Profs and Prophets, Profits and Proofs

An afternoon visit to Cambridge University
September 9, 2010

Roy Lisker

A Riddle: Why do the residents of Cambridge, England refer to themselves as "Cantabridgians"?

Answer: It refers to their tendencies to be long-winded and pedantic. They "can't abridge"!

The Cam River

  London, 9 AM : I started out from London on a clear morning , bracing, not chilly. It had been that way since my arrival in England the week before. Showers would come in the late afternoons around 3 and last for about an hour. It was a welcome change in climate: in the 4 days I'd spent in Boston before boarding the plane, the mean temperature had hovered between 90 and 95 F (31 to 35 C).

  The early morning train from London's King's Cross station dropped me off at Cambridge Station at 10:54 AM (Very precisely, as are all announcements of time and place on British Rail.) From a telephone on the quai I put in a call to Dr. Robert Anderson.

  Robert Anderson was the director of the British Museum between 1992 and 2002 . In addition to his varied career as a museum curator he is also an archaeologist and a specialist in English science in the 18th century. The latter was a great help in finding common ground for our conversations : I know nothing nothing about the administration of museums, but I do know something about 18th century science, if for no other reason than my growing up in Philadelphia.

  Anderson instructed me to take a taxi from the train station to the Fitzwilliam Museum, then wait for him on the terrace under the Greek columns at the main entrance . It turned out to be a 5-pound taxi fare for a very short ride!

  Anderson arrived in about 15 minutes. Decades in sedentary occupations have given him the appearance and manner of a jovial curator: pudgy, slow-moving, very much the academic establishment.

Dr. Robert Anderson

  Establishments aren't my strong suit. When I described him to a friend he was amazed that we didn't immediately begin shouting at each other! Yet in fact I found him very likeable, intelligent, generous, the ideal host and guide through the university city of Cambridge , itself a kind of outdoor museum or "theme park" of universities!

  Sitting over tea and pastry in the cafeteria of the Fitzwilliam Museum we embarked on a conversation covering 18th century medicine in Edinburg and Vienna , Joseph Priestley in Pennsylvania , the life and work of the chemist Joseph Black, and other appropriately arcane topics.

  I'd always believed that Joseph Priestley had emigrated in 1794 to my home town of Philadelphia. Not quite: Priestley lived in Northumberland, a town to the north of the city. It still exists today, although I'd never heard of it. We discussed the possibility that he may have lived there to escape the recurrent epidemics of Yellow Fever, compounded by the quackery of Benjamin Rush!

  Before leaving the Fitzwilliam Museum , Anderson asked me if there were any displays in its collection that I'd like to see. I mentioned the Impressionists. He remarked that the fondness of Americans for the Impressionists always amused him. Charitably I did not respond with the standard rap about the reputation of English painting . On the way to the small number of Impressionist paintings hanging in the Fitzwilliam we passed through a room filled with Madonnas painted in the Italian Renaissance. I commented that the choice of subjects may have been a bit simpler for artists when they were obliged to take their subjects from a single book. Anderson smiled: one has to learn, he pointed out, how to look for the subtle ways these artists got around such restrictions.

  Anderson is a natural-born tour guide. Who, other than a past director of the British Museum, could possibly be better, to lead one through the mossy meandering maze of mausoleums of mind, matter and money, that unique amalgam of artifacts and architecture that comprise the great, ancient, academic town of Cambridge in England !

This is the administration building of the university. Anderson was concerned that I not confuse the colleges with the university. The 31 colleges are independent; their administration is coordinated by the university. The colleges in Cambridge are not, in general, specialized. there are 3 colleges exclusively for women, and even one Methodist college.

  Anyone can get a full college education in English history merely by strolling about its 31 colleges, its immense library and university administration buildings, endowed from the 13th century by a succession of monarchs, clergy, academics and plutocrats. (And by viewers like you!)

  It is an enriching experience to stroll through and around the Cambridge colleges, revisiting historic events of civil wars, sectarian conflicts, monarchs and their reigns, changing styles in art and architecture, and, inevitably, the advance of science since the 17th century. In this regard the name of "Cambridge" blazes brilliantly around the world like a supernova, newly minted on that day on which Isaac Newton decided to take a rest from his alchemic researches by studying the discoveries of Copernicus, Galileo, Kepler , Descartes and other trouble-makers.

  Anderson led me through a row of colleges on Trumpington Street , the main thoroughfare, and down nearby abutting sidestreets: Peterhouse College , Pembroke College , St. Catherine's College and others.

