Showing posts with label shadow. Show all posts
Showing posts with label shadow. Show all posts

Thursday, July 2, 2020

Nightfall


the twilight-loving bats    begin to flit about
-- Washington Irving ,“The Legend of the Enchanted Soldier”, in The Alhambra (1832)


The shadows of the valley
grew deeper and deeper,
until all was dark.
-- Washington Irving ,“The Legend of the Moor’s Legacy”, in The Alhambra (1832)


They sat on the boarding-house porch  and saw the sun plunge  into the same crack in the earth  from which the night emerged.
-- Zora Neale Hurston, Their Eyes Were Watching God (1937)

Wednesday, February 19, 2020

Damascus, in the Grand Mosque



The court was half full   of afternoon shadow,
  and half  of sun …

-- Gertrude Bell, The Desert and the Sown (1907, repr. 2001), p. 150



Sunday, July 1, 2018

Sierra Nevada monostich



The shadows of the valley  grew
deeper  and   deeper

till all was dark…


-- Washington Irving, “The Legend of the Moor’s Legacy”

Thursday, November 27, 2014

Alexander Grothendieck


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


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:


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



[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:

~

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:




~
Sotie : 
le mathématicien  et la conspiration Riemann
~



[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:


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 ντίνοος 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:


 
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:

* 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.)

Monday, September 16, 2013

Der Mann ohne Eigenschatten (weitergespiegelt)


In a lengthy novel, more admired than read, Robert Musil depicts the initially spring-fevered, ultimately autumnal society of Vienna under the Hapsburgs;  the novel opens in 1913.   Its title is the haunting Der Mann ohne Eigenschaften (literally, a man without qualities or personal characteristics) -- haunting despite or rather because of the nagging fact that, like some paradox in a dream, it makes no sense.  The concept is looming and formless -- something best unmentioned, or to scare the children with.

Yet now it occurs to us (and we seem to have been the first to notice this), that the familiar “plain-text” title with Eigenschaften   is a Deckname, a cryptonym for something … darker, yet lying phonetically  just beneath the surface.  And so exactly does this key  fit that lock, that the hidden mechanism  springs open at a touch:

~  Der Mann ohne Eigenschatten ~

So what would be this “Eigenschatten”?   
There is a technical meaning of the term, defined in Wikipedia:

Der Eigenschatten (auch: Körperschatten) eines Körpers  ist der Schatten, den der Körper auf sich selbst  durch sich selbst  verursacht. Dabei sind aber nur Schattenflächen gemeint, die auf den jeweiligen schattenverursachenden Flächen liegen. Anders formuliert ist der Eigenschatten die Menge der nicht beleuchteten also die der Lichtquelle abgewandten Seiten.

But that is not the meaning that concerns us here.  We allude rather to one who, for grievous diabolical reasons, can cast no shadow -- who has no shadow to call his own.

I'll just take this, now ... you won't feel a thing ...

The notion is familiar to students of German literature:  it is the central plot-device of Chamisso’s celebrated  novella Peter Schlemihls wundersame Geschichte, in which the hapless title character (a Pechvogel, and eponym of all later schlemiels and schlemazels) sells his shadow to the Devil -- a bad bargain.
(Cf. additionally  the opera by Richard Strauss, “Frau ohne Schatten” (1919).)



~
~  Posthumous Endorsement ~
"If I were alive today, and in the mood for a mystery,
this is what I'd be reading: "
(Ich bin Adelbert von Chamisso, and I approved this message.)
~        


The eerie image of the man-without-a-shadow -- penumbrous dual of the shadow-without-a-man --  yet came to our author  innocently enough.   From Karl Ude’s introduction to the Goldmanns Gelbe Taschenbücher  edition of the work:

Die Erzählung ist entstanden aus einer zufälligen Frage an Chamisso, der sein Reisegepäck verloren hatte,  ob er nicht auch seinen Schatten verloren habe?

