Interview recorded in Gray, Maine.
Interview conducted by PoS collaborators:
Babak Ashrafi, Karl Hall, and Sam Schweber.
Edited by A. Martínez and S. S. Schweber.
I've come to realize that one of the most important dates in
all of history is the date when people started making videotapes.
And that will vie with the date that Gutenberg invented printing.
Or very close to it. While we were coming down in the car, I
was thinking that it would be really helpful to us if you could
go back to your days as a graduate student. I think we know something
about the background for your undergraduate days. I think it would
be helpful to go back to Caltech and have you tell us about learning
physics and, in particular, learning quantum field theory, renormalization
and all those things at Caltech, beyond what you said in your
I came to Caltech in 1956, and what I didn't realize was that
for all practical purposes, I had already completed a Ph.D. Working
with Arnold Arons specifically during junior and senior year.
I did a project, I wrote it up. It was never really published,
but it could have been. I spent a year taking courses at the same
time that I - just for kicks - worked in the nuclear physics laboratory
on an experiment which was supposed to reproduce parity violations,
but never succeeded.
Were you already learning some many-body theory at that stage?
No, I didn't learn any many-body theory. It's just that I had
done all the work of a thesis and I was clearly self-propelled
then. I took courses, but it was boring.
You did nuclear physics at Harvard or at Caltech?
No, at Caltech. This was after I'm finished with Harvard, I'm
at Caltech. And so the first year, I'm taking courses like the
quantum field theory course. I can't remember. I had taken the
chemist's quantum mechanics course at Harvard, so I think I was
taking quantum field theory first year, but I can't guarantee
And just to go back, when you said you essentially had done old
thesis work already when you came to Caltech, can you say specifically
what is it that you had done?
I did a theoretical study of calculating propagation of sound
in an ocean that had both a layer at the top of both constant
temperature and sound velocity and then a thermocline underneath,
which means a variable sound velocity. That meant there was a
shadow zone because sound rays would come up to the surface, the
rays would reflect and then go down again in the surface zone,
they were caught because the rays were straight. There was a special
ray that would come up, just graze the surface zone and then head
down; and there was a shadow zone beyond this special ray. I worked
out the theory of how the sound penetrated into that shadow zone.
Arnold Arons, who was supervising, didn't know the mathematics
that I was looking at, but he was, in a sense, probably a better
supervisor than anybody I had at Caltech. So, once at Caltech,
I did an experimental project in my first year, basically for
Willie Fowler and people like that... I forget who.
Tell us about your courses.
I was just taking courses, and of course, at some point, in the
period that was either the first year or the second year, I took
the quantum field theory course.
With [Richard] Feynman or [Murray] Gell-Mann?
No, it was neither of them. It might have been [Robert] Christy,
I'm not sure. I also became friendly with Jon Mathews. He and
I would go on hikes and talk. Gell-Mann and Feynman were the big
cheeses, but I spent very little time actually with Gell-Mann,
and with Feynman. The third year I was there, Gell-Mann was off
in Europe. Gell-Mann had urged me to come, too, but I wasn't ready
for that. And so during the third year, there was a seminar that
was run by Feynman, and that was very interesting. Feynman read
my thesis because Gell-Mann was still away.
This was all the time when Feynman and Gell-Mann were doing weak
And how far did the quantum field theory course go? I mean, if
it was Christy, did it included renormalization and all of these
Oh, yes, at the heart of it, it was just QED-type renormalization.
One of the texts that I certainly studied at the time was [N.
N.] Bogoliubov and [D. V.] Shirkov. I think there was some other
texts that we had, but I forget what it was.
Bogoliubov and Shirkov didn't appear in English until 1959. So
does that fit with what you're talking about?
Oh, so it could well be that I read that afterwards.
Berestetskii: does that ring a bell?
You mean Akhiezer and Berestetskii? I remember...
It wasn't so widely available because it wasn't officially published.
It was simply translated by the AEC or something like that.
Right, right, it was widely circulated.
Well, there's no question that the field theory course I took
in either in 1956 or 1957 or 1957/1958....
Did it get as far as something like Gell-Mann/Low or Bogoliubov/Shirkov
-style renormalization theory?
No. That part I read on my own, I'm pretty sure.
Well, it could be that you saw the Bogoliubov and Shirkov article
in Nuovo Cimento.
I know I came away with that book, so I'm sure there was another
book that we were using. And I know I reacted very negatively
to the book, too. It was so ad hoc, I couldn't stomach it.