Cloister. Robert Anderson in profile.

Our first stop was at Peterhouse College.

This tablet in memory of Godfrey Washington, grand-uncle of George Washington, hangs on a wall near the entrance to the chapel of Peterhouse College

  As we passed by the buildings of Corpus Christi College (under reconstruction), Anderson explained to me that it is considered one of the holiest sites in the Christian world. It is the repository of the manuscripts of the Gospels of St. Augustine, (not to be confused with the earlier St. Augustine of Hippo) the man who brought Christianity to England . They were sent to him by Pope Gregory in the 6th century.

  Before going onto Queens' College and the immense King's College,( founded by Henry VI in the 15th century and completed by Henry VIII in the 16th) , Anderson shunted us off onto a side street so that he could show me a wall plaque.

This plaque is on the wall of a pub where Crick and Watson proclaimed their male chauvinism monopoly on the discovery of the structure of DNA.

  "What about Rosalyn Franklin?", I asked. Anderson laughed: "She was down in London. " We made another stop a short distance to look at another plaque:

  This plaque locates the former site of the world renowned Cavendish laboratory. On it one can read tributes to J. J. Thompson and James Clerk Maxwell.

  Anderson continued to point out various colleges and landmarks until we came to the site of the building that had housed Isaac Newton's alchemic labs. The building itself was demolished long ago. All that remains is a bit of lawn, and, predictably, an apple tree.

This apple tree outside the walls of Trinity College was grown from a cutting taken from the original apple tree on Newton's farm. One can see that it has had its share of storms and rough weather. The holy aura that surrounds it does somewhat enhance the impression it makes. The story of the apple may just be a fiction. However it was told by Newton himself in his old age.

  Anderson related to me that a delegation of chemists had visited these grounds a few years ago to search for traces of the mercury, antimony and bismuth used by Newton in his alchemic experiments. The results were inconclusive.

  This excursion set me to thinking: although the colleges in Cambridge date back to the 13th century, the major faculties were established in the 15th and 16th centuries. Their founders were a fool, a tyrant, and a lecher: Henry VI, Richard III, Henry VIII. Was it not remarkable that such black-hearted, ignoble, odious people should have, all the same, recognized the growing importance of the new sciences coming out of Italy, then made provision for them by establishing institutions of research and learning? Was it not even more amazing, that from their beginnings, in the centuries of endless civil war lasting from the 15th through the middle of the 18th century, that these institutions would have served as the foundation for the richest treasurehouse of scientific discovery anywhere in the world?

King's College Chapel

  Queens' College (note spelling!) was founded by Margaret of Anjou, wife of Henry VI, then re-founded by Elizabeth Woodville, wife of Edward IV . Sculpted above the entrance one finds a pair of figures, part deer, part goat. Anderson told me that they're called "Yales". He'd often wondered if Yale University had gotten its name from these mythical beasts. The truth does not always make the best story: the founder of Yale was, of course, a man named Eli Yale.


  King's College took one hundred years to build and is still standing today. Close by stand some very modern structures of Selwyn College and Cripps Court. They look as if they were thrown together in 3 years and will be torn down in 30.

  Anderson walked with me over to his car and drove us to Clare College , where he is a fellow. Inside we walked up to the high cafeteria on the second floor.

  It was time to meet some honest-to-goodness Cambridge seers !

Intro: A short excursion into the history of mathematics at Cambridge

  It is one of the curiosities of scientific history that, from the time of Isaac Newton and well into the 20th century , Cambridge University has played a leading, even dominant role, in every science except Mathematics.

  One can go further: many of the modern sciences were invented here: Celestial Mechanics, Calculus and Geophysics, Evolution , Electro-magnetism, Statistical Mechanics , Atomic physics , Molecular Biology (Crick and Watson) . Even the word "scientist" was invented by a Cambridge don, William Whewell.

  There is no simple reason for this. The sordid and ludicrous quarrel between Newton and Leibniz over the invention of the calculus is often given as a reason for the isolation of England against the powerful development of mathematics on the Continent. It must also be noted that Göttingen, the most important center for mathematical research until the 1930's, was founded in 1734 by George Augustus in his function as the Elector of Hanover , while, as George II of England, he authorized large grants to the colleges of Cambridge and to its library. Nor should one overlook the charter granted by him to Columbia University in 1754. From King George II to George W. Bush...!

