It is rather obvious but it is helpful to remind ourselves periodically that explanations only go so deep before hitting a wall, as Emmett explains:
“When we make the statement hedged about with so many qualifications it might be argued that we are making it a necessary statement by putting the necessity in; that we are saying in effect that if the wire is of such a kind that the other end will move when I pull this end, then if nothing happens to prevent it going so the other end will move when I pull this end, then if nothing happens to prevent it doing so the other end will move when I pull this. “We can couch the statement in such a form that it carries with it necessity or theoretical certainty, but the events which are being described are the events of experience. The fact that, usually, if we pull one end of a wire the other end moves is derived from experience and it is a fact which we come to see and absorb very early in life. As soon as we start touching or seeing material objects we experience events similar to this. And to the question Why it should happen no answer seems possible except that it just does. It is to events of this kind, the simplest sort of link in the chain of cause and effect, that all chains can be reduced and in terms of which they can all be explained. “When we are investigating or analysing we want to postpone for as long as possible the answer ‘It just does — it’s a fact of experience — look around you and see.’ And indeed one of the main points of an investigation, of asking a ‘why’ or ‘how’ question, is to discover more intermediate links. But the answer ‘It just does’ is bound to come eventually.”
– E.R. Emmett. Handbook of Logic. Totowa, NJ: Littlefield, Adams & Co, 1967.
Tony Leggett won the 2003 Nobel Prize in physics for his work on superfluid helium-3. Rebecca Tan interviewed him during his visit to Singapore last month:
Tan: “You took a rather unusual path to a career in physics, doing your first undergraduate degree at Oxford in classic philosophy, known colloquially as the Greats. If you could go back in time, what career advice would you give to your 17-year-old self?”
Leggett: “Do the same, I have no regrets at all. Had I gone into physics initially, I would have missed the enormous intellectual benefits I would have gotten out of my Greats education.”
– R. Tan. “A Word to Young Physicists in Asia.” Asian Scientist (2 Feb 2015) [link].
Comment: Unfortunately the world is different now. Leggett describes in this interview how he was able to go into physics based on one individual seeing some promise in him despite having almost zero background. This was at Oxford in 1959. It is very unlikely that anything like that could happen today.
The implicit question that arises from Leggett’s response is whether we are greatly losing out as a field by not letting more come into the fold from alternative backgrounds. Smart people with different perspectives make a better and more energetic community overall. Who wouldn’t want to see what Lionel Trilling, or Maya Angelou or Edward Said would have produced if they had become physicists?
Cicero in about 50 BCE explaining the heavens:
“The universe is held together by nine concentric spheres. The outermost sphere is heaven itself, and it includes and embraces all the rest. For it is the Supreme God in person, enclosing and comprehending everything that exists, that is to say all the stars which are fixed in the sky yet rotate upon their eternal courses. Within this outermost sphere are eight others. Seven of them contain the planets — a single one in each sphere, all moving in the contrary direction to the great movement of heaven itself. The next sphere to the outermost is occupied by the orb which people on earth name after Saturn. Below Saturn shines the brilliant light of Jupiter, which is benign and healthful to mankind. Then comes the star we call Mars, red and terrible to men upon earth.
“Next, almost midway between heaven and earth, blazes the Sun. He is the prince, lord and ruler of all the other worlds, the mind and guiding principle of the entire universe, so gigantic in size that everything, everywhere, is pervaded and drenched by his light. In attendance upon the Sun are Venus and Mercury, each in its own orbit; and the lowest sphere of all contains the Moon, which takes its light, as it revolves, from the rays of the sun. Above the Moon there is nothing which is not eternal, but beneath that level everything is mortal and transient (except only for the souls in human beings, which are a gift to mankind from the gods). For there below the Moon is the earth, the ninth and lowest of the spheres, lying at the centre of the universe. The earth remains fixed and without motion; all things are drawn to it, because the natural force of gravity pulls them down.”
– Cicero. “The Dream of Scipio,” in Cicero: On the Good Life. Penguin, 1971.
Comment: This passage was originally written by Cicero sometime between 54 BCE and 51 BCE. The “Dream of Scipio” is in the last volume of his six volume set entitled On the State. Much of those six volumes is lost to us now. However, we do know that the device Cicero used was that of a conversation between Scipio Africanus the younger and others. The passage above is Scipio Africanus the elder coming in a dream to explain the heavens. It is a nice summary of what Romans of antiquity knew and thought of astronomy and cosmology. Of course, Cicero got much of this from the Greeks, but he had to synthesize sources and make decisions, especially on the ordering of the planets and the Sun (he sided with Pythagorus over Plato). Presumably he consulted with others as well, and it is fair to say that this is likely to be the Roman view of the cosmos in approximately 50 BCE.
