An Interview with Bernie Alder

Bernie Alder

BA = Bernie Alder
GAM = George Michael

GAM: Today is March 5, 1997 and we are talking with Bernie Alder, one of the earliest scientists to come to the Laboratory. Bernie, please begin.

BA: To start right from the beginning, I was born in Germany as a Swiss citizen in 1925 and, when Hitler came to power in 1932 or 1933, I moved to Switzerland. And then I came to the United States with my family in 1941, just before the United States went into the war.

I did my undergraduate work at the University of California, Berkeley (UCB) in Chemistry, and I was interrupted by the war. I very nearly got into the Manhattan Project; just slightly too young, they tried to get me into it, but it wouldn't work. So I went into the Navy and then came back and finished my undergraduate degree at Berkeley in Chemistry in 1946. I got my Masters in Chemical Engineering in 1947 and then went to Cal Tech in 1948. I think that's where I first got introduced to computers actually. That's presumably what you're most interested in.

That's sort of an interesting story. I was working for Kirkwood, who was the expert in statistical mechanics, liquid theory, etc. We were trying to figure out according to this theory whether hard spheres had a phase transition to the solid phase and we used a rather complicated nonlinear integral equation that had to be solved and we could only solve it on the computer. We only had IBM mechanical computers that were programmed by a plug board. Then I ran across a man named Stan Frankel, who was the head of the computing organization that had just been created at Cal Tech. He came from Los Alamos. I think he was an unrecognized genius in the business. We soon realized that solving this nonlinear integral equation didn't have a unique solution. We got into the intermolecular instabilities. And then he or I or we came up with the idea, it's hard to trace this down, to use the Monte Carlo method to solve this hard sphere problem. I don't know how much technical detail you want?

GAM: I'd like it all.

BA: We tried something that didn't initially work. We placed the hard spheres into a box randomly to make a dense system. Of course, when you try to place them in randomly, and the thing that we realized almost immediately was wrong, you have to try again and again. For example, if you tried and it failed because it overlapped with one of the existing spheres, you tried again until it fits. Well, there are three things wrong with that. It isn't quicker to do, you can easily show that statistically it isn't correct and, thirdly, you can't get very high densities by just randomly putting things in a box—you've got to arrange them in an orderly fashion like oranges in an orange box. Anyway, we immediately realized that, so we started out with a configuration, a solid like order configuration, and then jiggled the particles according to the pulse rate distribution. And that is, in fact, known now as the Monte Carlo Method—it was presumably independently developed at Los Alamos by Teller, Metropolis, and Rosenbluth. They actually got all the credit. My guess is we did it first at Cal Tech. It's not that difficult to come up with that algorithm, which, by the way, I think is one of, if not THE, most powerful algorithms.

GAM: It still is, yes.

BA: The most powerful ever developed on computers, because you need computers just to do this enormous amount of juggling in the box; you can't do that by any other mathematical or analytical technique, and for the first time really solves numerically what is called the Many Body problem.

Anyway, we juggled these particles and realized that on this mechanical IBM computer we couldn't go very far. Then Stan Frankel actually went to England, to Manchester, where they had a FERRANTI Machine. Which may have well been the first electronic computer.

GAM: Can you give us a date on that?

BA: My guess it's the summer of 1950 that he went over. I was still working on my Ph.D. thesis. He was really well known in computing circles. He actually put the Monte Carlo Method on the FERRANTI Computer and ran it all summer. I think it was before Los Alamos had electronic computers available. Anyway, we ran it and he came back. The thing that happens, Kirkwood did not believe in my boss, my thesis supervisor, he didn't believe in him at the college and, of course, he had communication with Los Alamos. The fact is, we never published—you can't publish something your boss doesn't believe in! In the meantime, Teller, Rosenbluth and Metropolis independently published. There may have been some collusion or communication of ideas that I couldn't recall, but they had the machines, so they published and we published only years later. There is, in fact, a footnote in the Metropolis paper giving us credit of having independently developed it. That got me a connection with Edward Teller and when he came to Cal Tech, he persuaded me to become a consultant. At that time, after I finished at Cal Tech, I became what was then called a Wrakov instructor which each professor started out with at Berkeley. I think Teller was at Berkeley when Livermore was founded—in 1952, I guess.

GAM: Yes.

BA: I think I was almost immediately a consultant primarily because I knew Teller, and I was used primarily to help with the equations of state. I was probably the only man to devise the equations of state in the early history of weapons development at Livermore.

