Star Trek ministich

a planet-size base   that hangs in the heavens

like a Christmas bauble,  with inverted boulevards

and skyscrapers  curving around  inside

[-- Anthony Lane, reviewing the latest Trekkie offering, in this week’s New Yorker]

Alexander Grothendieck

From the graceful pen of Edward Frenkel  comes this appreciation of the prodigious mathematician Alexander Grothendieck:

http://www.nytimes.com/2014/11/25/science/the-lives-of-alexander-grothendieck-a-mathematical-visionary.html

Frenkel’s summary of Grothendieck’s approach  is phrased in distinctly Platonistic terms:

Grothendieck’s genius was to recognize that there is a “being” hiding behind a given algebraic equation (or a system of equations) called a scheme. The spaces of solutions are mere projections, or shadows of this scheme.

That formulation goes beyond the basic assumptions of mathematical Realism, adding a quasi-personalistic, quasi-spiritual metaphorical dimension.   We might epigrammatize the matter thus:  bare-bones Realism (embraced by most mathematicians as a lower bound) is to the view attributed to Grothendieck, somewhat as deism is to theism.

Frenkel concretely illustrates this (neo-)Platonistic / Plotinean stance of  seeing the relatively concrete and familiar, as but a pale and lesser projection of some higher, transcendent, but paradoxically more solid Reality (which dwells in Platonic heaven, sipping some higher-dimensional nectar), in his justly celebrated book for the layman:

Imagine a world in which natural numbers are replaced by vector spaces;  that is, instead of number 1  we have a line, instead of number 2  we have a plane… Addition of numbers is replaced by the direct sum of vector spaces,  multiplication by their tensor product.  The number 3 is a mere shadow of the 3-dimensional space, reflecting only one attribute of this space, its dimensionality.

-- Edward Frenkel, Love & Math (2013), p. 155

That insight is superficially reminiscent of Bertrand Russell’s definition of, say, the integer three as being not basic, but the rather the (infinite) set of all triads { {Moe, Larry, and Curley}; {Huey, Dewey, and Louie}; {the Andrews Sisters}; ..}  Russell’s move always struck me as, at best, an obscurum per obscurius (or even a clarum per obscurius);  at worst, a parlour-trick.    Frenkel’s suggestion likely goes much deeper -- indeed, to a depth I am in no position to assess.

Finally, without the structural richness of Frenkel’s proposal, but perhaps more accessibly, this from a pair of noted philosophers-of-science:

The abstract objects of thought  such as “numbers” [or] “perfectly straight lines” .. are real parts of nature, even though they do not exist as particular things, but as the relations or transformations of such particulars.

Morris Cohen & Ernest Nagel,  An Introduction to Logic and Scientific Method (1934), p. 372

~

Frenkel reminds us that Grothendieck, dramatically and notoriously, Threw It All Away, resigning his institute and seceding from the mathematical world, upon learning of its defense funding.   Frenkel points indeed to the possibility that even a subject so “gloriously useless” (as it was seen back in G.H. Hardy’s day) as number theory, can have crucial cryptographic applications which, in turn, invite subversion by the intelligence community.   He states, indeed, that such subversion did take place, at the hands of a three-letter Agency too numinous to name, in the case of Elliptic Curve Cryptography.  Yet ironically, that very field was pioneered by a theoretician politically of the far left, Neal Koblitz.  (I knew him slightly when we were both math majors and antiwar activists at Harvard, and recall him fondly here.)

[ A parallel:   For a highly entertaining, though painful, account of Simon Norton,  once Conway’s collaborator, but who likewise Threw It All Away, see the book by Alex Masters, The Genius in my Basement  (2011) ]

I never met Grothendieck, nor so much as approached the foothills of his cloud-surmounting summits;  but my introduction to mathematics did come via one of Grothendieck’s students, Robin Hartshorne, here portrayed:

http://worldofdrjustice.blogspot.com/2011/12/adventures-in-algebraic-geometry.html

We touch upon Grothendieck tangentially in several essays;  here they are:

worldofdrjustice.blogspot.com/search/label/Alexander%20Grothendieck

[Another parallel:  Grothendieck’s abrupt withdrawal from mathematics, and his sometimes surly subsequent comments on its practicioners, recalls that more recent self-reclusion of the Russian topologist Grigori Perelman, who quit his institute in 2005, with the remark that “I have been disappointed in mathematics and I want to try something else.”   Now, to anyone who grasps the subject, disappointment with mathematics is almost inconceivable -- it’s like being disappointed with the Universe, or with penguins, or with life itself.   Other statements he has made suggest that his quarrel is not with math per se  but with certain mathematicians.