  Yet it appears that for many of the learned doctors in the Cambridge colleges, Mathematics was not regarded as a real science. This seems to have been the wilful whim of William Whewell himself!

(See Mathematical Visions: The Pursuit of Geometry in Victorian England, by Joan L. Richards, Academic Press, 1988)

  It was but a short step from that conclusion, to the strange view that since Geometry was a science, it could not be a branch of mathematics!

  Up to the beginning of the 19th century, Euclid's Elements appears to have been the cornerstone of a Cambridge education. Sticky controversies revolved, like the legs of exponential spirals, around the ontological nature of mathematical truth : is mathematics a "real" science like biology or physics, or do a certain absurd class of eccentrics merely jiggle their arbitrary axioms to see what they come up with?

  The "reality" of mathematics pivoted on the role in nature of the geometry described by Euclid's Elements. Thomas Huxley, notorious as the champion of evolution, supported the "arbitrariness" plank. At the other extreme, Lewis Carroll composed a 225 page play ("Euclid and his modern rivals", available for free download at Euclid and his modern rivals in defence of the assertion that Geometry is REAL, in the same way that potatoes in a potato field are real. He was defending not only mathematics, but Cambridge University.

  To my knowledge "Euclid and his modern rivals" has not yet been picked up by any producer on Broadway or London's West End; but short excerpts make for delightful reading. One sees the extraordinary transformation from the charming, witty, dreamy Lewis Carroll of the Alice books, into the dodgy, stodgy bird known as Charles L. Dodgson , bristling all over with pedantic feathers.

  Intermediate postures were maintained by James Sylvester and Arthur Cayley, the greatest British mathematicians of the 19th century. Although the "reality" of mathematics might not be so obvious as the shape of a building, they thought that it should still be included among the "real" sciences. It is fortunate for us that Sylvester brought this perspective with him when, in 1877, he set up the first mathematics research department in the US at Johns Hopkins University in Baltimore.

  A third opinion is familiar to us: "Although mathematics is just a higher version of Tic-Tac-Toe, it trains the mind marvelously." This view was defended by Whewell himself. It was hotly contested by others, who pointed to actively engaged mathematicians and remarked: "See how bent out of shape they all are!"

  Recall that this was an age when too much cerebration was deemed to be a cause of insanity, particularly when done by women. Before John Hamilton invented the chronometer in the 18th century, many stories circulated about people who'd gone insane from their obsession with the longitude question! The mathematical contributions of the gifted Mary Fairax Sommerville were suppressed until after she'd raised several children and gone through two marriages: her loving parents didn't want her to do damage to her fragile woman's brain!

  All in all, it appears that , until well into the 20th century, Cambridge was not a good place to either learn mathematics or do mathematical research. Yet , in this same period, Cambridge was phenomenal for physics, a subject in which the real reality of the things that are really there was rarely questioned, at least before the quantum theory came along.

  Aristotelian and Symbolic Logic fared better because they were classified under Philosophy. Fired up by the earnest intention of restoring some order to the hierarchies of knowledge, many attempts were made to nudge mathematics into philosophy. For a century or so the super-saturated air of Cambridge University rang with learned debates over why 2+2 = 4, that is to say the why of arithmetic as opposed to its use in calculation . It was "Much ado about Nothing" all over again ( Recall that the slow-witted Europeans had only picked up the pragmatic use of "zero" as a place holder from the Arabs only as late as the 15th century . ) The search for the why of mathematical ideas, as opposed to their what or the how, dominated mathematical thought a Cambridge University far more than anywhere else . Fundamentalist Hegelianism may have had a hand in these strange convolutions .

  Throughout the 19th century, mathematics at Cambridge University became thoroughly bolloxed up in arguments about its pure relationship, or lack thereof, to science, philosophy, geometry and the cosmos, with the end result that very little interesting mathematics - Arthur Cayley excepted - came out of Cambridge. That had to wait until the arrival of J.E. Littlewood, G.H. Hardy and S.I. Ramanujan (a life-saving injection from the land of Brahmagupta), and their work in number theory at the beginning of the 20th century.

  The definitive attempt to force mathematics into philosophy was made by Bertrand Russell and Alfred North Whitehead. They wrote a long and perplexing treatise, the Principia Mathematica , through which they attempted to prove that number, that is to say the key concept of mathematics, could be derived from Aristotelian Logic, enriched by some concepts by Frege.

