Kenneth Wilson
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ORAL HISTORIES
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Preferred citation
In footnotes or endnotes please cite AIP interviews like this:
Interview of Kenneth Wilson by Tian Yu Cao on 1991 December 10,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
www.aip.org/history-programs/niels-bohr-library/oral-histories/34476
For multiple citations, "AIP" is the preferred abbreviation for the location.
Abstract
In this interview, K. G. Wilson discusses the development of the renormalization group. Topics discussed include: Andrew Pickering; the Kondo problem; Ken Johnson; Francis Low; Freeman Dyson; field theory; A. A. Katanov; Michael Fisher; G. Jona-Lasinio; Carlo Di Castro; Franz Wegner; Alexander Patashinski; Valery Pokrovsky; Curtis Callan; Kurt Symanzik; University of Washington Department of Physics; research on teaching physics; s-matrix theory; Peter Carruthers.
Transcript
Cao:
[???] I want to so [???] most important things. [???] Because there are several different questions. One question about history, your connection with [???] a lot of personal connection [???] of history.
Wilson:
Yeah.
Cao:
[???] Your idea may be too [???] for them to understand at that time, and some people even said that [???] long after [???] can understand your profound idea also. And also some people even said your [???] So maybe you can tell me something about, something your mind [???] more profound ideas [???] historical [???]. Another question I want to ask of you, and you can take any one as first, is about discovery of [???] and the revival of [???] because I had a [???] had something to do with the revival of [???] just want to listen to you. What do you want to take first, history or [???]
Wilson:
Why don't you do the history first?
Cao:
Oh yes.
Wilson:
I mean what I noticed, I mean Pickering has an excellent history of you know what happened in the [???], really excellent, and then most of the people who work, you know, in the sociology side of things responded to that by saying the history was unimportant; they will just discuss the philosophy. So I think it's extremely important to do the best one can on the history. Of course you're just talking about my memory, which is not very good.
Cao:
Actually I had already read your [???]
Wilson:
Right.
Cao:
So some background [???] I already got. Then you just tell me the essential pieces, crucial [???]
Wilson:
Okay.
Cao:
Then I will ask you some detailed questions about your contact with others.
Wilson:
Okay. Well I guess the history probably starts when I was a graduate student, the [???]. And I don't remember if I said anything about that in the Novell [?] lecture.
Cao:
Oh yes. You said something. Then after that a small [???] about three week ago I talked to [???] very important [???] about [???] He said when they studied the [???] in 1954 [???] went [???] office and with [???] Did you know that?
Wilson:
No. Don't know anything about that.
Cao:
[???] But he said even 1954. You didn't know that also.
Wilson:
No.
Cao:
I suspect maybe [???] told you that he had this obscure argument.
Wilson:
Well, you have to understand that as far as I know I never discussed it with Gilmonde [?].
Cao:
Aah. [laughs]
Wilson:
Because you see, what I was doing with Gilmonde was I was, uh, he wanted me to apply, uh, he wanted me to use the fixed source model for K [???]
Cao:
Yeah.
Wilson:
And that was what he was interested in.
Cao:
Yeah.
Wilson:
And I started looking at [???] theory sort of as an interesting mathematical system but lost interest in the Ks and at that point Gilmonde lost interest also, besides which he was going off to France. So the last year I was working on my thesis it was on my own and Gilmonde wasn't there. And that's where most of the work that they, a lot of the work that they did on the fixed source theory at that time was done actually at Harvard while I was starting my Junior Fellowship.
Cao:
[???] What attracted you about [???] as a group? [???] you learned that [???] renormalization [???]
Wilson:
That's right.
Cao:
[???]
Wilson:
Well, I couldn't understand the paper of Gilmonde and Rowe [?], so I had to learn it from [???]
Cao:
Oh.
Wilson:
See, that book had this big chapter on it, so—
Cao:
So you [???] understand [???] said in their book? So many people complained they couldn't understand. Even [???] said, "I cannot understand the [???]"
Wilson:
Well, I couldn't understand either [???]
Cao:
[laughs] So what [???]
Wilson:
Well, let's see. I mean, what happened, I mean sort of the first thing that happened was that I constructed — I started looking at the high-energy behavior of the [???] theory, and I then discovered that there were series expansions there that I could recognize analytically and I could sum them up. And that was a paper I wrote and never published, but I don't think [???] at least I don't think I published it.
Cao:
[???] some connection with your paper published in 1975?
Wilson:
I don't think I ever published this particular stuff. I mean, that I had, although, let's see. What was the paper in '65?
Cao:
I didn't [???] several other papers. [???]
Wilson:
It is conceivable that — Anyway, what I had was exact sums of —
Cao:
[???]
Wilson:
Well at any rate I had run through the series to enough orders to see that there was a rule there. You could complete the rule and then [???] high-energy limit of the [???]. And that sort of got me interested in [???]. I mean I had read [???] and Chertoff [?] when I was — before that. But that was just because that was the text for our [???].
Cao:
So [???] you had never had a conversation with Gilmonde?
Wilson:
As far as I know, I never had a conversation with Gilmonde [???].
Cao:
And also [???] when you were at MIT you tried to talked to [???] and that he was not interested in that. Is this true?
Wilson:
That I have no memory of.
Cao:
No memory. Well he said you told him [???].
Wilson:
Could be, but — Okay. So, I don't remember. Well, I could try to see if I have [???] paper in my files here. Okay. Now, at this point there is no reference to Delmon [?] and Lowe [?]. There is a reference to a discussion with Gilmonde [?].
Cao:
[???]
Wilson:
So this was probably [???]. I don't know. But anyways, if it is published, you can find it [???].
Cao:
[laughs] So, when you — What attracted you to the Renormalization Group at the beginning of the 60s? You didn't have a [???].
Wilson:
Well, it was impossible to understand it. It was impossible to understand it, because what it said was that if you have the solution of the theory then you can derive the solution the theory.
Cao:
Yeah.
Wilson:
Right? It was circular. Because you had to start with a complete solution, given in the [???] theory, and —
Cao:
[???] it's valid. Assuming the validity of the [???] theory.
Wilson:
Right. I mean, so in effect, from the [???] sense you would solve the theory, and then it led to a set of equations which allow you to solve the theory. Now it wasn't completely circular, because when you saw the equations you got the solution in the form of these sums of, the sums of the [???] were given to you where before you [???]
Cao:
Do you think that maybe I have to take [???] in this kind of —? There are some people complain that the Renormalization Group Theory is usefully only when you are able to solve the complete theory.
Wilson:
Right.
Cao:
Which [???] Renormalization Group in the 70s. Is [???] such group?
Wilson:
Well, I mean there are a few cases — but unfortunately only a few — where in fact the Renormalization Group theory solved something that had not, uh, science previously didn't solve. There was the approximate recursion formula, which I wrote down, but of course which was not much different from what Dicen [?] had written down, except I had more of a, I had a different logic behind the recursion formula than Dicen did. And I guess the most notable example was the condo [?] problem. Because there I generally got a solution which nobody had gotten before, and I got it by a pretty large scale [???] computation.
Cao:
I am not familiar with condo problem. I talked to [???] about solution of condo problem. [???]
Wilson:
Well there is now — See, what happened was, I did a numerical solution, and not only did I do a numerical solution, but I put [???] solution, do sort of an experimental type error analysis on it, but came up with a number. And then ten years later Notton Andre [?] in the U.S. and Wheatman [?] in the Soviet Union came up with their analytic solutions to the condo problem, including a value for the number that I had calculated numerically. And their value was exactly at the limit of error that I had calculated.
Cao:
[???]
Wilson:
[???] 1 percent.
Cao:
Oh. [???]
Wilson:
Well, I'm sure that [???] is suspicious of their analytic solution, but what's amazing is that it did agree with the numerical solution that I did [???]
Cao:
Of course for him it's easier to accept the numerical solution. [???] to be universal applicability. Is there something [???] history.
Wilson:
Okay, well the next thing that I remember, and it's presumably [???] lecture was the work that I did on [???], part of the [???], which simply had the benefit of focusing my mind on that. The only thing that is in between is the work that I did trying to solve the [???] and getting exactly nowhere with that, but getting more and more frustrated with [???]. That was when Esnitcher's [?] theory was all the rage and everybody was doing it, and I got more and more frustrated with it; it was not a proper framework of doing or accomplishing anything.
Cao:
At that time you were quite isolated.
Wilson:
Right.
Cao:
[???] communication with other physicists?
Wilson:
Well, I went down to MIT all the time. I mean, at Harvard I was adulated, but —
Cao:
MIT?
Wilson:
MIT, I talked to Ken Johnson and Francis Lowe [?] and all those people. I used to go down there and have lunch with them. I mean, it is still true that I was isolated compared to the kind of things that happen today. But I had just come from CERN, where [???] in touch with everybody. So, oh, and then of course I had long had in mind that I wanted to look at the [???] behavior. And I started that in earnest when I was sitting in a hospital in Yugoslavia.
Cao:
Yugoslavia?
Wilson:
Yes. I spent six months just travelling around Europe, and I wound up with the usual Third World stomach problems in Yugoslavia and I was in the hospital trying to get over it.
Cao:
Can you remember which year?
Wilson:
That was '63.
Cao:
'63.
Wilson:
That was in the summer of '63. And that's when I started working on what became the operative [?] product [?] expansion.
Cao:
Yes. Well there are some interesting questions about your first [???] product expansion. [???]
Wilson:
It wasn't rejected. It was sent back for reworking.
Cao:
But did they suggest you to consult other paper by Ken Johnson?
Wilson:
No no. It was, well let's see. Okay, maybe it was. It was whoever did the paper on the tearing bomb.
Cao:
Johnson.
Wilson:
Okay. So —
Cao:
Johnson 1961 paper.
Wilson:
Right. And I think if I remember correctly, the review [?] did mention that paper.
Cao:
[???] very interesting. Ken Johnson's 1961 paper played an important role in your later paper, because you follow his work step by step. And [???] the story told me by [???] that you [???] and then there was some suggestion to you to consult Ken Johnson's paper, and Ken Johnson's paper is important [???] all these things. And you [???] your paper.
Wilson:
That's right. Well, what happened was — I mean, I saw that the assumptions I made were incorrect [?] because the solution of the [???] model didn't agree with the assumption. And so at that time, instead of resubmitting a paper, I started working and trying to understand how you reconcile [???]
Cao:
But I am more interested not in the result but in the motivation. What was your motivation at that time? At that time the [???] Outside of [???] what's your motivation?
Wilson:
Well, my motivation was, having studied the strong coupling approximations, [???] that I wanted to make [???] theory work.
Cao:
So you still tried to take [???] your vehicle?
Wilson:
That's right. My vehicle was [???].
Cao:
I see.
Wilson:
There wasn't very much one could do with field theory, and so I had to find some kind of puzzle to work on. And it wasn't that I was — I had no conscious plan for what my work on field theory would be, when there was a problem which affected field theory, then that was what I wanted to work on, and there were several things. There was the mismatch between what I had assumed and the operative product expansion paper and theory model, so [???] about that. And then I kept thinking about the fixed source theory, and I can't tell you why I was thinking of that in connection with the Renormalization Group, [???] it was, and it was — oh, well the other thing was that, having worked out the operative product expansion for the full field theory, one thing I did was something to try to work that out for the [???] model.
Cao:
How could you get at the idea of [???] expansion at that time? It was a new idea at that time.
Wilson:
It was a new idea at that time, and what it involved was, I had worked out very complicated formulae for how amplitudes was, if you had a Feinemann [?] amplitude and you had some high momenta [?] and some low momenta, I worked out a complicated formulae for what happened in that case — how the sort of dependence on the [???] separated from the dependence on the low [m ], and at some point realized that I should recast that in terms of position theory space rather than the [???]. And I can't tell you what motivated me to do that.
Cao:
But maybe you can tell me what [???] of this idea. There must be some, you must have some precursor, where you get your inspiration about the expansion of [???]
Wilson:
Well, I mean the first thing that I did was I work out a [???]. It was just part of sort of my general thrust to try to understand what was going on with high-energy. And I don't remember — I mean, that's when I started doing that [???]. Oh, I know what it was. There was this stupid thing by TDV of the — it was a model of [???].
Cao:
[???] Component model?
Wilson:
No. It was — They talked about it at the '62 Rochester conference, so if you look at what they presented at the Rochester conference, I think that [???].
Cao:
[???] paper? I'll try to find out.
Wilson:
Okay. So I had, I think, if I remember correctly, and my memory is very weak on this, that I had started trying to make sense of that.
Cao:
Oh, I see.
Wilson:
And found — and I think I somehow found that in order to do that I had to be able to study this question of amplitude which had some high momenta and some low momenta. I don't know whether I could ever reconstruct the details of that. But, anyway, I got started on that problem and just — So, I mean what happened was I had — the first thing I had was a momentum [?] space [?] version of the operative product expansion.
Cao:
Yeah.
Wilson:
But then I got the idea of trying to restate it in X [?] space rather than momentum space and —
Cao:
What did you [???]
Wilson:
Well that's when the whole thing became much more transparent — which is why the only thing that I wrote down was the position spacing [?]. Because a lot of different things get mixed up when you [???] transform it [?]. The coefficient functions and the matrix opposite get mixed up in funny ways. So it was much easier to boil down the thing to a set of rules when it was on the position [???], and then I just presented the world with the results. Except that you know I didn't publish the paper.
Cao:
Yes. But before that did you have any encounter with Dicen's paper, that Dicen 1951 paper? You said you studied his paper carefully and then — but afterwards [???] this paper.
Wilson:
Oh that was, let's see, that was the paper where we try to do some kind of division between high momenta and low momenta or something like that.
Cao:
Yeah. And also try to establish some connection between the low momentum to high momentum.
Wilson:
Yes.
Cao:
Essentially the idea of [???]. But didn't [???] When did you encounter this paper?
Wilson:
That's a question, and I don't know.
Cao:
[laughs] In the early 50s Dicen was so [???] You put it in the footnote and you said you studied it. And also you mentioned this in your [???]. So [???] get some inference from this paper, but actually there is nothing concrete you can [???] Just a vague idea, but there is nothing concrete there.
Wilson:
Well, I think when I remember reading it, and, let's see. Where did you find the first reference to it?
Cao:
Oh yes. In the '61 paper maybe. I think [???] Also in your [???] you mentioned this.
Wilson:
But we want to find the first reference to that.
Cao:
[???] footnote in this [???]
Wilson:
I wouldn't expect it to be that late.
Cao:
Oh, quite late. In the 60s you mentioned that.