Also, this gets beside the point, I helped establish the explosives station at site 300. I worked with that, but that was an experimental phase of my career, I don't think you would want to pursue that.

Then an interesting question came up which, in a physics sense, was the 64 dollar question, whether hard spheres had a phase transition. It turned out that the Los Alamos people failed to find it, for some reason that I didn't understand. We had predicted there would be one—it stood ultimately on shaky ground but, nevertheless, I believe it was something that had to be cleanly settled in the Monte Carlo Method. They failed to see it. What happened to me, I taught for three years at Berkeley in Chemistry, then took a Guggenheim abroad. When I came back, I worked part time at Berkeley and part time at Livermore, and eventually the computers, as you said earlier, dragged me to Livermore and I gave up the Berkeley position.

But the hard spheres business still bugged me and, so I thought, well there's another way to try to see whether the hard spheres have a phase transition and that is to develop molecular dynamics, which has since become a competitive and extremely powerful methodology. Also, we solved the POSTUM many-body problems, but the molecular dynamics can also solve the time-dependent or transfer problem. Then, I got Tom Wainwright whose office was down the hall from me, interested in these questions, and I said I needed somebody to talk to and work with, and he became very interested. We actually developed, in relatively short order, molecular dynamics.

GAM: Yes, I remember.

BA: It's sort of interesting that people predicted, I think including Teller, that molecular dynamics would never be competitive computationally with Monte Carlo because it was so much more complicated. But it turns out, when you finally get down to doing it, it's very competitive. I guess that must have been about 1955 or 1956.

GAM: Well, as background in a sense, I remember Edward Teller saying, at one of the LMG meetings, that we're now through with this testing thing, so let's get to do some physics with these machines and you and Tom came up with your molecular dynamics scheme. I remember Chuck Leith came up with the business of simulating neurons and a few other things like that.

BA: Right, Project Moron, right. At one point Chuck and I...I guess it was the LARC, or was it the UNIVAC?

GAM: The UNIVAC and then the 704 and then the LARC. The LARC didn't show up until about 1960 or so.

BA: OK, I remember only Chuck and I competing for machine time. But it was a very friendly competition. Anyway, we developed molecular dynamics and that really swept statistical computing.

GAM: Well, your method was a really important thing all over the world.

BA: Oh yes, there isn't a university department that doesn't do both Monte Carlo and molecular dynamics.

We then went back and reinvestigated the hard-sphere phase transition. We found, actually, beautiful pictures of solids in equilibrium with liquids,

GAM: Yes, I remember those pictures.

BA: Which, I think, got on many covers of freshmen textbooks and into Scientific American, it really swept the field. Then the Monte Carlo people, particularly Bill Wood of Los Alamos, went back and redid more carefully my Monte Carlo methods, and found the hard-sphere phase transition.

GAM: I remember back in 1958, during the Hardtack Phase I test series in the Pacific, you sent out stuff to me there and I ran hundreds of hours of STEP calculations out there.

BA: I remember that and I am very thankful to you for that, George. We needed a lot of statistics because this liquid-solid phase transition is a very rare event. It's very hard to do that and machine time was THE important thing at that point, to get a large amount of statistics. We did two things, we taught all our friends and buddies to help us run and we also developed an agreement with Sid, which I think became very important too, and that was to utilize the machines in a maximum way to compute. Whenever there was an idle moment we had an algorithm where we could just get in there, whenever the scheduled computation couldn't run. We fixed our programs so that they were ready to run in an instant. In this way, we could get a few seconds or whatever, that would otherwise have been unused, So, we started to help other people to do the same thing to utilize the computers really fully.

GAM: It used to annoy the A Division people, even though they couldn't use the time, they didn't like it that you were getting so much time. Actually though, their design codes were very complicated especially compared to your Molecular Dynamics program, and it always took extra time to get them started.

BA: Right, but they got clever over the years too, and started doing similar things to try to utilize all their time. But early on, it helped Sid Fernbach to acquire more machines, because even though people didn't know what the machines were being used for he said, "Look, they are being 99 odd per cent utilized, we need more machines". In that political sense, it was very important. We managed to abscond with a fair number of machine cycles. Anyway, we settled the hard-sphere transition.

GAM: Well, wasn't it sort of an unusual thing to build in, this hard-sphere thing had a model, though, for potential wells so you could model the sphere, at least, from the potential point of view as inelastic.

BA: Well, would you deal with soft spheres or...

GAM: With soggy spheres?

