Interview: Vera John-Steiner, Philip Davis, Reuben Hersh

John-Steiner: I'm going to ask a couple of questions based on things Reuben said once about your collaboration and see to what extent you have similar ideas. One of the things that he said was that mathematicians are particularly eager to collaborate because it's very difficult to live in one's own head and that collaboration helps to overcome the problems of that very internal way of elaborating ideas.

Davis: I think you are speaking of collaboration within mathematical research. I think that's true. that the people are much more isolated than perhaps the outsider thinks, and that they get mutual encouragement and support and also verification. They go over their ideas and say, "this is right and this is right," and they may say "Aha — but you forgot something; what about that case?" It's really a mutual support society. Usually it's two people, it could be more. Now this is mathematical, you said — not book writing — Are you talking about collaboration in research or in book writing?

John-Steiner: Well, I really want to get to the particular collaboration that you two have engaged in. Perhaps the comment about mathematicians in collaboration that he made was more general than your particular collaboration.

Davis: We have never collaborated on math research, only in book writing.

John-Steiner: In the process of book writing have you ever had experiences where, rather than dividing labor in deciding I will do A and you will do B, you actually engaged in the process of thinking together?

Davis: I think that the process of thinking together was informal. We would talk a little and bang out several things, or straighten up certain things, like, "How do I feel about this?" or "How do you feel about this?

John-Steiner: Can you remember a specific instance?

Davis: No, I can't remember one. I remember doing it frequently, I remember doing it under all circumstances. I remember doing on the trip from Albequerque to Taos and back, on those back roads, we would bang out certain things.

John-Steiner: When you say "bang out", was it sort of the overall notion for the book or certain particular ideas?

Hersh: We would try out certain ideas. We would try out ideas, thinking that they might later be incorporated into something that one of us would write. And that's my impression of the way it worked in many instances. I remember once I was in Mt. Vernon visiting my parents and you came down from Providence by train — we met in Rye.

Davis:We met on the beach.

Hersh: We spent the day walking along a deserted beach and it was really great. I hadn't had a chance to talk to anybody about that stuff.

Davis: I don't remember the "stuff".

John-Steiner: Do you remember what the "stuff" was?

Hersh: No, but I can guess because it was the kind of thing, probably, that we always talk about. It's something that I can't quite bring back but it has something to do with mentally handicapped people learning math, or not being able to learn math. Generally, what we talk about is that we've learned, our feeling, I think, that most of the people who are in the math business are totally mixed up and confused about what they're really doing. Particularly, being trapped or hung up about certain illusions and shibboleths. And it's just a pleasure to find out that, if we disagreed, usually we would come to some new thinking after a while — not just stick to our disagreements — each of us could actually learn something from the other.

John-Steiner: When it came to new thinking, was it hard to reconstruct the actual disagreements? Did you come to new thinking in a way continuing the conversation? Do you remember any disagreements that may have been productive.

Davis: I think we had numerous disagreements. I'm very vague now on specific details. I remember numerous disagreements because although our philosophies were sympathetic and almost alike, they were not identical by any means. I remember simply saying to myself — well, this is his position, it's valid, and let's write it up that way. While he would write it up and I'd look at it, I would write something else and he would look at that. There was a back and forth in some pieces. We made an agreement early on that we would essentially never tell the outside which paragraphs who was responsible for. The outsider often wanted to know this. I don't know why, but he did. And we wouldn't do this. This was joint work, and we're both responsible. In fact, one or the other wrote it, and the other criticized it. That's the basis on which we were operating on those books.

Hersh: We decided to use the first person singular, not plural, and quite a few people were quite annoyed about that. They seemed to think that they had a right to know who the "I" referred to. That's why it was so clever of Ian Stewart to give us a mutual name.

John-Steiner: Oh, he's the one who made up —

Hersh: Dervish. Unfortunately, it was never widely adopted in the literature. But that was the idea, that this was a persona, a fictitious single person that didn't have to be Hersh or Davis. But some people are very literal minded.