Wilson:
That's [???]. Okay.
Cao:
[???] these footnotes [???] Dicen said a lot of things in his paper, but actually he didn't.
Wilson:
Okay. I mean I suspect that I was doing that early in the 60s.
Cao:
The early 60s. So what's attractive [???] of this paper?
Wilson:
Dicen's paper?
Cao:
Yeah.
Wilson:
Well, I think that's — I mean, I don't remember ever studying Dicen's paper from the point of view of really expecting to learn very much from it.
Cao:
But [???] got some insight [???]
Wilson:
It might have — There's just no way I can — I mean, I remember reading the paper, but I don't remember how it affected my thinking.
Cao:
And you found this paper interesting, and something attract to you. Because actually in this paper I can find some vague idea of the [???] Maybe this appealed to you.
Wilson:
Well, I mean it was clear the — I mean, there were a lot of papers that I had to read which I couldn't understand. Nothing would go on [???] itself.
Cao:
Including [???]'s paper?
Wilson:
Yes.
Cao:
But when did you really understand the [???]
Wilson:
Well I mean, I mean I had to reinvent the Renormalization Group before I could understand —
Cao:
Only after that you — [laughs] [???]
Wilson:
And as I say, the thing that was the problem with the Yaman Lowe [?] paper was it was circular. It said you could only solve the problem after you had solved the problem.
Cao:
[???]
Wilson:
And I kept, I mean, I kept trying to find some way of doing it that wasn't circular, and that was sort of the reformulation of the Renormalization Group so you could set it up in such a way that you could say what the Renormalization Group equations were without having already solved the problem.
Cao:
Can you make an explicit statement about your work on [???] theory and your work in your first paper of operative product and expansion. What's the connection between these two?
Wilson:
Oh. Well as I said, once I had the operative product expansion, one of the things I did with it was to try to see what would those ideas mean if I was working with the fixed source theory instead of the full field theory.
Cao:
I see, I see, I see. [???]
Wilson:
And then, again, it was a question of looking at a separation between high momentum and low momentum.
Cao:
I see.
Wilson:
And then what I started looking at were the wave functions, the actual ligand [?] functions of [???] fixed source theory, which depended on wave function from 1 meson, 2 mesons, 3 mesons, and I was looking at what would happen when you'd sever it. And some mesons had high momenta and some had low momenta. And it was looking at the structure that I could see that there was this structure that would become much clearer if I did the [???] momentum slice [?] model.
Cao:
[???]
Wilson:
That was certainly very important. But the connection was that, since I had this technique of the operative product expansion, and I didn't know what else to do with it, I applied it to fixed source.
Cao:
Oh I see. So actually the important [???]
Wilson:
Pardon?
Cao:
[???] important preparatory work was done.
Wilson:
Yes.
Cao:
But you didn't get [???] back through until 1966 also [???]
Wilson:
Well the first breakthrough — Well, I mean the operative product expansion was a breakthrough, and then —
Cao:
But you didn't publish it at that time.
Wilson:
I didn't publish it because of that referee's report.
Cao:
But in your mind you still felt the idea essentially correct.
Wilson:
Oh, I mean what I had done was correct. I mean, you will discover that all the way through there are things which I don't publish because I don't consider them complete yet.
Cao:
Oh, I see. Not complete not because of its incorrectness. Oh I see, I see. Hmm.
Wilson:
See, it was not complete because it did not agree with the tearing model [?]. I mean, I had made an assumption which simply didn't agree with the tearing model. I mean, the work was perfectly correct if you restricted yourself to [???].
Cao:
I see.
Wilson:
Because then the assumptions were incorrect. But I mean you have to understand that all this time my focus was I wanted to do field theory of [???].
Cao:
Yes, yes.
Wilson:
I had no interest in what the properties of [???] theory was. No. interest.
Cao:
I see.
Wilson:
And so, something that was interesting from the point of view of [p tion] theory was not interesting to me.
Cao:
Yes. It addressed a problem. Some theorists say that you had a more ambitious idea about the [???]. You want [???].
Wilson:
Well, I mean from the time that — I mean, right from the time that I started my research as a graduate student I knew what I wanted to do, and what I wanted to do was [???]. For instance I consciously rejected working with Gilmonde on the weak interactions because it was clear to me that you could not understand the weak interactions without understanding the strong interactions first. That was an assumption in which I was dead wrong. [???] But that was my assumption, that was what was driving me, was that sort of the core of the problem at that time as far as I could see was the strong interactions. And everything that I did, starting, you know, I made Gilmonde give me something that had to do with the strong interactions. And then I never relinquished that. And I'm still trying today.
Cao:
[laughs] Actually Gilmonde's idea [???] just to try to sidestep the [???]. They want to calculate the [???] factor. The [???] factor [???]
Wilson:
That's right.
Cao:
You want to find some dynamic theory to solve that problem from fact actually.
Wilson:
Well, it wasn't just if I want [???] factor —
Cao:
Yeah, more than that, more than that.
Wilson:
It was a whole problem of, I mean, my feeling was the only thing that could work was the field theory and strong interactions and I wanted to understand field theory. And the thing that was really sad about it was the only thing I knew about field theory was —
Cao:
The basic.
Wilson:
Well, it wasn't the only thing we knew. We knew two things about field theory — one, that p[???]tion theory would not work, and the other that there was no specific model that conceivably could be the description of strong interactions at that time. That was very clear. But even despite that, I wanted to understand how to solve a field theory and strong coupling because I didn't think anything else had the remotest chance of success.
Cao:
Yes. Maybe we can take these three lines of reasoning and follow your later work. Because [???]
Wilson:
Okay. Well okay, so then what happened in I think it was in, it was either '64 or '65, Ben Whittem [?] gave a talk on his scale theory of critical phenomena.
Cao:
So we approach it as critical phenomena. What is so critical to your understanding of the whole problem.
Wilson:
Oh yes.
Cao:
[???]
Wilson:
I mean, from the time of, I think it was from the time of Whittem's talk — of course I can't give you, be precise on this sort of thing, but I certainly remember going and listening to his talk and being puzzled by it. But I think from that time — I assume it's from that time that I started thinking about the possibility that critical phenomena wouldn't illustrate the kind of problem that I was thinking about.
Cao:
Why did you get such a hunch at that time?
Wilson:
Well, we have to fill in something here. I mean, let's see, I'm pretty sure this is after — I mean I started thinking a lot about how do you solve a field theory.
Cao:
Yes.
Wilson:
I mean, I know that you weren't going to do it analytically. So I did a lot of thinking about how would you solve the field theory numerically.
Cao:
Step by step.
Wilson:
I mean, how would you set it up so you could put it on a computer.
Cao:
Mmmm. Yes.
Wilson:
I mean, I was fascinated by computers. I spent a year, even though it was futile, trying to solve a strip approximation on a computer.
Cao:
In the years of '64-'65?
Wilson:
No. The strip approximation was what I spent most of my time on when I was a Junior Fellow. This was after I had done my thesis. My thesis was over, I turned it in, and then mostly what I was doing for the rest of my period as a Junior Fellow was I was going — And that was one reason I was going down to MIT, because I would get one run per day from their stupid machine.
Cao:
Oh. So you were fascinated by a computer even in that time.
Wilson:
Yes. And so I mean I wrote a program. I didn't know how to debug computer programs at that time, and you got — The turnaround at MIT was you got one run per day. You know, and so I had to go down to MIT every day to get the results of my run.
Cao:
[laughs] Maybe this kind of [???] Your access to computer actually influence your thinking maybe. Can we say that?
Wilson:
Yes. Certainly. And then when I came to Cornell there was a little machine that they had in the laboratory of nuclear studies, Control Data 160-A [?]. I actually had started with the Datatron [?] 210 or something like that. The machine they had at Cal Tech when I was a graduate student. And John Matthews and I had written a program [???] rocket [?] coefficients. So the computer runs through all this, and I was thinking about how would you [???] strong interactions from the numerical point of view, because I was skeptical there would be any analytical [???].
Cao:
I see.
Wilson:
And now at some point — and I think this was before I started thinking about critical fund [?] — I got the concept that the right way of putting a cut-off into a field theory so you can even think about it, was to use a lattice [?].
Cao:
Yes. So you saw some similarity in your thinking and that [???]
Wilson:
Well I mean, once I was thinking about what a field theory looked like on a lattice. And I did some numerical computations just on free field theories on a lattice, and that was [???] things I ran in the 160-A just to get experience. But it was, as I started to think about what a field theory was, what [???] on a lattice, and then it became easy to see that a [???] and a field theory were very similar.
Cao:
[???] make it clear that your idea also to use field theory in the lattice, you got this idea before 1975 or after 1975?
Wilson:
I believe that I had it before. I think that was the reason I got interested in the [???].
Cao:
So Williams' idea became a receptacle for you, because you already had some idea, but not his idea.
Wilson:
Well see, I don't know if I had that at the time I listened to the Williams [???]. I have no [???]
Cao:
Something in your conscious or unconscious, subconscious.
Wilson:
I mean I know at some point I was struggling with the question of what did he really mean by having a theory with a cut-off, and especially what did you mean by a theory that you could actually compute. You see, in the conventional ways of introducing a cut-off didn't make a theory that you could compute. Whereas if you put it on a lattice, then you could start thinking of something that was computable.
Cao:
[???] about cut-off. You were studying — you spent some time in Cornell.
Wilson:
Yes.
Cao:
[???] And he introduced the cut-off in [???] calculations first of all, one of your [???] successful calculations.
Wilson:
Yes.
Cao:
Did you have any contact with him? And what was your understanding of cut-off in [???]
Wilson:
Well my understanding of the cut-off as far as I can remember was the standard one. You, [???] cut-offs in the diagrams.
Cao:
But there were two different understandings of cut-off. One [???] and another is a [???] What was your understanding?
Wilson:
No, no. I'm sure that what I had learned was the standard thing you did in preparation for [???]
Cao:
[???]
Wilson:
Now, but I had I think at this point, I had done the blocking for the fixed source theory. So I was beginning — There the cut-off was more than just a formal device [?]. But I came up against this question, that if I was gonna do a field theory numerically, I'd have to somehow —
Cao:
[???]
Wilson:
I had to have something which I could take seriously [???] arrive at something which was computed.
Cao:
[???] high-energy physics there is a new school [???] They take their cut-off very seriously. But all these physicists attribute to you [???] because you first introduced the idea that we have to take the cut-off very seriously. So I just want to know, when did you get the idea? When did you have a shift from the formalistic [?] [???] then?
Wilson:
Well as I say, what I remember — and I don't guarantee that my memory is correct — is that the shift was precisely as a consequence of trying to ask the question, "How would you compute a field theory?" I mean, "How would you set it up so that you could actually use it on a computer?" And the standard way of doing cut-offs would not have worked. I mean, it was not only that I wanted to be able to do it on a computer; I wanted to do it on a computer away from perturbation [?] theories. So you did not have to, you know, it was already clear you could compute a perturbation theory if you wanted to [???] order. But that was not what I wanted. I wanted to take the field theory, I wanted to be able to ask things like, "What does it do in the strong coupling limits?" and I wanted to be able to do that on a computer.
Cao:
You wanted to do some work with computer then after you [???] so that this new theory can be adapted to [???] computer. Can we say that?
Wilson:
Yes. And further along the way I posed the question — I mean I knew that the computers that were available at that time were ridiculous for this problem, but I just asked, "If you had a computer which was powerful enough but still finite — I mean, it could not do an infinite calculation, [???] finite could be as large as I wanted, "How would you formulate the field theory in such a way that you could do that?"
Cao:
Oh, I see. You just wanted to get a new formulation [???]
Wilson:
Right.
Cao:
All this was happening before 1975 when you got in contact with the idea of [???]
Wilson:
I can't tell you at what point in this thinking process I heard Williams' talk. I just can't tell you, because that's [???]
Cao:
Anyway, around this time you had such an idea.
Wilson:
Yeah. But anyway, my memory is that because I knew that I was thinking about lattice theories that that made it natural to look at the IZ [?] model just because, I mean, I was beginning to see that the essence of the problem was just how many degrees of [???] measured by the large number of lattice points you had to deal with.
Cao:
Then [???] you did not understand what Williams said, and then only after [???] you saw something unique.
Wilson:
Well I mean, Williams had made a set of assumptions, which I couldn't see any reason why you would make those assumptions. Because he basically assumed a result. So, you know, he assumed certain things were a homogeneous function of a certain nature, and he just assumed it.
Cao:
You couldn't see the reason why.
Wilson:
There was no reason.
Cao:
Yes. And afterwards Katanov [???] there was some reasons for that.
Wilson:
Yeah, well Katanov did a version of the renormalization with the scaling. His scaling ideas of course were much more based on the Renormalization Group's ideas than [???]'s group.
Cao:
In his '66 [?] paper he didn't mention the name of the Renormalization Group.
Wilson:
No. He knew nothing about — The Renormalization Group —
Cao:
Essentially the idea is the same. [???]
Wilson:
The Renormalization Group was the name that the field theorists had invented, and there was no reason for Katanov to know anything about that.
Cao:
But the idea is essentially the same.
Wilson:
Yes.
Cao:
[???] introduced the name of the Renormalization Group to [???]
Wilson:
Well, no. I think that honor goes to [???] Lucenio [?] and Castro and Yonan [?] Lucenio.
Cao:
Which year? In 1964?
Wilson:
Well, you'll have to look up — Their papers were later than that, but I mean I certainly didn't write anything until well after Yonan Lucenio and Castro had written [???]
Cao:
I see. And there is a very interesting question that I want to ask you, because there are four persons getting involved in this: Williams, Katanov, and [???] you. And what's the [???] relationship and what's the [???] paid by every physicist [???] What for example Fisher [?] in this development?
Wilson:
Well, I mean the most important function of Fisher was, after I had studied the IZ model and I started learning what Katanov had done, I mean then I started talking a lot to Michael [?], because he had a comprehensive knowledge of what was happening in statistical mechanics, and you know, just because I had read Katanov's paper and listened to [???] didn't mean I knew nearly enough about sort of the — I needed to know the way people thought about critical exponents and things like that.
Cao:
Or [???] information you have to —
Wilson:
Usually you hear about this from them from the newspaper report. I mean, they hold their press conference in Stockholm and then the radio and TV and the newspapers call the recipient. But they placed a special phone call to me to explain why it was not going to Katanov and Fisher and myself. Because that was what everybody has assumed that was what it was going to do, that's what they should have done. But they didn't.
Cao:
They didn't.