BA: Soggy spheres, yes. I mean of course, that's sort of historically interesting. We stuck to hard spheres because they are several orders of magnitude faster than if you do the same thing for soggy spheres and sticky spheres. Because machine time was so valuable, for hard spheres you can solve the collision dynamics algebraically, rather than as a differential equation. And that gives enough of an advantage numerically. And, it turns out ultimately, it was in fact the key problem, because it has all the essential physics in it and from a theoretical point of view it's a much easier thing to deal with as well as numerically.

GAM: I remember the stir of excitement that ran around the Lab when you were talking about simulating boiling too.

BA: Right, right, now for boiling you do need the sticky, soft spheres. We put on a square well and we saw the gas liquid interface. That also got into a lot of pictures. Those pictures may have well been the earliest graphics examples of use.

GAM: Not quite, but they were certainly early, I made thousands of feet of films for you and that guy in Berkeley.

BA: You helped us a lot, yes.

GAM: It was fun, I remember that.

BA: Yes, that guy in Berkeley, you know that's sort of interesting, this was the Berkeley Physics series. You know there was a Harvard-Berkeley Project at one time to rewrite the freshmen physics text. Fred Rife, who was the Berkeley guy if you recall was, in fact, heavily involved in the statistical mechanical section of that freshmen physics series. And he asked me, and with your help, I succeeded in making some pictures.

The thing that was sort of interesting there, and is still being used, let me explain that to you, is this problem of irreversibility. Freshmen have a very difficult time understanding the concept of irreversibility. The point was, if you remember this, you had a box to be divided into two and, in the first demonstration, we had four particles in the left side and none in the right hand side. And you run the system, and then you run it backwards, and you can't tell what irreversible is. When you run it forwards, and run it equal time backwards, the four spheres end up being on the same sides again, but it's not an unusual event because it's a natural fluctuation. But, if you put a hundred particles in, and you run it on half the size and half the size of the box and none on the other. You run it forward, it mixes, of course, all up and then you run it backward and a hundred particles end back up in the left hand side, of course, because the equation is motion reversible. But, then everybody laughs, because you recognize it's a terribly unusual event with a hundred particles. So that got on the cover of the freshman physics book. We tried something that was a film loop that demonstrated just the thing I was talking about dynamically. They were trying to sell that loop with the book. I don't think it was a commercial success, but it was used a lot. Many fashionable physics professors have told me they have used that demonstration to teach the concept of irreversibility.

GAM: There were lots of similar things like that going on through the Commission on College Physics.

BA: Yes, that's right, I'd forgotten the auspices of this however. But that service became very well used.

GAM: Well, yes, it was great stuff, it was very good use of the computers.

BA: I agree. Graphics were very primitive in those days, and we needed helpful people like you to make the thing go. I think we spent about three months just getting these film demonstrations working.

GAM: Yes, well things have gotten much better now, but it was more fun then.

BA: We only had black and white then, now they have color and sound. Anyway, that was sort of interesting, this whole hard spheres transition. Using the computers for education purposes was extremely important and selling it to the academic community a worthy task.

GAM: Along the way, we sort of covered the first fifteen or twenty years of the Computation Department, but how close did you work with Sid making decisions here, there, or elsewhere? You were an advisor to him, weren't you?

BA: Yes. The things that we did that ultimately turned out to be very important. We founded the Methods of Computational Physics, the book series. I had a friend in the publishing business and we were chatting one day about all this material developed at Los Alamos and Lawrence Livermore on hydrodynamic phenomena, and that we should publish it and get more people in the academic world to participate. So we started that. There was a huge problem about declassifying all this material, but we brought out close to twenty volumes. Each book dedicated to a specific field, such as statistical mechanics, quantum mechanics, fluid dynamics, solid state, and that was the early, extremely important project of getting more people involved in the field. Sid used all his friends, I did a lot of the legwork, but I used to run into him and ask, "How do we get this going"? and so forth.

Then we started the journal Computation, which is still a key journal.

GAM: Yes, it is a very good journal.

BA: Because we realized the books took several years to produce and we needed a quicker communication means.

GAM: I still have some of those journals. They are still the best treatment for that early stuff, very good stuff.

BA: The journal still has, even today, the key articles, the key intellectual developments.

At the end of Sid's career, speaking of publications and so on, he sort of had the idea of starting a division within the Physical Society. You know, they have the Energy Division, the Plasma Division, Materials Division. So we had a Computation Physics Division. He, at that point, was no longer associated with the Laboratory, but we met occasionally, and he had a desire to do that, so I really worked at it and helped him get that going. We went to the American Physical Society for support. It's a very successful Division, and it became a Division almost immediately. We got some 2000 members without even trying.