“Atlas bearing the heavens” http://www.aip.org
“In three studies, we found that students who took notes on laptops performed worse on conceptual questions than students who took notes longhand. We show that whereas taking more notes can be beneficial, laptop note takers’ tendency to transcript lectures verbatim rather than processing information and reframing it in their own words is detrimental to learning.”
– P.A. Mueller, D.M. Oppenheimer. “The Pen is Mightier Than the Keyboard: Advantages of Longhand Over Laptop Note Taking,” Psychological Science vol. 25, 1159-1168 (2014) [link].
Comment: The implication is that the slowness of writing requires the brain to process lots of information into a smaller number of words that the student must come up with him/herself, thereby requiring more engagement with the material while being presented. Makes sense to me. It should also be noted that this is a study about today’s students who are much more used to the computer than to writing. The results would be obvious for people of my age, who grew up with more longhand writing, but I presume it was less obvious to researchers that the result would stand for the very young. I hope that means spiral ring notebooks will be around forever.
Robert Graves channeling the 12-year-old future Roman emperor Claudius describing his lessons on writing and communicating effectively:
“Athenodorus told me [Claudius], the very first day of his tutorship, that he proposed to teach me not facts which I could pick up anywhere for myself, but the proper presentation of facts. And this he did. One day, for example, he asked me, kindly enough, why I was so excited; I seemed unable to concentrate on my task. I told him that I had just seen a huge draft of recruits parading on Mars Field under Augustus’s inspection before being sent off to Germany, where war had recently broken out again.
“‘Well,’ said Athenodorus, still in the same kindly voice, ‘since this is so much on your mind that you can’t appreciate the beauties of Hesiod, Hesiod can wait until tomorrow. After all, he’s waited seven hundred years or more, so he won’t grudge us another day. And meanwhile, suppose you were to sit down and take your tablets and write me a letter, a short account of all that you saw on Mars Field; as if I had been five years absent from Rome and you were sending me a letter across the sea, say to my home in Tarsus. That would keep your restless hands employed and be good practice too.’
“So I gladly scribbled away on the wax, and then we read the letter through for faults of spelling and composition. I was forced to admit that I had told both too little and too much, and had also put my facts in the wrong order. The passage describing the lamentations of the mothers and sweethearts of the young soldiers, and how the crowd rushed to the bridgehead for a final cheer of the departing column, should have come last, not first. And I need not have mentioned that the cavalry had horses; people took that for granted. And I had twice put in the incident of Augustus’s charger stumbling; once was enough if the horse only stumbled once. And what Postumus had told me, as we were going home, about the religious practices of the Jews, was interesting, but did not belong here because the recruits were Italians, not Jews. Besides at Tarsus he would probably have more opportunities of studying Jewish customs than Postumus had at Rome. On the other hand, I had not mentioned several things that he would have been interested to hear – how many recruits there were in the parade, how far advanced their military training was, to what garrison town they were being sent, whether they looked glad or sorry to go, what Augustus said to them in his speech.
“Three days later Athenodorus made me write out a description of a brawl between a sailor and a clothes dealer which we had watched together that day as we were walking in the rag-market; and I did much better. He first applied this discipline to my writing, then to my declamations, and finally to my general conversation with him. He took endless pains with me, and gradually I grew less scatter-brained, for he never let any careless, irrelevant, or inexact phrase of mine pass without comment.”
– Robert Graves. I, Claudius. Penguin Books: London, 1986.
Comment: These are very good lessons on writing scientific papers as well. Among the writing sins implied above, repetition and getting side-tracked off the main argument are perhaps scientists’ biggest writing sins. However, repetition is often viewed as a good technique to emphasize the main points of the paper. Claudius, or rather Robert Graves, would disagree.
BICEP2/Keck and Planck joint analysis casts doubts on detection of gravitational radiation from inflation
From the conclusions section of joint analysis paper released last night by the BICEP2/Keck Array and Planck collaborations:
“The final result is expressed as a likelihood curve for r, and yields an upper limit r < 0.12 at 95% confidence. The median limit in the lensed-ΛCDM+noise+dust simulations is r < 0.075. It is interesting to compare this latter to dust-free simulations using only BICEP2/Keck where the median limit is r < 0.03—the difference represents the limitation due to noise in the Planck maps, when marginalizing over dust. The r constraint curve peaks at r = 0.05 but disfavors zero only by a factor of 2.5. This is expected by chance 8% of the time, as confirmed in simulations of a dust-only model. We emphasize that this significance is too low to be interpreted as a detection of primordial B-modes.”