Wilson:
And, you know, that was because the [???] prize two years before had gone to the three of us, and that had set up the expectation in everybody's mind that if there was gonna be a Nobel award for this it was would have been the three of us. And I still maintain that's what they should have done.
Cao:
Then what's the essential contribution of Fisher?
Wilson:
Well —
Cao:
[???] extension?
Wilson:
And there were two components there. I mean, first of all I had to learn — In a sense what I [???] was the paradigm that the people in statistical mechanics were operating on, because they thought about the critical point, and to get that paradigm I had to get that from [???] Fisher because he knew it better than anybody.
Cao:
I see. Another [???]
Wilson:
And the other tough moment [?] was in his office together, looking at the question whose answer was the epsilon.
Cao:
Yes.
Wilson:
I mean, I was trying to figure out what was going on with the solutions of the [???] formula [???] and I was just confused about it, and it was with that discussion that he and I had that sort of resolved the sense of confusion and made it clear that there was something specific happening in four dimensions, and the way to look at it was to look at not at four dimensions but close to it, and as soon as we had resolved it that was the problem and I knew what to do and I went off and did it. But, let's see, here we come to a, I mean, this is I think an extremely interesting point from the view of history, because the Renormalization Group would not have taken off the way it did if all the people had was my numerical paper — the ones that the committee cited [?] my new numerical paper, which preceded the epsilon expansion. Now Franz Wagner [?] had come to Cornell specifically to learn about numerical stuff. So it's conceivable that it would have taken off through that route. But the epsilon expansion paper is what enabled everybody to get into the act.
Cao:
So, are you suggesting that actually the epsilon expansion provided some theoretical basis for [???] work?
Wilson:
Not only did it provide a basis for understanding numerical work; it provided a basis for doing some.
Cao:
Ah. Why it is so important? Maybe you can explain to me.
Wilson:
Well, I mean, physics is people discovering [???], that's what physics is about. But there wasn't very much that you could discover based on the [???]. Very difficult. Whereas the thing about the epsilon expansion, it opened up all kinds of problems that you could solve, and you weren't subject to the limitations of the approximate recursion [?] formula, which I had all kinds of questions about. By making this in the form of an expansion it was much easier to know where you were at, and a much broader range of problems that you could address. People would have found it extremely difficult to do with the numerical [???]
Cao:
Then there are two questions I feel difficult to understand, and you can help me.
Wilson:
Yes.
Cao:
First question is, what's the relevance of expand, of epsilon expansion to the Renormalization Group? The other question is, what's the ontological [?] basis for the epsilon expansion? I mean, what's the physical meaning, real meaning of this epsilon expansion?
Wilson:
Well, you see, what happened was, after — Once the epsilon expansion was there, then the Renormalization Group became sort of the paradigm while the epsilon expansion became the technique.
Cao:
Technique. Yeah.
Wilson:
I mean people started learning, in statistical mechanics, they started learning the paradigm of the way of thinking about the problem provided by the Renormalization Group, but they used the epsilon expansion was the technique by which they actually [???] numbers [???]
Cao:
I see.
Wilson:
But this is information you have to get from the people who came into the subject. You can't get this from Michael Fisher and myself; you have to get it from the other people, like Brisand [?], Wallace —
Cao:
David Nelson. I talked [?] to him.
Wilson:
And a key person to talk to is Franz Wagner, because if anybody could have taken it from the numerical equations directly it would have had to have been him.
Cao:
I see. So actually you say that there is a reverse order of the understanding, where you inventioned something then you took the epsilon expansion very seriously, afterwards when the Renormalization Group pattern had become established. When people came later, they learned the Renormalization Group at first, but then [???] explained other techniques.
Wilson:
Well, I think — I mean, as I say, you have to talk to the other people. I mean, the point about the epsilon expansion is a lot of people realized they could do this. And you'll have to find out from them more specifically. But, I mean, what in the end developed was this blend, and you'll have to talk to them about how they arrived at this blend of understanding the formal concepts of the Renormalization Group. And by the way, Michael Fisher did a lot to help the rest of the [???] learn those formal concepts, and his review articles were very important for that. And so they, but what they learned was the formal concepts of the renormalization [???], and they learned the techniques of the epsilon expansion.
Cao:
So that's the contribution of Fisher, not Fisher [?]. What about Katanov?
Wilson:
And remember also that Michael had been one of the people to develop the scaling theory.
Cao:
Yes.
Wilson:
I mean, Ben [?] had developed, Katanov had developed it, Michael had developed it, Patashinsky [?] and Porkovsky [?] I think had also developed it. A number of people had developed from their own point of view what the scaling theory was. But Michael gets as much of the honors as anybody else. So, but I mean is sort of, he had been a driving force behind the whole development of the theory of [???]
Cao:
[???] personality? [???]
Wilson:
The most important thing he had I think was he had a comprehensive knowledge of what was going on, and so he could everybody unders — I mean, he was a teacher of everybody in the subject, with the except of Cyril Dolm [?], who was teaching [???]
Cao:
Yeah. When did the concept of universality get into the program?
Wilson:
I mean the universality was developing along with the development of the [???], although I think in some sense that had been earlier. I mean, Katanov was of course very focused on universality [???]. So, but there I think you have to talk to the people in the subject. I mean, it's not my place to tell you who is responsible for universality, since that was clearly coming out of the statistical mechanics side of it.
Cao:
Then, what was your contribution, essential contribution to this?
Wilson:
Well, the contributions I made were first of all — Katanov, in writing his thing, assumed something that he could not produce. He assumed there was some way of going from a theory at one scale to, you know, he said if you had an Eising [?] model with this lattice spacing there was some way of producing an Eising model at the next lattice spacing. But there was nothing you could figure out from his papers as how you would do it. So the approximate recursion formula is the first actually concrete procedure by which you could accomplish that. I mean, with all kinds of caveats and approximations with it. It was a sort of a model that allows you to see how you would actually do that. Then there was the epsilon expansion, which was jointly between Michael and myself — which is what really released everybody to go work on this. And, but, but, you know, embedded in the approximate recursion formula was — See, what was there that was much more powerful in a sense than what Katanov had done was the concept that you could have a transformation, but that a transformation was not something that transformed two variables like Katanov does; it was a transformation on a completely arbitrary [???], which meant infinite numbers of parameters [???] To characterize that Hamiltonian [?], you had to do a transformation in that space to define the full renormalization. And in some ways you might say that was the most essential point, because that sort of set the framework for being able to think about the whole problem without making approximations when you were thinking about it. And with that I was very careful because, I mean, I didn't get it published right away but in '72 or '73 I published a formal paper where I showed an example where I could prove that despite having an infinite number of parameters that you could still have a transformation that made sense and control its properties. And I don't think very many people read that paper. It's sort of an archival paper, but you know, it's sort of like publishing the details of how you actually did an experiment that worked.
Cao:
There is something very interesting —
Wilson:
Well, let me finish. I mean, the point was that that was in the end the statement of my understanding of Gilmonde and Lowe. And Gilmonde and Lowe, the essential problem with it, was that it was a transformation on just one variable [???] And there are all kinds of — It was a very complex set of assumptions that allowed you to solve the Renormalization Group in terms of one transformation and one [???] And you could only do it in [???] theory and etc., etc., whereas in the form that I gave it, it was now completely general, and you could think about problems that had no connection with [???] As I say, there are only a few cases where that has been made to work. The condo [?] problem is the primary one where [???] actually taking that concept of a transformation on an arbitrary Hamiltonian, doing a —
Cao:
[???] new idea, yeah.
Wilson:
Yeah, and doing a numerical computation based on that and getting a number which was actually accurate and [???] best information we had.
Cao:
But there is a problem about the Renormalization Group flow, the transformation of the Hamiltonian space.
Wilson:
Right.
Cao:
Is there any guarantee for existence of [???]
Wilson:
No.
Cao:
If there is no guarantee, [???]
Wilson:
No, because I mean then it becomes a problem [???] I mean, when you have a space, and if you can characterize a space as bounded in some sense, even though it's an infinite space — it is compact, in other words — then you have a transformation and [???] turpological [?] transformation [???] I mean there are things you can say about that, even if it's not [???]
Cao:
Yes, but you see [???] discuss this question with various physicists, because the [???] of the Renormalization Group [???] the transformation within the homotoneous [?] base is so powerful in connection to [???] physics, no problem about that. But its usefulness [???] in the existence of [???] If there is no [???] solution, [???]
Wilson:
Well, I mean the next thing you think about is a [???]
Cao:
Yes. But even [???] every cycle is not guaranteed.
Wilson:
No. Nothing is guaranteed.
Cao:
Not even guaranteed. Then the question raised by field theorists, they said in the quantum field theory you cannot find [???] theoretical model in which there is a fixed [???] solution.
Wilson:
Well I mean, that's nonsense. I mean, it's just that we haven't found one in four dimensions.
Cao:
Yes, this is the question. [laughs] Because you see [???] How can we find the fixed point solution? Where is the [???] of fixed point solution? I can't answer that and so I want to ask —
Wilson:
Well, of course the other thing is the fixed point that we use in the theory of strong interactions now is the [???] field fixed point [?]. I mean—
Cao:
Yes. The only theory is the free theory. Yeah.
Wilson:
Well, I mean, in the case of esontotic [?] freedom, [???] so, I mean, that was one of the, I mean, one of the great ironies of this whole story, right, is I produced the operator [?] product, I said I would not publish it because it was not [???] enough—
Cao:
You didn't [???] You should have done that just a step further, yeah.
Wilson:
Yes. But, I mean, quite aside from the question of whether I should have discovered it or not, the irony is, I mean, all the evidence [???] you know in the late 50s and the 60s was here was a strong interaction problem, so it was natural to think about, that that was a problem, and you had to address that problem. And so, you know, I was very careful to focus all my research on strong interactions and not to publish things that would not be relevant to that problem. And yet, because I was looking at the high-energy behavior, right, there was no need — If, I mean, if our picture of quantum thermodynamics is correct, there was no need ever to go beyond [???] theory to deal with [???] That's not to say that we aren't going to find other theories in these main unified theories which bring you back to the same [???]
Cao:
Maybe part of the reason you didn't discuss that was that you didn't pay attention to the [???]
Wilson:
That's why I didn't discover it. Because I never had the energy to go learn about [???] theory to know what's going on, and so I just made the assumption that since every other theory had no, you know, it all went the other direction for every theory I knew about, I just assumed that it was always gonna be the case and I didn't need to pursue it.
Cao:
Also there was a controversy between you and [???] and [???] about the [???] They told me that you always insisted that all the [???] can absorb into [???] normal scale dimension, and they thought it was impossible. Do you remember this controversy?
Wilson:
No.
Cao:
Maybe we should attend to the history again.
Wilson:
Okay.
Cao:
Within the time you get involved in statistical mechanics in 1965-66 and your works on the statistical mechanics again in the 70s at some [???], you published the most important paper I suppose about the operative product expansion in 1968. Why did you, once you got involved in statistical mechanics, come back again to do some work on field theory?
Wilson:
Well, that was because the only reason I was doing statistical mechanics was [???]
Cao:
Just because you want to do some work on the strong interactions.
Wilson:
That's right.
Cao:
So [???] about the scale [???] Can you tell me this history? When did you get involved in the scale argument? Because you said that you never got this idea from Gilmonde.
Wilson:
Right.
Cao:
Then there was some previous work from [???] and several people. Did you [???] all these papers?
Wilson:
Well, I mean, the papers that I knew about are of course referenced in the 1969 paper. Now —
Cao:
You mentioned Ken Johnson's paper, 1961, and Mark's [?] paper, 1968. You read these papers.
Wilson:
Well of course. And at the same time I, I mean, what I was learning from the paradigm of statistical mechanics was to, I mean, all that was helping me to understand the concept of scale endurance, I mean how it should be formulated. Because, I mean, that whole scaling theory was telling you that you were dealing with a scale [???] theory, and I was relying on that whole paradigm from statistical mechanics to sort of put some kind of order into how to think about the field theory when I could no longer use preservation theory to tell me what to expect.
Cao:
So you put a [???] You want to get rid of the [???] theory?
Wilson:
The, well — I mean, the title [???] was basically saying that I was not relying on the connection with classical canonical [?] quantum [?] [???]
Cao:
I see. Why did you think that the canonical formulation is not so good? Because around the same time there were some very important discoveries about the anomaly [?]. You know that result. Because [???] was your student, and he informed you of this development.
Wilson:
Well, I mean, are these things referred to in the '69 paper?
Cao:
Oh yes. You discussed their work and you even put it a little bit further and to expand the [???] and also [???] that he informed you of [???]
Wilson:
Oh, I'm sorry. There was the axial vector anomaly [?] within piezio [?] [???] which I certainly knew about, no question.
Cao:
Yeah.
Wilson:
But that's separate I th —
Cao:
Separated from the scale anomaly.
Wilson:
From the scale anomaly. I mean, the statement that canonically you should have had scale endurance, and yet in perturbation [?] theory the scale invariance [?] itself has violated this separate — At least, I think that's separate from the actual vector anomaly, which prevented you from having axial [???], conservation of the axial.
Cao:
And so at that time you didn't see any connection between the [???] vector anomaly and the scale anomaly, no connection?
Wilson:
I don't think that had been discussed as a — I don't think that had been discussed as an anomaly, because at that point — as far as I can remember, and we can check the references — the only people talking about scaling variance were [???] and [???] Jukeef [?] was very focused on this axial vector anomaly.
Cao:
He didn't discuss that. He said that he got involved in this only in 1970-71, much later.
Wilson:
That's right, that's right.
Cao:
And you developed the idea of scale anomaly in [???]
Wilson:
But you see I didn't develop as an anomaly. Right? I didn't tell you here is a diagram — I mean, for the pi-zero to two gamma there was a diagram that you calculated, and that diagram showed you why [???] conservation [???] As far as I know I never looked at the scaling from the point of view of being an anomaly in a current [?]. And I don't think Mack [?] and Castro [?] [???]
Cao:
No, they didn't [???] that. Only [???]
Wilson:
So I think that all developed later, as far as I know.
Cao:
There is something very interesting and very important historically. [???] and Rumiyaki [?] were the first persons to develop the scale anomaly connected with the current [?], but I suspect and they [???] they get some idea from your 1969 paper. Because you developed the idea of a normal scale dimension.
Wilson:
That's right.
Cao:
In [???] there is a scale anomaly in your paper.
Wilson:
Well, implicit, I mean implicit, but I never developed [???] saying here is what the current is and here is the anomaly.
