly recently that I realized that I must just like doing things that other people are not doing. Partly because of the way I get to a telescope, which is relatively seldom.
When you first began finding evidence for dark matter, I guess that was a little bit later...
Yes, it was the extension, right after the M31 [program], the Andromeda program.
Do you remember, did [the dark matter] come as a surprise to you?
It's very hard to tell. It's very hard. I think I learned slowly. Well, I guess the answer has to be yes. Of course it was a surprise, because if it hadn't been a surprise, we would not be sitting here talking about it.
Do you remember anything about how the community [responded] — unless you wanted to say more about [the last question]?
What I was going to say is we would take about four spectra a night. That's about all we could fit into 2 or 3 hours, and I would develop each one. We would take turns guiding the telescope.
Was this with Kent Ford?
Yes, Kent Ford and I. I would develop the plates. He built the instruments, and I sort of did the science, but we always observed together because we both liked to. I do remember my puzzling at the end of the first couple of nights that the spectra were all so straight. My first ideas were, by today's ideas, just totally wrong. The first thing that came to my mind when I looked at these very straight spectra was that there must be some kind of feedback mechanism. If the stars got too fast, they were slowed down, and if they got too slow, then they were speeded up. It just didn't look like a random occurrence. The idea of a distribution of matter that would just give you that [velocity distribution] really didn't enter my mind at first. I remember consciously thinking that, and that's about all. So it just shows that your intuitive ideas or whatever, the first thing you think of, in that case, is apparently just irrelevant. It doesn't have that much to do with [my current thinking] in that case. I was really thinking more in terms of observables than the distribution of matter.
When you did realize that it meant something about the distribution of matter and dark matter, do you remember, as you began talking to people about this, what the reaction was?
The reaction was two-fold. In fact, historically, we've left something out. After I finished the early M31 work, which was in the early 1970s, then I went back to the large scale motion problem in the mid-1970s.[14] My going to the rotation curves was, again, to get away from the controversy of the large-scale motion [research]. Therefore, I really loved it, because the rotation curves were so flat.[15] Observationally, it was such a nice program. All you had to do was show someone a couple spectra, and they knew the whole story. In a sense, it was a wonderful observing program, because when you [ask] what were people's reactions, there was never any doubt on anyone's part that these rotation curves were flat. You didn't have to show them measurements. You didn't have to argue. All you had to do was show them a picture of the spectrum.
Well, they could have doubted the data.
No, no one did. It just piled up too fast. Soon there were 20, then 40, then 60 rotation curves, and they were all flat. My recollections are that no one doubted the data. And it was just a joy to have that kind of a program, after a program where you had to go through deep analysis and everybody doubted the answer. The fact that the rotation curves were flat, I think, was doubted by no one — at least in my presence. The interpretation was more complicated. I think many people initially wished that you didn't need dark matter. It was not a concept that people embraced enthusiastically. But I think that observations were undeniable enough so that most people just unenthusiastically adopted it.
So you felt in this case that you didn't have to go out and promote the meaning of the work?
Not at all, because there already was a theoretical basis. Ostriker, Peebles, Yahil,[16] and others had come [out] with very good ideas that [dark matter] ought to exist, independent [of observations], for other reasons, for stabilizing the disk. The ideas had been around for a while.
Not very long, though.
No, a couple years. That's right. But the observations fit in so well, [since] there was already a framework, so some people embraced the observations very enthusiastically.
Let me turn now to your reaction to some outstanding cosmological problems, some of which may be related to your own work and some not. Do you remember when you first heard about the horizon problem?
I remember [hearing about it in] the mid-1970s, because I spoke at a summer course at Erice, and Roger Penrose was also teaching. I sat in his courses because I had so much to learn. In fact, my husband and my youngest son came over toward the end because we were going to climb Mount Etna. I even insisted that they sit in, saying, "It doesn't matter whether you understand what he's saying. It's just such remarkable stuff that you ought to be exposed to it." So that would be the mid-1970s. Earlier than that, I don't have any clear recollection.
But he talked about the horizon problem?
Yes.
Do you remember, when he talked about it, what your reaction was? Did you regard it as a serious problem? How did you think about it?