 
[Note:  I use the term “dual” here  in its mathematical sense;  yet the kindred notion of Doppelgänger  is here curiously appropriate.]


*
For another, exceedingly strange story,
and not unrelated in theme,
try this:

*



~

Orthoëpic interlude

So -- how do you pronounce the guy’s name -- Chamisso?
The man was French in origin;  and the worthy Webster’s New Biographical Dictionary, to which I myself, as editor, contributed not a few pronunciations (though not this one), gives -- for its pronunciation in English -- a value of orthographic “ch” which derives from French (here I translate into “newspaper-style” transcription):  sha-MISS-oh.   But the name is quite odd, for French or for German;  I do not know how his drinking-buddies called him.

An idiotic stab at the pronunciation is offered here for internauts:
http://www.pronouncehow.com/english/chamisso_pronunciation
Ignore it.
 
~

To resume.  
The man was, as we say, French, of noble origin (whence the “von”) and had to flee the overexuberant antics of the French revolution.  He spent the rest of his life dedicated to German life and letters.   With what results, we mention here.



And yes, I am aware, there is a parallel, between his Lebensbahn and mine -- ich, der ich Fremdling und Flüchtling bin,  nun jetzt in Herbstesalter,  in deutschem Kulturgut  fummelnd
Yet there is a more deep-cutting parallel:  and this, between Chamisso and Schlemihl.   For Chamisso himself was a Mann ohne Eigenschatten -- living in dreadful exile, his roots quite sliced, condemned to stammer in an alien tongue.


*
Für psychologisch tiefgreifende Krimis,
in pikanter amerikanischer Mundart,
und christlich gesinnt,
klicken Sie bitte hier:

*

[Update 6 Aug 2013]  An interesting article by Costica Bradatan  explores the writerly bilingual dilemma here:

In her exploration of the Catholic religion, “Letter to a Priest,” written the year before her death in 1943, Simone Weil noticed at some point that “for any man a change of religion is as dangerous a thing as a change of language is for a writer. It may turn out a success, but it can also have disastrous consequences.” The Romanian philosopher Emil Cioran, who was one such writer, talks of the change of language as a catastrophic event in any author’s biography

~

To recur to the thorny subject of the Eigenschatten.
The poet and mystic Christian Morgenstern  has discoursed in rhyme  upon this matter:

Das Lied vom blonden Korken

Ein blonder Korke spiegelt sich
in einem Lacktablett –
allein er säh’ sich dennoch nich,
selbst wenn er Augen hätt’!

Das macht, dieweil er senkrecht steigt
zu seinem Spiegelbild!
Wenn man ihn freilich seitwärts neigt,
zerfällt, was oben gilt.

O Mensch, gesetzt, du spiegelst dich
im, sagen wir, – im All!
Und senkrecht! – wärest du dann nich
ganz in demselben Fall?


This we have managed, by a heroic feat of compression, to reproduce, for a world-wide anglophone audience, the original dozen lines by a mere six:  thus doing our ecological bit to stave off the impending Global Pixel Shortage (“Peak Pixel”):

A cork upon a mirror stood;
though had he eyes, ‘twould do no good,

because he stands on self upright,
his mirror image -- out of sight.

E’en we! beamed forth  beyond the sky
see not ourselves  with inward eye.


(This miracle of minimalism we achieved by means of Korf’s own invention,
described by Morgenstern  in “Die Brille”.)