Cao:
You didn't say that, you didn't say that.
Wilson:
But you see, but there's a reason, you see. Because what I am saying, you see, what— The scale anomaly came up when it became necessary to really study perturbation theory, because in perturbation theory there had to be an anomaly which that perturbation theory is not scale [???]
Cao:
I see. And you [???] the idea of perturbation in your theory.
Wilson:
That's right.
Cao:
Oh. I didn't see that. Oh, yes.
Wilson:
[laughs] So there is no scale anomaly in my paper, because scale and variances [???] It is only the — See, and the point is that I was talking about these anomalous dimensions, and where they come from is, they come on one hand from the [???] model, but that was too specialized. There was no justification for saying what happened to the tearing model would be general, but then I had all these paradigms from statistical mechanics, which exactly says that there will be scale invariance but it will have [???]
Cao:
So it's not [???] You this as incompatible, because you rejected the idea of perturbation, and the scale anomaly comes from the perturbation —
Wilson:
That's right.
Cao:
Oh, I see. [???] more complicated [???] to discover this. [laughs] And another thing, actually you believe that there will be scaling laws, or once you get to [???] dimension of the field. And they claim that it's impossible. [???] field operator, you still have something more than that, so the scaling [???] is not always —
Wilson:
Sorry?
Cao:
The scaling [???] —
Wilson:
Well, I mean, there's just tremendous confusion about which scaling laws we're talking about. See, I talked about scale invariances and [???] but with [???]
Cao:
The scaling [???] approximate [???]
Wilson:
But, well, I have to find out what you're talking about. But I remind you that at the time that I wrote that paper scaling meant something completely different. It was [???] scaling and [???] everybody was fussing about, and that was the scaling that could not [???] according to my theory [?].
Cao:
Oh yes. I understand this. That's totally different. Because his study entails [???] no interaction in it. Your scaling [???] entails of something [???] more than [???]
Wilson:
[???] scale invariance in the sense of an actual transformation, you know, a rescaling of all positions or all momentum. I was talking about a theory that would still be scale invariance in that sense but just that the operators would have different rules for how they —
Cao:
Different dimensions.
Wilson:
They were in different dimensions under that scale. Whereas [???] scaling depended on particles actually being free particles, and of course Feinemann was the one who really set up that [???] model to really make that explicit, that that was the underlying assumption of [???]
Cao:
[???] argued with you in that paper and also in their memory, that they say that [???] impossible to have a field theory [???] scaling laws without some extra term in it. And they say that there is always something more than the [???] scale dimensions in field theory, and —
Wilson:
I mean, they may well have said that, and there may well have been arguments. I have no memory of it, but you can't rely on my memory for anything.
Cao:
But actually in your [???] papers published around 1969 to 1973, [???] you had two very ambitious ideas. One is that you tried to develop a field theory of strong interactions without perturbation, and this idea wasn't, didn't — Some physicists found it very difficult to implement.
Wilson:
Yes.
Cao:
The other idea is the [???] Renormalization Group flow idea.
Wilson:
Yes.
Cao:
Also field theorists found it very difficult to assimilate it, because they cannot find the [???] Everyone said that Kim Wilson's idea is so profound that we should have learned something from him, but [???] they cannot learn something from [???] Then a very interesting story that Steven Weinberg [?] and [???] something from your [???] from their conversation with David Nelson, your student, one of your students?
Wilson:
David Nelson was a student of Mark Fisher.
Cao:
Mark Fisher in Cornell [???]
Wilson:
[???]
Cao:
He attended your seminars. He [???] your idea in the language they [???] understand that. Can you see the reason why field theorists cannot understand your work? Everyone knows that at that time there was a Kim Wilson there, very good, wonderful ideas, but we can't understand them. Why? Why they cannot understand? You worked first as a field theorist. You were always interested in the field theory.
Wilson:
Well, I mean, the reason is very simple. I never gave them the steps by which I arrived at anything. I just gave them the results, and they couldn't work on it really. I had done eight years of work to be able to write that paper, and all I did was I gave the results; I never gave them the scaffolding [?] which made that work [???]
Cao:
Why didn't you give them scaffold so that they can understand easily?
Wilson:
Well I tried, but it was, I mean, I tried to write a paper that would really explain why the operative product expansion worked, and I have — I think I eventually threw it out. I mean, it was this thick.
Cao:
Oh.
Wilson:
And I just didn't have the necessary practice at that point in how to really pull out the essence of something illustrated with some simple example that would help people —
Cao:
To understand.
Wilson:
Right.
Cao:
Now there is one question particularly I want to talk to you, about Kim Wilson — no, no, no — Ken Johnson.
Wilson:
Yes.
Cao:
Ken Johnson also published a paper with Baker about the Renormalization Group in 1969.
Wilson:
Yes.
Cao:
And [???] he had extensive discussions with you. Can you remember the [???]
Wilson:
Johnson, Baker and Willy published papers not in '69, but much earlier.
Cao:
Much earlier. In '69 they also published a paper on the Renormalization Group.
Wilson:
Yeah. But you see they had published earlier a statement about electrodynamics —
Cao:
Yeah.
Wilson:
Which, I mean it had not been published in '63 when I started working on this, but as soon as they published their paper I knew from my work on the operative product expansion that their paper was wrong. And I spent a lot of effort, you know, just showing that it was wrong, and telling Ken Johnson that what they were doing was wrong.
Cao:
And then during the time of 1978 and '79, certainly you had discussions with Ken Johnson.
Wilson:
Well, every time that he published a paper, there was a discussion.
Cao:
Can you remember something significant about these discussions and how they —?
Wilson:
Well, all that I remember about it was that that was one of the motivations that — I mean, that sort of gave me something to do to keep working on the operative project expansion. Because I had to use it, you know, I had to, I mean, it was from the viewpoint of the operative product expansion that I knew that what they were saying was wrong, but then I had to actually work it through so I could go argue with them.
Cao:
You didn't find any [???] insight in their work important to your development?
Wilson:
Well, I mean, I couldn't get the insight from their work, because they had it wrong.
Cao:
[laughs] You really [???] some credit to Michael Fisher and Katanov and these statistical [???], but actually you cannot find something [???] on some field theorists. [laughs] [???]
Wilson:
Well, I mean that's unfair. I mean, Ken Johnson played a very important role in inspiring the research that I did. You don't have to be correct to inspire research.
Cao:
I see.
Wilson:
I mean, there's the famous referee's report by Pauly [?]. This paper is not even wrong.
Cao:
[???] with Pauly. You mean you are —?
Wilson:
No. I'm just saying there's a standard story about Pauly that he gets this paper to referee, and the report he sent back was very short. It said, "This paper should be rejected. It is not even wrong."
Cao:
Not even wrong. [laughs]
Wilson:
Well, I mean Ken Johnson's papers were wrong, but they were wrong in a very interesting way.
Cao:
That's very interesting, yeah.
Wilson:
That gave me something to pursue, to [???]
Cao:
Can you single out one, even just one paper, published by a field theorist which you think was helpful to your work?
Wilson:
Well, there's no question that the paper that was most helpful was Gilmonde and Lowe.
Cao:
But you didn't understand that!
Wilson:
But I spent most of my time trying to understand it. It gave me something to do.
Cao:
You understood it only after you, yourself, [???]
Wilson:
But I mean —
Cao:
Still they provided some inspiration?
Wilson:
I mean they provided a very strong direction for everything that I did.
Cao:
Oh, I see, I see. [???] Then what's your assessment about [???] work?
Wilson:
Well, I mean, Callen [?] and Samansik [?] were involved with reworking Gilmonde and Lowe so that everybody could work with it. I mean, it was sort of — they did the function for the field theorists that Michael and I did with the epsilon expansion [???]
Cao:
But their work was wholly based on the idea of scale [???]
Wilson:
Yes.
Cao:
Is this something new? Or actually they just get the idea from your [???] the scale argument?
Wilson:
I mean they had to develop a different approach to the problem. Clearly there were things in that paper that were — I mean, you have to find out from them the extent to which they were inspired by the 1969 paper —
Cao:
But they say that. They mention that used your opinion in the paper.
Wilson:
And so I think, I mean, it's the usual story. They couldn't work with the — You know, it goes back to, what was it, Hamilton couldn't understand LeGrime [?], so he had to work that all over again.
Cao:
Something I found, the resurgence of the scale argument is very important. And certainly [???] your work in 1969 that the [???] Mark's work.
Wilson:
Yes.
Cao:
And what's the major difference between your scale argument and his scale argument? Why —?
Wilson:
Because they didn't, I mean, Mack did not have the concept of anomalist dimension.
Cao:
Oh yeah. He didn't.
Wilson:
And you see that was inspired in part by the tearing model and in part by the statistical mechanics. And I wouldn't — I mean I wouldn't have done it just based on the tearing model. At the same time, Ken Johnson's paper on the tearing model was very important, because it set me up for thinking that way.
Cao:
But he didn't have an idea of anomalist dimension there. He [???]
Wilson:
Well, he just didn't — I mean, he had the anomalist dimensions in the tearing model, and they were right there, but he never, as far as I know, he never suggested that that would apply to any other theory besides the tearing model.
Cao:
[???] Ken Johnson's work [???] statistical mechanics.
Wilson:
So I mean it's not fair to — I mean, there is a very strong field theory background pushing this whole — You know, whether it's Johnson's paper, whether it's Gilmonde and Lowe, [???] Cherkov — And then of course at the time of the 1969 paper I had to integrate everything with all the work on current algebra and anomaly and all the specific pieces that are in the paper have [???] field theory [???]
Cao:
But that was interesting, because your type of [???] was [???] current algebra.
Wilson:
Right.
Cao:
Why you took the current algebra as so important? Because current algebra —
Wilson:
But everything I do is based on the current algebra in that paper.
Cao:
Actually you tried to replace the current algebra. Because current algebra was based on the commutators [?]. You tried to —
Wilson:
I never changed the commutators. The commutators and currents are still there and still correct.
Cao:
Still correct?
Wilson:
Right. I mean, the core statements about the current algebra are still correct. I haven't changed that. I haven't changed anything that [???]
Cao:
You tried to develop something more powerful —
Wilson:
That's right.
Cao:
— with operating expansion. But once people get operating expansion, they don't want to use the commutator.
Wilson:
No. The point is, the current algebra is still there, but the current algebra, as always, was [???] I mean, the current algebra did not give you a complete statement about the field theories.
Cao:
No.
Wilson:
See, but there was a body of things which I didn't even have to talk about that came directly from the current algebra, like the soft [???] theory. Those are still correct; they are still derived in exactly the same way. But I gave, I was supplying a framework in which you could go beyond the current algebra itself, and that you could understand things that go beyond just current algebra — because of that further framework. And that was the whole power of the operative product expansion, was that it was more— I mean, the current algebra was there as a subset of the operative product expansion, but was not the whole story.
Cao:
A subset with some [???] because of the anomaly. Do you know that Ken, uh, Johnson and Lowe's paper about the [???]
Wilson:
About the what?
Cao:
The danger of formal manipulation of current algebra. [???]
Wilson:
You'd have to show me what paper that was. And again, it probably depends on whether it was referred to in that article.
Cao:
You didn't refer their article. You know, since time of 1966 there was some realization of the defect [?] of current algebra, and there was a work by [???] and Sutherland [?] about the [???] and —
Wilson:
Yes. Oh. You're saying that there are defects in the sort of canonical picture of currents and about how you have to do operators and how you have to define operators at the point and things like that.
Cao:
Yeah, yeah.
Wilson:
I think that's correct, and if my memory serves me correctly, I knew about those papers at the time that —
Cao:
And during that time also you referred to a work by Schwinger [?], [???] Schwinger terms, all these things —
Wilson:
Schwinger terms stuff, I mean, I certainly knew that that already existed.
Cao:
And also you knew the results of [???] and [???] for all those [???] But you still believe that [???]
Wilson:
Well, I mean the — I mean, people already knew that you couldn't take everything that you learned from canonical field theory about currents, you couldn't take seriously. You'd have to talk about these various anomalies that were not part of the canonical theory of currents. But the basic — And see, the point is, the current algebra that remains correct is the algebra of the chart.
Cao:
Yes, that's true.
Wilson:
The Schwinger terms have to do with directives of delta functions that disappear when you actually form the algebra of the charges [?]. And so all the people were saying was that you had to be careful when you did the commutators of local currents as opposed to the commutators of the charges because the currents are more than just charges, and it's only the algebra of the charges that has taken over a change.
Cao:
That's very interesting. You said that [???] agree that the canonical formulation is not enough.
Wilson:
Yes.
Cao:
And one manifestation of this [???] that there were several kinds of anomalies there, that's one thing.
Wilson:
Yes.
Wilson:
Another thing is your 1969 paper. You develop a formulation which is more powerful than current algebra and the formal manipulations [?]. You developed an operative product expansion, but you even didn't try to establish a connection between these two things — the existence of anomaly and the operative product expansion.
Wilson:
Yes.
Cao:
Even though you introduced a [???]
Wilson:
That's right. Well, all I did was said that when you made these two postulates of the scale invariance and the operative product expansion then you could start understanding things. But what people were unwilling to do, just as I was unwilling to do with [???] Ben Whittem's thing, is that it was too arbitrary to them to have those two assumptions. And so they weren't really willing to — and I didn't do anything to [???] You know, I published a paper and I just went on working. You know, I didn't go into PR [???]
Cao:
[laughs] So afterwards you spent your time on the lattice [???] theory.
Wilson:
Well, I mean, I think from the time that that paper was published, I was I think at that point I was spending most of my time developing the statistical mechanics stuff.
Cao:
Right.
Wilson:
Well, let's see. Let's be careful. I mean I went out to SLAC for a sabbatical.
Cao:
Which year?
Wilson:
That was '69-'70. I was out there at SLAC. I did give some lectures on things I was thinking about. I was trying to — At that point I had an idea for how to try to do the Renormalization Group numerically —
Cao:
Within the [???]
Wilson:
Well, I was trying to do it for a quantum field theory. But at that point there was no difference. It could be either one. I wrote a big computer program when I was down at SLAC. In fact, if you talk to them and you find the right person, I was famous for having written this huge program, spent a month on it, made one run and said that it doesn't work [???]
Cao:
One point we can make is that the computer played a great role in your thinking. That's a very important sociological [???] question, yes. Then you also spent a year in Princeton. Because the physicists there always say, "Oh, Kim Wilson came here and [???]" and —
Wilson:
Yeah. That was in '72. That was not a whole year. That was one semester.