I'm an observer. I really feel very much that I'm an observer, and I tend to relate what we know about the universe to what has been observed. So my feelings about cosmology, I think, are probably much more loose and relaxed than [those of] many people. Maybe this does come from starting with Gamow, from my early work. I think many of the models are brilliant, and some of them probably have some parts that are right. But, personally, my attitude towards many such theories is that we're still groping for the truth. So I don't really worry too much about details that don't fit in, because I put them in the domain of things we still have to learn about. I really see no reason why we — and include all of us in this generation — should just have been lucky enough to live at the point where the universe was understood in its totality. I think the best thing I can say is that I didn't worry about it any more than any other facet of details that don't seem to fit. I think as telescopes get bigger, and astronomers get cleverer, all kinds of things are going to be discovered that are going to require alterations in our theories. The horizon problem doesn't exactly come into that kind of situation, but I think, science consists of just continually making better and better what has been usable in the past. So all I can say is I would put it in the domain of something that needed attention.
But you did think that it needed attention?
Yes, I think so.
So you took it as a serious problem?
I took it as a problem. Yes, I think so.
I mean something that would require a solution at some point?
Yes.
You may not be able to think back this far, but when you thought of it as a problem that required a solution, did you think that the solution might be in the initial conditions of the universe? Did you think in those terms?
I don't even think I thought in those terms.
Did your view of the horizon problem change any after the inflationary universe model?[17]
Oh, I thought that was pretty clever. I thought that was fine. I liked that very much.
Let me ask you about another problem, the so-called flatness problem.
That I consider a real problem.
Do you remember when you first heard about that?
Much later. A few years ago really.
Did you regard that as a serious problem when you first heard about it?
Yes, I did and I still do. I don't know whether you're going to ask me what I think omega is?
No, I won't ask that.
Well, then let me tell you. I see no reason why omega should be one. I really don't know why the universe should be that finely balanced, and that comes from the observations.
When you say you see no reason, you mean that the observations say that it is not one?
That's correct. The observations tell us that [omega] is 0.2 or something, and all kinds of theorists can tell me that 0.2 is awfully close to one and go through the flatness arguments. I do see that as a problem. I don't understand that at all.
When theorists say that if it's 0.2, then it should be one, do you accept that argument?
And therefore think it's one? No, not at all. I believe the observations, and I believe the observations are telling us that it's 0.2, and I'm not convinced by arguments that tell me that 0.2 is so close to one that it has to be one. No. I think there is some kind of a problem there, and it has to be solved, but I'm not convinced. I was going to say that I understand the problems, but maybe I don't understand the problems. I mean I don't understand what the solution to the flatness problem is going to be, but it is not yet so troublesome to me that I'm willing to say that omega is one. I think it's fun. I sort of enjoy it. I often ask myself what's cosmology going to be like in 500 years. I presume they'll have solved the flatness problem, or they'll know that omega really is one in a way that will satisfy an observer and so forth. I think if there were no problems, it wouldn't be much fun.
I certainly agree with that. When you talk about solving the flatness problem or finding that omega is equal to one, do you mean reconcile the fact that omega is 0.2 with the reasons that theorists think it should be one?
That's correct. That's exactly right.
So that's your version of the flatness problem?
That's exactly right. That's how [I see it] at the present time. But I'm very willing to admit that if we could really understand, if we could learn about the distribution of dark matter or how much dark matter there was or what it was, then there might be good observational evidence that omega is more than 0.2. So part of the problem might go away. I don't know.
I think that's very funny.
What?
That part of your view of the flatness problem is that it may be a problem that theorists have.
That's correct.
I don't want to misquote you. I want to understand clearly what you are saying here.
No, that is really what I'm saying, that somehow or other the theory has put them in this position of saying what they do, and that something may be missing. I remember, in the early and middle [periods of the] large-scale motion problems, some of the people I admire most telling me that you can't have large-scale motions because any irregularity since the early universe — would be damped out. I mean they gave me all these reasons, which impressed me — [indeed] really terrified me — as to why you couldn't have large-scale motions. But if you ultimately get to the point where everyone believes that there are large- scale motions, that that is what the observations show, then the theorists just have to tell themselves that they have missed something, and they have to go back to their drawing boards and fix up their theories. That's fine; that's progress.
