“Zero Dark Thirty”

Hier neubearbeitet/updated here:
http://worldofdrjustice.blogspot.com/2013/12/zero-dark-thirty.html

Happy Feast-of-Saint-Andrew !

Today’s the day.

Here we see him with the instrument of his affliction, the chi-shaped cross that now bears his name.

For an engaging essay about Andrew, try this, by our good friend Dr Massey:

http://magnaliadei.blogspot.com/2013/11/saint-andrew-mans-man-of-god.html

Sky Wars

Hier neubearbeitet/Updated here:
http://worldofdrjustice.blogspot.com/2013/12/sky-wars.html

“What is Mathematics?”

[Updated here:
http://worldofdrjustice.blogspot.com/2014/01/what-is-mathematics-expanded.html ]

Semantics, local and global

[The distinction between the local and the global view, with increasing enrichment of the latter, has brilliantly characterized geometry (and cosmology) for the past half-century or so.  Addressing a different problematics, we proceed in that spirit  here.]

In math, the familiar notion of a function  normally (and only-ever in one’s earlier education) assigns some value to each of a set of points.  Later, one studies function-like entities, or functions sensu lato, whose mandibular gape is more capacious, taking in as argument, not merely a point, but a variable region, or even another function:  thus we come to study things called functionals, densities, and distributions.

In the simplest popular literature, such as the Hardy Boys on which my generation of masculine rascals was raised, semantic interpretation is local, even punctual.   The interpretation may well be more than literal, and require certain background conventions for proper appreciation, but the meaning may nevertheless be derived directly from the sentence in question -- it does not require any sort of “contour integral” through surrounding text, mapping its textual neighborhood into a richly layered semantic space.

Thus, consider:

            Joe’s jaw dropped.

This, our legent lad is to understand, denotes, primo, that Joe’s mouth widened somewhat, involuntarily; and that, segundo, this reflex was caused by emotionally tinged surprise. 

Such associations are to some extent conventional, and thus vary across cultures.  Part of the value of such digestible and repetitious reading as the Hardy series, is to inculcate such simple mappings.  To accomplish this does initially require the learner to pay attention to immediate context:  as, a preceding

There beneath the Christmas tree stood a shiny red roadster.

followed by

“Jumpin’ Jehoshaphat!   This is the best present ever!”

in which case the jaw-drop manifests surprise plus delight;  or else

There on the kitchen floor lay Aunt Gertrude, bound and gagged.

followed by

“WTF ?!??!!!”

(well, not that exactly), in which case the concommittant to surprise is rather dismay.

Surprise is the common factor, and persists for all later instances of falling jaws, even in the absence of such circumambient clues.   That there exists some attendant emotion  is likewise a given, with some (surprise, dismay) being much the most common, and others being almost ruled out (perplexity, embarrassment, boredom).  What objectively occasions the surprise in each new instance can be described as a matter of simple statistics, derived from such considerations as the relative likelihood of encountering a beribboned roadster on Christmas morn, versus a fruitcake, say, or a set of Lincoln logs (or, for adults of a Glengary Glen age, a set of steak-knives);  and whether Aunt Gertrude is a conventional reserved sort of elderly lady, or whether, rather, she is given to bouts of self-bondage, like that MI6 agent whose corpse was found found in his bathtub.  Such frequency-profiles are of course relative to culture, and their calculation and application go beyond the content of the immediate sentence under interpretation, but they are soon solidified into background assumptions tacitly available to anyone competent in the culture, and need not be specifically keyed by the ambient text.

In time, one accumulates great hordes of such things, no longer needing any contextual guidance to interpret such conventional gestures as

Frank slapped his forehead.

Iola blanched.

Clint’s eyes narrowed.

Wolfe frowned and polished his glasses.

and so on and so forth.   As one’s literary experience proceeds, other, no longer culture-wide but character-specific physical indicia may be acquired:

Merlin’s thumb tingled.

(Cf. “By the pricking of my thumbs, something wicked this way comes.”)  But once acquired, their interpretation is straightforward, and purely local.

~

Consider, now, a character  not from any series, and whose acquaintance we have only just begun to make, in a character-crowded tapestry, the novel Martin Chuzzlewit:  to wit, Tom Pinch.  And consider this line, appearing isolated in a paragraph all by itself:

Mr Pinch opened his eyes wider, and looked at the fire harder than he had done yet.

Whatever can this mean?