GAM: So after this journal got started, I remember seeing all over the world references to the Fernbach, Alder things, OK? As I said, I have some in my own library that I think are great. The best treatment for the initial ideas of hydrodynamics and things like that that I've ever seen. But I was thinking more in the sense of dealing with Sid. Yes, I know you guys pioneered this business of publishing the Computational Books too, which were very good. But I was thinking more of the day to day like when you were going to work out some strategy for getting a new machine or work out some strategy for equitably sharing the time available on the computers. Were you involved in any of that?

BA: No, he did the acquisition of the computers, I never did any of that. I always wanted the biggest and the best, but I really couldn't help him with that.

For example, the use of the spare cycles was an issue that we felt very strongly about and he pushed it. I'd say, "Why don't we do that?" and he implemented it. He'd get people to agree, not only in the Lab, but also outside the Lab. That was a big problem.

GAM: That seems so obvious!

BA: Yes, but people wouldn't initially agree.

GAM: It's just a dog in the manger act..

BA: Well, you know what the people in the Lab say: "You're cutting into our time this way", and then we'd show that swapping information each way was trivial in terms of time used. But there were also intellectual considerations, where you couldn't let outsiders use a government machine that was dedicated to weapons. Machine time was really a valuable commodity in those days. To use it for this whole equation of state business was based on the development of Monte Carlo. Anyway, I remember he had a hard time getting agreement both inside and outside the Laboratory.

Our communication was extremely informal, I ran into his office, or he looked me up, or we met in the hall, or we had lunch, or just chatted. It was never formal; we respected each other. He was always interested in developing new ideas and encouraging more use and intelligent use of computers. But I took the sort of intellectual end and he took the more administrative, practical, and political ends. He was very good at that. We had lots of fun trying new things.

GAM: I don't know if it was the Laboratory or Sid, but you had some excellent support in MaryAnn Mansigh, who was devoted to your project all the time. And, I remember, Norman made some interesting contributions about developing a neighborhood concept that made STEP run much faster.

BA: That's right, in those days, people like me didn't really program. That was dirty work and, even then, very time consuming. So, I worked through a programmer. MaryAnn Mansigh was my loyal twenty-odd year programmer. I tried to get her to be more innovative, but she preferred to stick with a very conservative approach.

GAM: She did what you wanted her to do.

BA: She did exactly. Nowadays, that is no longer practical. Now, you have Physicists with PhDs who are trained in the computing business, but that just wasn't available then. And, if you do more sophisticated computing, you need people who know both programming and physics.

For example, we spoke to Norman about speeding up the hard sphere algorithm, the molecular dynamics algorithm, and you don't have to search the whole system for the next collision, you just need to know the domain. Intellectually, it's not a very difficult thing, you just need a neighborhood or domain decomposition, whatever fancy name they have now, but it's neighborhood search.

GAM: It was innovative at the time.

BA: Yes, but in retrospect, nothing was really difficult. That's, of course, the beauty of being a pioneer in the field. Do the easy things—get the cream off the top. It took Norm quite a few months. He had other things to do, but he actually coded the nearest neighbor algorithm, and this speeded the thing up.

GAM: Yes, I remember him on it. He was my office mate.

BA: He is a brilliant guy.

GAM: Indeed, he is.

BA: He wasn't assigned to do this, he was just interested. We were all interested in doing this stuff, no formal arrangements—we just did it. It was an extremely fertile environment.

The interesting thing is that neither the Monte Carlo algorithm nor the Molecular Dynamics algorithm have significantly changed since their inception. Once we made these, what we think now are, obvious improvements, basically, people are still using them. Monte Carlo, of course, is easily parallelizable, which we couldn't do in these days with Molecular Dynamics—which can't be made parallel even when people think they can. But, basically, the arguments are unchanged. The original algorithm is still valid. When people first build something it's not always the most efficient version.

GAM: Well, that's true.

BA: It turns out, we build an algorithm that is close, I have not seen any significant changes.

GAM: Just apropos, if nothing else, is anything of this stuff being carried on today?

BA: You mean the Monte Carlo or Molecular Dynamics?

GAM: Yes, that you were involved with at the Lab.

BA: Oh yes.

GAM: How about Jim Belac, I was always impressed with the stuff that he was doing.

BA: There are a number of people who are trying to build Molecular Dynamics into bigger and bigger systems. We were stuck in the early days because we only had memories of a hundred words. We could do, maybe, a hundred particles at most. Well, they can now do ten million particles, and Belac is one of those people who just, by brute force, does bigger systems. Runs them maybe longer, on much more capable computers, but that's not my cup of tea.