Davis: I found it very convenient. this agreement that we made. Of course I took credit for a lot of parts that I didn't write and probably couldn't have written.

Hersh: Well, thanks. I think what happened is that both of us took credit for the whole book. People just assume that anything they like in there is mine. Sometimes it's very embarrassing to let them say that, but a —

Davis: It was, but —

Hersh: It's kind of a double your money business, huh, two books for the price of one.

Davis: It's a useful way of multiplying one's own words.

John-Steiner: The other thing that you said in '85, you mentioned something about a certain kind of loneliness of academic life. You also said that sharing ideas endows a greater reality to the intellectual process. I'm just wondering whether either one of you have any ideas as to the effect of communicating at some distance? After all, you were not in the same department, and this has been a very effective collaboration. There may be some advantages to not collaborating when you are next door to each other, in achieving a balance between spending too much time together or not enough; also in creating a special time like you described.

Davis: When the books first came out a number of people commented or raised the question of how we were able to do it at such a distance. It really was a trick, actually. I said, well you know there's the telephone and letters, and we did get together on a number of occasions. I never thought about the virtues of distance, but I suppose now there was an advantage to distance. I suppose, in a sense, if you room too close you get on one another's nerves. The distance meant that we had pieces that we sent back and forth sort of independently of the other. So I think the distance was an advantage.

John-Steiner: The other thing that comes up about the benefits of distance is that having too much time to talk may take some time away from writing, from a balance between "talking time" and "writing time".

Davis: Well, I felt that there was a certain optimal amount of time that I wanted to talk and mull this stuff over before writing. I'll say to myself, "I'm saturated now and I know what I want to write now. I think I have it straight."

Hersh: That's absolutely true, but you had no difficulty making that clear when I was in Providence. It wasn't necessary for me to be in Albequerque in order for you to control the amount of time we spent together. Just that you know what you want and say so. I had one research paper which was done with Y.W. Chen, whom I'd never met at the time, and we never spoke on the telephone either. On the other hand, I have done six collaborations with people in my department, so I don't think it's really an issue. Once you have the same idea, you can each write your part, and it's a minor matter to put them together. And having that same idea, I think, is merely a matter of having a similar viewpoint, a similar desire as to what you want to do. And that was why Phil and I worked together so easily, because what we had in mind was so similar.

John-Steiner: Can you give a two-sentence summary of what that original similar idea was?

Hersh: Well, actually that's not true. Because my idea was to recreate the philosophy of mathematics and Phil's idea was to take some lecture notes from a course he had given on mathematics for the intelligent lay person and produce a book on that subject — which are two entirely different ideas. Our original idea was that he would write his book with my moral support while I would write my book with his moral support.

Davis: Originally two books, my book and Reuben's book, but they would both carry both our names. It didn't work out exactly that way.

Hersh: What happened was really that I was unable to carry out my ambition, which was not only to reconstruct the philosophy of mathematics, but to do it in a style comparable to Bertrand Russell or Henri Poincaré, and to do this in one semester. So I failed. But I produced about a hundred pages of manuscript, and Phil agreed to take it. It was really amazing — I don't understand how a book created in this way could be tolerable let alone successful.

John-Steiner: Well, once you started to link the two things together, do you remember making a common outline for the chapters?

Davis: Well, what we had to do was interesting — we wrote a lot of stuff and then we presented it to the publisher. The publisher said "This is great but I think it's a little too long. We have to cut it by 10 or 15 percent." Then I remember torturing myself, how am I going to cut this back? What am I going to cut out? And then after we'd cut it out, hopefully put the stuff back together so it was coherent. This is where Hadassah came in, she helped me very much.

John-Steiner: You just didn't know what to throw away.

Davis: I won't say that that cut-back was traumatic, in the sense that I said, "Look, this that I have written is precious." I never feel that. I didn't know what to throw away. I now that there were a number of things that we had and they're still in the bottom of boxes, they were in the original manuscript and got cut back.

Hersh: You remember John Dee? He's gone. That was one.

Davis: That's right, it was an interesting story of sixteenth-century mathematics and science.