[Note:  I shall pause here, pending future leisure to expand, and meantime let you ponder this, and to seek its context if you will, in Chapter 6.]

Tom has recently been sent to fetch Martin Chuzzlewit fils at the inn, to be Mr Pecksniff’s new architectural apprentice.  When we first meet him, coming in from the cold on a frosty night, he too engages in a bit of hearth-staring:

The stranger became thoughtful, and sat for five or ten minutes  looking at the fire in silence.

Here the significance of the action is quite different from that which applies in Pinch’s case.  Yet, different in a deep way, which requires psychological excavation to uncover:  not different in the merely algebraic way whereby x may denote, now 2, now ½, or his may be co-indexed, now by Frank (“…stroked his chin”), now by Rico (“… hefted the Lugar in his hand”).

Though born to wealth and privilege, Martin has recently been evicted from the good graces of his elderly uncle and theretofore-presumed bequeather-to-be.  And since (like half the characters in Dickens, it sometimes seems) he is otherwise an orphan, he has seen his “Great Expectations” (Martin’s phrase; where have we heard that before?)  evaporate before his eyes (which, had he been a Hardy Boy, would have “popped” at the news, along with his plummeting jaw).  He is accordingly a great fire-starer, by way of absorbing the warmth he feels to be his due, and of brooding upon his wrongs.  Here we see him later, at it again, with poor Pinch huddling on a neighboring footstool:

Beyond that, Martin is not (yet) a deep character, further than what we have seen, and indeed is typical of Dickens as being sharply (though, to a beginning reader, somewhat subtly) delineated, repeatedly bodying-forth a certain trait of character.  This is the sort of thing that has led some critics (unjustly I believe) to dismiss the Dickensian menagerie as caricatures.   It is likewise part of Dickens’ craft, to throw this character’s essence into greater relief, by means of characteristic physical gestures;  further, in the case of Martin, by the juxtaposed contrasting figure of Tom Pinch, who is something like Martin’s dual or inverse.  Where Martin was born to privilege, Tom was born to none.  Whereas Martin continually frets at any crumb that might be missing from his own bounty, Tom is grateful -- truly, deeply grateful -- for any scrap that might fall from the table of his betters.  (Dickens offers a literal picture of this, in Tom’s delighted feasting upon the wilted leftovers of the departed Misses Pecksniff.)

Tom Pinch is more of a puzzle -- more of a mystery.   On the face of it, he is a simple fellow, almost a simpleton;  certainly that is the opinion of the various Pecksniffs.  But there are a deep roots to Tom’s humility, to which the instincts of a Christian will quicken.  He is less a village idiot, than a Holy Fool.

And now these polar opposites are confronted.  Martin speaks casually, heedless of his snubs towards Pinch.  Pinch, from his good heart, never quite perceives these, just as he does not from the Misses Pecksniff.   Martin’s pretentions are likewise dutifully seconded, just like those of Pecksniff.  (Martin on his family’s failings, which fortunately “haven’t descended to me”; he must “be very careful that I don’t contract ‘em.”  “’To be sure,’ said Mr Pinch. ‘Very proper.’”)   But at length, Marvin’s account of his haughty rebuke to his elder relative, is too much for poor Tom to swallow whole.  It is his glimpsing that flash of Satanic pride -- that non serviam -- which sets Pinch to staring, wide-eyed, sightlessly, into the fire:  into the depths of the fiery pit.

To resume the mathematical metaphor:   This ignispective image is visually equivalent for Martin as for Tom, but means something a bit different.  It represents, if you will, the punctual intersection of two life-curves;  and its meaning in momentum-space is given  not by the locus alone, but by the tangent.

Happy, umm, Th*nksg*v*ng

[Update November 2014]  Since people are still viewing this old post, it’s best to update.  BLUF:  Stand down.  There seem to be few or no mainstream attacks against Thanksgiving  this year.  Go figure.  In fact, the principle MSM article that came to our notice, was the spread of Thanksgiving paraphernalia to the land of our former colonial masters, England.

For this, as for so much else,  

we give thanks.

~ Original Post, 2013 ~

First Columbus Day.    And now -- what -- is Thanksgiving too  now Politically-Incorrect?