Cao:
One semester. You gave out a series of lectures?
Wilson:
That's right, that's right, and that's one, [???], Brisande [?] —
Cao:
That was very important for them, because they appreciated it very much. Especially Wilchuck [?], because he [???] important work, and he said, "I got my idea from Kim Wilson's [???]" Do you get similar feedback from these field theorists?
Wilson:
It's not in my memory —
Cao:
[laughs]
Wilson:
— that I was getting much back from them. I could be very wrong about that.
Cao:
So now I get the impression — I've said it before — if you [???]
Wilson:
Well I mean I published the paper in '69, you know, and I just published it. And then the next thing that happened sort of that I was aware of was Murray Gilmonde started talking about it.
Cao:
Oh. You had a conversation with him?
Wilson:
Well, no, no. There was a conference I think in Coral Gables [?] where he started saying people should look at this.
Cao:
You mean in '69?
Wilson:
No, no, this was around '70 or '71. [???] But you can find out. There was a conference in — I think it was a [???] conference at Coral Gables where he first started telling people they had to look at this paper. And I don't know that anybody paid much attention to it until then.
Cao:
Now what was the reason that you didn't [???] fascinating development in the early 70s? There's so many things that happened in the field theory —
Wilson:
Yes.
Cao:
— that they discovered [???] and [???]
Wilson:
That's right.
Cao:
So many things. And QCD and the [???], there were so many developments. But you didn't get into the mainstream. You developed your work —
Wilson:
But you see I was always late. I was always late. I mean, I was the last person to understand current algebra. Of anybody who was important in the story of current algebra, I was the very last person to understand it, and I was several years late.
Cao:
Actually you put an end of a [???] [laughs] [???] no serious work on [???] Of course [???] but that's different.
Wilson:
Yeah. And so just as I learned the current algebra several years late, I was not — I mean, I was building what you call a mental model of the situation which was very different than anybody else's [???] model, and I only learned current algebra when I was ready to bring it into my own mental model, or my own paradigm.
Cao:
I see.
Wilson:
You know, he wasn't spending his time focusing on [???] one person. I mean, he has explicit trouble with me, and I don't remember what he says about Gilmonde, but clearly Gilmonde did his own paradigm. And then [???] he has a whole history [???] which comes down to just two people [???] [Bowling alley or airplane noises in background make several minutes inaudible here — Transcriber] But I mean Pickering is more interested in building sort of the group interactions and how they're affected than talking about what happens when you finally get down to one person or two people, except in the case of [???] because [???]
Cao:
[???] paradigm in your case in a different sense. [???] easy access to computation and your paradigm provided some easier way to make some calculations and publish them and certainly spread over [???] academic journals, then he [???] question [???] appropriate [???] for the advancement of science where suddenly a new paradigm dominated a whole [???]
Wilson:
Yes.
Cao:
And [???] had some suspicious. [???] There are some cases; a lot of cases cannot be covered by the paradigm. And so many exceptions and so many doubts and —
Wilson:
But this is the essence of what [???] is talking about. [???] the revolution there is always a competition between a new paradigm and an old paradigm. I mean there's a competition, and that's a social competition. It's not a — I mean —
Cao:
Social competition or intellectual competition?
Wilson:
Well, it's a social competition based on rules of an intellectual nature. Right? The rules are intellectual, but the competition is social, in the sense that in the end what seems to be more plausible — As you say, there's always extrapolations beyond the actual data involved in the paradigm, and the paradigm, the whole point of a paradigm is to allow you to extrapolate from an incomplete set of data to a mental model which incorporates data that you don't have yet.
Cao:
You mean a kind of idealization?
Wilson:
It's an idealization which allows you to say not simply we can understand this particular experiment or that particular experiment, but we can say here is our expectation as to what will happen when the experiment hasn't been done yet.
Cao:
With some predictive power.
Wilson:
Right, with some predictive power. I mean, and not simply predictive power, but an ability to understand something.
Cao:
[???]
Wilson:
[???] for something that hasn't happened yet. And then there's a competition that takes place, you know, and the rules are very reasonable, I mean that you start identifying those experiments that would give different results according to the two paradigms, and people who [???] perform the experiments, and you try — And the way it is supposed to happen is the paradigm that wins is the one which is most successful in handling the experiments —
Cao:
But once there is competition between different paradigms, I think the situation is healthy.
Wilson:
That's right.
Cao:
But do you that think now, at this moment, is there any competition within the context of statistical mechanics [?] between the Renormalization Group program and the other paradigm?
Wilson:
I don't think so. [???]
Cao:
[???] there is a dominance of the Renormalization paradigm.
Wilson:
Well, I mean, what you're asking, I mean can a paradigm win prematurely from this competition, [???] of course it can win prematurely. Because it comes back to Feinemann's [?] statement, right? I mean, as scientists we don't demand an infinite number of examples to produce [???].
Cao:
Two examples. [laughs] So, because actually I had a sense that [???] suspicious maybe there is a premature dominance [???]
Wilson:
Yes.
Cao:
And maybe he's wrong, maybe he's right, I don't know. [???] premature? [???]
Wilson:
Well, I mean my statement would be, in a certain sense it's always premature.
Cao:
Yes, I think that's good. [???] if you find it's premature then you produce some [???] example maybe it can be improved to [???] Oh yes, I see.
Wilson:
Because it is always based on a finite number of examples, and because it's always based on a finite number of examples you never have a formal proof that it was right to reject the old paradigm. On the other hand, the issue is not was it right but is it useful.
Cao:
But now [???] in the controversy of the [???] theory [???] But you always have ideas [???] forward step by step and can never get to the end. Actually [???]
Wilson:
Well, I mean my side is, I have [?] taken a side, but not from the point of view — I mean, I'm just saying — I mean, this is sort of what I have learned from doing the Renormalization Group.
Cao:
Yes. Actually [???] explicit in this approach.
Wilson:
Yes. I mean, that what we see is an effective [?] field theory, and what we see is always gonna be an effective field theory. And you see, we now come between the difference between me and being a philosopher and mathematician. I mean, I say if we cannot get it from the data [???] it has no value.
Cao:
You were interested in Pickering's work because you [???] the subject [???] want your cooperation [???] and we hope that you can comment to [???] And this will be a [???] book, and this will be just an introduction.
Wilson:
Okay.
Cao:
And I hope, and [???] also expressed his hope that you can find some time to read it and [???] comment. Because there are several sections that are wholly devoted to your work, and there will be two chapters describing your work in the book.
Wilson:
Yes.
Cao:
And also a lot of philosophical discussion about the Pickering and the [???] in the last section here. And it will be published soon, but we hope we will get your comments to improve it. If you have any disagreement with this paper, please tell us.
Wilson:
Right. The only thing I cannot guarantee is how long it will take me to produce this, because [???]
Cao:
[???] If you have time, then just tell us. Because you see you will be the essential figure of this [???]. Because the history of Renormalization [???] since 1950 to 1980. We don't say nothing about Renormalization in the 40's, so just describe the evolution from [???] and [???] and also we discuss the possibility of [???]
Wilson:
I mean saying that you have to be careful about [???]. I mean you have to be careful about laying the groundwork. The Gilmonde-Lowe [?] paper will be extremely important.
Cao:
Yes, certainly, yes. [???]
Wilson:
And in the treatment of the [???] I did not do the [???] mechanics [???] and that's where you have to be careful about not overplaying [???]
Cao:
Oh yes. We will pay enough attention to Gilmonde [???], [???] Gilmonde and Lowe's paper provides the essential idea there, and also people say there are four persons in the program, and you and Mac Fisher [?] and then Katanov and [???] and [???] certain Michael Fisher provided some [???]
Wilson:
The other place you will run into trouble with this —
Cao:
Yes, tell me.
Wilson:
— is with the role of the Russians. Because the Russians were making the connection between statistic mechanics and [???]. You have Patashinsky [?] and Prokovsky [?] in the middle 60s and you have McDowell [?] and Pollykrov [?], and I think it is — I don't know if you've tried to interview McDowell and Pollykrov about this, but you should do so.
Cao:
Yes. [???]
Wilson:
McDowell and Pollykrov are both in the U.S.
Cao:
In the USA now?
Wilson:
Yes. They both [???] McDowell is at Princeton, and Pollykrov I think is at MIT, but I'm not sure.
Cao:
Oh, [???] at MIT I can find [???]
Wilson:
So you should interview them. I mean, they will give you a different version of the story than anybody else.
Cao:
Oh certainly. But [???] what about the [???] Did they exercise any influence on you in the [???]
Wilson:
I met them about '72, something like that.
Cao:
The [???] had already taken.
Wilson:
The, let's see — I mean, there are two questions. [???] questions [???] influence me, and the question is did they influence the subject, and there is always this issue of priority, who did what first.
Cao:
Oh yes. [???] That's a question I would ask you. When you met them, you had already published your paper in 1971 [?]. Is that right?
Wilson:
Sure. That's right.
Cao:
Of course David Nelson [?] gave me several references of Russians they published in 1969, [???] and about the [???] arguments [???]
Wilson:
I mean there was a lot of work done by the Russians, and, you know, if you're gonna do a history you sort of have to sort that stuff out. And of course the other people who are gonna be upset are [???]
Cao:
Pardon?
Wilson:
Decastro [?] and Yonin Lasinew [?].
Cao:
Oh yeah.
Wilson:
[???] in a sense they're right.
Cao:
Mmm. [???] We'll take notice about that.
Wilson:
Right.
Cao:
But as far as the Russians are concerned, we are suspicious about their real influence in this country.
Wilson:
I mean they lacked influence in this country, but —
Cao:
But they have influence in the subject.
Wilson:
But I mean in a certain sense, if you are writing history —
Cao:
They made [???] contribution.
Wilson:
I mean, their influence was limited for social reasons; not intellectual reasons.
Cao:
I see. But still there is some influence upon the American scientists. [???] they know [???]
Wilson:
I mean I think the period of big influence came later. I mean they have general [?] contributions which are picked up in the West and [???] citation index and you can find out when their papers start being referred to.
Cao:
Yeah, so Russians and the [???] Do you have any suggestions — because that's very important, because we have to widen our scope, because up until now we have focused solely on the U.S. [???]
Wilson:
I mean in a sense I have a big advantage over [???] and so forth by being at Cornell — being right there with [???] and Michael Fisher, which they didn't, I mean —
Cao:
They knew everything, and they told you.
Wilson:
Yeah, I mean, in that sense I had a tremendous advantage in being able to have access to them on a routine basis. And —
Cao:
Could you read the Russian?
Wilson:
No.
Cao:
Then how can you have access to their ideas?
Wilson:
Their papers were translated.
Cao:
Translated. Ah, I see. And then they were introduced to you by Fisher?
Wilson:
Well, I mean my real awareness of them, let's see. It's hard for me to say when my awareness of them started. I mean of course I had actual conversations with them when we started having these exchange visits [???] with the Russians.
Cao:
[???] much later?
Wilson:
That began in the early 70s. I'm pretty sure I knew about Yonin Lucenio and Decastro and I probably talked to — I think I talked to Yonin Lucenio at some point. In that whole period I can't tell you when that was. I probably won't be able to give you dates as to when that was. And part of your problem is that you'll find I'm sure that I had talked to them before I had totally formulated my ideas.
Cao:
I see. So do you really think you got some idea from him?
Wilson:
Well, I don't know.
Cao:
[???]
Wilson:
I mean, you have to record — I mean, the history, what you want to be able to record is who talked to who when. Right? And I can't give you always accurate dates on these things. And some things you cannot resolve. Some things you cannot decide who influenced who. I think you will find in the end that everybody will agree that I did things that went beyond what I could have learned from anybody.
Cao:
That's true. [???] final results of that, yeah.
Wilson:
And so a lot of it is, you know, some people who want partial credit for this and that sort of thing. But when you talk about Whittem and Katanov and Fisher and myself, and especially Whittem and Fisher and myself, I think the fact that we were right there in the same place made a big difference. And nobody knows what the history would have been if I had stayed at Harvard for instance, because then I would have had much less access.
Cao:
Is it the idea or example of the [???] You yourself symbolize this interaction.
Wilson:
I was certainly not the only one building that. See, that's one of the things they want credit for, is the idea that they were making the link [?].
Cao:
Yeah.
Wilson:
Now, you know, I always have the feeling that, I mean, I've made a lot of mistakes in my career of not publishing things that were in fact revolutionary because I didn't think what I had done was complete.
Cao:
[???]
Wilson:
I mean, the operative product expansion, of course I should have published that. It's ridiculous that I didn't publish it, in retrospect. I invented wave widths [?], you know, and I told a few people about it, but I never — I think there is a paper now which publishes the work that I did on wave widths, but you know, I did it in '74 or '75 or something like that, and I never published it. It's now in print, it's only a year ago, and I have never seen the [???]
Cao:
Do you think I can get a copy of your first paper of [???] and also this paper? Maybe this unpublished paper will play some [???] your ideas.
Wilson:
Well I mean, if you are gonna do a history, I would think they would be very important.
Cao:
Yes.
Wilson:
I managed not to throw it away.
Cao:
Oh, it's a pity. You yourself didn't keep a [???]
Wilson:
Well, I had a copy for a long time, but —
Cao:
[???]
Wilson:
You know, all the preprints got distributed and [???]
Cao:
Can I have this copy?
Wilson:
Sure.
Cao:
Thank you.
Wilson:
But I mean coming back to the issue — I mean you come down to a question of where you give credit, and that is, as I say, I didn't publish things which I should have published because I said, "This is incomplete. I'm not gonna publish it." But it's clear that was a mistake. And then when you look at the work of the Russians, say Yonin Lucenio and Decastro, I mean in a sense it's in my sense incomplete, but that doesn't mean that they don't get credit for something. Because all of science is incomplete in the end.
Cao:
That's true. Because they had published these [???]
Wilson:
They have publications. You know, you look at the date of publication and you can [???] See, you have a problem. I mean, a lot of the stuff that I do, you know, I don't publish the things that I do, so it's sort of haphazard whether there's anything written in print. So, on the one hand in order to build the history you have to try to build sort of the history of what I was doing to get some of these papers that were published.
Cao:
That's why I ask you for a copy of this and a copy of your 1964 paper. And it's a pity I cannot get it.
Wilson:
Well, as I say, if you asked around at MIT, you might find somebody who still has kept a copy.
Cao:
I'll try very hard to get it [???] Because certainly your [???] is a very important paper.
