Mechanics of Geomaterials
Edited by Z. BaÅ¾ant
Â© 1985 John Wiley & Sons Ltd.
William Prager:Â Personal Recollectionsâ€
Philip G. Hodge, Jr.
â€ Text of a speech presented at symposium banquet.
Professor BaÅ¾ant, Professor Rice, Professor Drucker, distinguished colleagues, welcome guests, or â€” to put it concisely â€” friends.
Shortly after I accepted the kind invitation from Professor BaÅ¾ant to deliver a â€˜Banquet Speech related to Pragerâ€™ I obtained a copy of Jay Barryâ€™s (1982) book Gentlemen under the Elms, with essays on eleven of Brown Universityâ€™s famous professors, including, of course, William Prager. â€˜Aha,â€™ I thought, â€˜this talk will be easy to prepare.â€™
I already had quite a collection of articles on Prager. These included two ASME documents: an account of his acceptance speech for the Timoshenko Medal from ASME in 1966 (Paul and Hodge, 1963) and a copy of his nomination form for Honorary Membership in 1970. I had a 1968 article from the Brown Alumni Monthly (Anon., 1968) about his triumphant return to Brown after five years of â€˜exileâ€™ at IBM in Zurich and the University of California, San Diego. I had my own introduction of him for the Timoshenko medal, and H.G. (Geoffrey) Hopkins had sent me a copy of his urbane presentation when Prager was awarded an honoris causa by the University of Manchester. I could refer to two â€˜birthday cards:â€™ one written by Dan Drucker (Drucker, 1973) for his 70th birthday, and Jim Riceâ€™s beautiful â€˜Laudatioâ€™ for his 75th (Rice, 1979; Prager, 1979). And I had two bulging folders of personal correspondence extending over thirty-some years. All I had to do was to put all this material together in a talk.
I began my preparation by carefully reading Barryâ€™s essay. And I found that everything I wanted to say is already there in well-written detail. How Prager worked with Prandtl in Goettingen, and how he accepted a professorship in Karlsruhe in 1933 only to be fired by Hitler. How he went to Istanbul, and what he accomplished in eight years there. How Henry Wriston brought him to Brown in 1941, and what Prager did there during and after World War II. The statistics are there, too: twenty-some books, over 200 papers, lists of awards, proficiency in four languages, the journal editorships. And finally, the essay is replete with personal glimpses and anecdotes contributed by such people as Dan Drucker, Harry Kolsky, Paul Maeder, Jim Rice, Paul Symonds, and his secretaries Eleanor Addison and Frances Gadjowski.
It was soon obvious that the only way to literally adhere to the publisherâ€™s original title of â€˜William Prager â€” the scientist and the man,â€™ would be to spend the next 75 minutes reading Chapter 5 of Gentlemen under the Elms to you, a task which would tax your patience and my vocal chords â€” and probably provoke a suit for copyright infringement.
So, let me refer you to these other sources for most of the public record which constitutes William Pragerâ€™s illustrious career. I will make passing reference to a few well-known facts, but for the most part I want to share with you some of the personal glimpses I had of this exceptional man who was my thesis adviser, mentor, and friend.
* * * * *
A prime requisite for achieving success in life is to be in the right place at the right time. For me the right place was the Graduate Division of Applied Mathematics (GDAM) at Brown University at the end of World War II, and the right time was seven oâ€™clock in the morning â€” any morning.
I was a conscientious graduate student, and fully expected to work sixty hours or more a week at my studies and research. However, unlike normal people, I preferred to start work before sunrise and to eschew burning the midnight oil.
According to Barry (1982, p. 92), Pragerâ€™s rigidly regular schedule called for 10.30 bedtime, up at 4.30, and not later than 6.30 to work. Thus, for an hour or so in the early morning we were the only two people in GDAM. Usually we each worked in our separate offices. Occasionally I would have a question related to my work, and he would always interrupt his pursuits to discuss it with me. And on rare mornings when he didnâ€™t feel like working, he would come in my office, perch on a desk corner, and reminisce.
Thus, I knew some of his history in the late 1940s â€” well before the laudatory articles and speeches spread the knowledge. And there were little differences.
For example, Barry (1982, p. 79) says that Hitler had him dismissed from Karlsruhe â€˜because of Pragerâ€™s strong anti-Nazi views.â€™ As I heard the story from him early one morning, Professor Prager was singled out because he was the youngest full professor in Germany and the object of some jealousy. Therefore, the universities didnâ€™t protest as strenuously as they might have over a more established professor, and Hitler had been able to set a precedent.
The harrowing details of how Bill and Ann Prager and their 12-year-old son, Stephen, came from Turkey to the United States in 1941 by way of Baghdad, Karachi, and Capetown may be found in many places. But to me, the tension they were under was brought home most sharply when he talked about how for over two months they had lived fully packed and ready to leave on 24-hourâ€™s notice.