Field theory in general or renormalization theory?
The renormalization procedure.
Do you recall at what point you became familiar with the renormalization
group, say, Gell-Mann/Low?
Sometime toward the end of my second year, I started working
with Gell-Mann. I went to Gell-Mann and he gave me a problem to
work on and suggested I start working with fixed source theory
of K-particles, where he wanted me to do things involving strong
and weak interactions. And it's when I read about fixed source
theory that I began to learn about renormalization group and realized
it could be applied to fixed source theory, and I don't know whether
there were papers that I read about renormalization group and
fixed source theory, or I worked it out for myself, but in playing
around with this, sort of trying to learn what was going on, I
discovered that there were great simplifications that took place
when you took the fixed source equation and took them to high
energies, and when you did a leading log approximation. In the
end, I discovered that those equations, simplified at the high
energies -- you could get exact solutions. That was part of my
thesis. And that was the initial thing that sparked my interest
in the renormalization group. I remember when I presented my thesis
to a seminar, and this was when Feynman was there, but not Gell-Mann.
I went through all this exciting mathematics and toward the end,
someone said, "Yes, that's fine, but what good is it?" I
remember Feynman's answer as "Don't look a gift horse in
So you come away from Caltech having really worked hard on renormalization
group methods and the thesis is essentially what gets published
No, the thesis was never published. I don't remember if I actually
ever published the exact solutions of the fixed source theory.
So at that time, who else did you know who was looking at issues
with renormalization groups?
No one. There was the work coming out of Russia. I mean the papers
of Bogoliubov and Shirkov. I don't know when they stopped publishing
on renormalization theory. I don't think they did anything through
the 1960s as far as I know.
I think Shirkov was off doing strong interactions.
And so you feel pretty isolated in terms of people not understanding
you or knowing what you did on your thesis when you talk about
it. You come back to Harvard afterwards.
Yes, I come back to Harvard, and at that point, I picked up with
S-matrix theory and I tried to work with Mandelstam's bootstrap
approximation and I tried to program a numerical solution. I tried
to use the MIT computer and that went exactly no place, because
I could look at the output only once a day. And you can't do computing
on that basis.
Your interest in computing and the relevance of computing and
all of these things comes from where?
That gets started in graduate school. Jon Mathews was the one
who took me over to the Jet Propulsion Lab... It had some kind
of machine which ran on paper tape. I think it was some kind of
Burroughs machine. He showed me how to use it and I did simple
programming things with it. I forget whether I was actually able
to do anything useful or not, but I certainly got interested.
So I was fascinated with computers starting from that point.
And the philosophy which stems from saying that unless you can
get numbers out... stems from where?
All through my undergraduate days, I was fascinated with the
question of how you approximate mathematical equations in order
to solve them.
And when you say you were fascinated, what stimulated you to
think that way?
Well, the strength I had, starting much earlier, was in mathematics.
I learned calculus from a book that was given to me when I was
in the eighth grade (in ninth grade we were in England for a year).
There's no question that I had learned the essence of what calculus
was all about before I went to England. I wasn't able to do very
much... I went to two years of prep school after ninth grade and
I wasn't able to do very much then because there wasn't anyone
around to work with.
But the fascination of approximation... Somehow, you were willing
to consider approximate solutions. And perhaps that was the best
one could do.
That's right. That certainly built up as I went through the math
courses as an undergraduate. And, of course, it was strengthened
by the work I did with Arnold Arons. Here there was a need to
actually do a problem and get approximations. And I remember early
in graduate school, one of the things that happened at the end
of the first year of graduate school, I had signed up to spend
a summer working at Los Alamos on plasma physics. I was going
to see what that was like. And then the whole Los Alamos group
was going to go to this big international meeting and so I quick-switched
to go to General Atomic and worked with Marshall Rosenbluth instead.
So I spent a summer working on plasma physics and I think it was
at that point that I got fascinated by the guiding center approximation
for the motion of particles in almost constant magnetic fields.
I remember working a lot on trying to understand -- you first
have to study that circular motion and then you have to extract
from that a set of equations for the motion of the center and
the whole concept of that kind of approximation. So whenever something
involving approximation would come up, I would always sort of
keep working on it.
And at this point, this was all on paper, or were you using computers?
This was all on paper. I did do a dogwork project for Arnold
Arons on the osmotic pressure of sea water. I don't know if we
had a desk calculator at that point or not.