There are some very recent developments that we are trying to work, and which we may want to briefly discuss. One of the problems, is it's computationally very expensive to run fluid dynamics compared, of course, to Navier Stokes, right? And people are trying to bridge this gap between Molecular Dynamics, the Particle Method and the Continuum Method. The Particle Method you can't run more than 8 seconds and maybe run 10 to the 6th or 10 to the 7th particles. But that's not going to get you to turbulence or whatever. So, our most recent ideas for extending Molecular Dynamics is to do what is called "Imbedding". Imbedding a particle method into the continuum. So only, for example, where you need detailed particle information—it's sort of an adaptive algorithm; within an adaptive gridding. That may extend Molecular Dynamics by many orders of magnitude. That's our latest idea that works very well with parallel machines. It's amazing that people have not done that actually. But that's a relatively recent thing still to be done.

GAM: I think it's amazing that people have not done a lot of things and I must admit I don't know why. Some things are hard to do, I suppose.

This thing you are talking about with adaptive gridding and so forth, I worked with some aspect of it with Garry Rodrigue. He was busy trying to put it on a sound mathematics foundation.

BA: There's this group of people with Phil Colella and John Bell, I'm not quite sure they fit into your time history, but I brought them to the Lab and they are the ones who really made adaptive gridding work. And it is highly successful, but that's within Navier Stokes. One puts the gridding where the action is basically. The latest thing we are talking about is extending that when the gridding gets very fine, very small scale, then you put in a particle algorithm instead of the diffusion method. That's very successful.

GAM: And you are carrying that on now both at the Laboratory and at Berkeley?

BA: Yes, well, one of the groups, the Bell, Colella group has left to go to LBL and we are working with them as well as a newer group here at the Lab under Steve Ashby. We're trying to work with this group to try to do the same adaptive gridding and imbedding algorithms.

GAM: Yes, I've heard of them.

BA: The other thing that is a significant development in the extension of Monte Carlo Methods, which I've personally been involved with at the Lab with a man named David Seperly, is solving the quantum many body problem. Solving the Schroedinger equation by Monte Carlo method which has been a pioneering effort also. I think we did a superb job on that. It has its technical difficulties with the Fermion problem, which is one of the deep instability problems in numerical algorithms, which has not yet been corrected.

GAM: Where is David now?

BA: David is a Professor at the University of Illinois. The key thing we did there, which is one of the key papers that has been published in Condensed Matter was the uniform electron gas, the jellion. That turns out to be a most cited paper, or was, at least, a few years ago, in Condensed Matter. That was sort of interesting. There were three papers written up of ours, or mine, in the hundred-year anniversary issue of The American Physical Society. They published significant papers in this issue and they picked three of ours. One was the hard spheres transition; one was the discovery of the long time tail in the auto correlation function, which completely overthrew the existing kinetic theory. The fact that there was a long-term memory and not a Markov process involved. And the third was this condensed matter thing. All these were developed at the lab where all those marvelous computers are held.

GAM: Beyond that, the computers are there, but so are the people who have the skill to use them.

BA: Yes, you need an idea. You see the problem is you can do intellectually interesting things on the computer instead of just engineering things. You can do really innovative discoveries and that's my bag trying to use the computers to gain more insight into Physics.

GAM: That's what it's really for.

BA: I think so. Well, that's what it's usually for, it's now used for sending e-mail back and forth.

GAM: Something here about reverse evolution?

BA: Right, it's astounding what computers are being used for, let me go back to one other thing that is sort of interesting, my admiration for Stan Frankel at Cal Tech, who worked at Los Alamos during the war and then came to Cal Tech. Very few people know of him because he never got tenure at Cal Tech and then went off to some oil company as a consultant.

But in 1949 or 1950 he was most interested in building a personal computer. He was fiddling in his lab trying to build a small personal computer.

GAM: It was virtually impossible then, the components didn't exist.

BA: That's right, he didn't have a semi conductor. But his idea was way ahead of its time.

GAM: It would be nice to have more of a detailed description of that for others to read later on.

BA: You should get a hold of Stan Frankel. I lost track of him after we wrote our paper on the Monte Carlo Method with him which was published in the middle 1950s, a year or two after Teller and Rosenblum's paper. I've lost track. I know he was at some oil company.

GAM: Speaking of Teller, were there any of your interactions with him that you can remember?