We touched on the inflationary universe model a moment ago. I gather you heard about the flatness problem after that model. What is your view of the inflationary universe model? Do you take it as a working hypothesis? Do you think it's kind of speculative?
I would take it as a working hypothesis. No, I don't think it's highly speculative. I don't think it's much more speculative than the big bang, and that in its time was awfully speculative. I don't know enough physics, really, to know how far back you can trace the physics. I feel comfortable, as most physicists would, [extrapolating] way, way back — whatever numbers people give you — 10-46 seconds or something. But I have no intuition — let me put it that way — between that point and the really initial big bang. I think I'm willing to look at any model that people want to put in, because I don't know any way to refute those models. The simple, conventional big bang was a very general framework that described only a few things, and now [Alan] Guth and others have [put] details [into] that era. I look upon it as a working model. However, let me just go on and say that, for an observer, it doesn't make a lot of difference at the present time because, except perhaps for the cosmic background radiation, we have very few observables from that time.
So when you say it doesn't make a difference, do you mean that your observing program and your projects are not going to be determined by [the physics of the early universe]? Is that what you mean?
I don't mean that they're not going to be determined by it, because in fact, if someone was clever enough to think of some observations that might be very relevant, they might be directly determined. But, by and large, the observations I make, and the observations that most observers make, are much closer, much younger. We're not observing in that domain. I guess we all hope that we will learn something that will be relevant, that will tell us [about that era].
When you observe omega, it's related [to that era] because inflation makes a clear prediction about omega. Possibly [inflation] could be ruled it out altogether, if you could prove for sure that omega is not one.
That's correct.
Let me ask you a sociological question. In your view, why has the inflationary universe model gained such wide support?
I don't think I'm capable of answering that question. I don't know.
Let me ask you about another observational result and a group of observations leading up to it. When you first heard about the work of de Lapparent, Huchra and Geller,[18] how did you react to that work?
I thought it was spectacular.
Did it present any conflicts in your own view of things?
None whatsoever. None whatsoever. Of course not.
Yes, because you've done related things.
Yes, that's right. In fact, the only thing that bothered me about it was, [with] these wonderful wedge diagrams, [some] people didn't understand that they weren't really looking at spatial diagrams.
But velocities.
Yes, velocities, because I did worry about large-scale motions. So I even tried figuring out how you could turn them into a spatial diagram. But I thought they were lovely.
Taking into account a large body of work besides the Geller, de Lapparent, Huchra work - your own work on the large-scale motions and the work of the Seven Samurai[19] and all of that work which has shown that the universe is more inhomogeneous than might have been present in simple models - has that altered your view of the big bang model at all, or of the validity of model, the assumptions of the model, that kind of thing?
It certainly has convinced me that we're not living in a homogeneous, isotropic [universe]. I mean these things that I really suspected in the back of my mind, I can now say publicly. I'm not sure the Robertson-Walker universe exists. I can think of more questions to ask because of what they've done, which go more in the direction of making things more inhomogeneous, and I've at least asked some of my theorist friends some of them. No, it hasn't concerned me about the big bang - maybe because I just don't put my mind to it. If someone came out with a different model that could incorporate such large-scale inhomogeneities, I would be delighted to see it, but until then I will just live with the big bang model.
Yes, but...
I'm not quite sure what you mean. Are you asking is it all gravity?
I guess I'm asking whether you feel like some of these things threaten the big bang model, in your own opinion.
I wouldn't use the word "threaten," because as I say, I don't believe that 500 years from now — I hope 500 years from now astronomers still aren't talking about the same big bang model. I think they won't have done their work if they are.
You think we might have an altered view of things.
Surely. Things have to be altered. And so these are the kinds of observations that will get some theorists thinking about how to incorporate them, sure. I still believe there may be many really fundamental things about the universe that we don't know. I think our ignorance is probably greater than our knowledge. I wouldn't put us at the 50-50 point of knowing about the universe. So how correct the big bang model is, is not a worry of mine at all.