What kind of exposure did you have to statistical mechanics at
I had to pass a thermodynamics course, which I did by never going
to lectures, just reading [Enrico] Fermi's book and taking exams.
But I don't think I had to learn anything more formal than that.
When Gell-Mann handed you the problem of the three-dimensional
I didn't do anything with it.
Did you look at it? Did you research it?
No. I think that was my going into his office and asking what
he was working on, and he wrote down the Ising model and told
me it would be nice if I could solve it.
Do you remember BCS being discussed when it comes out in 1957/1958?
Feynman got interested in that stuff shortly after it came out,
but I didn't keep track of that myself.
Feynman was giving a set of lectures at Hughes Aircraft at that
stage, things which involved the polaron, BCS, all of these things.
I didn't pay any attention to that.
You didn't look at the notes or anything like that.
So you went to Harvard as a Junior Fellow and you were still
looking at problems of quantum field theory at that time?
Once I started working with Gell-Mann, I was solely in quantum
field theory until I come back to the Ising model in 1965.
That includes S-matrix work?
Yes. What happened, from the time I go to Harvard, the big project
I tried to do was work on S-matrix theory. But then I had to figure
out something to do because I kept having to wait for the turnaround
on these programs, so a couple of things happened. I got interested
in the strong coupling approximations, fixed source theory and
what had happened there. Gell-Mann had talked about it in a set
of lectures that he gave, which I attended. I suspect what must
have happened is that I must have taken the field theory course
the first year and then there was sort of a topical course given
by Gell-Mann the second year and I was listening to Gell-Mann's
lectures and not understanding a lot of what Gell-Mann said, but
in figuring that I wasn't going to understand it I supposed it
was just Gell-Mann. Then I come to Harvard and I become curious
about strong coupling because there's a person named Helmut Jahn
visiting Brandeis as a postdoc and it quickly became frustrating
to me that Helmut Jahn understood this and Gell-Mann had lectured
about it (the strong coupling approximation), and if Helmut Jahn
could understand it, I knew I could. But I couldn't read the papers.
I mean, I had the papers in front of me, I read them, and they
didn't make any sense. And finally I realized I had to reinvent
the approximation for myself and as soon as I sat down and said, "How
would I approximate this?" it then turned out not to be very
difficult. But I did have to stop trying to read the paper and
work it out.
Would you happen to have those lectures?
Gell-Mann's lectures? No. I don't know that there were any lecture
notes. I just know he lectured on them.
Who were you working with or talking to while you were working
There was hardly anybody at Harvard. So what I used to do was
go down and eat lunch with people at MIT: Francis Low, Ken Johnson
and those people. And that was very interesting. That set me up
for what got me going in early 1963/1964. Partly it was looking
at the work of Johnson and Marshall Baker and trying to figure
out why I didn't agree with it.
The canonical history of high-energy physics or quantum field
theory is that starting in the early 1960s, quantum field theory
goes into disrepute... Did you have that sense that you, being
committed to quantum field theory, were in the minority and you
were a little bit outside the fold?
I knew I was outside the fold, and I didn't care. I had just
come to one of these presuppositions that Gerald Holton talks
about. I had come to the presupposition that S-matrix theory was
going no place, that field theory was the only way to go, so I
decided I was going to work on field theory. That was my rule;
I was going to work on field theory and do the best I could, but
that was what I was going to work on.
Do you recall what people like Low or Johnson or maybe Gell-Mann
made of the direction that you picked? Was this an issue of discussions
for your lunches at MIT?
Not as far as I know. Because remember, when I'm at MIT, what's
happening is I'm working on the strip approximation, I didn't
really discuss that with anybody. It was numerical work so there
was nothing to discuss. I had just come back from CERN where I
had worked on another thing altogether and that was the multiple
production processes and very simple models of multiple production.
And there's an article on that that I published in Acta Physica
Austriaca which was a set of winter school lecture notes I gave
on that, and there was one or two papers with [D. Amati] and [A.
Stanghellini] from my period at CERN. I started working on the
strong coupling theory, but I didn't publish anything on that
until I got to Cornell. The only other thing that happened was
a conjecture by [Freeman] Dyson that I got fascinated by. So I'm
sort of all over the map. I felt isolated at Harvard. There's
no question, but I found people to talk to at MIT, but it was
more for lunchtime conversation than "Can you help me with
Did you ever tell Francis [Low] about the work you had done for
your thesis? Did he understand what you were doing, given in part
that it was on renormalization group methods?