For a poignant glimpse of the daily routine of this semi-recluse, try this:

http://www.lepoint.fr/monde/le-genie-qui-s-est-retire-du-monde-30-09-2010-1246189_24.php  ]

~

In other cryptographic news … This week’s New Yorker has a review by Anthony Lane of “The Imitation Game”, which takes us back to the WWII code-breakers at Bletchley Park, with mathematician Alan Turing at the center.   With his welcome skeptical eye, Lane punctures the movie’s superstar approach to the material:

No word is breathed, for instance, of the Polish cryptographers who did much of the heavy lifting on the project  before Turing came on the scene.  As for the cracking of codes, it is shrunk to single, Oh-my-God epiphany, triggered by a comment in a pub.

That last motif is strikingly reminiscent of the trumped-up Eureka moment ascribed to Gauss in the movie “Die Vermessung der Welt” (which we reviewed here), whose insights into differential geometry were supposedly engendered -- in a flash, on the spot -- by a buxom mädchen handing him an apple from the knowledge-tree.

Another warning-sign:   The role of Turing’s  Comely Female Sidekick (de rigueur in Hollywood these days) is played by Keira Knightley, an overactress whose pornographic approach to proximity to great men of science, in the movie “A Dangerous Method”, we earlier had occasion to denounce.

~

[Late-evening update]  And now, fellow devotees of that supreme queen of the noösphere, math -- now that we have all stuffed our tummies with turkey, and are sprawled upon the couch:  as we are probably not just now engaged in settling the Hodge Conjecture (and making but scant progress if we are), let us rather refresh the neurons with a bit of mathematical merriment:

How Now, Round Cow

~

Sotie : 

le mathématicien  et la conspiration Riemann

Борис Березовский

~

[Update, 30 November 2014]  Further thoughts.

(1) Integers as shadows

That epigram, that petite phrase,  “The number 3 is a mere shadow of the 3-dimensional space”, continues to intrigue.  Further thoughts on the subject here:

From Finitude to Infinity

The point being that Frenkel/Grothendieck are here proceeding in the less-familiar opposite direction.

(2) “Goodbye to All That”

The catchphrase “I Threw it All Away” is from Bob Dylan.   An earlier more familiar expression is “Goodbye to All That”, the title of a memoir by the poet Robert Graves.

To fascinate a public beyond the circle of connoisseurs, a mathematician (or physicist, or chess-player) needs to sport some quirk, some handle onto which the layman can hang his attention.  That is massively true of Turing, first because of his role in the thrillingly clandestine -- and militarily crucial -- cryptographic factory at Bletchley park;  and more recently -- and less relevantly, from any mathematical standpoint -- by reason of his personal predilections (held in common with such extra-scientific figures as Ἀντίνοος and the Baron de Charlus) which at present have reached an apogee of public celebrity.   On a more modest scale (no blockbuster biographies, no movies) the careers of Emmy Noether or Ada Lovelace come to mind.

For anyone not a member of the identity-groups in question, such chance affiliations are mathematically and philosophically boring.   But not so a figure like Groethendieck, who reached intellectual levels that most of the rest of us can only pant and sigh for -- then threw it all away, in a contemptuous gesture.   For that is a challenge to all of us, whatever our private identities;  it calls into question the very value of the ‘it’ for which we so painfully and vainly strive.

A well-known example from chess:  Bobby Fischer, who withdrew from the sport at the top of his game.

Or, in the sixteenth century, the pioneering anatomist Vesalius, who, having published the book that settled his fame forever, and still a young man, left the field and became a simple physician to a valetudinarian Emperor.

A grey-area variant of this motif is found in the case of Simon Norton.   True, he voluntarily withdrew from the field;  but in view of his later pointless eccentricities, we cannot avoid the suspicion by then he had largely Lost It.

That variant motif forms the spine of Rebecca Goldstein’s fascinating mathematico-philosophical novel,  The Mind-Body Problem.