How to talk to your children about Thanksgiving's ugly history

http://www.latimes.com/opinion/opinion-la/la-ol-thanksgiving-history-children-20131126,0,1226806.story

(One strains to imagine the nationwide epidemic of family dramas that presumably led to that post. Little Susie, a teardrop suspended from her button-nose:  “M-m-mommy … This turkey t-tastes like genocide …”)

A reader retorts:

Thanksgiving Day is about neither history nor patriotism -- nor is it about Indians -- it's a day we set aside to give thanks -- to God or our families or fortune -- for what we have, as much or as little as it may be.  Period.

It's rather pitiful that a petty little prig chooses to dwell not on thanks but on resentment, though it's no surprise that a pompous mediocrity like The Times chooses to publish her.

[Update] No worries -- The politically correct term this year is “Thanksgivukkah”

http://www.washingtonpost.com/lifestyle/style/where-is-it-thanksgivukkah-year-round-at-home-with-the-nava-jews/2013/11/27/a4d65e02-554e-11e3-8304-caf30787c0a9_story.html?hpid=z1

That chimeric coinage “Thanksgivukkah”  rivals that of Gröfaz for sheer phonetic grotesquerie.  It looks as though it should rhyme with “F*ck ya” (which is indeed the message to those whose ancestors founded this nation), but presumably some other pronunciation is intended.

Note:  This newly-minted wordoid “Thanksgivukkah” is something of a lexicological mayfly, not expected to see long wear:  Hanukkah and Thanksgiving are not expected to coincide again  for over seventy thousand years …

~

Oof, and now this:

http://newsbusters.org/blogs/pj-gladnick/2012/11/26/slate-writer-racism-could-explain-white-turkey-meat-preference

[Flash update!]  Our crack research team here at WDJ Worldwide Enterprises ® (Headquarters:  Geneva) has dug into the matter and uncovered the real reason for the previously unexplained preference for white meat.  The answer might surprise you!  It has to do with the game of chess.  Here, the White pieces get the first move, which gives them a slight advantage over Black.   This explains the otherwise puzzling preference for tender turkey breast over the dried-out, tough and sinewy drumsticks.

~

Our Thanksgiving-related woes have been noted abroad.  Here, in Switzerland:

Fest unter Druck

http://www.nzz.ch/aktuell/international/auslandnachrichten/black-thursday-an-thanksgivukkah-1.18193626

 

*

Falls Sie im Doktor-Justiz-Sammelsurium

weiterblättern möchten,

Bitte hier klicken:

http://worldofdrjustice.blogspot.com/search/label/Deutschtum

*

[After-thought]  If the apostles of goodthink (what the French these days call bisounours) imagine that, by posting such an edgy op-ed as their corporate contribution to the holiday spirit, they are bringing us all together for a thoughtful dialogue, followed by singing kumbaya around the fireside and sewing-circle, they are -- simply as an empirical matter -- sadly deluded.   The dissenting reader’s-comment with which we opened this post, is actually relatively measured;  more typical are such testy replies as the following:

THERE’S A REMOTE CHANCE THAT INDIANS WERE NOT LIVING IN A HIPPIE COMMUNE WHEN WE GOT HERE
The accepted narrative for Native Americans is they were all playing Ring Around the Rosie until we blew germs on them and they all fell down. Though he had a helluva time getting it published, Lawrence H. Keeley’s War Before Civilization debunks that myth. The book describes common traditions such as mutilating a body AFTER it was killed to ensure the victim was doomed in the afterlife. We learn of mass graves with hundreds of scalped cadavers a good half-century before Columbus got there. Indian traditions have many wonderful traits, but let’s grow up a little and allow for the possibility they were simply incompatible with the modern world. For Christ’s sake, when we got here they hadn’t even invented the wheel.

Happy Thanksgivukkah

countered (from the opposing wing, the Atavist camp) by such blasts as

The so-called Thanksgiving story imparted to most American schoolchildren is a triumphalist, sectionalist Yankee national origin myth.

Although the on-the-air-heads in the Fluff Room (which has replaced the Newsroom at many media) cannot perceive it, posting a piece like that at a sensitive time like a solemn national holiday, makes as much sense as putting up Dylan’s “Masters of War” to mark Veteran’s Day, or a historical account of the doctrine of Jewish blood-guilt for Yom Kippur.

~     ~     ~

Other holiday-related posts:

   * Fourth of July

   * Veterans Day

   * Hallowe’en

   * Christmas Eve

   * Christmas

~

For a selection of individual detective stories,

available for your Nook or Kindle,

visit this site:

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

~

.

Homology versus Analogy in the taxonomy of tetropods

[Excerpt from a sort of novel or extended meditation in progress, Life With Each Other]

Laura was a practical person; yet, out of the blue one day, as they were reading next to each other in bed, she remarked:  “We don’t look much like dinosaurs.”