Saturday, May 18, 2013

CHAOS, COINCIDENCE, CORRELATION, CONSPIRACY


Daily life is a tissue of loose ends, shot through with snarls and dropped stitches. That society nevertheless does not unravel, seems due to the fact that most people, though in detail unpredictable, are essentially similar and basically sane; due additionally to conservative/equilibrating structures evolved over the centuries; and perhaps to some further, anti-entropic factor, still obscure  but whose presence we may suspect (guardian angels would be the simplest explanation; something equally speculative though less intuitive, concerning negentropy or self-organizing systems, could also be alluded to).  Things pretty much jog along and usually eventually work out; but the details of any particular transaction  often may not bear looking into.
            One gets a glimpse of this  whenever, by some chance, a particular circumstance must be looked into further – something went a lot or a little bit wrong,  that, for some reason, this time, needs to be corrected or explained  and not just brushed aside as usual.  One often finds, upon turning over a rock long left undisturbed, a welter of wriggling vermin: errors previously unsuspected, data missing or misfiled, notes contradicting what one had previously believed (while their author has since left the company, or died prematurely).  Normally, none of this is sinister, but simply shows, on the human level, an analog (not an effect;  a metaphor, merely) of the underlying quantum uncertainty and atomic chaos  which nevertheless  ultimately manages to cohere in this coffee cup or that paperweight  sitting placidly, bien sage, on your desk.  If, however, the original affair is shady, the unexplained details which investigation unearths  lie in its shadow.  Let one instance stand for all: the celebrated “18-minute gap” in that tape, during Watergate.  Personally I find it utterly plausible that the gap resulted from the same gremlins that hide our spectacles, lose our umbrellas, and eat óne out of each pair of laundered socks.  But in context, it did look suspicious.
            An instinct not to let go of such suspicions  is buttressed by cases in which investigation of some misdeed,  severe enough to catch the atte.ntion of the media or the D.A.,  reveals a pot-pourri of previously unreported malfeasance, as in the Watergate affair.  Novelists and cineasts take the trend a satisfying step further with variations on the “Blow-Up” motif, in which a chance following-up of some minor discrepancy, out of mere curiosity, leads to a Vast Conspiracy. 
            The problem becomes acute when the stakes are high, the affair complex, and the discrepancies numerous (as they inevitably will be in any far-reaching affair, even absent any sinister underpinnings).  As, the Kennedy Assassination, or 9/11.

            We are currently witnessing a whole industry, tying our current President and his associates – both laterally (the present Administration) and longitudinally (the Bush family, going back to Prescott) – to all manner of skullduggery.  At the far fringe are the conspiracy theorists (stronger in Europe than here) who initially maintained, and some still maintain, that 9/11 was actually planned and carried out by a U.S. cabal, the airplanes being remotely controlled from the ground. A tad less extreme is the allegation, popular among some less reflective Arabs, that Israel did it.  Another tad, the position that,  while the op was indeed al-Qaeda’s, the Administration knew (sub-position 1, more florid) that that attack was due on that day, or (subposition 2, more reality-based, pointing to the August 6 memo) knew in a general way that such a thing might happen, and deliberately did nothing, so that they could use it as an excuse to proceed with their nefarious plans.  Certainly there have been agents provocateurs in history; but I tend to disbelieve in any gross such allegation concerning a present-day American administration, since every potential conspirator must be aware that, the way things stand in America today, no conspiracy broader than two twins in a cave  can stay secret for long – people write books and go on talk shows  to expose much milder grievances. 
            More centrist – if only with respect to such as these – is the new movie, “Fahrenheit 9/11”.  To his credit, Michael Moore does not even allude to such darker fantasies – indeed he indirectly exonerates the Administration, or at least Bush himself, of complicity,  if only through imputation of cluelessness. Bush’s blank look while the WTC attack vied for his attention with the Pet Goat, is itself a piece of evidence against all but a watered-down version of the last of the above-listed positions.  (Moore himself voiceovers a plausible thought-balloon in keeping with the last one, along the lines of: “Dang, wasn’t there some memo about something like this? Maybe I should have spent more time at the office and less on the golf course.”)  In one of his books, Moore hints at something more conspiratorial, but there fingers the Saudis (he really doesn’t like the Saudis), not the Illuminati or the Carlyle Group. And in the film, he does raise a number of other serious suspicions, none – again to his credit – original with himself, but dramatizations of charges explored at length by serious journalists in books. 

