Amazing Teachers I
Our oldest daughter started her senior year in high school with a list of books given to the entire class by the English teacher. These books were not to be discussed formally because some parents might not approve. Reading them was not encouraged. It was a short list. Among others, I remember “Catch Twenty-two” and “Lysistrata”, the Greek play in which the women abolished war by withholding sex until their men stopped fighting. The teacher kept her word and never mentioned any of the books on the list, the students frequently brought up points from these books in class discussions of Shakespeare, “The Tale of Two Cities” and other books on the curriculum. Surely at least some of the students benefited from this extra learning about the breadth of material available in literature.
Our youngest daughter was home schooled from age 9 to 11 while we were in Afghanistan. What she and her sister, 2 years her senior, learned around the neighborhood was much more interesting than book learning, so they got that out of the way in part of the morning. A side effect was unnaturally efficient study habits. Winifred was quite articulate and told the junior high, to which she returned, when she thought they were wasting her time. Many of her classmates greatly disliked gym and were amazed when she was excused with no medical or parental excuse and with no specific request. The culmination occurred when she insisted that a pop quiz on the rules of speedball had nothing to do with physical fitness.
Her social studies teacher in high school redeemed her from academic oblivion by finding out what she was interested in, ecology and the environment. After several months of extra reading at his suggestion he gave her the assignment to teach the unit about the environment to all the sections of his freshman social studies classes. And she willingly did it at the appropriate time of year throughout her high school career, even returning during spring break during her first year in college.
Back to academic oblivion: She has a bachelor’s degree in engineering.
Amazing Teachers III (the ice cream cone theorem)
C. E. Palmer taught me mathematics from 8th grade through high school. I never found out what the C. E. was for, but I learned a great deal about what math is for.
Mr. Palmer always had extra credit questions on our tests and quizzes. These questions had not been part of the curriculum but were vaguely related to what was being studied. His sporting proposition was that if you got some of that difficult stuff right, that compensated totally for stupid numerical errors in the main part of the exam. As a matter of fact if you did only the main part and got it all correct, you still got 100 for a grade.
Needless to say I looked forward to these extra credit questions (some of them might have been tailor made for me, a possibility recently divined by retrospectoscope). One of these extra credit items I still remember because I worked on it for several months and obtained a partial solution, which impressed Mr. Palmer. Much later I learned that this particular problem was a classic unsolved problem in mathematics posed by Fermat 300 years before. It is called Fermat’s last theorem because it was discovered after his death written in the margin of a book with the intriguing comment that he had an elegant and simple proof for it. The problem is very simply stated: Expressions in the form ax +bx =cx have no Diophantine (only integers permitted) solutions for values of x greater than 2. Incidentally Fermat’s last theorem was proven within the last 10 years. It took the experts several years to decide that the proof was complete and valid, all 99 pages of it. We may never know whether Fermat really did have an elegant and simple proof. Mr. Palmer was a straight shooter. I am convinced that if one of us had come up with a proof, he would have gone public in our behalf and the individual would have gotten a bye to M.I.T.
But my most memorable encounter with Mr. Palmer occurred when we were studying conic sections in algebra (circles, ellipses, parabolas, and hyperbolas). They are called conic sections because they are the only curves that can be formed by a plane cutting a cone. However in algebra they are defined by quadratic equations, equations containing x2 instead of just plain x. I asked ,”How do we know that the geometrical and algebraic definitions result in exactly the same shapes? There might be subtle differences” Mr. Palmer thought rather briefly and replied, “That is a very good question, and I don’t know the answer.” The great lesson that I learned from this was that an authority figure’s reliability is enhanced when he promptly and forthrightly states that he doesn’t know, a much bigger lesson than the details of the example. I was fortunate to learn this at such a young age..
About 10 years later while browsing in the library of the AeroMed Lab at Wright-Patterson Air Force Base I stumbled on proof that these curves are identical in a book “What is Mathematics” by A. J. Courant of the University of Chicago. If you ask me about it at a party where they have paper napkins, I will show you the proof. Then you will understand why it is called the ice cream cone theorem, a factoid gleaned from a patient. The theorem is remarkably simple, but it wasn’t discovered until 1860- something. I took the proof to Mr. Palmer, who was still teaching. He remembered the occasion from 10 years before and was especially grateful for my insight that he had taught me something much more important for the rest of my career than mathematics.
William Meldrum PhD. was the head of the chemistry department at Haverford College when I attended in the early 1940s. He himself taught the freshman course for those of us who had taken chemistry in high school. I well remember the following points from his first lecture. 1) Significant figures: When measurements are multiplied or divided, strings of numbers may be created which have no physical significance. He illustrated the point by showing us how to multiply and divide without even creating the meaningless decimal places. (this was in the days of slide rules before pocket calculators). He also showed how taking the difference between large numbers destroys significant figures. This has been part of my scientific armamentarium ever since. 2) “There will be no demerits for dirty lab notebooks! Copying them can only introduce errors.” This was eminently sensible to me. I had resented this “wheel-spinning” activity in high school.