Sometimes he talked about Prandtl. His favourite story, of course, was about the student who plotted some numerically obtained data and suggested that the points lay on a semi-ellipse. Prandtl took one look and said, â€˜No. An ellipse is symmetric; this problem is not. Try a cycloid.â€™ Looking for the cycloid, the student returned to his equations and was able to prove that it was indeed the correct solution.
A balance between intuition and rigour, and a gift for, in Einsteinâ€™s words, being â€˜as simple as possible â€” but no simplerâ€™ were Pragerâ€™s trademarks. For my first assignment as a research assistant Professor Prager asked me to write up, as a paper, a theorem he had presented in our plasticity class. It took me weeks to flesh out the proof that he had intuitively sketched in a few minutes, but eventually I did it for the general three-dimensional case. He suggested I apply the method to a simple beam problem. I did, and in the process discovered a mathematical error in my proof which was rather subtle in general 3D tensor notation, but glaringly obvious in a single scalar dimension. It was a lesson in the value of simplicity which I never forgot.
One August morning when I was working in shorts and T-shirt (which I still do), Professor Prager, who could look formal in slacks and a short-sleeved, open-collar shirt, commented on the changes he had witnessed. Prandtl had once complained about a graduate student who had come to his office on a hot day without putting on his waistcoat. Stiff-collared shirt with tie and jacket were considered insultingly informal! There was no censure in Pragerâ€™s telling of the tale. He had his own standards of dress and conduct, but he had no desire to force them on anyone else. He was just amused at the contrast.
A lot of nonsense had been written about Pragerâ€™s formality. It was present on the surface, but his humanity easily shone through it. One afternoon a burly delivery-man stamped into the GDAM with a package and bellowed â€˜Is there a guy named Prager here?â€™ (He pronounced it â€˜pray-ger.â€™) We, the students and secretaries, were horrified at the sacrilege, but Prager wasnâ€™t fazed. He came out of his office, signed as requested, and thanked the man.
Speaking of formality, formal calls had not gone completely out of style in 1948. One spring Sunday my wife Thea, year-old daughter Sue, and I all dressed in appropriate finery and set out for the Pragerâ€™s house. In our anxiety not to be late we appeared at the door about 15 minutes before the agreed-upon hour of 2 p.m. Professor Prager was ready for us, but Mrs. Prager was doing some last-minute things in the kitchen. (This was a lesson to us not to be early for social calls!)
Now, many people have mentioned that William Prager was not noted for â€˜small-talkâ€™ but preferred to sit in comfortable silence for any length of time. However, after a minute or so he sensed that Theaâ€™s efforts to start a conversation were becoming desperate. So he picked up Sue and told us what a beautiful baby she was. I think we were all relieved when Ann Prager came in, and quickly put us at ease.
Apparently the event also made an impression on Bill. Twenty-some years later he was giving a talk at Washington University in St. Louis where Sue was a graduate student. When she introduced herself after the talk, he seemed very pleased as he reminded her of the day heâ€™d held her in his lap.
When I left Brown in August 1949 we began a lengthy correspondence over the book we were writing. His first letter began â€˜Dear Hodgeâ€™ and was signed â€˜W. Prager.â€™ I responded with â€˜Dear Professor Pragerâ€™ and signed â€˜Phil.â€™ He immediately switched to â€˜Dear Philâ€™ and in letters of September 21 and October 3, signed himself â€˜Bill.â€™ When it happened twice I assumed he meant it, and from then on we were â€˜Philâ€™ and â€˜Billâ€™ to each other.
Let me tell you about our book (Prager and Hodge, 1951). To the mechanics community it says a lot about plasticity; to me it says a lot about William Prager.
In 1948 the Office of Naval Research asked Prager to prepare a survey report on the status of plasticity, and he assigned the job to me. It was a typical professorâ€“student relationship: heâ€™d say generally what should be in a chapter, Iâ€™d write a draft, heâ€™d red-pencil it all over, Iâ€™d write another draft, and eventually weâ€™d converge.
Chapter 9 started out with a typical history. I submitted a first draft. Prager suggested numerous changes, corrections, and additions, and he also completely rewrote the introductory paragraph. By the time I responded to his ideas the manuscript was a mess so I recopied it all, in my own handwriting â€” including the opening paragraph exactly as he had written it. Draft 2 was returned with several further changes, but on the first page Prager had written only â€˜An excellent first paragraph.â€™ I reread that paragraph the other day; it still sounds good!
After many months, eleven chapters containing 396 pages were issued as GDAM Report A11-S2: â€˜An Introduction to the Mathematical Theory of Perfectly Plastic Solids,â€™ by P.G. Hodge, Jr. Period. Prager insisted that only my name belonged on the cover and that there should not even be an acknowledgement page.
As we neared the final chapters, Prager, ONR, and John Wiley decided that the material should have the wider distribution of a published book. Prager completely rewrote what I had done, and showed it to me for suggestions. Here was I, with the ink still wet on my Ph.D. diploma, telling William Prager how to improve his writing! I may have suggested a couple of things to be included, possibly clarified a mathematical point or two, and spotted various typographical errors. I did prepare the problems and the index, but it would be exaggerating to say that ten percent of the final book was mine. But Prager insisted that we share equally in the infinitesimal royalties. In fact, he sent the manuscript in as â€˜Hodge and Prager,â€™ and only agreed to have his name first when Wiley pointed out it might sell better that way!
