On Brilliance and Boredom

Our substantial essay on mathematical depth and difficulty, and the very different intellectual rungs on the ladders of those who attempt to reach it, has been repeatedly updated;  time perhaps to give a taste of these.  For the full essay, click here:

Oligophrenia mathematica

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[Fifth appendix]   From a lecture by Professor Messing in Princeton, March 2002, in allusion to Robert Langlands of the Princeton Institute for Advanced Studies:

Langlands, with characteristic humility, wrote:  The virtue of Dieudonné theory  is that, for mathematicians of middling ability, it lets you translate difficult problems in abelian varieties  into straightforward problems in linear algebra.

I can well believe this.  I personally attended Professor Langlands IAS lecture series (autumn 1999);  in the first of these he stated that he'd wanted to be a physicist, but physics was "too difficult", so he had to settle for being a humble mathematics professor at the Institute for Advanced Studies.   Nor was this a pose;  his whole manner is that of straightforward humility, very … Canadian. 

John Conway, one of the most brilliantly elflike of mathematicians, confessed to a similar trajectory, during his time at Cambridge.  In a lecture at Princeton University (17 XI 1999) he confessed:

I studied Quantum Mechanics with Dirac.  Quantum Mechanics is hard to understand, even when you can answer the questions on the exams.  And I couldn't answer the questions on the exams anymore.

After his lecture, I went up with him to his office, and the sense of his almost Franciscan combination of humility and playfulness  was confirmed.   His small and crowded office (Princeton has an enormous endowment;  this is the way they treat their stars?)  was a four-dimensional playpen (of which, with my limited vision, I could perceive only three) of mathematical mind-toys, stacked up here and there, hanging from the ceiling, projecting from the walls …

[Sixth appendix]

Alex Masters, The Genius in my Basement  (2011)  [a book that treats of the  downfall of Simon Norton, once a key collaborator of John Conway]:

At Trinity College in Cambridge, there was a man who scored a double first in his undergraduate degree, took his PhD in the flash of an eye, and still gave up in despair  and became a tuba player.

How much more poignant, with the humble, doleful tuba, rather than piano or violin!

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[Seventh appendix]   On a related note:

In the moving coda to her splendid examination of the meteoric careers (or perhaps, fireworks-like, including the eventual fizzle) of a pair of brilliant (counter-)Freudians, In the Freud Archives,  Janet Malcolm, all passion spent, has a last interview with the man she has so closely followed, and not-unsympathetically depicted (and who would later sue her), Jeffrey Masson.   He says this, he says that;  and then she says:

“You know, as you’ve been talking, I’ve had the feeling that you’re bored with what you’re saying.”

The prodigy, his own passion likewise depleted, concedes that this is so.   He has seen farther than others, and has already said, and re-said, all that he has to say.  And then adds, fatefully:

“For people who are truly smart, like Bob Goldman, there really isn’t much they want to do, or can do.  The truly smart people seem to do less and less.  It’s terrible.  The dull have taken over.”

This chilling observation put me in mind of my best friend in high school, Ted Franklin, whose gifts in math and physics  lay far beyond my own.   I had an excursus in Europe before following him to Harvard, shortly after which time he had dropped out.   I did get to room (informally) with his erstwhile roommate, the brilliant math major David Collins -- who, however, himself promptly parachuted out of the university -- leaving the undergraduate mathematics to the tortoise, myself.  Both of them went on to quixotic social projects, and then I lost track.   Somehow neither one managed to stay sufficiently interested  to wind up doing anything intellectually really interesting.   They thought of themselves as rebels, but in that way they were more like Edwardians.   Leaving the field to us dullards.

How valid Masson’s plaint may be, in psychology or philology (two fields in which he greatly distinguished himself), I do not know.   But enormously smart people are doing deeper things than ever before, in mathematics.   They are not bored.

Physics and Physicality

[This piece dates from a decade or so ago, when our family was living in Princeton.  It is scheduled to appear in a book of essays, Princeton Follies, expected to be released this autumn, along with another wicked bit of satire ("Poetry Alive and Well in Princeton"), reporting on the social scene in the Micawber bookstore on Nassau Street.  So herewith, a sneak peak.
Oh and -- authors?  Don't bother to sue;  Dr Justice is a yachtless pauper.]

PHYSICS AND PHYSICALITY

            This afternoon  Rebecca Goldstein kicked off the reading season at Micawber Books, presenting her new novel Particles of Light.  She first came to the world's attention in 1983 with The Mind-Body Problem, a title as witty and apt as any in this century, set in the world of Princeton University and the IAS.  I read it shortly after it came out in paperback, having heard neither of book nor author, but intrigued enough by the title on the spine to pull it from the crammed shelf of a Cambridge bookstore, whereupon the cover seals the fate of any male reader who gets that far: a captivating nude painted by Balthus.  I had not at that time heard of Balthus either, but I had heard of nudes, and swiftly inserted this one into the inconspicuous interior a stack of blameless scientific reading and headed for the cashier's.

            (Ah, why not confess it all, since St. Peter knows it anyway.  It was in that very Cambridge bookstore, on that very day, browsing, that I happened upon, and was tempted to buy, but did not buy, a slender overpriced volume, by some trendy overrated litterateur, called: Spanking the Maid.)

            The book turned out to have all the novelistic virtues – funny, good plot, good dialogue, a heart.  But what really intrigued me was that whenever (as frequently) she referred to physics, philosophy, or linguistics, three areas in which I had some preparation, she got things exactly right, not just in the factual sense  but in the sense of the ethos of the field.  (She has herself a Princeton doctorate in philosophy, and her husband is a physicist.)