BA: Well, we certainly talked a lot in the early days of our mutual interest of the Monte Carlo Method and molecular dynamics. I was very much in favor of starting the Department of Applied Science at Livermore of which I am one of the founding members. Edward and I worked together in that. Neither of us stuck there very long, it was sort of awkward.

GAM: The one person I heard who was against it was Emilio Segre. Everybody else...

BA: It's very complicated, I don't want to get into that, it's a physics thing. Berkeley physics was opposed and then it got into Davis and Davis physics opposed it. It was the political connection of the university with a weapons lab, and ultimately it ended up in the sort of awkward Engineering Division. They forced it down their throat, and it's been a sort of stepchild of Livermore and a stepchild of Davis. I'm still involved with the Department of Applied Science. I ultimately went back to it. They wanted me to come back and help them organize it. I was on a bunch of committees and now that I am retired, I occasionally help them with advice. That department is being reexamined. The idea was to use the Laboratory as a training ground because it had unique equipment such as the computers, the high explosive facility, and lasers to get students trained in the advanced and multi-disciplinary research. It has worked to some extent, but not nearly as well as I think it should.

GAM: Well, maybe after the smoke had cleared, the degree of cooperation that one extracted from the various parts wasn't all that hot. I remember I taught out at DAS for a bit and I was told that that's on me, it did me no good at the Lab.

BA: It was funny, the Lab supported, in principle, education.

GAM: Yes, but only in principle.

BA: The hierarchy did, but when it came to the nitty-gritty people, they wouldn't do it. So it changed that.

GAM: So, it worked out a little bit. And I will tell you in the computing area, there have been some very, very, talented people that got produced at DAS.

BA: And it turns out, that half the graduate students still want to go into computational physics. But the staff at this point is very low. I'm trying to remedy that in my retired status. Teller has never really spent enough time out there to make it flourish. Even in the old days, my guess is it got so politically complicated at the end that he didn't want to deal with the Davis section and just sort of gave up.

GAM: Back to a semi-technical question. One of the things that seems to be a great concern in the Monte Carlo Method is its spread across an arbitrary number of processors. How do you keep the seed from being inbred or being repeated over and over again?

BA: Are you talking about random number generators?

GAM: Yes.

BA: They now have random number generators that they can test. You see, because the machines have gotten so big there's a danger that the random number generator has a periodicity. They now have tests that know how long it takes for random number generators to repeat or to get back to the same initial state.

GAM: But, from the technical, or philosophical, point of view, it's obvious that that's got to be avoided if you intend to use it?

BA: Oh, by all means, and you can test that very simply by generating random numbers and just plot them. And use the generator to see whether the area you are trying to cover is uniformly covered. Whether you have stripes or empty regions.

GAM: I remember doing that many times and seeing holes in the circular distribution.

BA: Then you know you have a problem, right? Exactly! That's a highly technical thing. Actually, Chuck Leith got involved in that.

GAM: Oh, really, I didn't know that?

BA: I just ran across that. He published a paper in our Journal of Computational Physics with some woman who is not at Livermore on the Randomness of Other Memory Generators and trying to make sure that they are random over these many more samples. But there are tests.

GAM: But you are telling me that people recognize that there is a problem and they're doing something about it?

BA: Right, and massively parallel computers force you into that because the numbers are used so many more times and you need so many more different runs.

GAM: Well, I think it's rather germane to the question in these ASCI computers that they are trying to foist off on the scientific community right now.

BA: Right. Oh yeah, we are planning to use the ASCIs, the blue machine one of these days.

GAM: It's fine to use it, you know, if you could leave the politics out of it, and the hype, I think it's likely it could answer some interesting physical questions and it would be worth it. Many of those questions are the same ones that we talked about thirty years ago and you couldn't do it then because you didn't have the machines.

BA: Right, you couldn't solve them very fast. You must have a perspective, I personally think you know, people get all excited about a computer that has a power of 10 or a 100 times more powerful than the one they have. But the problems that you need to solve are almost so complex that even that factor is not very important. So, not only do you want bigger machines, you have to be clever about usage, if you can. For example, turbulence or three-dimensional hydrodynamics, those are problems that can eat up an arbitrary capacity on any computer we're ever likely to see. So you have to be clever.

GAM: Well, Great, can you think of anything else that you'd like to add before we turn this thing off?

BA: Well, have we answered all the questions?

GAM: Well, it's not the questions so much, it jogs your memory, OK? I think you've covered everything you wanted to say here, and I want to thank you for taking the time to revisit this memory lane.