Hersh: I thought it was a story of hanky-panky.

Davis: He had a minor role in the history of mathematics.

John-Steiner: I'm still wondering whether there was a point at which a shared outline was made. It doesn't sound like it.

Hersh: The problem was to find some order. It was basically an unsolvable problem. Some critics said it was a bumpy ride. And I certainly agree.

Davis: It was a bumpy ride to some extent because we thought of the thing more in terms of short pieces. We definitely thought of it as a collection of short pieces which would have a kind of coherence.

John-Steiner: Like a mosaic.

Davis: Yeah, like a mosaic, but not that smooth. Because of the fact that both of us worked on the writing, we realized it would have to be more like a mosaic than an oil painting.

John-Steiner: Do you think that part of the success of the book is precisely because the short pieces provide different entries to different readers?

Davis: Well, I always thought so. I know I find that kind of book attractive. Because you can go in here and you can go in there and you don't have to read the thing from start to finish. I thought so, and maybe some readers found it attractive.

John-Steiner: Then this was not a clear-cut decision at the beginning — it sort of emerged like this?

Davis: I think it emerged because we both had written a number of individual essays which were published in different places. And so the natural length of our pieces would be between three and four thousand word maybe.

Hersh: Well that was certainly one of the things that made it bumpy, that a great portion was taken out of the drawer and those things were not written to fit together.

Davis: We took some things out of a drawer.

Hersh: We never really tried hard or considered it necessary to make them fit in smoothly. The trouble is that some critics in the reviews didn't look at it that way.

John-Steiner: One of the things I find interesting, watching you work, is that the length of your essays are virtually set, like certain people run for a certain distance. I don't know about your work, Phil, but for Reuben there is a cohesion that runs for a certain length.

Davis: At the outset I saw a lot of Reuben's material. It consisted of short pieces. And he used to say, "Well, these are just jottings or something that have to be worked on more," and I looked at them and I said, "There's no need to, they're okay, they express the idea adequately.

John-Steiner: You played the role of confirmation for him at a very crucial stage. What did he do for you?

Davis: Well, he also confirmed that this material that I had been writing was interesting, and the philosophy it expressed, either explicitly or implicitly, was very consistently his own. On the level of technical writing, Reuben was a very fine editor, and he could take my stuff and essentially copy edit it. Then he used to be pissed off when I would agree with him and he wanted to fight. He was looking for a fight about all these corrections he had made, but I said, "I accept 'em."

Hersh: It was very disconcerting. I wasn't looking for a fight, but I was expecting it.

John-Steiner: It's interesting, because one of the things you said in '85 was that collaboration requires a certain clicking of personalities, and you had enough to talk about, so there was some involvement and interest and so on. But at the time it doesn't sound like there were endless battles about minor little things. The disagreements, if they existed, were really easily resolved.

Hersh: I just remembered something — I don't know if you remember it, but I was amazed at the time — and still am. This was shortly after we first met or first started talking about philosophical things. I told you I had been trying for years and years to write a book and I just couldn't get started, and you said I should just tell you whatever I thought and you would write it down. I just could not believe that anyone would say that.

Davis: Well — I'd had some experience like that. I did a book with Rabinowitz — the book was an advanced monograph that consisted of reviewing many, many current research papers, and there was some standard material which I simply wrote myself out of my own knowledge. Then we came to the more specialized stuff and I said to him, "You read the papers and tell me in your words what's in them." He was a terrible writer — he subsequently learned how to write — and he would must summarize in his own words what was going on in such and such a paper and then I would rewrite it.

John-Steiner: Did you tape it or were you taking notes while he was talking?

Davis: No, he would write it down in some form. His prose style was terrible. I simply took what he had summarized and I rewrote it. So I was experienced in doing that sort of thing, on the basis of that experience, which was previous by ten years maybe or something like that, because we did several editions of the Rabinowitz book. I said, "Sure, tell me and I'll write it down. I'll be your Boswell."

John-Steiner: Did you actually —

Hersh: We never did that actually. But just your offering to do that impressed me so much.