Besides the few things that I have mentioned, has any other development in the last 10 or 15 years changed your thinking very much — your conception of the big picture — either your own work or other people's work?
I've been very impressed with the Davis, Yahil, Strauss work[20] in attempting to start from the distribution of galaxies and predict what motions would be. That's on a smaller scale, within some tens of megaparsecs or something, but I like that approach very much. That seems to me a fundamental way to study the relatively nearby universe. I've been very impressed with their diagrams. I'm not sure they're right, because it's not clear that the IRAS sample that they use is a complete sample. I guess what I'm saying is, in the past - starting with what I did, and what almost everyone else has done - we've used galaxies as test particles in the gravitational field and you have asked how fast are they moving, and what does that mean. But to start with a distribution of matter and to predict what the galaxy should do is somehow, to me, a very satisfying way of doing this problem. I've been impressed with that. Other than that, I guess, I would say I've been impressed with how little we still know. The Seven Samurai[21] have 300 galaxies. The number of galaxies, whose distances we know well, independent of the Hubble expansion, is beginning to get near 1000.
That's very small.
It's incredibly small. There is a lot to do.
Let me take a quick digression. One of the things that I've been interested in is to what extent scientists use visualization in their work, whether it is important to visualize a problem that you are working on or not. Does visualization play any role in your own work?
You mean visualizing the universe or…
I mean either visualizing the universe or visualizing the particular problem that you are working on. Does that play a critical role, or is it not so important?
I'm not sure I understand. I have to see my spectra. I mean I look at spectra. When I come back from an observing run now, when everything's on tape, the first thing I do is make a picture of each spectrum. [Also] I go observing with a picture of each galaxy, which is probably more than most people do.
You mean an actual photograph of the morphology.
Yes. So at that level I look at things, but...
It is a vague question and everybody relates to it in different ways.
Yes, so at this very low, fundamental, observing level, sure. I sometimes ask myself whether I would be studying galaxies if they were ugly. I really do, and I'm not sure. I mean I see ugly bugs. My garden is full of slugs. I sometimes think, well, maybe if I started studying them, they wouldn't appear [to be so ugly]. I battle the slugs because they ruin the flowers. I don't know. I put that at the other extreme. I think it may not be irrelevant that galaxies are really very attractive.
We mentioned a little bit about your attitude towards theory. How do you think theorists and observers have worked together in cosmology over the last 10 or 20 years? Do you think it's been a successful working relationship or do you think one has gotten way ahead of the other? How do you feel about that?
I don't know. Maybe I'm not a good person to answer that, because I really tend to work pretty much alone. I personally don't often interact with theorists at all. I don't see anything wrong with the way things have gone. I think it's hard to point to many observations that have been made because theorists said we should. Now maybe you could argue that the dark matter has been [an example of that]. But at the time it wasn't.
It sounds like in your work that was not the motivation.
No it wasn't at all, and I don't know why. In retrospect, I can't remember theorists standing up and saying, "Galaxies have heavy halos, so go find rotation curves because they'll be flat." You know, I just thought of something. When you asked me what the response to the flat rotation curves was, [I remember that] the first set of galaxies we observed were very high luminosity galaxies. We published an Astrophysical Journal letter.[22] I had forgotten that the response I got from many people was, "Okay, but that's because you did the high luminosity ones."
The selection effect. Of course, it's hard to explain even for the high luminosity ones.
That's right. But their point was when you go to the lower, or the lowest luminosity, they [will] all have falling rotation curves. I really had forgotten that, and these were some of the people you have on your list. So it wasn't so well expected that people said, "Okay, that's what they predicted and now you've found it."
I'm glad you remembered that. That's interesting.
Well, it was amusing, because by then, I had been convinced they were all going to be flat. That's irrelevant, but the point is that by then I found that a strange attitude. In contrast, let me say in all honesty, [that] when we did the M31 rotation curve and that was virtually flat, we weren't smart enough to make a great thing about it. We live in a diverse world, and some people like to think and some people like to observe. We interact in some places and, by and large, I think it helps us both — the observers and the theorists.