Wilson:
Okay. Well I mean, this is the sort of thing you have to wrestle with in building a history, is what is it that [???] deserves credit and then— Because obviously, I mean especially if you — I mean, to do a history properly, you want to disentangle the social aspects from the intellectual aspects. I mean, that is in sort of the essence of the question right now. And, I mean there's no question that my being right next to Whittem and Fisher made a difference, and I don't know whether anybody can ever disentangle how much of a difference it made.
Cao:
If we carefully are interested in the [???] direction has already set for you for many years.
Wilson:
That's right.
Cao:
[???] But the direction was there, and the main vehicle was there. The idea, and some [???] and you will certainly go [???] this direction.
Wilson:
I would have gone in that direction, but I don't think there was any possibility of my writing a paper in 1969 without the [???]
Cao:
But the one thing I find a puzzle. How many influences you received from [???] paper.
Wilson:
[???]
Cao:
M-a-c-k [?] Mack's paper.
Wilson:
Right. Well, I mean it was less of an influence than some of [???] other things. Because what I was really relying on, as I said, was the tearing model and the —
Cao:
Yes. I suppose Johnson's paper was important for you, because you go through all the steps of his paper. [???] paper provides [???] for you.
Wilson:
Well, okay. I think the thing is, that I think — See, I don't think Johnson ever talked about scaling things [?] in his paper, if I remember correctly. He just, he was the solution, right? But I don't think he [???]
Cao:
He didn't use this word.
Wilson:
He didn't use [???] So I think, I mean what I got from Mack and [???] was they actually formulated that this was in variance of the theory.
Cao:
In variance of a [???] especially.
Wilson:
No. They just talked about field theory having this special kind of a variance called scale [???], which you could formulate on the same basis as variance [???] and [???]. I mean, you know —
Cao:
Oh, I see.
Wilson:
And I don't think Johnson said anything about that.
Cao:
No. That's different. Yes. [???] Thank you. Thank you very much. [taped turned off, then back on...] And more than history in the traditional sense. We want to do a history, an exercise in factual independence [?]. Because normally historians always accept what scientists say.
Wilson:
Yes.
Cao:
In that case, this is a project still going on, and a lot of different ideas, different suggestions, and we have to take sides. And we have to make some judgment. Maybe some judgment different from some cases and agree with some cases. So it's more difficult a task for the —
Wilson:
I mean, quite apart from that, I mean, what I would say is this. I mean, I think you are gonna see in the next few years enormous pressure on the scientific community to recognize social obligations in respect to teaching [?], and to recognize that research on learning is a fundamental requirement of a research scientific department. I mean because they cannot perform their teaching function without it. And they are resisting, as you know very well. I mean, the pressure hasn't gotten strong enough so that they realize yet that they are resisting an overwhelming pressure, but that pressure is going to explode in the next few years I think.
Cao:
Why do you think the next few years are so crucial for [???]
Wilson:
Because the educational reform is not going to be able to proceed unless this happens. You know, you've got a $240 billion business which is failing — I mean it's in bankruptcy basically — and they are not gonna pull out of it, uh, I mean the whole system is gonna have to be reformed, but part of it is gonna be the reform of the scientific departments and their teaching [???] The only department that has reformed in this sense so far is at the University of Washington, the Physics Department at the University of Washington.
Cao:
[???] you mean?
Wilson:
Right. And I mean they have a little group there that does cognitive research, research on how students learn physics, and they build course curricula based on that. And every science department is gonna have to do that; they are gonna have to recognize that that is an explicit obligation on their research side, to do that kind of research. And they are gonna have to define it, that that is a legitimate part of physics research. Because the social demands that the universities perform their teaching functions — The universities accept that they have a teaching function, but they do not accept right now that they have to do it right. But to do it right they are gonna have to do research on [???]
Cao:
That's true. Yeah, yeah.
Wilson:
And what is stopping that is the — I mean, there's a number of psychological hang-ups stopping it, but one of them is that the scientists do not want to accept that research on learning has reached the same state that research on quartz or anything else has; that there is a paradigm, and that you can rely on it, and you can build from that paradigm. But one way of sort of hitting the scientists on this issue is with the social aspects of their own research. Because they know that. They don't want to admit it, as you know very well, but they know it. And so the more that this is done and done carefully and done right, the easier it will be to use that as part of the levers on the scientific community to accept that they have to accept research on learning [???] legitimate research area.
Cao:
And what do you think work on the history of science can a play a role in this?
Wilson:
Just by documenting in a way that the people that have to agree with it, this is the way it happened. There is a social aspect to this. It is not — you know, it is not that, you know, from — Galileo used to say that, he would talk about the little books of mankind and the great book of nature. And I think the book was a new thing [???] The scientists from that time to this have said that we are reading the great book of nature as something that's independent of ourselves.
Cao:
That's not true.
Wilson:
And, you know, [???] what it leaves out, it leaves out the incompleteness of any scientific investigation — which opens the possibility for multiple representations of what it is you've actually learned. Now what the historians of science are trying to say is that there could be incommensurate representations — because it is finite, there could be two things which have no relationship to each other. They both could accommodate a finite amount of data. And of course in a sense, I mean some of the most severe paradigm shifts have involved precisely that, that there was a certain amount of data that was perfectly well represented by the paradigm before and the paradigm after it. And they couldn't — I mean, the caloric theory, I don't think there's any way that you can rebuild the caloric theory [???]
Cao:
Impossible. Cannot translate [???]
Wilson:
Right. So, I mean in that sense they are perfectly correct. And sort of anything that we build is suspect because it is incomplete. On the other hand, what Pickering does not point out, is the degree to which the way we judge a theory is based on our previous theories. I mean, we still use Newton's laws as a paradigm for what a law should be like. And see, one of the things that was driving me in the way I approach things, was I knew that. And I looked at S [?] matrix theory, which was [???] looking like it, and that did not fit the paradigm of Newton's theory.
Cao:
I see.
Wilson:
Even the fixed source meson theory, even though it was wrong, it was the right paradigm. And the reason I knew it was the right paradigm was that you could approach it from different points of view and you could still deal with it. You could do a recoupling point of view or you could do a strong coupling point of view, but you could work with the theory that way, and you know, there are many different ways you can work with Newton's laws. But there was only one way you could work with S matrix theory, and to me that was garbage. And since it was garbage, I said I wasn't gonna do it.
Cao:
[???]
Wilson:
Right. The concept of S matrix theory qualified as a theory when we already knew what a theory is like, because we knew Newton's laws and we knew Maxwell's equations and we knew [???] equations, and S matrix theory did not belong in that league. And it didn't take me, you know, it took me a year to figure that out, and then I said, "To hell with it."
Cao:
[???] it was a fashion, and so many physicists converted to S matrix theory.
Wilson:
That's right.
Cao:
So you resisted that and —
Wilson:
Well, I tried it. I spent a year struggling with it. You know, that was when I was doing this thing with the strip [?] approximation.
Cao:
I see.
Wilson:
And there was even an unpublished manuscript on that I think that I wrote.
Cao:
I still didn't clearly understand what you said. You said now it's very important for scientists to realize the social —
Wilson:
You cannot separate this work, as research physicists cannot be separated from a social environment [???] I mean, the heart of their resistance to physics education being a part of the — Well, see there's two parts to this. There's one, there's the resistance to recognized research on learning as legitimate research. They say, "That's social science research. That's nonsense." There's another part to it, they will not accept — I mean, what you are saying and what Pickering is saying and what [???] is saying is, that the basis on which you do physics is not simply that you know Newton's laws and you know [???] and Coon [?] was very explicit about this. It is the set of examples that you have worked —
Cao:
You have some puzzle you have to solve.
Wilson:
I mean, your active knowledge of physics depends not only on the stuff that is written in the great book of nature, but it is the problems, the puzzles that you have either solved or you have worked through as far as your training —
Cao:
Now I see your point. Now I see your point. So the research is so crucial for your teaching activities, this idea.
Wilson:
But what I'm trying to get at, you see, if you say that, that — People, they like to talk about the accumulation of knowledge, but they do not include the problems that you solve as part of the accumulation of knowledge; they deny that that is part of the historical record of physics.
Cao:
I see.
Wilson:
They deny that. But you see, what is being done in the research and learning is to start to categorize the actual problems that enable people to learn physics. But they won't consider that to be part of the accumulated knowledge of what physics is.
Cao:
Yeah. In our work we always try first to set out what was the problem to be solved. In this context [?] the scientists, the physicists try to develop some ideas, some [???], some vehicles to tackle these [???] problems. I think in your case that's also true. You have some problems to solve, and you try to find some means to solve this problem, and because of this [???] something from that, and [???] find some vehicle to solve my problem about strong interaction —
Wilson:
What I'm trying to say is the following. I mean, the physicists who [?] accepted it, the problem that was a puzzle to me in a sense that that's something you can publish, you can write about it, that's okay, that's an acceptable part of research. But a problem that is needed for a 10-year-old kid to learn about electricity, you know, the problem that does a better job of teaching a 10-year-old about electricity than another problem, they will deny that that belongs to the historical records of physics.
Cao:
I see.
Wilson:
Right? I mean, if it's a 10-year-old kid, it doesn't count. If it's me, that's okay.
Cao:
[laughs] [???] easier to persuade then.
Wilson:
That's right. But, I mean, where do you put the boundary? You know, it's like the old story, you know the old story that ends, "Okay, all that's left is to negotiate the price." I mean the question is, where is the boundary? I mean, where do you say this problem as opposed to this principle or this law is legitimately part of the research record [?].
Cao:
I see.
Wilson:
And I say that it's ridiculous to say that a 10-year-old kid is somehow disenfranchised from this discussion.
Cao:
I see. Certainly we accept [???] I think. But the problem certainly is the part of that whole sense about scientific [???] no problem. And we certainly [???] agree with you.
Wilson:
But what I'm saying is, there is going to be a violent [?] discussion of this whole problem as the pressure builds on the scientific departments that they have to, part of their societal function is to do this research on learning. And they are resisting that, you know, they — The resistance hasn't started to build because they haven't felt the pressure [???]
Cao:
And when the pressure increases, the resistance will increase.
Wilson:
That's right.
Cao:
But when you said there was such a [???], what do you mean exactly? You mentioned several times.
Wilson:
Well, it's [???] misconceptions research. I don't know if you dug into that at all. But, I mean, what you need to read is this book.
Cao:
[???] good book?
Wilson:
That summarizes on this research on learning and how it affects teaching.
Cao:
It's a new book.
Wilson:
Yes. It's 1990.
Cao:
[???] I'll try to read it, because you [???] Isn't he a [???] physicist?
Wilson:
Yes. He is a superb physicist.
Cao:
In which area? Because I didn't know his name.
Wilson:
Well, you see, he worked in areas of classical physics. In the end he stopped doing regular research to work totally on teaching problems, but I actually did — My first research project was done under his direction.
Cao:
Really?
Wilson:
Yes.
Cao:
So how many [???] are you doing now? [???] suppose that you are doing these kinds of things.
Wilson:
Well, I mean the thing that is in this book is something that I'm now working on, but that was only since I came to Ohio State.
Cao:
When did you come here?
Wilson:
Three years ago.
Cao:
Three years ago. Before [???] Cornell?
Wilson:
That's right. But what I am saying is, I mean, what he is talking about there is very important from the point of view of, if you're talking about the history of science from a social point of view, then what you are doing is closely linked with the kind of research that's discussed here.
Cao:
Oh, certainly I'll read this book. Yeah.
Wilson:
And, as I said, it just happens that as an undergraduate I was, '55 and '56, I happened to do research during the summers down in Woods Hole [?] and was directed by Erins [?].
Cao:
I see.
Wilson:
But that was, I mean, that was not this kind of research that's recorded here; that was just regular physics research, but it was in the propagation of sound rather than [???].
Cao:
So there is an important development now. You see, at first, in the early 50s the United States [???] established a [???] called the history of science.
Wilson:
Yes.
Cao:
Original motivation was to provide something for undergraduates to understand what science is, because the history of science will help them to understand what science [???]
Wilson:
Well that was Gerald Holton, right?
Cao:
Gerald Holton and [???]
Wilson:
Well, Arnold Arantz [?] was closely tied with Holton also, and Gerald Holton knows him.
Cao:
[???] help teachers help scientists.
Wilson:
What the history of science can do, is to help research scientists recognize that they cannot isolate themselves from the social sides of their subject.
Cao:
[???]
Wilson:
And I say that because they are going to, I mean the pressure for them to do that is going to grow very rapidly.
Cao:
But [???] your expertise, your research interests, your funding [???] other social factors.
Wilson:
Well, I mean the social pressure will be on the teaching side of it, [???] people that are not going to be physics majors. Although the situation is so bad that even physics majors are not being taught properly. But the point is, that what is mixed up, I mean the resistance that will build up is a resistance to any social interference, any social component to their research.
Cao:
I see.
Wilson:
I mean, they want to keep the research in their minds pure. You know, very well, they don't want to admit that there is any social impact into it. They don't want to have anything to do with anything that is actually social science research. They reject everything having to do with that. And so, I mean we have to attack them in multiple places. You know, we have to attack them directly on the teaching problem, but we also have to attack them on this history of science problem that there is a social component to that. And it's all part of breaking down their defenses that says that hard science research has no human components — a statement which is sheer garbage. I mean, it's a misconception. And when you read about the misconceptions here, it's the same kind of thing, this is a misconception — I mean, your problems with most scientists when you try to go into this social side of history is the same kind of misconception that prevents them from accepting research on learning as part of a legitimate part of their physics research [???]
Cao:
That's interesting, because before today I supposed you were a pure scientist. Actually you are willing to accept all social impact on your own research even, because you try to persuade other scientists to accept the idea that the social [???] teaching.
Wilson:
Well, we have two positions posted here at Ohio State for people in physics education. And so the faculty is having discussions about, "What does that mean [???] physics educator?"
Cao:
[???] education. What is [???]
Wilson:
Well, it would be the same kind of group they have at Washington, I mean which does actual research on how students learn — and develops courses based on that research.
Cao:
That's wonderful. Two positions?
Wilson:
Two positions. They're advertised in the October issue of Physics Today.
Cao:
Oh, maybe I try to apply. Do you think I can apply?
Wilson:
You can certainly apply.
Cao:
[???] January issue of Physics Today?
Wilson:
October, this past October.
Cao:
I didn't know that. What would be the deadline?
Wilson:
The deadline I assume is not passed yet. I mean, as far as I know we are still accepting applications.
Cao:
Oh, I see. What would be the requirement for that position?
Wilson:
We're actually not sure — Well, you can read the ad, but —
Cao:
[???] junior position [???]
