FROM THE HISTORY OF PHYSICS

MEMORIES OF PROFESSOR P. EHRENFEST*)

G. E. Uhlenbeck

I have been accorded the great honor of being awarded the Oersted Medal for achievements in the teaching of physics. It is very gratifying—and it came to me as a pleasant surprise—to receive recognition for one’s everyday work. This is especially pleasant when one is engaged in teaching, which is a rather “abstract” occupation, consisting only in the fact that you tell something, and in which one so rarely has occasion to experience the feeling that one has succeeded in doing something substantial.

Naturally, in such cases the recipient of an award tries to understand what exactly he has managed to do so successfully, especially if he, like most of his colleagues—teachers of physics—has studied at no pedagogical institution and has not even attended lectures on pedagogy, so that in any case he does not officially know, and probably never did know, how one ought to teach. I say specifically “officially,” because personally I distinctly feel the circumstance that I was taught how to teach—primarily by example, but also together with certain instructions. The man who taught me was the late Paul Ehrenfest, professor at Leiden University in Holland, who, in my opinion, was a truly outstanding pedagogue. Therefore it seems to me quite appropriate at this meeting to try to tell about some of his methods and about the very characteristic devices he used in teaching students.

1. Allow me to begin with the technique of giving lectures. I can still hear Ehrenfest’s exclamations, pronounced in the mixed German-Dutch language typical of him and addressed to a student appearing before the audience:

— Please begin writing in the upper left-hand corner of the blackboard!

— Please do not erase until your listeners have seen what is written!

— Please do not speak with your face buried in the blackboard, etc.

All these may perhaps be rather trivial things, but one need only attend a few meetings of the American Physical Society to be convinced how often these simple rules are violated. But, of course, these rules concern only the purely external side of lecture technique. As for the manner of presenting the very subject matter of lectures, here we learned chiefly from Ehrenfest’s own lectures. It is not easy to say at once what made them so magnificent. Partly, without doubt, it was their clarity. But that was by no means all. Lorentz, for example,

*) Am. Journ. Phys. 24, 431 (1956). Address delivered by G. E. Uhlenbeck on February 2, 1956, before the American Association of Physics Teachers on the occasion of the presentation to him of the Oersted Medal for outstanding achievements in the teaching of physics.

also distinguished himself by the remarkable clarity of his lectures, but his lectures were often so “smooth” that it was very difficult to grasp the center of gravity of the whole argument. Therefore, at the end of a lecture one could often lose the thread and forget what all this was being done for. This never happened in Ehrenfest’s lectures. He always emphasized himself, and demanded that others emphasize, the der springende Punkt (the decisive point) of the argument. He always asked: “Was ist der Witz?” (What is the point here?) or would say: “Why do you mention this here? Does this seem amusing to you, or is it really essential?” As a result of this approach, I still remember the primary causes of many difficulties, especially in questions of statistical mechanics, with which one had to deal in those days and with which one often has to deal even today.

The famous Ehrenfest clarity of exposition should not be confused with rigor. Indeed, he rarely gave a strict formal proof. But he was always able to give an all-embracing survey of the subject of exposition, clearly singling out the questions already settled and the questions that remained open. Ehrenfest liked to repeat: first explain, and then prove. And he always began by sketching a proof or making some assertion plausible to such an extent that the listeners could grasp it “on their fingers.” He was always resourceful and ingenious in inventing simple models that helped to clarify the essential features of the argument. (Recall the “tree in the wind” model for explaining the H-theorem ¹ and the model for explaining the nature of irreversible processes ².)

He liked to say that anyone who can obtain, by a logical route from given premises, only the necessary result does not understand the inference itself. For in that case “he can dance only on one leg.” One should always see all the connections of a given theorem, so that the successive mastery of the subject is very much like untangling nets.

He liked to repeat that all the most profound conceptions inevitably turn out to be frivolous, and that “jede Konsequenz führt zum Teufel.” (Every logical consistency leads to the devil.) But, of course, everyone must try to clarify the situation of things and must ask questions. Ehrenfest loved questions and often ended lectures or articles with a series of questions. Many of us remember one of Ehrenfest’s last articles, “Einige der Quantenmechanik Betreffende Erkundigungsfragen” ³, and in their time derived much from it and from the answers given in connection with it by Pauli ⁴.