  The project came to grief when Kurt Gödel proved that arithmetic could never be fully axiomatized. This didn't seem to have worried Russell very much. He only threw in the self-referencing towel when his prize disciple and nemesis, Ludwig Wittgenstein, convinced him that his work in logic was both void and devoid of content: devoid because Logic is a subject devoid of content, void because Gödel had rendered his work null and void.   Whereupon Russell stopped doing philosophy altogether and went into popular writing, telling the public why he wasn't a Christian, how to be happy in marriage, how to institute scientific eugenics, how China had always been ruled by benevolent artist/emperors like Augustus John and Lytton Stratchey, and why the barbarous Russians, rather than the civilized Germans, were the natural enemy in World War I. See Ferment Magazine Bertrand Russell

Michael Nedo and the Wittgenstein Archive

  I was well aware of these fixtures of the Russell-Wittgenstein contretemps before Dr. Robert Anderson placed me next to Michael Nedo at the dinner table in Clare Hall. Michael Nedo is the director of the Wittgenstein Archive at Cambridge University . His crowning achievement is the editing of 6 volumes of Ludwig Wittgenstein's writings. Before dedicating his life to the memory of the great Meta-Stoic, he'd been a mathematician, zoologist, and physicist working at the Max Planck Institute .

  The Wittgenstein Archive was originally established at the University of Tübingen, then transferred to Cambridge in 1978. Nedo has been at Cambridge since then , the first 10 years at Trinity College, currently with Clare College. He speaks excellent English with a strong German dialect (I did not ask him to pronounce "William Whewell!"). He looks very healthy and energetic, with the kind of bushy white hair and mustache that is a German stylistic cliché (Think of Albert Schweitzer) .

  I was placed by Nedo's left. To his right sat the sculptor Helaine Blumenfeld. Across from us sat a much younger scholar, close shaven and tall, a colleague of Nedo's from Berlin. I don't remember his name.

  When I'd met Anderson that morning, he asked me if I was a Museophile or a Museophobe . I replied that it depended on the museum. In the matter of Ludwig Wittgenstein however I am definitely a Wittgensteinophobe. I told Michael Nedo that there is a class of philosophers such that, once I've read their biographies (notably Descartes, Russell, Wittgenstein, Heidegger and Sartre) I lose all respect for and interest in their philosophy. My opinion of Wittgenstein was formed from a recent reading of his biography by Ray Monk .

  "Aha!" Nedo beamed, "But you see, sir, Monk is just a journalist, not a scholar (See Journalists and Scholars )

  " He writes for a publisher who just wants to make money from the public. That's why there are so many pointless pages in this book given over to Wittgenstein's alleged homosexuality, his attitudes towards his Jewishness, and so forth. Monk slanders philosophers because it sells his books."

  "Few major figures are so misunderstood as Wittgenstein. To take one example: he was interested in the foundations of mathematics all his life . His notebooks are filled with a wealth of insights on this subject. All earlier editions of his notebooks totally misrepresent this work. Previous editors have taken bits and pieces of Wittgenstein's writings, jumbled them all up, then published them like a jigsaw puzzle.

  "My editions of Wittgenstein correct this impression. They combine photographs of the actual pages of the notebooks, with transliterations of the texts and commentary. For the first time one can see how Wittgenstein's thought is worked out through the pages of his notebooks."

  Nedo and I concurred that Ray Monk's biographies tend to become more and more negative as they go along. His biography of Bertrand Russell took him ten years. I had the distinct impression that Monk had grown disgusted with his subject after the first 5. By the time he got to Volume 2, he had nothing good to say about him. Nedo promised to send me excerpts from his editions of Wittgenstein's writings which will correct my false judgement of him (Nedo has a reputation for being absent-minded. He's never sent them.)

  Somehow we got onto the subject of modern-day Vienna. Here, Michael Nedo became himself a kind of Ray Monk - he had just about nothing good to say about the fabled city of music !

On Music : "Wittgenstein's brother Paul was a terrible pianist. The family helped him in his career because they didn't want to hurt his feelings."

  "What about the Concerto for the Left Hand that Ravel wrote for him after he lost the use of his right arm in World War I?

  "The family paid for it. Musical life in Vienna today is completely empty. You look at the announcements in the papers and what you find are Eine Kleine Nachtsmusik and Fledermaus.

On Intellectual Life: "There are lots of institutes in Vienna named after famous people: Mach, Freud, Wittgenstein, Boltzmann, Mozart. Nothing at all is happening in them. It's a waste of time to attend their events."