Wilson:
Probably one senior position and one junior position is what it'll come out to be. So I mean, we'll probably look for creativity and all nice kinds of things for [???]
Cao:
I see. [???] nice things. Thank you for all your suggestions. [???] the development into your language.
Wilson:
That's right.
Cao:
Ah. So, then what part did the [???] It was originally a talk by you?
Wilson:
I mean, that was the outgrowth of my lectures.
Cao:
Yeah, in Princeton. They were afterwards published.
Wilson:
Yes. Right.
Cao:
What's the importance of this lecture? Anything new and original [???] It was very influential, and everyone [???]
Wilson:
Well, I mean I think there is some stuff in there that I had not published previously.
Cao:
I see.
Wilson:
I mean, there are some — I mean certainly there are formulations of the Renormalization Group that had not previously been written down. And you know, as a sort of review — I mean, reviews like that are very important, because they make it easier for other people to get involved. And you see, I had done nothing in the nature of review before that, and the fact it wasn't really that I did the review. I mean, I gave the lectures and [???]
Cao:
Put the notes. Yeah.
Wilson:
But it's very difficult. I mean, this is difficult stuff, and without something like a review, it becomes harder for — I mean, they could, people could pick up on the epsilon expansion [?], but of course it became much easier when [???] had a review which really tried to build up from scratch what the formal ideas were.
Cao:
I see. Another person maybe you remember, Caruthers [?].
Wilson:
Yes.
Cao:
Caruthers published a paper about [???] 1970. Did you have any contact with him?
Wilson:
Caruthers? Yeah, I mean he was at Cornell, right?
Cao:
[???] Cornell. He was junior [???]
Wilson:
Oh, sorry, you mean Kruther [?].
Cao:
Caruther. C-a-r-r-u-t-h-e-r—
Wilson:
Well, there's Caruthers. How do you spell it?
Cao:
Ca-ru-thers.
Wilson:
Okay. Yes. He was at Cornell.
Cao:
Your student?
Wilson:
No, no, he was another member of the staff. I mean he later moved to Los Alamos.
Cao:
Yeah. He did some work parallel to yours about the [???] based on the scale argument.
Wilson:
I mean, I cannot place, you know — I mean, this discussion is simply not ringing a bell with me, so I can't —
Cao:
Ah. You can't remember. Ah.
Wilson:
But he certainly knew what I was doing, and so, and there's nothing very surprising that there would be a paper about this. [???] But you'd have to show me the paper and then I might be able to tell you more about it.
Cao:
I myself [???] some parallel development [???] So you didn't [???] very much. You cannot remember it [???]
Wilson:
Well, I can't say it was appreciated or [???]
Cao:
You just can't remember.
Wilson:
As I said, you cannot rely on my memory.
Cao:
Oh yeah. [???] You introduced a very important idea. Maybe somebody did it before, a statistical continuum limit.
Wilson:
Yes.
Cao:
What is the idea you used [???] yourself? Or there was somebody introduced this [???] before?
Wilson:
I'm not aware that anybody really did. I'm not aware of anybody who discussed it in [???]
Cao:
[???] before your introduction. Can you say more about this idea? When did you get this idea? Because [???] deep foundation [???] physics.
Wilson:
That's right. That's right.
Cao:
How could you develop this idea?
Wilson:
I mean that sort of characterized all the work that I was doing.
Cao:
Yes.
Wilson:
I mean what people had relied on up until then was the canonical part of this, that they said you had a classical continuum of [???] differential equations. And the whole concept of [???] differential equation [???] derivatives [???] differences. And the whole renormalization theory was developed in such a way that you made changes to the classical continuum limit without ever saying that was what you were doing. And that was, I mean that bothered me from the beginning, from the time that I learned about field theory that, I mean they had this way of doing renormalization.
Cao:
[???]
Wilson:
Yes. I mean, when I was [???] the field theory, and they started, you know, in the field theory of course they said well, you derive these formulae from canonical field theory. They have infinities in them, and so we forget the formula, but here is a set of tools by which to make these things finite. Right? And it drove me up the wall.
Cao:
So you were not satisfied with the old renormalization theory.
Wilson:
Right. I mean, it was a joke really. There was no formal basis for what they were doing.
Cao:
That's true, that's true.
Wilson:
And so, I mean, one of the themes — and sort of everything I was doing, was I still had that problem of, what was the basis for renormalized field theory?
Cao:
I see. So that's something on your mind constantly.
Wilson:
Now it turned out that that issue was essentially the whole issue that the people in critical phenomena were wrestling with, except that the — I mean, formally the limit, they were taking a different limit. They were taking a limit in which the correlation went to infinity, where the finite lattice [?] [???], and the statistical continuum limit is simply that you let the lattice spacing go to zero [???]
Cao:
[???] direction, yeah.
Wilson:
So I mean, if you understand the critical phenomenon, then it's not a very profound concept. Of course if you're coming from the field theory side and you have never mastered the statistical [???], then it is a very deep concept because you don't have the paradigm [???] mechanics to tell you that it's something we already have a lot of understanding of.
Cao:
There's something which is a puzzle, because actually in their calculation, in the calculation of relation of [???] theory, there is something [???] in it which corresponding to your idea of counting your [???]
Wilson:
Say that again?
Cao:
Something hidden in the calculation of the quantum [?] field theory.
Wilson:
Yes.
Cao:
Which actually is corresponding to the idea of statistical continuum [???]
Wilson:
That's right, that's right. And, you know, Gilmonde and Lowe's thing is sort of the first statement of that, which you know that's the first stage in the reformulation of renormalization theory so you can really understand what kind of limiting process you are talking about.
Cao:
When did you coin the word or term of statistical [???]
Wilson:
Well, I think it was not much before the first paper where I mentioned it.
Cao:
Why did you choose the word of statistical continuum?
Wilson:
That was specifically from the —
Cao:
[???]
Wilson:
Well, I mean we're dealing with — In all cases it's models which have a statistical character — whether it's [???] statistics or [???] statistics. And without a statistical component to it, you don't get into these kind of problems [?].
Cao:
So actually you had an idea that [???] renormalization. The classical and the standard for renormalization.
Wilson:
Well you can't say that that is understanding. There is no understanding in the classical way of doing it.
Cao:
Classical formulation of renormalization. Then you have a new understanding of renormalization based on the idea of statistical continuum [???]
Wilson:
Right. Well, I mean there's, the statistical continuum limit, there's the formal statement that you were trying to set things up like on the lattice and take the continuum limit, and then there is the Renormalization Group formally which tells you what it is possible to say about that thing. And then of course that then gets back to, I mean, if there's a fixed point there's a certain limit that you can talk about, and we don't really know what would happen if you sort of had a transformation which was say chaotic in the classical sense of chaotic, because we never encountered that.
Cao:
Are you familiar with the subsequent developments in [???] field theory after the popularity of the Renormalization Group equations? For example, [???] development [???] field theorists [???]
Wilson:
Yes.
Cao:
You see, [???] Have you received this? [???] introduction of the book about the history of renormalization. Certainly you are an essential [???] of this whole book. Why? Because we think that — we agree with you, there was too different [???] renormalization. [???] classical went by [???] and that the other was something developed based on your idea of the Renormalization Group.
Wilson:
Yes.
Cao:
And there’s this one [???], because field theorists say that all of Kim Wilson's idea is based on the existence of fixed point solution.
Wilson:
Yes.
Cao:
Then [???] field theory actually almost [???] cannot find any model which has that fixed point solution. Even so, still we find [???] very important. Why? Because of the Renormalization Group impression people develop the idea of [???] high-energy modes, [???] Afterwards the cut-off we discussed in this way.
Wilson:
Right.
Cao:
Cut-off become very serious things.
Wilson:
That's right.
Cao:
And we try, all these field theorists abandoned the idea to get a unified [???] everything from this. You have to go step-by-step, and every step is so crucial for the understanding of the nature. This means a hierarchical structure of the universe. You cannot get a homogeneous structure of the universe. There is some [???] struggle. [???] All this comes out from the renormalization [???] Because it's very important. But still there is something profoundly difficult. And actually, [???] your ambitious program [???] model of the field theory didn't work.
Wilson:
Well, what happened was in the part of the Renormalization Group that works from the field theory side was the part that was linked to the free field fixed point. I mean, the [???] freedom is not a fixed point theory, but is a theory that is coupled to the free field fixed point. You know, the concept of a fixed point which is unstable.
Cao:
I see.
Wilson:
And that is explicitly a part of my theory, but then you have to be completely fair about this. That was part of Gilmonde and Lowe's theory too.
Cao:
Yes. [???]
Wilson:
There was nothing that I did — I mean, if they had really understood Gilmonde and Lowe, they could have done everything that they did without referring to me.
Cao:
[???] If you look at Dicen's paper at a distance, it was very important. If you look at it closer, then you cannot use it. In some cases it also had such an impression. [???] When they look at it closer, and they tried to use the Renormalization Group, [???] in your work they cannot define the [???] They just cannot use it. Do you think it's true?
Wilson:
Well, I mean there was one more paper that I wrote that was influential, and that was, "The Renormalization Group and Strong Interactions." But [???] I mean that was the paper that I had written in 1970. I mean, that was the paper where I logically should have [???] models and found what they did. Because I discussed various options for strong interactions, leaving out the one option that was correct.
Cao:
[laughs]
Wilson:
Describing all the other options.
Cao:
I remember this paper, yeah.
Wilson:
But I mean despite the fact that I did not do [???] freedom and did not discuss that option, nevertheless you will find there's a certain amount of influence from that paper, and that was a paper that [???] The 1969 paper was very difficult, but by the time — I mean, after they started learning something from the statistical mechanics, then they could use the paper that I wrote and for example this whole concept of fine tuning. I think you will find that when you have a scale or particle mass you have to fine tune it to bring it down to the normal range of masses [???] I think you'll find that the concept of fine tuning dates from that paper in 1970, and one they had picked up some of the stuff from statistical mechanics they were able to use that.
Cao:
But actually you yourself developed your language in the [???] areas. What was the result of this work?
Wilson:
Of my thing about lattices?
Cao:
Yeah.
Wilson:
Well, I mean of course that ended up with a paper on lattice [???]
Cao:
I mean, is it acceptable to other field theorists?
Wilson:
Well, I mean there is now a whole army doing [???] So that's part of the field theory —
Cao:
What's the [???] of this approach? I mean, [???] lattice theory, [???] theory.
Wilson:
Well, the lattice [???] simply that I formulated the, my way, as I said, my way of just being able to understand what the [???] theory was about, was to set up the lattice version of it. And now in fact Pollykrov at the same time did the same thing, except that I went one step further, that I looked at the — I realized there was a strong coupling expansion for the lattice phase [?], which nobody else realized. But of course strong coupling expansions were always on my mind, and I found when you did this lattice scapes [?] theory and you did the strong pumping expansion it gave you, in a qualitative sense, it gave you the real world. I mean, it gave you protons and it gave you mesons and, you know, was actual bound states, and you could actually calculate them as bound states in this theorem [?]. And so that work has inspired [???] and then —
Cao:
[???] still working now.
Wilson:
That's right.
Cao:
But after 15 years or 16 years, is there any substantial results that come out from this approach?
Wilson:
Well, I mean there are partial results. I mean it was very difficult, and you know, I tried to do this myself and found it very difficult to get the computer to really produce something that was more than was in, that was really a major step beyond what I had done by analytic —
Cao:
I see. Power of computers is not enough?
Wilson:
The — I mean what is happening now is, people can argue still about what has really been learned from the numerical computations, but I have seen now what has happened in other fields in using the computer, and it can take them a long time. They have to, the computers have to get more powerful, and the algorithms by which you use the computers have to get more powerful too, and eventually you reach a point where they are powerful enough, so you start producing a lot of science. Now, they haven't crossed that barrier to start producing a lot of science in the lattice gauge theory [?], but I think one can now reasonably confidently predict that it's gonna happen. You know, it might be 10 or 20 years, but it's gonna happen.
Cao:
There is a [???] last two questions.
Wilson:
Yes.
Cao:
In your 1969 paper, you [???] some explanation not expressed today about the source of the [???] You suggested that it may be this anomalous [?] dimension of the [???] from the necessitor for renormalization.
Wilson:
Yes.
Cao:
Was that true?
Wilson:
Sure.
Cao:
What was your understanding of the renormalization, at that time, in 1969?
Wilson:
Well, at that time I knew perfectly well — I mean, I knew about the Renormalization Group transformation.
Cao:
Yes.
Wilson:
I mean, the paper that I published in about '71, there's a long paper which is where I prove in a model, I prove in one of these momentum slice [?] models that there is a Renormalization Group that involves [???] but I proved that you can define the space in which [???] show that each time you did the transformation [???] I already knew that. I mean I had done that work about '67. I just didn't get it all worked up for publication until '71. So I knew that I was already thinking in that context, and it was in that context of the Renormalization Group that I knew that if you had a fixed point you were gonna come out with these enormous [?] dimensions.
Cao:
[???]
Wilson:
Well you see at that point I was saying I knew that the tearing model worked, and I knew that the statistic mechanics works, so I said let's assume that. Let's assume that.
Cao:
It's plausible.
Wilson:
Yeah.
Cao:
So can you state succinctly what was your understanding of renormalization [???]
Wilson:
I mean my understanding of renormalization was that you had to define [???] That's sort of the right way to set it up. And you would have to formulate the limit in terms of setting up a Renormalization Group transformation, and you had to understand what kind of behavior you got depended on the kind [???] you got. Now I had focused on the fixed point. I mean I know that — I mean [???] does not require fixed points that do that, but on the other hand I also knew that the only examples that I had had fixed points. [???] I knew that if you had a fixed point you got this phenomenon with the [???] and I knew that [???] statistical mechanics paradigm and the tearing model paradigm. And that's all that I demanded. I had no counter-examples anywhere. So I solved my problem. I mean, I no longer had a contradiction between the product expansion and the tearing model. So that was all that I needed. You know, there was nothing to tell me that I was incomplete. I mean, there were no concrete things like the tearing model to tell me that my paradigm was incomplete, so it was time to write [?] it in. But remember I'm a physicist; I'm not a mathematician. So as long as all the examples that I had fit the paradigm it didn't matter to me that the formula then would allow other [???] You know, if I had been Arthur Jaffee [?] I might have said this was not [???] satisfactory.
Cao:
As a physicist, part of the argument is enough.
Wilson:
I remember one time in conversation when I was a graduate student Feinemann, and someone asked him a question, "What do you need in order to be able to make the statement in general?" Feinemann's answer was, "You need at least two examples."