1. Secondly, allow me to dwell somewhat on the course of study in Leiden as it was in the twenties. Students began attending Ehrenfest’s lectures several months after the first candidate’s examination. In the first year Ehrenfest expounded Maxwell’s theory and always concluded it with electron theory and a part of the theory of relativity. The second year was devoted to statistical mechanics, which ended with an exposition of the theory of the structure of the atom and quantum theory. The lectures took place three or four hours a week, and there were long intervals between them. Thus the scope of the exposition was much smaller than what is presented under present-day conditions. Ehrenfest never assigned and never invented problems; he simply did not believe in them. He considered valuable only those problems that naturally arise before the student himself. All attention was always concentrated on physical ideas and the logical structure of the theory. And I must say that, although, perhaps, we were not taught how to calculate, we firmly knew what the real problems of physics consisted in. It is difficult to describe how this was achieved. One

...one of the reasons undoubtedly lay in the absence of technical details. Only the foundations were examined carefully and systematically put into the students’ heads; in the remaining time Ehrenfest gave an astonishingly brief—so to speak, bird’s-eye—survey of all current news, with the most characteristic results and references, skillfully awakening the students’ interest. In my view, this is the best method of teaching a subject, considerably better than the strict, complete, and systematic exposition now accepted in our universities. As for me personally, even when teaching the most elementary physics courses I achieved the greatest success by combining the careful study of the foundations with conversations with students on topics that were not compulsory for them.

The second reason was the seminar, which was held throughout the year, every Tuesday evening. It resembled a priestly service. A student, once admitted to the seminar, was obliged to attend it without fail. Ehrenfest even checked attendance. This seminar was always the culminating point of the week. On first attending, it seemed very difficult to understand what was happening at the seminar, but very quickly a participant in the seminar grasped the “jargon” and in this way gained the possibility of at least an oral acquaintance with the newest research. The discussions were always encouraging in character and often proceeded very animatedly. It was always instructive (although sometimes not altogether pleasant, especially if you yourself were the speaker) to hear Ehrenfest summing up the discussion, and often the entire report as well, so that everyone, including the speaker, ultimately understood what all this was needed for.

1. In conclusion I should like to say a few words about what Ehrenfest did, probably, for the very main problem of education—namely, for the problem of preparing a student for independent research. He usually worked with only one student, and practically every day in the second half of the day. He discussed with this student either a problem on which he was working at the time, or a recent article in a periodical that he wanted to analyze in detail. The work progressed rapidly, and the blackboard was used. When there was no longer any room on the board, the main points were entered in notebooks. I personally became convinced that if at the beginning of such lessons everything was absorbed, if one may put it so, by the tips of one’s fingers, then by the end of the lesson you were already mortally exhausted. This happened especially because it was necessary to follow all the details; it was considered the gravest sin to say that you had understood some point when in fact this was not the case. This circumstance was always in the end discovered! The astonishing thing was that after some time the fatigue disappeared, and a year later you were already working on an equal footing. And gradually the suspicion began to creep into the student that he knew the subject even better than Ehrenfest. This moment meant that the student had stood on his own feet and had become a physicist. I tried to apply this method, to the extent to which I could apply it, in working with my own students, and I can confess that I was most satisfied when some of them told me that they experienced similar feelings while working with me, especially the feeling of extreme fatigue at the beginning of their training.

I think that Ehrenfest’s method proceeds from the fact that one of the basic requirements for a researcher is belief in oneself or, if you like, courage*). And Ehrenfest’s method, the only one of all those known to me,

*) This applies even to such outstanding scientists as E. Fermi. In an article dedicated to Fermi’s memory,^5 B. Pontecorvo relates that Fermi acquired confidence in himself precisely during his stay in Leiden, thanks to his association with Ehrenfest. Fermi considered that this was the most valuable acquisition for him during his study abroad.

allows a student to acquire this quality. It is very revealing that at a certain moment the learner feels himself at least the equal of his teacher! Ehrenfest did not say in vain: “Weshalb habe ich solche gute studenten? Weil ich so dumm bin.” (“Why do I have such good students? Because I myself am not very clever.”)

To follow his rules precisely, one must not only possess his didactic abilities, but also maintain the one-to-one student–teacher ratio that he practiced—a rule from which we are departing more and more at the present time. I do not presume to say what Ehrenfest would have advised in the face of today’s crisis in education. I would like to have had the opportunity to ask him about it. But there is no doubt that his advice would not have been a rejection or even a weakening of the student’s personal relationship with his teacher. In his time the problem of mass scientific education did not exist, or at least it was of secondary importance. If he suddenly had a significant number of students, he tried—and usually succeeded—in assigning to each of them responsibility for the instruction of those who were less prepared. He organized, for example, a physics club that bore the by no means accidental name “The Leiden jar” (“the Leiden jar”), where the best-prepared students conducted seminars, as far as possible in the same style in which he himself conducted seminars for them. The leaders of such seminars were required to inform him of the appearance of capable students.

Perhaps the hope that something similar can be carried out in our colleges is a pure utopia. However, I think that all this fully deserved mention, since, as I have already noted, Ehrenfest’s individual method is unique of its kind.

References

1. P. and T. Ehrenfest, Enz. der Math. Wiss. IV, Art. 32, p. 19.
2. P. and T. Ehrenfest, Phys. Z. 8, 311 (1907).
3. P. Ehrenfest, Zs. Phys. 78, 555 (1932).
4. W. Pauli, Zs. Phys. 80, 763 (1933).
5. B. Pontecorvo, UFN 57, 349 (1955).