– P.A.R. et al. (BICEP2/Keck and Planck Collaborations), “A Joint Analysis of BICEP2/Keck Array and Planck Data.” January 30, 2015 [pdf].
Comment: Unfortunately the excitement was short lived over the earlier claim by the BICEP2 collaboration of gravitational radiation effects on early universe microwave background radiation. This was a prediction of inflation theories, although the size of the effect is unknown (“model dependent”). The current result suggests that galactic dust, which mimics the signal but is of little cosmological significance, was larger than BICEP2 originally thought. Non-zero B modes and inflation theories are not disproved by this new result quoted above, but the exciting prospect of finding evidence for them is not supported either.
The BBC has a short, popular article on this latest development here for those not technically versed on the subject but wish to know about this important result.
“What have we been doing all the centuries but trying to call God back to the mountain, or, failing that, raise a peep out of anything that isn’t us? What is the difference between a cathedral and a physics lab? Are they not both saying: Hello?”
– Annie Dillard. Teaching a Stone to Talk. Harper Perennial, 1992.
Comment: It is often remarked that physics and mathematics are dreary subjects that are impersonal and lonely. Humans are a social species, who crave contact, discussion, gossip, and interactions of all kinds with people. History, psychology, social science, medicine, and law are all fields that “make sense” from this perspective. What drives the physical scientist and the mathematician? It is a craving to discover the “other” — that which is greater and more enduring than us weak humans.
Abstract of my recently released notes:
“In this note integrals over spherical volumes with rotationally invariant densities are computed. Exploiting the rotational invariance, and using identities in the integration over Gaussian functions, the general n-dimensional integral is solved up to a one-dimensional integral over the radial coordinate. The volume of an n-sphere with unit radius is computed analytically in terms of the special function, and its scaling properties that depend on the number of dimensions are discussed. The geometric properties of n-cubes with volumes equal to that of their corresponding n-spheres are also derived. In particular, one finds that the length of the side of such an n-cube asymptotes to zero as n increases, whereas the longest straight line that can fit within the cube asymptotes to the constant value . Finally, integrals over power-law form factors are computed for finite and infinite radial extent.”
– J.D. Wells. “Rotationally invariant integrals of arbitrary dimensions” [pdf].
Comment: The above is the abstract to some notes I wrote for upper division undergraduates and beginning graduate students on rotationally invariant integrals. The undergraduate interest would mainly be in the integral dimension computations needed for many straightforward applications in mechanics and electricity and magnetism. Graduate students, who are already familiar with those results, would find more interesting the discussion for arbitrary fractional dimensions. These kinds of integrals are used, for example, in dimensionally regulating quantum field theory computations that are otherwise divergent.
Cicero channeling Pythagoras on the value of studying nature:
“Some of us are enslaved to glory, others to money. But there are also a few people who devote themselves wholly to the study of the universe, believing everything else to be trivial in comparison. These call themselves students of wisdom, in other words philosophers; and just as a festival attracts individuals of the finest type who just watch the proceedings without a thought of getting anything for themselves, so too, in life generally, the contemplation and study of nature are far superior to the whole range of other human activities.”
– Cicero, “Discussions at Tusculum”, in Cicero, On the Good Life. Penguin, 1971
Comment: It should be remarked that Cicero invokes Pythagoras here as getting it almost right, but later says that Socrates, whom Cicero deeply admired, had it right when he “took the initiative in summoning philosophy down from the heavens.” In the end, according to Cicero (On Divination, II), there is but one source of real happiness. It is the “proposition which brilliantly illuminates the entire field of philosophy — the proposition that moral goodness, by itself, is sufficient to make anyone happy.” Nonetheless, I’ve met many physicists who appear to agree more with Pythagoras than Cicero, and of course many who appear to agree with both. After all, the two are not incompatible.
Recently there has been much discussion about radically reforming university education. Many of these reforms advocate the elimination of the lecture. The Atlantic magazine profiled last August the upstart Minerva Project, which is a “university” predicating itself on no lectures. This is thought to be revolutionary and new to our times.
However, anybody who has been in the education business knows that these ideas and close variants of them have been talked about and tried and abandoned and tried again for many decades, if not centuries. My personal view is that social science researchers’ ability to quantify the value of a proper lecture may be severely lacking. But that discussion is for another time. Instead, what I wish to do is demonstrate how long-standing this debate is.