John-Steiner: And it must have freed you too in some way.

Hersh: Well, I felt that this could be a way out. I guess just that kind of willingness to take second place —

Davis: It didn't work out that way — we didn't do it that way, but we thought of the possibility at the beginning.

John-Steiner: So there is clearly some trust involved too in collaboration in that statement when you say, "Just tell me and I'll write it down"

Davis: Well, my trust in him was, when he said something it was right. He would get it right. I wouldn't trust myself to get it right. I knew he would get it right.

John-Steiner: I think there is a real complementarity too. Reuben's a very careful editor and I would, just like you, feel that if a particular phrasing or particular way of structuring it appears right to him, I would trust him too. My involvement is not at that level. As a matter of fact, I showed him the "Scientific Thinking" chapter when I was working on it and he was paying attention to editorial changes, and I got very angry, and I said, "But how about the ideas?" And you said, "Well, they're all right, but have you noticed that you did this and that" and so on and so on, and that was the first time that I had witnessed the very careful way in which he works.

Davis: He's very careful at working with text. Of course there are plenty of times when you change something around and it can be this way or that way and he changed something around that I thought was valid the other way, and I said "No — what difference does it make whether it goes this way or —"

John-Steiner: You are a person who's done a lot of collaboration. One of the things we talked about in the car this afternoon was the Glass collaboration, the illustrator.* And one of the things that interested me as you told the story was that your letter to what became your illustrator was the beginning of a project where in a way she saw some possibilities there that stimulated you to go further with it.

Davis: She said, "No, this is your thing and if you do it I will illustrate it." I said "Okay, but I can't write a children's book. I have no desire to write a children's book. I'll write something that I would like you to illustrate." And so we struck that agreement and I did it and she spurred me on to doing it.

John-Steiner: This "spurring on" is one of the things that interests me, just like what you discussed earlier in terms of your seeing things in all those short pieces was a confirmation that in a way spurred him on. That's different from the later real division of labor where it comes to the details. But this early recognition of the promise of an idea seems to be a very crucial aspect of collaboration.

Davis: Also the personal relationship — you're working with a person. You like that person, you want to work with that person, you want to join with that person. That's important.

John-Steiner: That's another thing that I'm sort of holding for later and that is one of the things you said in '85. The personalities have to click. That sense of really enjoying the other person.

Davis: Well — personality has to click. I have tried collaboration with a number of people that simply didn't get off the ground for a number of reasons.

John-Steiner: Can you mention a couple?

Davis: Yeah — I tried with this fellow Chaitin, Gregory Chaitin, and there I thought, he's a very talented genius in a way, I suppose, and I thought again, I would be Boswell, but he was much too egotistical for me to work with or for him to want to work with me, and we simply couldn't agree on a title.

John-Steiner: Did he collaborate with anybody else, ever?

Davis: Probably on papers, but probably not on a book.

John-Steiner: So it's possible to collaborate with somebody on a short piece of work, even though eventually there isn't that sense of mutual trust and liking.

Davis: A number of collaborations simply couldn't get going. Do you remember some of the others?

John-Steiner: The collaborations that fail mostly don't ever get started.

Davis: Now I've heard of other people that have collaborated, let's say, and they write a chapter, two chapters, three chapters and it breaks down — for whatever reason — nothing ever happens. But I think that what happens in my experience is that if I can get going then it will finish.

John-Steiner: Is there something about that mutual commitment too that makes the process work? That is, once you know that you really want to work together, that commitment keeps a long work going in a way that's much harder to do when one's alone.

Davis: Well, I think ideally both have to be stimulated by the same idea, the same goal, and I can conceive of a situation that people are just pulling themselves apart and it adds up to zero.

Hersh: Have you heard about the collaboration of Courant and Friedrichs on their book on supersonic waves? Cathleen Morawetz was a graduate assistant, she was handling the manuscripts. She says that Courant would write something and she would perhaps edit it and show it to Friedrichs (Friedrichs had been Courant's student.) Friedrichs would say, "No, that's much too vague and sloppy" and he (Friedrichs) would do it over correctly. And then after she had corrected Friedrichs' manuscript she would show it to Courant and he said, "No, it's much too complicated, no one could read that." So he would do it over. And so on. And each chapter went that way until they just got sick of it and stopped.