Theodore William Richards, a graduate of Haverford College in 1885, had won the Nobel Prize for Chemistry in 1914 for his determination of the atomic weights of 30 of the chemical elements to six and seven significant figures including the fact that the atomic weight of lead had values of about 206, 207, and 208 depending on from which of three ores the lead was smelted. When Dr. Richards was asked for his interpretation of this, he replied “I do good work. These were the values I obtained. I have no further explanation.” The concept of isotopes had not been conceived until a few years later when radioactivity was discovered revealing that primordial lead and lead as a radioactive decay product of thorium or uranium have three different atomic weights with one and two extra neutrons in an atom of the thorium and uranium derived lead compared to lead which had been in existence since before the formation of our solar system. Dr. Meldrum pointed out what a cogent example this was of intellectual honesty.
In honor of Theodore William Richards those of us who took Dr. Meldrum’s course in inorganic quantitative analysis were asked to recapitulate the details required for such meticulously accurate weighing. Two of these details were calibrating the weights for our analytical balances instead of taking the weight manufacture’s word for the values, and correcting for the buoyancy of air which varies with barometric pressure and humidity. It was a privilege to be taken to the fringes of knowledge and technique in an undergraduate (sophomore) course.
George Hoyt Whipple, M.D., Dean of The University of Rochester Medical School (New York) for many decades surrounding my graduation in 1946, instantly recognized any student or former student of his and knew a surprising amount of detail about each of us. We knew he was special from his introductory session for new students. He started out by telling us that the school had selected 65 of us from 1200 applicants that year and all should do well. Specifically he said we were fellow scholars cooperating in learning. There should be no destructive competition because there was no such thing at Rochester.
To dramatize the point he said we would be given no grades, but the office would keep grades in case of the need to transfer to another school. Twice during the first two years the final exam in a course was canceled because we had all mastered the material. So why waste everybody’s time with an exam? And the faculty did know us all very well from our laboratory sessions, so we had no reason to doubt their judgment regardless of any conflict of interest. Only one student flunked out of the seven classes that were present during my years there.
The introductory session had a heavy emphasis on the health of students with substantial contributions from the school, so we could realistically be expected to follow the advice. For example the school had a subsidized cafeteria to promote a healthy diet. Of course there was no compulsion to patronize it. Simply stated it was the best deal in town both for gustatory and financial reasons. Also we had Tuesday and Thursday afternoons off for athletic activities. There were squash, handball, basketball courts and other gymnasium equipment for the exclusive use of medical students. Most of us became hooked on physical fitness. Real “bang or the buck” for the school, since we have remained healthy and active longer than most people, increasing the value of the university’s investment in our education.
George Whipple was a pathologist. His course was like none I have heard of from colleagues trained in many schools. We were expected to do six autopsies, under supervision of course, not just be there but do all the work. Decades later when I was willing to help out doing autopsies in small town funeral homes, my colleagues have been surprised that I had not had more training than the sophomore medical school course in pathology. And every Wednesday at 11 AM we all put on rubber gloves to feel and cut the abnormal organs available from the previous week. There was nothing armchair about Dr. Whipple’s course.
Dr. Whipple had some human foibles. Psychiatry was an elective course for seniors. I remember on occasion being the only student to show up for a scheduled session. When Dean Whipple retired, some committee wasted no time hiring a world famous psychiatrist from Cincinnati. And as a fulltime faculty member, I hasten to add.
I was not aware of another foible of his until after graduation. He had taught us that gallstones were quite likely to be big trouble on an emergency basis, and that all reasonably healthy people known to have gallstones should have an elective removal of their gallbladder. This foible came to light when he had an emergency cholecystectomy in New York City where he had been attending a meeting. Confidentiality has its limits or all graduates would not have found this out rather promptly. George Whipple probably sheepishly “came clean” by suggesting that the truth be spread among his friends: He had known about his gallstones for years.
This has been a very incomplete eulogy of George Whipple neglecting many more spectacular accomplishments such as a Nobel Prize. I am sure he would agree with my emphasis of his influence on almost countless students. I am also quite confident that he would be enthusiastic about recent advances in psychiatry.
John A. Frantz, M.D.
July 29 to October 23, 2002
Summary of Amazing Teachers I through V
Three of five of these episodes involved the beginning of a course of study or the beginning of an entire career. Parents and other teachers have opportunities to say uniquely memorable things on such occasions