People, Challenges, Impact on Applications: A Glimpse of the History SiteJuly 6, 2006
Heroes of the SEAC. Philip Davis (left) and Philip Rabinowitz, National Bureau of Standards, 1952.
The following passages are from two of the 20 "Oral Histories" now available at http://history.siam.org. The excerpts (slightly edited) are from interviews of Philip J. Davis (conducted by Bill Kolata and Gail Corbett, April 15, 2004) and Cleve Moler (conducted by Thomas Haigh, March 8 and 9, 2004).
An Absolute Miracle
Bill Kolata: Let's move on to your career at NBS. The computing environment had changed by then?
Phil Davis: The computing environment had changed considerably by then. The first-generation digital computers were there, and there was one called the SEAC (the National Bureau of Standards Electronic Automatic Computer, the first electronic computer with an internally stored program of the U.S. government and the first of three computers built at NBS). That was in 1952, which is when I went there, and that was the hotshot computer in its day. There was a great group of people there, an inheritance from a thing called the Math Tables Project of the WPA (Work Projects Administration). . . .
Kolata: They didn't use any computers other than the electrical-mechanical computers?
Davis: In those days, at the beginning, those were the only things that were available. Some of the people there were from England---John Todd, Olga Taussky, and others---and from Switzerland---Peter Henrici and Walter Gautschi. They were all there but at different times. NBS became the leading outfit in the exploration and development of methods for scientific computation using the newly developed electronic computers. . . . And then, of course, as the computer spread, the knowledge and technique spread, and the primacy of the group (at NBS) was diffused a lot. In those days, one of the nice things about it was that we had very much freedom to develop what we could. I was never given a specific task really; I might have taken one, but I was never given one. What I thought that I would do was to develop a certain method in partial differential equations---the solutions of which I knew how to get---and see whether it worked.
Kolata: You mean whether the numerical technique you were using worked?
Davis: Whether the numerical technique worked, and was the right thing, was expeditious, was competitive with others.
Kolata: At NBS, you met Phil Rabinowitz and later did some work and wrote a book with him. How did that happen?
Davis: Phil was a crackerjack programmer. I had only programmed one thing in my life on that old system, which has what was called a four address system; he was crackerjack at that. So we worked together, and I would work out the theory, lay out the algorithms, and Phil would do the programming. And that worked out very beautifully. Now in a number of these things that turned out to not be too hotsy-totsy, we had to do a lot of approximate integration; so I got interested in doing approximate integration in a more sophisticated way. And that led to the book. We did a fair amount of work on Gaussian integration, which was a very hard thing to do in the precomputer days.
Kolata: You have a fascinating story in your book Mathematical Encounters of the 2nd Kind (Birkhauser, 1997) that led to you and Phil being called "Heroes of the SEAC." That story is worth retelling.
Davis: Well, the story---it still is true---is that when you write a piece of code, a program or something in code, it almost inevitably has bugs in it, so you run it. We had laid out a program for doing the Gaussian integration; it was tricky---I didn't know whether it would work or not. I was following some leads that came from some advanced stuff in orthogonal functions, on the zeroes of orthogonal functions, and I brought that advanced stuff in---it came from a book on orthogonal polynomials that Gábor Szegö had written (Orthogonal Polynomials, Colloquium Publications, Volume 23, American Mathematical Society, Providence, Rhode Island, 1939), which I was familiar with. I had no notion under the sun whether or not this scheme was going to work, so I laid it out for Phil and then I did some of the programming. But I said, I can't do the double precision stuff; you do the double precision stuff. I figured we had to go to double precision, which is 20 figures; otherwise, we'd get junk. He laid that out. I still have the program sheets back home. I didn't want to throw them out. And then we put it on the SEAC. You had to type it out in those days, and put it on wire; then you shoved the wire in and you pushed the button---and waited. Lo and behold, it started outputting numbers, which seemed to be good. It was a miracle, an absolute miracle, from two points of view: first of all, that the programming was correct, and second, that the algorithm was working. And this being a rare case, they named us "Heroes of the SEAC." In those days that was a takeoff on "Heroes of the Soviet Union," because when one heard about heroes of the Soviet Union they were highly regarded people and they got prizes and so on in Moscow, so this was a takeoff on that.
In the Cracks Between Math and Computer Science
Tom Haigh: What was George Forsythe [Moler's thesis adviser at Stanford] like to work with?
Cleve Moler: Wonderful. He wasn't harsh, he wasn't demanding, he was inspiring, he would give you guidance when you needed it. He told me one time, not just about me but about everybody, "It's our job as professors to teach you students what we know and then get out of your way," and I've always remembered that. I'm thinking that about MathWorks today. There are young people at MathWorks today working on parts of our software that I've always been very much involved in, and I don't always agree with them, but I'm getting out of their way. It's time for them to do it their way, and Forsythe would have had that attitude.
Haigh: One of the things, as someone who's not trained in this specific area, I'm having some trouble with is understanding which bits of mathematics are particularly important for which application areas. So, could you say a little bit more about the specific disciplines in which this book [Forsythe and Moler, Computer Solutions of Linear Algebraic Systems, Prentice-Hall, 1967], might have been used most?
Moler: Solving systems of simultaneous linear equations, I would argue, is the most important topic in scientific computing. They come in many forms. This particular book handles fairly small systems, and modern computing today solves much larger systems to which this software doesn't apply, but still the topic is there, so I can't think of an area of scientific computing which doesn't rely on solving linear equations. Control theory and signal processing. . . . My wife was just looking for a hearing aid for her mother on the Web and came across hearing aid companies, and these guys use MATLAB, and they use what's become of this software in designing hearing aids. All the big codes at the national laboratories doing weapons effects are solving systems of simultaneous linear equations. Wall Street, predicting stock prices and futures prices, and so on, does this. Statistics, automobiles, aerospace, any place.
Haigh: Did academic specialists in numerical analysis have a good sense of the kinds of problems that people in disciplines were working with, and of what was and wasn't useful?
Moler: No, I don't think so. There can be a pretty wide separation of it, if you look at the kinds of computations that are going on in the automobile industry, or in the aerospace industry.
Haigh: At that point if you'd had to choose one or the other, would you have called yourself a mathematician or a computer scientist?
Moler: Well, that's always been a question. I have a joke, I don't know if you know what the Lorenz attractor looks like, that chaotic system with the butterfly. I have a map that shows that orbit, and I say this is numerical analysis trying to decide whether it's mathematics or computer science. It's attracted by both centers, but as it gets too close, it's repelled, and it's different at different places; it has a lot to do with personalities of people involved and history of people involved. Today numerical analysis really falls in the cracks between math and computer science. I can't think of any place where it's a central discipline in either department. Here at the University of California at Santa Barbara, I'm actually visiting here teaching a numerical analysis class that is one of the possible required courses for undergraduates in computer science. It's rare that computer science students take numerical analysis anymore.