            It has been correctly observed that the basic motivation behind some of the most persistent of conspiracy theorists  is not mere irrationalism, but a perhaps excessive penchant for rationality – demanding to make sense of things that, well, don’t.  The distinction is hard to spot, since any empirically competent, level-headed investigator  tends to get swallowed up in a crowd of crazies.

            Another possible determinant, perhaps less often observed: in ascribing a pattern to the welter of events, as deriving from a plot, the theorizer may be acquiescing in a demand for personalization.  For, the confusing flux of the world  often lacks palpable causes.  Surely it can’t just all be random – one suspects deep dark forces at work. A plot puts a face on it.  But usually this is an explanatory short-circuit. For indeed there are forces, as deep and dark as those of hydrodynamics, but they are not even rational, let alone personal.
Empirical question: Does a tendancy towards florid conspiracy-mongering  correlate negatively with religious belief?  It is an observation  due perhaps to many, but prominently expressed in many a delightful story of Father Brown, that superstition tends to flow into the vacuum left by an absence of faith.  Perhaps belief in a heavenly Father – however distant, however inscrutable – leaves one less likely to imagine that the world’s workings may be ascribed to some shave-pate villain in a bunker somewhere, stroking a cat.
Against this, however:  the observed fixation of Book-of-Revelation-style evangelicals  on the Antichrist, working through the New World Order.  They do, so they say, believe in God;  a lot of good it’s done them.

            There is a healthy kernel to the epistemological attitude which, in its pathological exfoliation, becomes conspiracy-mindedness: a simple stance of “Wait a minute.”  For as Locke observed, and as subsequent scientific and historical discoveries  retrospectively further buttress: that “some (and those the most) taking things upon trust, misemploy their power of assent, by lazily enslaving their minds, to the dictates and dominion of others, in doctrines, which it is their duty  carefully to examine.”  (Essay I.iv.22)
            In an unhealthy development, skepticism becomes  not a key to inquiry, but a pose of imperviousness in the face of counter-evidence.  Michael Rutschky, in a recent contribution to the Sueddeutsche Zeitung, described the situation in Germany, where “Ich bleibe skeptisch” has become a slogan – not, like that of the fabled Missouran (“You’ll have to show me”) inviting actual demonstration, but issuing a warning that, whatever evidence you may bring, it will be dismissed as smoke and mirrors. This sclerotic ‘tough-mindedness’ in the face of empricism  is often coupled with a soft side for Verschwörungstheorie.  At an extreme, this leads to political infantilization.  That the phenomenon seems more to be met with in Europe (at least, comparing their educated reading public with that of America, and setting aside the seething cauldron of the Web sites and talk shows) may cohere  with an objective semi-infantilization or anyhow sidelining  of Europe itself, in the age of the unilateral hyperpower.


*
The detective versus an unnamed evil thing:
A tale of madness, and of the uncanny --
Murphy Calls-in a Specialist
Available for Kindle or Nook

*
[Footnote May 2013: 
The above was written ca. 2005;  since that time, the fragile cortices of many of our countrymen have cracked, while paranoid fantasies sprout like weeds.  Yet the circumstances tend to reinforce the conjecture above, that hands far from the tillers of power  are freed for idle mischief.   When in office, Republicans are crafty and cynical; when out, they lose their moorings.]

[Sidenote]  There is a quite respectable practice of trying-to-see-hidden-patterns everywhere:  it's called Science.  For which see:

http://worldofdrjustice.blogspot.com/2011/10/consilience.html


That practice too  has its pathologies, which perhaps someday time will allow us to notice in this place.

We find both kinds of nisus united  in the figure of Newton.  On the one hand, his scientific Principia side; on the other, his esoteric researches (alchemical and theological), which bulked equally large in his life.  Re the latter, David Berlinski remarks (Newton’s Gift (2000), p. 68):  “Secretive natures are quite prepared to believe that the history of human affairs  is largely the history of a great many secrets."