“I’ve noticed that myself, “ Ronald replied thoughtfully.  “It’s hard to believe that we’re cousins.”

“Yes, I guess you’re right,” said Laura, who was familiar with the basic facts of paleobiology.  “We’re more like cousins than actual descendents.”

Ronald looked pensive, then brightened, as offering a sort of amical compromise.  “But we’d look a lot more alike if dinosaurs wore clothes.”

“That’s true!” Laura gasped, and almost clapped her hands.

“ `How pretty you look today, Mrs. Brontosaurus, in that nice new poke bonnet. ‘ ”

The Physics of Snow-Bunnies

Snow-bunnies inhabit their own funny geometry.  They scamper and frisk every whichway, yet every trajectory a snow-bunny takes, is a geodesic.  That’s why the rapid movements of snow-bunnies are so effortless.

When a snow-bunny runs into a black hole, they cancel.

Since snowbunnies move infinitely quickly, infinity has a different meaning for them than it does for us.  But it’s still pretty big.

They run, and they run, and they never stop, lest  like a photon  they cease to be.

[Learn more about our fleet friends the snowbunnies, here.]

Chess Challenge (further updated)

[ Zur Problematik des Schachspiels "im Zeitalter seiner technischen Reproduzierbarkeit"]

We earlier marveled at the proliferation, in our generation, of musical prodigies (performers, not composers, though).  In athletics as well, performance is just plain better than it ever was.

Another human activity that has continued to improve is designing chess engines.   They have improved … alarmingly.  Not long ago, a grandmaster lost to a suitably programmed cell-phone.  The machines have won.

Ever since computers started whupping grandmasters, it has pretty much ruined the romance of the game -- much as similar technical developments scotched the potential vaudeville careers of mnemonic or calculating savants.  It’s a mug’s game, two alpha males knocking themselves out each to beat the other, when neither is as good as a machine.  From now on, human-only chess tournaments are like women’s soccer, or even the Special Olympics.

Granted, the computers’ prowess is itself a human achievement.  These things didn't just drift in from Andromeda.  We built them, we programmed them, we told them what to do.  We invented the heuristics that allowed performance to evolve to the next step.  Only, at some point, emergent factors take over, and our invention kind of gets away from us.  “The equations were wiser than I was,” as Maxwell said of his own.  And these Big Blues and what have you  start to stick in everybody’s craw.

So, a proposal:   Duffers, of course, will keep just duffing along, for fun.  But at the highest levels of play, we need a new mission.  And this, not to beat each other up, but specifically to target the machines.   This will be to a large extent a collaborative, rather than a purely competitive enterprise.  The game will be purified of the boardside antics, knuckle-cracking and cigar-smoke-blowing and a radio receiver in the ear.  More like the Apollo program, of putting a man on the moon.  Which man, did not matter.  Instead, collectively, passionately-yet-dispassionately, study the cybernetic style of play, probe it, discover its shallow spots.   Then strike a blow for us bipeds, for the honor of -- well, the warrior, really.   Colossus delendus est !

*

Für psychologisch tiefgreifende Krimis,

in pikanter amerikanischer Mundart,

und christlich gesinnt,

klicken Sie bitte hier:

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

*

And just how (you scoff) is such a development to come about?

Not in any way that we can imagine -- but then special relativity, quantum mechanics, and general relativity were unimaginable until they were born as fact.

Next time we'll be on the same side of the board...

Now -- it might be that chess is only somewhat less shallow than checkers (which fell to machines long ago), and that there is little room for improvement.  In which case, the contest isn’t interesting.   A hydraulic lift can heft more than any human weightlifter;  a computer beats humans within the current understanding of the game.

But it might be, that chess, as many say of Go, is deep indeed.   The way forward then would be to develop some entirely new strategy of play and lines of attack -- not necessarily stronger, in any meta-metric, than what we have now, but outside the ken of the computer.    The computers could start to lose.  Now, to keep the contest interesting, programmers would have to be forbidden from importing “the answers” into their programs:  it would be us against the cybernetic heuristics.   That is the only arena in which our Colossus may seem some sort of independent intelligence.  And if it eventually beats us then, um, somebody be ready to pull the plug.