Francis and I talked, but I have no recollection of whether we
ever talked about the renormalization group per se.
Or your thesis in particular. And starting in the early 1960s,
which was when you were at Harvard, Paul Martin is there.
But I don't think we ever talked. I don't remember ever talking
with him. I was doing high-energy physics at that point -- that
was where I saw myself. So I didn't talk to people about solid
It's not so much solid state as all the technology that Schwinger
and Martin had developed for many-body problems.
So by the time you come to Cornell, people don't really know
what you're working on. I mean on the surface, there are many
things that you're doing, but deep down, there's a commitment
to try to explore how far can you go with quantum field theory.
The people at Cornell had more of an interest to know what I
was doing than people at Harvard, because they were going to have
to make a decision... Of course one of the things that happened
was, as you may or may not be aware, is that they gave me tenure
after only two years and with no publication record. In fact,
there was one or two papers on the publications list when I was
taken for tenure and Francis Low complained that I should have
made sure there was none. Just to prove that it was possible.
Before then, when you were working on the work of Ken Johnson,
and you developed an expansion technique... Can you talk a little
about that? What was the issue you were addressing and how you
came up with this technique?
There were several papers by Johnson and Baker, related in some
way to the high-energy behavior in momentum space of quantum electrodynamics.
Finiteness or divergence of the Z-factor...
Something like that. I was skeptical, but that just gave me an
excuse to work on the things I was working on anyway, which was
just trying to understand high-energy behavior of momentum space.
I'd also worked on a conjecture of [T. D.] Lee and somebody else
which was on weak interactions, which involve renormalizability
and high energy behavior. So I just started working on the high-energy
behavior of Feynman graphs in momentum space... Things got more
and more complicated. I have no recollection of what it was that
triggered my thoughts of just freely transforming back everything
into position space, in which case, things became much more transparent
and that became the basis of the paper that I published.
You said you heard some lecture by Klaus Hepp, and the lesson
you took from that was that you should work in position space.
Do you remember anything about how that went?
I remember the locality requirements had to be stated in position
space. These commutators that have to vanish outside the light
cone. This was in the Nobel lecture?
So, it implies that you had followed all the things that were
being done by people doing renormalization theory...
I didn't follow it in detail. I knew that they were working in
position space. It didn't mean that I had worked through the formalisms
that they developed...
When you had looked at Bogoliubov's method of doing renormalization
and things like that.
Well, I knew the renormalization group and the concepts that
the axiomatic field theorists were working on.
So you write this preprint, stating the rules for your expansion
and then the referee suggested you look at the Thirring model.
So what's the significance of that exchange?
The significance is that when I set up the rules, I just used
perturbation theory so I was using canonical dimension for the
field operators and allowing logarithmic corrections because that
was what was coming out from the perturbation theory. But then
I looked at the Thirring model and discovered that the dimensions
are not canonical in the Thirring model. I mean, the dimensions
of operators changed depending on the strength of the interaction.
And I concluded that I was going to have to completely rework
the ideas so as to allow for non-canonical dimensions.
Were you aware that the referee was Arthur Wightman?
I never found out who it was.
Did he just point you in the new direction or did he just show
you that what you were doing was wrong?
You should have received a copy of the referee's report. The
thing that was important for me was that it said: “have
you considered the exactly soluble Thirring model?” Which
I had not, so I had to go look at it.
And then when you considered it, you realized that you left out
the possibility that the dimensions could change, and did you
have an idea of how to pursue this possibility? Or did it just
stop you cold?
It stopped me from publishing that paper. What could I do? I
mean I had the Thirring model. You can solve it. But I didn't
know what does this mean for field theory if it's not the Thirring
model. So here's this huge blank. So then I spent a long time
just trying to figure out how do I get more understanding about
high-energy behavior given that it could do that. The perturbative
approach doesn't work. So that sets me off thinking about a computational
approach to go beyond perturbation theory. And I particularly
get interested in the question if I had a computer big enough,
how would I do this computation. That became sort of a guiding
point to drive me to how to think about the problem. How can I
convert this from a problem of infinite number of degrees of freedom,
which you can't deal with anyhow, to a problem which is finite
even if it was so large that you would have to have an astronomical
size computer. I just wanted to convert it from an infinite number
of degrees of freedom to a finite number.
So the computer comes in by raising the question of how you program
it in such a way that you can try to get answers.