John-Steiner: So, it never got done?

Hersh: Oh yes, it's a famous book. The only book of its kind.

John-Steiner: In each chapter the series converges.

Hersh: But the point is that they never confronted each other — they just gave it to Cathleen. She later got her doctorate with Friedrichs. She's very much a Friedrichs type, actually.

Davis: I thought a lot about this. There's a lot of luck involved.

John-Steiner: Do you think that at the early stage there is that sense that you are expanding your ideas as a very sympathetic co-participant, that the ideas become so clear at that early stage? What I'm really struggling with is the distinction that I mentioned, thinking together versus division of labor.

Davis: Well, what I think frequently in cooperation, it's almost as though I have two brains. I have mine, and the collaborator's brains and they both pull it along, so it's sort of an amplification of the brain. I feel this very often, and when I don't understand something the collaborator understand it better, or I don't have any experience in this, and the collaborator does, and so on, and I think that's just great! I am more than myself.

John-Steiner: The reason I am talking about the early stage is because we frequently are raised to be very critical of other people's ideas. The critic can sometimes inhibit the creator. In collaboration the other person is the critic so you can let go, you don't have to be all that critical of yourself.

Davis: I have heard this of many collaborations that have failed. That they failed because of criticism of one thought and the other thought. And now I know from experience that when I collaborate, you've got to control this and I know how to control it — this super critical attitude toward my collaborator's work — I know how to control it.

John-Steiner: How about this super criticism toward your own work? A part of what collaborations may provide is that you have to let go.

Davis: There I expect the collaborator to correct me. I'm sloppy with myself — I might let it go — and then I expect the collaborator to — okay, that's where the sense is going to be.

John-Steiner: Right — my sense is that it can be very productive in terms of letting ideas come out and not inhibiting them by being too much a critic of one's own work.

Davis: I think that one can block oneself terribly by being too critical of one's own writing. I like the quote from James Thurber that was pointed out to me many years ago: "Don't get it right, get it written." So to some extent that's my motto, and I keep it in front of my eyes and having decided that that's the way to go then I use the collaborator to get it right. The idea of getting it written is very important and that brings up another thing that I think collaborations may founder on. Each person has a certain natural tempo and tempos are different. Unless you can somehow agree or match the tempo, the thing won't work.

John-Steiner: And that is something you don't know in advance. You may agree on a point of view but —

Davis: I can do it at a certain rate, he can do it at a certain rate, she can do it at a certain rate. And unless I see the feedback at my rate, then I can't go on with my work, as I have to get that — the tempo is very important.

John-Steiner: Any comments on either tempo or the critic within and the critic without?

Hersh: I'd rather just make some comments about the collaborations. I have collaborated with three other mathematicians on Scientific American articles, and with probably half a dozen on research projects, and I think it's fair to say that in every single case the collaboration was possible because they were projects that required a contribution that each collaborator could only make. If you know what I mean.

John-Steiner: So, complementary.

Hersh: Yes. That was the basis in the first place. Someone says let's do this. Why? Because it looks interesting and worth doing, and because I think that together we can do it, but I can't do it by myself. And in some case, the person approached isn't interested or it doesn't work. But if it does work, it's because that's the case. Now, of course, if the two people don't like each other or are grossly incompatible in terms of personality then it will be very difficult if not impossible. But that's the pattern I see in collaboration. You asked about thinking together. There have been some research projects where my collaborator and I actually would meet regularly over a period of time and struggle with the problem and, of course, each of our thoughts were necessary to finally get the solution. But even there the reason for doing this was that the problem involved both his or her and my area of expertise, so our thinking together consisted of our each bringing our own competence to bear on the problem and ultimately we would each write part of the paper — each separately. There could be other kinds of thinking together, where each person is fully competent, that they just work together to contribute to each other's thinking, but I myself have never done that.