At the end of this post I give an early reference from 1957 of professors discussing the elimination of the lecture. It is written by Vladimir Nabokov in his novel Pnin. Nabokov of course is the famous writer of Lolita and other outstanding literary works. He also emigrated to the United States and taught at Wellesley College and Cornell for more than 18 years. Pnin is a semi-autobiographical account of a Russian emigré literature professor taking up a non-tenured teaching post in Waindell College in New York. Timofey Pnin is lonely, devoted to his scholarly work, frustrated with his lazy American students, and somewhat clueless about the political machinations around him. Toward the end of the book he throws the academic party of the decade at his college, only to be told after it by a colleague that he will be out of his job by the next year.
It is at this academic party that three university professors at Waindell college get into a discussion about their frustrations in educating students. Hagen ventures after a few drinks to tell his colleagues his view that the lecture should be eliminated. Instead “phonograph records” should be made available once and for all. Not too different than us saying today that a video should be made once and for all, and no more lecturing (“flipped classroom”). It degenerates into teasing hapless Timofey Pnin, the host of the party, by saying, “The world wants a machine not a Timofey.”
Clements is the voice of teaching orthodoxy and his style is to put his own strong words into someone else’s mouth (Tom) and to make jokes to lighten the discussion (“We could have Timofey televised”). He ends the discussion with a dismissive “sure, sure” when Tom protests and implies that there is something to Hagen’s ideas of eliminating the “old-fashioned lecture.”
Nabokov was surely familiar with such debates during his time as professor at Wellesley and Cornell in the 1940’s and 1950’s. It is the same debate we are having today, sixty years later. Whatever position you might have on this question, keep in mind that it is not a new debate, and there may be reasons why changes advocated by the Hagens of the world were not so quick coming.
Excerpt from chapter 6 of V. Nabokov’s Pnin, 1957 (character descriptions given in brackets):
At a still later stage of the party, certain rearrangements had again taken place. In a corner of the davenport, bored Clements [philosophy professor] was flipping through an album of Flemish Masterpieces that Victor [son of Pnin’s ex-wife] had been given by his mother and had left with Pnin [Timofey Pnin]. Joan [Clements’s wife] sat on a footstool, at her husband’s knee, a plate of grapes in the lap of her wide skirt, wondering when would it be time to go without hurting Timofey’s feelings.
The others were listening to Hagen [German professor] discussing modern education:
“You may laugh,” he said, casting a sharp glance at Clements—who shook his head, denying the charge, and then passed the album to Joan, pointing out something in it that had suddenly provoked his glee.
“You may laugh, but I affirm that the only way to escape from the morass—just a drop, Timofey: that will do—is to lock up the student in a soundproof cell and eliminate the lecture room.”
“Yes, that’s it,” said Joan to her husband under her breath, handing the album back to him.
“I am glad you agree, Joan,” continued Hagen. “However, I have been called an enfant terrible for expounding this theory, and perhaps you will not go on agreeing so easily when you hear me out. Phonograph records on every possible subject will be at the isolated student’s disposal …”
“But the personality of the lecturer,” said Margaret Thayer [wife of English professor Roy Thayer]. “Surely that counts for something.”
“It does not!” shouted Hagen. “That is the tragedy! Who, for example, wants him”—he pointed to radiant Pnin—“who wants his personality? Nobody! They will reject Timofey’s wonderful personality without a quaver. The world wants a machine, not a Timofey.”
“One could have Timofey televised,” said Clements.
“Oh, I would love that,” said Joan, beaming at her host, and Betty nodded vigorously. Pnin bowed deeply to them with an “I-am-disarmed” spreading of both hands.
“And what do you think of my controversial plan?” asked Hagen of Thomas [anthropology professor].
“I can tell you what Tom thinks,” said Clements, still contemplating the same picture in the book that lay open on his knees. “Tom thinks that the best method of teaching anything is to rely on discussion in class, which means letting twenty young blockheads and two cocky neurotics discuss for fifty minutes something that neither their teacher nor they know. Now, for the last three months,” he went on, without any logical transition, “I have been looking for this picture, and here it is. The publisher of my new book on the Philosophy of Gesture wants a portrait of me, and Joan and I knew we had seen somewhere a stunning likeness by an Old Master but could not even recall his period. Well, here it is, here it is. The only retouching needed would be the addition of a sport shirt and the deletion of this warrior’s hand.”
“I must really protest,” began Thomas.
Clements passed the open book to Margaret Thayer, and she burst out laughing.
“I must protest, Laurence [Clements],” said Tom. “A relaxed discussion in an atmosphere of broad generalizations is a more realistic approach to education than the old-fashioned formal lecture.”
“Sure, sure,” said Clements.