I'm dying to ask you just what happens next? If you try to formulate
the question in a way that you can put in a computer, how far
did you get? Did you try it? Were you talking to other people
There was nobody to talk to. At that point, I'm constantly going
around in circles except...
You come back to the fixed source scalar model at that stage?
I continue to work on the fixed source theory. I sort of had
several balls in the air. One of them was to keep coming back
to the fixed source theory and there you have publications from
time to time. First, reducing it to a very simple model that you
can solve and then...
It's actually starting to peel away degrees of freedom.
You're right. This is when I start making models involving solving
and eliminating degrees of freedom, and it culminates in the work
that I did in 1969 when I was at SLAC, but talking to nobody about
it, in which I took momentum slice models and provided as best
I could a rigorous proof that it would converge despite generating
effective Hamiltonian of an infinite numbers of couplings. So
there's a long sixty-page paper on that proof.
When you do that, you're aware that there in fact is a length
scale which allows you to get approximate expansion. In other
words, cutoff dependence is relative to some length scale that
you have within the problem.
Well, remember what I did there was I did this momentum slice
procedure where there was a big separation of energy from one
slice to the next. And then I was able to do the approximation
of expanding in that energy ratio. Then, what I had done by 1969
or 1970 was a proof as rigorous as I could make it, although I'm
not trained in rigorous mathematics, that the process would converge
and even though the successive effective Hamiltonians generated
by the process had infinite numbers of couplings, that didn't
matter -- there was a convergence. You could prove a convergent
expansion if you had the whole thing large enough. And I wanted
to have that assurance that I wasn't just landing myself in the
soup by just imagining these Hamiltonians with infinite number
of couplings. That extends later to the treatment of the Kondo
problem where I was able to get rid of the artificial gaps between
momentum slices and still do a numerical calculation that was
feasible. And I kept trying to think about how do you set up a
field theory so that I could do the momentum slices. But that
didn't get me very far. Then, as I was playing with this stuff,
I began to start learning about the critical phenomenon.
We're now talking 1966 or thereabouts... 1967
Well, the first thing I do was attend a seminar by Ben Widom
when he's introducing his version of the scaling. And that was
1964/1965 or something like that... It's before I go out to Aspen
and start studying the solution of the solution of the 2 dimensional
Ising model as formulated by Dan [Daniel] Mattis, [Eliot] Lieb,
and Ted [Theodore] Schultz.
Essentially, very shortly after you come to Cornell.
Can we just take one step back? I'm just trying to understand
the linkages in your investigations. You worked in 1965 on momentum
slices and this all in the context of the fixed source theory?
And you said, "This work was a real breakthrough for me
and for the first time, I found a natural basis for renormalization
What drove me nuts was that in the Gell-Mann/Low framework, or
as Bogoliubov/Shirkov did it, you had to start with a complete
solution of the theory (obtained through perturbation theory).
Then you go back, and you work through the renormalization group
procedure. But I needed to get away from perturbation theory.
I needed to find some way to handle the problem so that I could
use the renormalization group as a way of solving the problem
instead of a way of analyzing the perturbative solution. When
I replaced the complete range of momenta by discrete and well-separated
momentum slices, that gave me a parameter to expand in, which
I could then use to actually get a solution in which each renormalization
group step deals with a finite and feasible problem. (namely,
the ratio of energies from successive slices)
Can you say a word about how scales or length come into that?
The way scales come into it is that for each slice, you have
a different energy scale. If one inserts large gaps between the
slices then the energy scales are different by enough so that
the ratio of the energy scales becomes an expansion parameter.
I mean the essence of the renormalization problem is that you
have these different energy scales and at the extreme they're
very far apart and you want to be able to expand. But of course,
you're prevented in real life by not having a high ratio of energies
between the adjacent scale. But by making the artificial momentum
slice models, with big gaps in energy between successive slices,
I made sure that every energy scale is separated from every other
energy scale by a large factor. Then the whole problem became
solvable even in the limit when you have an infinite set of scales.
So suddenly, in that approximation, I now had what I wanted. I
could solve the problem with an infinite number of degrees of
freedom in terms of reducing it to a sequence of problems, each
with a manageable number of degrees of freedom. But even with
momentum slices, there are still an infinite number of degrees
of freedom in each momentum slice. So I needed to conduct a formal
analysis to assure myself that I wasn't still in the soup because
of the infinite number of degrees of freedom in each momentum
slice. And so I worked very hard to make sure that there were
no problems in the momentum slice model that I wasn't aware of.