Cao:
I see. So it wouldn't be too —
Wilson:
I had two examples. I had the tearing model and I had the statistical.
Cao:
Oh, I see. [???] for field theorists. Because they want [???] and the tearing model is certainly not a realistic model.
Wilson:
Well, I mean the field theorists —
Cao:
QED [?] is not a model with [???]
Wilson:
So I mean the field theorists have the trouble of why — You know, it was like my problem was Ben Whittem [?]. I mean Ben Whittem gets up and announced that he is gonna assume there are these homogeneous [???] There was no way I could buy into that. Now at that point I had no knowledge of what Ben Whittem's thought patterns had been that led him to that. I had no access to that. And of course the field theorists had no access to the thinking that went into my statement that what has made these assumptions, because I didn't give them any assumptions [?].
Cao:
One thing [???] you can comment. Nowadays there is a controversy among field theorists. Some people, like [???], argue that the [???] theory is the most fundamental approach. You cannot get a [???] I talked to them a few days ago [???] so stupid. [???] As a fundamental physicist you have to develop some idea so you can develop some [???] Which one in your favor?
Wilson:
Well, we're back to the old question of the Greeks. The Greeks asked, if you subdivided matter, would you come to a fundamental unit and you couldn't subdivide it any further or would you keep going further?
Cao:
And what's the answer?
Wilson:
And we're back to that same question, and we have no more answer to it today than we ever did. I mean, we have taken the business of subdividing very much further than the Greeks were able to do it obviously, and I mean what we know is that you have to worry about gravity, and that defined the length. I mean [???] fantastically smaller than any that we've seen. So certainly from any practical point of view of you know working with the SSC [?] [???] when we're talking about phenomenological field theory, and I don't think anybody will disagree with that. There is a question if you reach the gravity you want, will you at that time reach a fundamental smallest length and you cannot go any further, or will you, will there be, will it keep going after that. And you know, we can no more answer that question than the Greeks could answer their question. And so, you know, you can choose up sides, because there's no evidence to support either side.
Cao:
You [???] side. [laughs] Can we say something about Professor Deaver's [?] objection to the —?
Wilson:
Okay, fine.
Cao:
Because his argument is that the universality assumption is not universally applicable. He [???] example. The most powerful argument, he said, was his example of [???] He said he had some argument with [???] Do you know that?
Wilson:
I don't think so.
Cao:
You don't think so. Then one thing I wanted to check with you, David Nelson [?] told me that actually all of his [???] example can be assimilated by your work with the attraction of the line [???]
Wilson:
Line of [???]
Cao:
You knew that?
Wilson:
Yes. That part I knew.
Cao:
You knew. And it was in argument with Lieb [?]?
Wilson:
Well, I don't remember having arguments with Lieb. I mean, all that I know is that the Baxter model [???] the line of [???], vertical line, and that meant a breakdown in your universality, because I mean you had to generalize the concept of universality, because instead of having a single fixed point, which will describe all members of the universality —
Cao:
So it's not enough?
Wilson:
They could pick any one of the fixed points on that critical line. And so you have to restate universality to say that no matter what model you come with, [???] fits into that universality class, they have to correspond to one of the points on that critical line. But you can't make it any — I mean, you have to know the specifics of the model before you find out which one. Now, I mean the thing about that is, is that it requires some kind of coincidence to have a critical line instead of a critical point. Because if you take a point on that critical line and you calculate the critical exponents that go along with that one point, one critical exponent has to be zero. If there is no exponent which is zero, you cannot have a critical line; the critical point is isolated. So it was a special property of the two-dimensional models that you could have a fixed point which had an exponent of zero and you could keep going along the line and that critical exponent wouldn't change. Because most models are complicated enough so that you expect, if you move from one point to another, which the critical exponents would change, because they are a function of where you are.
Cao:
I see. So [???] Pickering [???] and also Lieb also mentioned [???] and maybe something in your mind and in his mind are quite different. Why did you mention Pickering at first to me?
Wilson:
Well I mean you are doing the history of science.
Cao:
Yes.
Wilson:
Okay. Now, if you're doing the history of science, then obviously one of the very key works is [???] science of revolutions [?], and Pickering is in a sense an offshoot of [???].
Cao:
Yes, certainly.
Wilson:
But of course very interesting because [???] wasn't describing anything I was part of, whereas Pickering [???].
Cao:
Pardon?
Wilson:
Coon [?] is not describing anything that I was actually part of —
Cao:
Oh yeah. [???] oh yes, he say something about high-energy fields, yeah.
Wilson:
But one of the reasons I mentioned that is because — and what I'm actually spending most of my time on now is science education. And what is happening actually is not just science education anymore, it's just this whole educational problem we have.
Cao:
Yeah.
Wilson:
And front center in the whole educational reform issue right now is the question of whether the research and the cognitive research on how people learn — which is of course closely related to [???] — whether we have a paradigm there, in the same sense as [???], whether it's a paradigm that we can actually build applications on, the way we've built all kinds of applications on Newton's laws and so forth. I mean, we've built bridges because we know that Newton's laws are correct and will remain correct, right, and I mean you can sue somebody in a court of law if they didn't use Newton's laws to design their bridge. But now in educational reform, educational reform stands or falls on the question of whether we have a paradigm with the cognitive research, where you can design education based on cognitive research and it will work with successive generations of students. But the interesting thing of course is that none of my colleagues have accepted cognitive research as having any standing the way scientific research has. And the interesting thing about Pickering is, there he is, discussing the social aspects of scientific research, which the scientists in a sense, it's harder for the scientists to reject that, because it applies to the things they do know about.
Cao:
Yes.
Wilson:
And the fact that they rejected it anyway is, I mean, that's, getting the scientists to recognize that Pickering is right — not completely right, because I think he does not, you know, he just doesn't do a careful enough discussion of the social side of it, because it's so much of a [???] His book is just the phenomenology of [???] and interpretation.
Cao:
[???] is crucial, and which I disagree with him is that, do you agree that there is an internal logic of the development in the science? For example, the [???] of your idea was determined by the internal logic of the subject or determined by some social factor. What's the crucial [???]
Wilson:
Well, what he is saying is — the way I put what he says — is that the research that is done is incomplete because of the social factors in it [?]. And that's very clear in my own work. I mean, I was always incomplete. You know, I missed the, all the [???], because it was incomplete. Now the point is that, he had a snapshot going up to 1980 [?]. The research, the whole research that had been done at that point was incomplete, and that was what it made possible to have this shift and for him to say that it was incommensurate [?]. You know, he's right; the research that was done post the revolution [???] —
Cao:
'74, yeah, October revolution.
Wilson:
Mostly incommensurate with the stuff he [?] had done before, and the stuff that was done before was sort of written off. But you see for him to characterize that as if — he characterizes it as if that was the end of the story, where that is not the case. But, I mean, as it comes to this question that you raised of —
Cao:
Internal logic of the evolution of the [???]
Wilson:
When you talked about the phenomenological field theory versus the fundamental field theory. I mean that is basically not an answer to the question. I mean, for social reasons it is not answerable because there is no way [???] research in that [???]
Cao:
[???] different direction to go. [???] physicists at Princeton [???] took a different approach. [???] at Harvard, they go through the different directions, [???] even though most of them are not approachable, but still the directions are different.
Wilson:
Well, no, what I am saying is, I mean, I mean, you have a state of sort of research knowledge at any given time, and you just have to recognize that that is always incomplete, and it never will be complete.
Cao:
That's true.
Wilson:
I mean, the physicists have said several times, "We are now completely done." That [???] is nonsense. There is no way that we can have a complete set of knowledge about nature. It's not possible. Now, but the [???] report on my paper, the [???] famous remark that, "Problems are not solved; they are only more or less solved." Right? And, you know, the problem of sort of "What is the universe?" is a problem of that character, exactly described by the statement that it becomes more solved as time goes on, because we accumulate more knowledge and more understanding. But there are two things that you have to say. First of all, because our knowledge is incomplete, and incomplete in a certain sense of being finite instead of infinite, that means that there are always multiple representations that will fit the knowledge that we actually have. There always will be multiple representations. You cannot get away from that. And so that's part of the statement of the social scientists, although they don't say it that way. Because they talk about different theories, whereas it's really not so much different theories as multiple representations. And you always have the problem — I mean, what usually happens is beyond a certain point. There are [???] transformations between the record. You know, like between Hamilton's [???]
Cao:
[???] different versions of [???]
Wilson:
And, you know, there is always the business that you always have to be able to show that the classical physics was a limit of the quantum physics. Right? So again, [???] transformation, [???] multiple representations so there would be some type of transformation. Now, it is always conceivable that you could have two representations, which were in fact you couldn't do a transformation because both transformations correctly described the finite amount of data that we had to have but were sufficiently complicated so that that did not force them to have an exact transformation between them. I find it very difficult to imagine that we will get actually into that situation in things like Newton's laws, because there is so much data and there is so much — As I say, I mean it is reliable enough so that I mean you can actually sue somebody in court for not using Newton's laws. And that's not discussed in any of the books on [???] that I've read, and they have to be a little careful about not claiming, writing things in such a way that somebody would use as a defense, a bridge [???] could use against the bridge builder.
Cao:
But still there is a question about Pickering's thesis. His book titled The Constructing [???] [?] —
Wilson:
That's right.
Cao:
This construction was constrained by the social factors.
Wilson:
Yes.
Cao:
Come to your case, you developed the idea, actually initiated a new pattern of the Renormalization Group [???], it's a new paradigm, and actually you suggested that the evolution of your idea was constrained by your expertise and accesses to the computer.
Wilson:
Yes.
Cao:
To maybe support Pickering's thesis.
Wilson:
That's right.
Cao:
But, my question is that, do you think that there is any [???] problem [???] for the internal logic of the subject?
Wilson:
I mean, there are certainly constraints. I mean, you can think of all sorts of things that don't work because it does not fit the internal logic.
Cao:
The question is, which [???] a decisive fact in the evolution of your idea?
Wilson:
I mean, the evolution of my stuff is, like any science, is that you have a certain amount of information that you have to be consistent with. You have to be consistent with a certain set of information, and then —
Cao:
Information [???] you try to solve. Is this true?
Wilson:
Well, I mean, I have given you all kinds of examples. I mean, I had this thing that, I had the operative product expansion, I told you in outline how I came to be doing that. Actually it was Lee and Wick [?] were the ones who had done this stupid paper about something having to do with [???] boson [?]. I had worked on that for — That's what got me started. So I mean you can always track, and the only problem with tracking it is that I can't reproduce everything now that I did at that time. But you can always track sort of step by step, and there was some specific problem that I worked on, and it's exactly like [???] says, you have puzzles, you find puzzles and you work on them. And Lee-Wick [?] was a puzzle and I worked on it, and Ken Johnson, Johnson-Baker-Willy [?] was a puzzle, and I worked on that. And that's how, you know, a puzzle is something that doesn't fit the paradigm. And so you keep working on the puzzle, and by solving the puzzle you make the paradigm better [?]. And that's all that I was doing. And, you know, so, as I say, the internal logic is the thing that you keep getting these puzzles and you keep having to insist that the paradigm — There has to be a solution to the puzzle, and the paradigm has to be consistent about it.
Cao:
You see, so many developments in the 60s and the 70s, you didn't take any notice about this [???] These developments had nothing to do with your own evolution.
Wilson:
Right.
Cao:
Why? Because I suppose there was internal logical development of the subject [???] Renormalization Group approach.
Wilson:
I had taken a different view of things. I mean, I had taken the view that we had to solve the strong interactions, and I didn't pay attention to the [???] because it did not contain [???] and that was what I wanted to do was solve the strong interaction. And, you know, and so I was building a mental model, a paradigm of what it would be like to talk about a theory of strong interactions. And I absorbed other things when I was ready to absorb them.
Cao:
So the question is, all these are intellectual fact or social fact? [???] factor more decisive in your [???]
Wilson:
I mean, what I was doing was perfectly consistent with what Coon talks about. He talks about the terrific struggle to accept a paradigm. Right? And he talks about the normal mode of operation where you have the puzzles and people work on the puzzle. Now the only thing that it was different, in my case, and from what the case that Coon works on, is that I was building a paradigm by myself.
Cao:
[???] because you also [???] had some interaction with Michael Fisher and [???]
Wilson:
No. I had interactions with people, and those interactions were important, but I was not sharing my paradigm with them. [???] I was influenced by the various papers, you've got the papers, and the people that I talked to, but I was not sharing the paradigm with them. We were not working within the same paradigm.
Cao:
[???] can say that you initiated this paradigm. But afterwards a lot of physicists share —
Wilson:
No. After —
Cao:
After you set out [?] the paradigm.
Wilson:
Right. But in a certain sense, I mean it is, you know, having — It's only very recently, by the way that I read Coon's thing, and I only read, I only saw Pickering's book about a year ago, a year or two ago. But it is clear to me that the way I've operated is with an — In fact you can always find some aspect of my work where I'm building my own paradigm.
Cao:
Yes, that's true. I suppose that [???] closer to your case, and [???] always puts the emphasis on intellectual [?] fact, even though when he talks about the paradigm, paradigm [???] particularly and the styles are different, maybe substantially different, because he puts the emphasis on social factors. He puts more emphasis on the expertise, that this is [???] But I don't agree with him, because [???] the evolution of your idea just because [???] was determined by your access to computer. Can I say that? Or, the evolution of your idea is determined by the problem that you set for yourself to solve, determined by the tradition in the quantum field theory?
Wilson:
Well, I mean, look. I mean, Pickering does not state things carefully. I think that is his main problem, he just doesn't state things carefully. He is completely correct in saying that any person is limited by the social context in which he works. And I guess that's limited [???]
Cao:
Oh yes. Everyone knows it's limited, yeah.
Wilson:
Now the — He describes, in most cases he is describing sort of groups that are sharing a common paradigm — the different groups that form and so forth — and he had a special with [???] And he does not really explicitly allow for a case — And in my case, where I am as socially limited as everybody else, except that I don't have to work with a group paradigm.
Cao:
You're lucky. You can develop your own.
Wilson:
I was able to develop my own. I mean, I can see in retrospect. I mean, that was a very dangerous thing to do.
Cao:
Really. Yeah.
Wilson:
But on the other hand, I'm not the only person who's done that. I mean, Boseland [?] clearly developed his own paradigm and he committed suicide because nobody else would accept it. Murray Gell-Mann is a person who developed his own paradigm. So I mean there are a number of people —