And while Goldstein manages to craft a good read out of the tragedy, in the typical case of gradually fading powers, it is just sad.  Thus Lagrange, and other victims of Oligophrenia mathematica tardiva,  chronicled in the appendix to this essay:

De Stultitiâ

 

Other examples of burnout:  

Newton had a nervous breakdown a few years after publishing his Principia, and never did real science again.

Russell seems to have fried many of his math neurons in the course of writing his Principia (memo to prodigies:  Don’t try to write a Tenth Symphony, and don’t write a book called Principia).   He did much interesting philosophical work after that, but mostly with other areas of his capacious brain.

Somewhat in the spirit of the Stith-Thompson index of folkloric motifs, to I Threw It All Away (TaleType #1729a), we add:

* Taken all away (#1729b):    Persecution took them out of the game, at the height of their powers: Galois (permanently) and, for those who considered that he was hounded to death, Turing.  Temporarily: André Weil and Neil Koblitz (during their imprisonment -- though both managed to use their ‘time inside’ more profitably mathematically  than most of us do with all the free time in the world).

* Would throw it all away, if had to do it over again (#1729c):

Wolfgang Pauli in 1925:
"At the moment, physics is again terribly confused.  In any case, it is difficult for me, and I wish I had been a movie comedian or something of the sort, and had never heard of physics."

Schrödinger, to Niels Bohr:

“If all this damned quantum jumping were really here to stay, then I should be sorry I ever got involved with quantum physics.”

[quoted in: -- Roger Penrose,  The Road to Reality (2004), p. 516]

More such anecdotes here:

http://worldofdrjustice.blogspot.com/2012/06/on-truth-and-beauty-golden-oldies.html

* Should throw it all away, if that’s how they feel (#1729d):  String theorists who have wound up at the dead-end of the Landscape picture.  (“The reductionist voyage that has taken physics so far  has come to an end.  Since that is what they believe, I can’t understand why they don’t take up something else -- macramé, for example.”  More here.)

Life, Art, nabbed in Parisian love-nest !

In the following post,

     My apologies to M. le Président

itself repeatedly updated, as though with post-it notes, with each fresh whiff of scandal out of France, we apologized to the French President  for having called him “a crowd-courting doofus;  a lackwit wazzock”, and other things still more unkind.   Here, now, is the latest:

Anthony Lane, reviewing the new Tavernier film “Quai d'Orsay” (the title which Wiki gives it in English as well, though apparently it has recently been dumbed down for American audiences as “The French Minister”, rather the way the first Harry Potter book, “The Philosopher’s Stone”, had to become “The Sorcerer’s Stone” to cross the Atlantic), highlights the femme fatale character:

She is played by Julie Gayet, who was in the news recently as the woman to whom the real French President, François Hollande, was paying regular visits  on his little scooter.  And her character is called Valérie, which is the name of the partner whom Hollande was allegedly spurning for Mme. Gayet.  This is not life imitating art.  This is art going to bed with life  and staying there for the afternoon.

-- The New Yorker, 31 March 2014

A nice touch, that, by the way -- “his little scooter”.  This is artful of Mr Lane, suggesting that what the dumpling Hollande has   down there  between his legs  is pretty small, and goes putt-putt.

*

Si cela vous parle,

savourez la série noire

en argot authentique d’Amérique :

http://www.linguasacrapublishing.com/justiceexcerptdivorce.html

*

For further instances in which French sex and French politics  intertwine like the rose and the briar, try these:

           

            L’affaire  Masson  / Grosdidier

            The Muff of Mystery

            The World Cup of Crime

~

An after-reflection upon Mr. Lane,   the Art of Criticism, 

and the Meaning of Life

Well, no, precisely not, though that is just the temptation:  It’s just a mo-vie.   I enjoy Lane’s reviews the way I enjoy P.G. Wodehouse  -- reliably;  and sometimes there is rather more than that.   Yet in Googling his name, there in the very top returns were some absolutely scathing, venomous denunciations.  Bringing it home that, not only can you not count on pleasing all of the people all of the time (I think Abraham Lincoln said that):  if you so much as delight some people  some of the time, there will be others who downright  despise you.