You alluded to the similarity of your work to a conjecture by
Dyson developed a way of taking a field theory, putting in it
a dividing line between the low momentum part and the high momentum
part, and doing the perturbation theory on the high momentum part
before the low momentum part. I was, in the end, able to develop
more sophisticated versions of that as one way of setting up the
renormalization group. But he did not carry that to the point
of getting to the renormalization group concepts that Gell-Mann
and Low had...
But his conjecture was.... or maybe I misunderstood...
There were conjectures of Dyson, but I forget...
I think Dyson wrote a paper in Proceedings of the Royal Society
where he outlines this notion that renormalizations are high energy
effects that reparametrize the coupling constants in the theory
and made analogies with fluctuations and considered the smoothing
out of the low energy physics when you had intergrated out the
high energy fluctuations at short distances. I believe the conjecture
of Dyson that you give a proof of is a mathematical one that he
uses in some other thing, not necessarily in that problem.
The conjecture I studied at Harvard was about random energy levels,
which is really separate from anything else.
Can we take an interlude now before we move to Cornell? We've
been asking you questions about the techniques and the conceptual
development around renormalization groups and high energy limits.
What if we were to ask you about your history in using computers
to solve problems. So if we start with your work after graduating
from Harvard, when you had access to a Burroughs computer. Could
we just ask you to go back and tell a different story along a
different trajectory, which is how do you learn to be more sophisticated
and try things with computing?
Well, I first started working with computers at Caltech. And
Jon Mathews certainly introduced me to the Burroughs Machine that
was there and I learned to program it. I'm pretty sure I did some
of the work in calculating expansions for the fixed source theory
with that computer. By looking at the numbers, I learned that
I was getting expansions and I could recognize the analytic form
of the expansion from the actual numbers that were being printed
And you're talking mostly to physicists as you learned how to
It's just Jon Mathews who was interested in computers. When I
went to Harvard, I'm not sure whether there was anybody I talked
to about computers.
Did your father use computers? Did you know of his models for
getting infrared spectra? Did things like that play a role in
What I remember from discussions with my father was that he used
get very wrought up about computational quantum chemists. Garbage
in, garbage out. That set me up to spend some time at Ohio State
studying quantum chemistry. I had done a little bit towards the
end of my stay at Cornell, but took it more seriously while I
was at Ohio State. And so then I had to find out from my father
who were the good people. And he knew them, he had a list of them.
And who did he say were the good people?
There was [Isiah] Shavit. There was Ernie Davidson, John Pople
from Carnegie Mellon. What's interesting about this is that later
when I became interested in the history of physics and [Thomas
S.] Kuhn's book, one of the characteristics of the pre-paradigm
phase he discusses, and there really are pre-paradigm phases --you
know, people don't want to admit that--is that everybody is arguing
with each other and somebody comes in from outside and tries to
figure out what's going on, like my father interacting with the
quantum chemists, they learn who the good people are. And yet,
they won't admit that there are good people, unless you ask them,
otherwise they are more interested in complaining about the poor
quality of the research by others in the field. I found the same
thing with Arnold Arons who knew the people in education research
and as soon as I asked him, he would tell me who the good people
were too. In that case, I discovered he didn't know all the good
people. And I didn't go back and check the names to make sure
I got all the good people from my father, but he certainly gave
me a good start.
And the criterion for being good? I mean what makes a person
These are the people who are smart, take serious problems to
The generative quality comes in?
For instance, consider quantum chemistry for a moment. What I
found was that the people who did the important work worked on
algorithms. They improved the algorithms for solving quantum chemistry
problems on computers. They couldn't do the calculations they
wanted to do, so they worked on algorithms. And it was the algorithmic
work that was absolutely essential. When the computers got better,
and they could do serious things, it was the work on algorithms
that made the difference and the people that my father knew made
contributions to serious algorithm developments. At the same time,
there was just a lot of stuff published where people were running
programs and they were paying no attention to whether they worked
or didn't work, and claiming all sorts of fancy things.
So the interaction with your father on that score is important.
Well, it's not important for the renormalization, but it's important
from the point of view of what I'm doing now. And I think it's
important, in the large sense, for what you're trying to do. I
mean a larger sense than just the physics of scales, though even
in the physics of scales, what I gather you're learning is this
phenomena of the physicist adjusting their standards to the difficulty
of the problem.
Continue reading part II of the interview.