Let me ask you what you think the outstanding problems in cosmology are. I don't expect you to go into this in any great length, but what do you think we should be working on?
Well, certainly, what the dark matter is, how much there is, how it's distributed. Hopefully, some of that will teach us about the conditions of the very early universe — whether it was hot dark matter or cold dark matter, if omega is just 0.2, whether it's all baryonic. I think those are fundamental problems. I think the question of whether it's just gravity moving things around, if there are large-scale motions — these are probably all related questions, those kinds of cosmological problems. Probably the one that we're most likely to be able to, I hope, address soon would be what dark matter is and what the distribution of it is — whether it's distributed like the galaxies or more uniformly. It's hard to think of good observing programs that will do any of that.
Maybe a little bit of it will come out of the numerical simulations, to whatever extent you can believe those. I have a couple more questions. One of them is a question about women in science. You've already made some comments bearing on that. Do you think that your experience in science has been different because you are a woman rather than a man?
Of course. Yes, of course. But I'm the wrong person to ask that question. The tragedy in that question is all the women who would have liked to have become astronomers and didn't. For those of us who have been successful in doing science, clearly the problems haven't been so great that we couldn't overcome them. By and large, if you ask a set of successful women, their answers would have to be that whatever the problems or differences were, they managed.
What do you think that some of the problems are that prevented other women from going into science who might have?
I think probably it's the way we raise little girls. I think it happens very early. I think also it's what little girls see in the world — I was going to say the universe — around them. It's an incredible cultural thing. I have two granddaughters. One of them — her mother and father are both professionals, her aunt and uncle who were visiting are professionals — she said her toy rabbit was sick. Her uncle said, "Well, you be the doctor and I'll be the nurse, and we'll fix it," and she said, "Boys can't be girls." And her mother realized that she never had seen a doctor who was a woman. By the age of two, she knew that men were doctors and women were nurses. So you may talk about role models and your thinking about colleges, but this happens at the age of two. It's a very complicated situation. I'm not sure how you handle this. I think it's a terrible problem; I think it sets in very young. Somehow or other, you have to raise little girls who have enough confidence in themselves to be different. I went to a DC public high school. I was very, very interested in astronomy, and I just could keep myself going by telling myself that I was just different than other people, that they just had different interests than I did. I wasn't really planning on telling you this, but it is so incredibly relevant. I had a physics teacher who was a real macho guy. Everybody loved him — all the males. He did experiments; he set up labs. Everybody was very enthusiastic. I really don't think he knew how to relate to a young girl in his class, and it became a terrible battle of wills. He never knew that I was interested in astronomy; he never knew that I was interested in science. The day I learned I got my scholarship to Vassar, I was really excited because I couldn't go to college without a scholarship. I met him in the hall, and probably said the first thing I had ever said to him outside of the class, and I told him I got the scholarship to Vassar and he said to me, "As long as you stay away from science, you should do okay." It takes an enormous self-esteem to listen to things like that and not be demolished. So rather than teaching little girls physics, you have to teach them that they can learn anything they want to. When I was at Vassar, I sent off a postcard to Princeton asking them for a catalog of the graduate school. Sir Hugh Taylor, the eminent chemist who was then the dean of the graduate school, wrote me a letter saying that [since] they wouldn't accept women, they wouldn't send me the catalog. Some things are better, but a lot of them are not. My daughter is an astronomer. She got her Ph.D. in cosmic ray physics and went off to a meeting in Japan, and she came back and told me she was the only woman there. I really couldn't tell that story for a long time without weeping, because certainly in one generation, between her generation and mine, not an awful lot [has changed]. Some things are better, but not enough things.
She also has you as a role model, which is better than the situation you had.
Yes, that's true. And she has other successful women scientists, but the numbers are still awfully small. I saw by the very last AAS [report] that came in, that the salaries are still down.
This is a pretty speculative question, so you may have to put aside some of your natural scientific caution. If you could design the universe any way that you wanted to, how would you do it?
I don't think I'm smart enough to design the universe. I used to think I could design a woman's plumbing. I used to think that if I had to design a woman's plumbing, I could have done a better job. But [the universe], I couldn't do it. I couldn't do it. I don't have that kind of a view.