Davis: One of the collaborators has to propose to the other one. They have to say, "Let's do something together. How about it?" And sometimes the other person says, "I'm not interested," or "I don't have the time." I certainly have proposed to a number of people a collaboration and they turned me down for all kinds of reasons. Unless you go out there and say what about it, you're never going to find a collaborator.

Hersh: Unless someone approaches you. If you seem to have something to offer, that people actually will want your help.

John-Steiner: But there seems to be — at least with you — a real clear commitment to collaboration that is for you a very important mode of working. Was it when you were very young, or has it been something that has been more the case recently?

Davis: I've written in both modes. I've written books by myself. The work is different, the feeling is different. I enjoy the collaboration. I get a kick out of it. I feel that my brains are magnifying, which is a nice feeling.

John-Steiner: Yes, I think there is something about that sense of — that's why I'm pushing about the early stage — that sense of real possibilities that can be quite exciting and then you sort of settle down and do the more detailed planning that is like any other detail, sometimes a chore and sometimes a pleasure.

Davis: No, it isn't always the brains though, certainly collaboration wi:th an illustrator is a different sort of thing.

John-Steiner: Yes, there is really a division of labor there.

Davis: It's a division of labor. Now, there I knew I have to control my critical comments and I decided at the outset, I have my own ideas as to what creates an illustration that I would like to see, but I don't know what you can do with it, and therefore I'd better shut up. So I didn't suggest anything. You take the text and you find those things that you would like to illustrate and that's what she did. And then when I saw them, it was different than what I expected. I expected my scenes to be illustrated and she didn't — she did her scenes — but her scenes were my scenes also because I'd written them. But this is a kind of initial disappointment that goes along with the exhilaration of seeing the nice things that she did.

John-Steiner: So it's more of a conscious decision to give the collaborator space.

Davis: I think there has to be a back and forth, you've got to give the other person their space, and if you can't do that — if your ego is so big that you can't do that, then that busts it up.

John-Steiner: So, really, people who collaborate well have an ability to step back at times. They don't always have to be in the driver's seat. They have the ability to move back and forth into different positions via the work.

Davis: Well, I would say that is the way I operate. One also hears stories of collaborations of different sorts where there is a principal author, maybe even a ghost writer. Let's say a public figure working with a ghost writer, which is a collaboration of sorts. And the ghost writer'd better defer to them, to the public figure, in some way.

John-Steiner: I'm just going to ask one more question on collaboration and that is on two brains — that's really the issue that is of central interest to me. When you know somebody well, is it possible that you can talk about the ideas that you have at a speed that is closer to the speed of thinking than when you talk to people who are strangers, and that part of collaboration that clicks is that you can tune into each other's thinking?

Davis: You don't have to say everything out. You say a couple of key words and the other person knows what you're talking about. That has to occur, otherwise it takes too long.

John-Steiner: Right! In other words, you begin to lose interest. Well, that was interesting to me today† while you were talking, it was virtually for Reuben, you know, he was sort of self-clued in when Carla made the comment and you came up with the SDI example and so on, that one could actually see a little miniature representation of the way in which the two of you are similar.

Davis: One reason is that I didn't understand the question.

Hersh: That's the difference between public and private.

Davis: That's right. In the public he came to my defense but afterwards he chewed me out.

John-Steiner: I chewed you out a little too

Hersh: He was thinking along my lines. That's why he came up with that example like that.

John-Steiner: So that was interesting for me to se because it was an example of how even though the two of you haven't been talking as much recently as when you worked together that mutual understanding was there.


This interview is quoted and discussed in Vera John-Steiner, Creative Collaboration, Oxford U. Press, 2000.

* It is not clear what "the Glass collaboration" refers to. Davis collaborated with the illustrator Marguerite Dorian on "Thomas Gray, Philosopher Cat" and with the illustrator Inger Sorensen on an unpublished work "The Kongekat". It is possible that this refers to one of those, and "Glass" is an error of some kind.

There is no information about the incident discussed here.