One of these counter-critics, writing in some New-York-based webzine, poured scorn upon Lane as a mere spewer of witticisms, with almost no knowledge of cinema;  and in particular (in reference to the movie under review, one of those vaporous martial-arts-cum-mysticism films) for having insufficiently spent his life delving into the splendors and subtleties of kung fu movies, or whatever it was.   His final, crushing verdict:  Anthony Lane’s reviews are so bad that they read like something out of a webzine.  (Oh, wait …)

Now, inside this animadversion lie perdu  two traits for which I specially value Mr Lane.   One, that he is no prisoner of the self-referential Cahiers-du-Cinéma-style film-crit hall of mirrors, but has windows on the world:  the review referenced above is informed with a sense of biography and of current politics.   Further, Mr. Lane knows his audience.   Probably few regular readers of The New Yorker (and I have been following that venerable weekly, though in part  pre-natally, since its inception in 1925) could by any possibility care less about puffed-up Oriental kick-‘em flix, however balletic the cinematography.  Mr Lane is not writing for the sort of pimpled basement-dwelling masturbators who batten on kung fu flix.   He reviews them, along with all the rest, simply because he is paid to do so, that is his job, whatever washes up on his plate that week.

As for the charge of wittiness, no doubt Mr Lane would own the soft impeachment.  He indeed is consistently witty, but also at least intermittently keenly perceptive, and occasionally (as here) capable of genuine moral seriousness.

[Note:  I had long suspected, based simply upon the archness of his writing (& yes yes, well aware, pot/kettle/black), that he might share with his countryman Oscar Wilde  more than the charm and English drollery (something that his ‘jacket photo’ on the New Yorker site  does nothing to dispel).  But no, turns out the man is a paterfamilias.  Some years ago,  I experienced an exactly parallel realization  regarding the arch and icecream-suited Tom Wolfe.]

[Afternote:   As for the Meaning-of-Life stuff, sorry, that lies above your service-level.  For that, you’ll have to upgrade to World of Dr Justice Prime ®.]

[Update 27 III 14]  The blushing vestal to get big buck$  in compensation:

http://www.lefigaro.fr/flash-eco/2014/03/27/97002-20140327FILWWW00183--closer-devra-payer-15000-euros-a-julie-gayet.php#xtor=EPR-31-[-closer-devra-payer-15000-euros-a-julie-gayet]-20140327-[titre]

The Overdue Notice … It Tolls for Thee

Back in my day, we were  as children  given very strict instruction in Library Etiquette.   No more would you raise your voice in that sanctum, in infantile mirth, than you would in church, or at a funeral.   Books were to be returned unharmed and on-time;  the concept of the Overdue Library Book was our first introduction to the notion of having a sin on one’s conscience.

The situation is somewhat reminiscent of that prevailing during Freudian/Victorian times, when children were subjected to overly-strict toilet-training, with odd and lasting consequences. 

In the current issue of The New Yorker,  in a typically witty review of the new movie “Moonrise Kingdom”, Anthony Lane writes, of a couple’s mad romantic encounter, before they go off on their great adventure:

Now they come face to face once more -- Sam with his canoe, gun, tent, and all-around scouting skills;  Suzy with her library books  and a cat in a basket.  [dbj: BTW, note the Harry/Hermione motif].  His most urgent concern, obviously, is the books:  “Some of these are going to be overdue.”

I totally get that.

At the Movies

For some years, Anthony Lane has been publishing witty and perceptive reviews in The New Yorker.  As one of but a handful of Americans who can currently make a living doing nothing but eating popcorn and keeping their eyes peeled, he certainly needs no assist from me.  We mention him in these spaces, not because of his having just now reviewed any mustn’t-miss movies -- indeed, the movies in question sound particularly worthless -- but because, critically,  a moral dimension enters, singularly well-expressed.  Indeed -- coincidence? -- this particular column, which you can read here

http://www.newyorker.com/arts/critics/cinema/2011/11/07/111107crci_cinema_lane

is in every respect  one of his better ones (that is saying a lot).

Thus, the present offering well illustrates the dual duty of a movie reviewer:

   (1) What when where why / nudity, backstory/ car-chases  well-done yes-or-no / Hollywood dish / musings as to how Dziga-Vertov might have filmed the same thing / …

   (2) Saving us from ourselves…