A few months later, idly wandering through the stately  and, for its provincial location, quite impressive  Worcester Art Museum, I came face to face with the actual painting, very much life-size, that graces the book's cover in miniature:  it was as surprising as though, opening your front door to get the milk bottles, you were confronted with a Botticelli in the flesh.  This was the subjective correlative:  The Mind-Body Problem was an icon of our age.

Goldstein followed up this beautiful debut  with something less good, and with a dreadful title, The Late-Summer Passion of a Woman of Mind;  then with something very much less good, The Dark Sister;  and then a collection of short stories, Strange Attractors,  that  in places  descends to the level of a Harlequin romance:  "His eyes were large and liquid and luminous – too luminous.  His nose is of an exquisite Hebrew model, but with a breadth of nostril unusual in similar formations”;  this written by "a governess and parson's daughter" for whom "a volume of headiest poetry is debauchery enough". ("Dreams of the Dangerous Duke"; sic.)  The books are progressively more seriously marred by what we may call the Pornography of Intelligence, consisting of gurgled tributes to the purported brilliance of someone (generally female, or the admirer of one) who does not actually ever get around to demonstrating that brilliance on the printed page.  As:  "And I told them of her meteoric rise to a brilliant, though as yet anonymous Fame;  of how her slender book of poetry had been printed, through the aid and connections of the Duke…. `Were you not the greatest of living Poets,' the Duke had told her, `you would have been either a mathematician or a musician.’ " (Or a philosopher, or a physicist, or a frigging concert pianist,  or the first violinist in space…)  A few years after this junk was published, she was given a MacArthur Genius Award, too belated to be an appropriate recognition of The Mind-Body Problem (especially as, unlike the Nobel, the MacArthur is meant to catch geniuses before they fully sprout), thus perhaps a sort of consolation prize for the later books, little read and ill-reviewed.  Her newest was sadly panned in last week's New York Times;  and it was with a certain foreboding that I went to her scheduled talk.

But that was to underestimate the force of the publicity machine, by whose exertions  the celebrated intercelebrate  and further inflate their celebration:  the book had drooling blurbs from the likes of Steven Pinker,  and even from the often acerbic Richard Dawkins, Michiko Kaku-caca be damned.   Nor was there any relaxation in the ubiquitous tensile tightly-inter-self-satisfied Princeton Smile  among those coolly, watchfully,  sipping the chablis with their thin lips --  a mannerism as catching as coughing or yawning, so that  fight as you might  soon your own face aches.  (Among the cozy Micawber bookstore personnel who put on the show, this rictus is widened and frozen to a Full Tooth aperture, so that bilabials actually receive labiodental articulation.)  The author herself was as yet mysteriously unseen ("Is she here yet?" “Have you seen her?”), which only increased the buzz.

Somehow I had pictured her as greying and getting stocky, as befits a philosopher of science.  Her jacket photo on Woman of Mind could be of a woman with nothing but mascara between herself and middle age, and who-knows how outdated that photo was at the time.  So I was unprepared for the vision of loveliness which, appearing out of nowhere, stepped demurely to the podium.  She wore a little bit of a thing of an off-olive-green dress, a hue inherently unbecoming, so that it could only be due to her own beauty that it so fetchingly complimented the equally strange tint of her hair – sort of a blonde that had become sun-tanned, which the sun had sweetened to honey with a hint of amber, to which poets despair of ever affixing a name.   That this was no natural color (matching neither the black of her earlier jacket photos  nor the brown of her current one)  no more detracted from its enchantment   than that the Venus on that half-shell  is a thing of paint.  Over her thin shoulders was draped  a thinner champagne sweater,  which soon – my heart stopped – dropped, with the drama of an ecdysiast  shedding her entire sheath.  Her head, like her body, is remarkably slender;  perhaps her brain became more brilliant as it was miniaturized, like microchips.

Much more than the usual author on a book tour, doing signings in a Barnes & Noble in is-this-Cleveland, she really could have schmoozed up this audience and flattered its yen for the inside dope, having written after all  the Great Princeton Novel, anyhow better than Fitzgerald's.  But all she said was, "I'm just going to read," and proceeded to do so – Storytime, children -- starting from page one, which consists of the single sentence, set proudly by itself, "The essential thing is that I hate her". 

(A pause, to let sink in, the bewildering-bewildered   disappointment of this.)

She proceeded to recite, in a delicious feline voice, the musings of a physicist (I think he turns out to be a ghost;  shades of the Dangerous Duke) on how he hates people, and how he isn't interested in things, though being really quite precocious, a fact dwelled on in extenso – not an auspicious strategy for drawing-in an audience, though ultimately, she told us afterwards, it's a love story.  (Having known a few physicists pretty well, I am baffled at how very far off this is.)   So far as I can tell, it's another bodice-ripper, but with enough glitzy glancing references to quantum mechanics  to give it what passes in our age for gravitas.

Ah, but enough – why satirize  or even summarize.  She said this and that; the crowd murmured, and dispersed;  as yet another shovelful of sadness  is tossed upon the coffin of my hopes.

It is evident that I read her first book one-sidedly, too exclusively emphasizing the former conjunct.  Since then, she has chosen increasingly to develop the body half of the dialectic.  And who should scant that?  The first novel was written, perhaps, by mere necessity; the latter are the works of one who can do anything she darn well pleases.  And this is what she pleases to do.

[© 2010,  David Justice]