On philosophy at the University of Vienna: "Well, you know, the Philosophy department at the University of Vienna is the largest in Europe: It has hundreds of students! But they're not doing anything at all. There is a historical reason for this. For many centuries the Catholic Church had a stranglehold on education. Philosophy was nothing more than a branch of theology"   (I happened to know something about this; in my novel Hysteria and Enlightenment , I discuss the efforts in the 1780's of the Austrian emperor Joseph II, Baron van Swieten and Joseph von Sonnenfels to create a secular society, and how their achievements were reversed by subsequent emperors, not excepting Napoleon.) When I brought this up, Nedo looked at me with approval - in a place like Cambridge U. , there's nothing new about erudition - then went on:

  "At the beginning of the 20th century there came the emergence of the Vienna Circle of philosophers inspired by the work of Ernst Mach, Schlick, Carnap, von Mises, Wittgenstein himself, and many others. It struck the Catholic reactionaries like a bolt of lightning, and devastated the philosophy department. Since then the department's been totally dysfunctional!"

  I pointed out that the publication of Kurt Gödel's theorems had totally devastated the Vienna Circle! I also observed that Bertrand Russell never understood what Gödel's Theorems really mean.

  "Yes. Bertrand Russell never understood Gödel's Theorems, but Ludwig Wittgenstein had a very good understanding of them. This comes out in his correspondence with Moritz Schlick."

(Note: this is apparently a hot topic in the Academy: there is a certain paragraph in Wittgenstein's writing's, (known as the "notorious paragraph"), which has led to much throwing around of battle-axes. Some say that it proves that Wittgenstein never understood Gödel's Theorems . Others say that it shows a particularly deep understanding of them!)

  I presented Michael Nedo with a copy of my coverage of the Einstein Centennial Symposium of 1979 at the Institute for Advanced Study. When he saw the name "Lisker" on it he became interested and asked me where this came from. I told him that it was a Jewish name from the Ukraine. Although he is Austrian, Nedo's question caused me no qualms: if he can deal with Wittgensteinian Jewishness, he can deal with anyone's!

  After the meal, Helaine excused herself, while the rest of us went into the high lounge for the ritual after-dinner high coffee. The conversation shifted to Cambridge politics and personalities. Nedo had been a fellow at Trinity College from 1978 to 1988. He described it as an intellectual desert; the meals at the High Table were the epitome of dullness (I can well imagine that! These, one recalls, were the events during which C.P. Snow wandered around asking the humanities dons if they could state the 2nd Law of Thermodynamics, and the science dons if they could describe the literary device of the "interior monologue"! See The Revelation of Dr. Snew )

  Most of the conversations at the high table consist either of reminiscences of former school days, or petty academic politics. If you dared to bring up a serious subject (Wittgenstein for example), people would stared at you briefly, say something like "Really?", then returned to their pedestrian gossip.   But then Michael Nedo himself related a truly juicy piece of Cambridge scuttle-butt! In 1927 Geoffrey Maynard Keynes brought the left-wing economist Piero Sraffa , refugee from Mussolini's Italy, to Cambridge . Sraffa is best known as the editor of the works of Ricardo, and for a book entitled "The production of commodities by means of commodities".

  On the day after the bombing of Hiroshima Sraffa bought up all the Japanese bonds he could lay his hands on. It made him rich. His argument was that the nature of the Japanese national character was such that the nation would work like an ant colony to climb out of debt as quickly as possible.

  In his will, Sraffa left all this war loot to Trinity College.Being told this was a cause for considerable anxiety among the board of directors: Piero Sraffa was famous for frequently changing his mind.

  The story is that when he was hospitalized in his final illness, a representative of Trinity College was seated at his bedside around the clock, to see that he didn't alter his will!

  Sraffa was fluent in half a dozen languages. He and his visitors conspired to speak in some language that the university representative couldn't understand! Ultimately Sraffa did not change his will.

  A nice story: how much truth is there in it? Does it matter? One way or another, Trinity has its own reasons for participating in the annual celebration of Hiroshima Day.

Final comment:

A survey was taken among a number of professionals involved in what one might consider, loosely, the analytic sciences. They were asked about their opinions concerning the concept of "space".

The engineer:"Space is real"
The physicist: "Space is where we drop our thought experiments."
The mathematician: "Does the reality of space matter?"
The philosopher: "Is space really real?"
The Wittgensteinian philosopher: "Is space really (really( really( really (really (really.............))))))?"

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