Let me ask you one last question. There is a place in Steven Weinberg's book The First Three Minutes[23] where he says that the more the universe seems comprehensible, the more it also seems pointless. Have you ever thought about this issue about whether the universe has a point or not?
Oh, off and on. And do I think it has a point?
Well, how do you feel about the issue?
I think I would agree with him. I think that the laws of physics being what they are, galaxies, stars, planets come into being, and supernovae come into being, and people come into being, and evolution is remarkable. I think it is remarkable. But I think it is a game, an amusing game. And some of us happen to be here, and we happen to have children, and they happen to be who they are. I don't think there is an enormous point to it all. [But for some of us, attempting to understand this universe is important and a major part of our lives.]
[1] J. Jeans, The Universe Around Us (New York: McMillan, 1929); Astronomy and Cosmogony (Cambridge, 1928)
[2] e.g. A.S. Eddington The Expanding Universe (New York: McMillan, 1933); The Internal Constitution of the Stars (Cambridge, 1926)
[3] R.A. Alpher, "A Neutron-Capture Theory of the Formation and Relative Abundance of the Elements," Physical Review, vol. 74, pg. 1577 (1948); R.A. Alpher, R.A. Bethe, G. Gamow, "The Origin of Chemical Elements," Physical Review, vol. 73, pg. 803 (1948)
[4] M.A. in Astronomy, Cornell University, 1951. Thesis entitled, "Evidence for a Rotating Universe as Determined from an Analysis of Radial Velocities of External Galaxies"
[5] M.W. Rossiter, Women Scientists in America: Struggles and Strategies to 1940 (Baltimore: The Johns Hopkins University Press, 1982)
[6] V.C. Rubin, "Differential Rotation of the Inner Metagalaxy," Astronomical Journal, vol. 56, pg. 47 (1951)
[7] M.L. Humason, N.U. Mayall, and A.R. Sandage, "Redshifts and Magnitudes of Extra-Galactic Nebulae," Astronomical Journal, vol. 61, pg. 97 (1956)
[8] V.C. Rubin, "The Local Supercluster and Anisotropy of the Redshifts," in Symposium in Honor of Gerard de Vaucouleurs (Springer- Verlag, 1988)
[9] Ph.D. in Astronomy, Georgetown University, 1954. Thesis entitled "Fluctuations in the Space Distribution of the Galaxies;" published in Proceedings of the National Academy of Sciences, vol. 40, pg. 541 (1954)
[10] Mark Kac, Enigmas of Chance: an autobiography, (New York: Harper and Row, 1985)
[11] G. Gamow, "Rotating Universe?", Nature, vol. 158, pg. 549 (1946)
[12] W.K. Ford, Jr. and V.C. Rubin, "Quasi-stellar Objects with Small Redshifts: 1217+02, . 3C 249.1, and 3C 263," Astronomical Journal, vol. 145, pg. 357 (1966)
[13] V.C. Rubin and W.K. Ford, Jr., "Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions," Astrophysical Journal, vol. 159, pg. 379 (1910); V.C. Rubin and W.K. Ford, "Radial Velocities and Line Strengths of Emissions Lines Across the Nuclear Disk of M31," Astrophysical Journal, vol. 170, pg. 25 (1971)
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[19] e.g. A. Dressler, S.M. Faber, D. Burstein, R.L. Davies, D. Lynden-Bell, R.J. Terlevich, and G. Wegner, "Spectroscopy and Photometery of Elliptical Galaxies: A Large-Scale Streaming Motion in the Local Universe," Astrophysical Journal Letters, vol. 313, pg. L37 (1987)
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[21] A. Dressler, D. Lynden-Bell, S. Faber, D. Burstein, R. Davies, G. Wegner, and R. Terlevich, "Spectroscopy and Photometry of Elliptical Galaxies. I. New Distance Estimator," Astrophysical Journal, vol. 313, pg. 42 (1987)
[22] See reference 15
[23] S. Weinberg, The First Three Minutes (New York: Basic Books, 1977), pg. 154