Even though I left Brown to go to UCLA in 1949, my relation with Bill Prager continued to grow. He was always willing to make suggestions about my work, and he also helped me in other ways. I donâ€™t think the words had been invented then, but William Prager was both my â€˜mentorâ€™ and my â€˜role model.â€™
California had a state law that required all state-employed professors to swear that they didnâ€™t belong to any subversive organization. Now, although I had once voted for Norman Thomas, I had never joined anything more subversive than the Boy Scouts, so I could sign the oath without fear of perjury. Still, I wasnâ€™t happy with the implications of the requirement. I visited Brown while I was still mulling over what, if anything I should do. Not only did Prager talk to me at length about the subject, but he arranged an appointment for me with Brownâ€™s president, Henry Wriston, to hear his views.
William Prager is, of course, as famous in Europe as in the United States. One of the few real regrets in my life is that I did not go to the 1952 International Congress of Theoretical and Applied Mechanics in Istanbul. Bill had offered to show me around the city â€” and who was better qualified? â€” but with a salary of $4,600, two children and a third on the way, and no contract support, I didnâ€™t go. I should have.
However, I did go and present a paper at the 1956 Congress in Brussels. I sat down next to Bill after my talk and a Frenchman got up. Judging from his gestures and rapid French, he was irate about something, but darned if I knew what. Prager leaned over and explained that the Frenchman wasnâ€™t criticizing my paper but complaining that it had gotten a better billing than his own had. When Bill, whoâ€™d been a member of the papers committee, asked me if Iâ€™d like him to respond, I murmured a heartfelt â€˜Thank you.â€™
A week earlier, also in Brussels, Prager and I had both attended an AGARD meeting, chaired by von Karman. This meeting was held in English or French with simulcast translation available for the other language. Prager, of course, spoke four languages including French and English in his own inimitable fashion. Von Karmanâ€™s introductory remarks were equally divided between the two languages, and Prager kept his earphones on the whole time, whispering to me, â€˜Iâ€™m letting the translator do the work.â€™
Iâ€™m not quite sure how it happened, but once long ago in Chicago I took Bill to Minskyâ€™s Burlesque â€” for a matinee, yet! As we left, he said, â€˜Sometime I must take you to the Folies BergÃ¨re.â€™ And in 1960 he did. I had to admit that in Paris the visible flesh was much more artistically presented.
But my chief memory of that evening was near the end of the show when the attractive mistress of ceremonies called on a gentleman from the audience to join her on the stage. Most of the audience was highly amused as she asked the man personal questions, kissed him, and made suggestive remarks and gestures, but Prager turned to me and said in a voice which conveyed absolute horror and utter disbelief, â€˜The young man seems to be enjoying it!â€™
When he was 60, Prager and several other people left Brown, and two years later he accepted a position at the University of California, San Diego. He went with promises of great support, many of which did not materialize. I visited him there in 1966, and he confessed he was somewhat frustrated. He told me, â€˜Older people are supposed to move more slowly and be more patient. I find I am less patient because I realize I have less time to get things done.â€™
William Prager visited Minneapolis on October 26, 1979, less than six months before he died. His colloquium lecture that afternoon was typical Prager: a profound idea in minimum-weight design, clearly presented without obfuscating mathematical detail, and applied to a trivial example to bring out its essential quality. That evening a group of six of us went to dinner â€” Bill, his son Stephen, Thea and I, and a young couple from our department. Bill seemed to really enjoy the evening with family, old friends, and new friends. Somehow it conveyed a perfect balance and a sense of continuity.
I didnâ€™t know, of course, that it would be the last time Iâ€™d see him, but I couldnâ€™t ask for a better last memory of a great man and a good friend.
Anon, (1968) â€˜Dr. Willi Prager: Applied mathâ€™s clean desk man,â€™ Brown Alumni Bulletin, December.
Barry, J. (1982) â€˜Gentlemen under the Elms,â€™ Brown Alumni Monthly, Brown University, Providence.
Drucker, D.C. (1973) â€˜Prefaceâ€™ (to special issue, edited by A.C. Pipkin), SIAM Journal of Applied Math, Â 25, 3.
Paul, B., and Hodge, P.G. Jr. (1963) â€˜Presentation of Timoshenko Medal to Professor William Prager,â€™ Â Â Applied Mechanics Division News, ASME, New York.
Prager, W. (1979) Reply,â€™ FENOMECH â€™78 Special Banquet, North-Holland, Amsterdam.
Prager, W. and Hodge, P.G. Jr. (1951) Theory of Perfectly Plastic Solids, John Wiley, New York.
Rice, James R. (1979) â€˜Laudatio,â€™ FENOMECH â€™78 Special Banquet, North-Holland, Amsterdam.