[Update 22 Nov 2013]  Chess is now a compulsory subject in Indian schools, reports the NZZ:

In Indien, seit Viswanathan Anand im Jahr 2000 erstmals Weltmeister geworden ist, hat die Zahl der professionellen Schachspieler im Land rasant zugenommen. Das Spiel ist zu einem Pflichtfach in Schulen geworden.

«Viele Kinder können heute nicht mehr stillsitzen. Beim Schachspielen lernen sie, sich zu konzentrieren und strategisch zu denken»

This is a welcome development.   Composed with our suggested “moon-shot” project  of pitting humanity versus machinery across the board, this will bring us back towards the origins of the game, in which both sets of pieces represented an army.  Instead of single combat as at present, it will be a pitched battle.

Home Guide to Mental Serenity

Simply count elephants!

I began talking with the driver.  He was an expatriate from San Francisco, an elephant expert who was spending his time counting elephants in the Thai jungle because he thought, “America is going crazy.  Going nuts, going to the dogs.  Going to the wow-wows.”  He went to Thailand to get his sanity back, and in Thailand he only trusted elephants.  He slept in the bush at night, and in the morning he got up, grabbed his elephant-counter, and just counted elephants.

-- Spalding Gray, Swimming to Cambodia (1985)

For more fun with elephants, simply click here !!

http://worldofdrjustice.blogspot.com/2013/11/here-come-elephants.html

“Hope You Guess My Name”

As part of the semicentennial commemoration of the assassination of JFK, the radio today, after playing Kennedy’s “Clear and Present Danger” speech about the missiles in Cuba, segued into a song I haven’t listened to in years:  the Rolling Stones classic “Sympathy for the Devil”, with its refrain

            Pleased to meet you -- Hope you guess my name!

The transition seemed jarring, until the song came to the verse

            I shouted out, ‘Who killed the Kennedys?”

            when after all, it was You - And - Me.

Now, ever since the very first time I heard it, that line has struck me as extremely lame, on several levels.  But there is no point critiquing it [*], since, after all, it is the Devil speaking:  The Prince of Lies.

[*] I’ll do so anyway.  Along with the line “For every cop is a criminal, / and allllll the sinners -- saints!”, it was well-calibrated to appeal to the sentiments of the layabout, shop-lifting hippies of the day.

One pictures the late-night rap sessions, amid the cannabis vapors --

            “Yeh-h, man -- we allll killed Kennedy!”

            “Far out, man …”    ]

~

Those unfamiliar with both the ecclesiastical and the folk take on the diabolistic tradition, will think nothing of that apparently pointless aside, “Hope you guess my name”.   But it is rooted in the nature of that master dissembler’s wiles and ways.  And that refrain, it now strikes me, likes at the back of the series of mystery stories I published awhile back, first in magazines and then collected in logical (indeed, theological) sequence,  as a book, I Don’t Do Divorce Cases.  They start of reasonably conventionally, but row progressively more strange, until one of them, a Miltonic memory, appears in the meter of Paradise Lost. 

In each, the detective, Michael Xavier Murphy, an outwardly lapsed or at least slovenly Catholic, must solve some little problem or other, assisted by his younger brother Joey, typically involving a purportedly missing person;  but each case is overspanned by a meta-problematic:  to guess the name of the Agent behind the client.  As the series progresses, the cloven hoof of Clootie projects ever more insolently out from beneath the hem of his sable mantle.  As, in the story, “The Temptation of Murphy”:

After he’s gone, Joey stares at me, something’s occurred to him.  ‘Hey Murphy -- we never even asked the name of our client!’

Bitterly:  “Whaddaya wann know ‘is name for, Joey?  You know who he is.

Anyhow, I commend them to your attention.  Further particulars here:

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

A subsequent story, published separately for Kindle and Nook, involving direct confrontation with His Satanic Majesty (a battle to which Murphy proves here unequal, since it involves another soul than his own, and must call in aid from a very special sort of specialist), can be sampled here:

http://murphybros.blogspot.com/2011/04/murphy-calls-in-specialist.html

Gradus ad Parnassum

We are familiar with the genre of spiritual (auto)biography.

First, our young enlightenee-to-be  experiences little but Unordnung und frühes Leid;  then, groping and grappling with shadowly intuited truths; then at some point there supervenes something supernatural -- most starkly, in the form of angelic intervention. 

Thus, Muhammad of Mecca, “enwrapped” (a detail telling in its biographical specificity -- this is not just all made-up -- it’s like the detail of Jesus doodling with his finger in the sand), alternately sweating and shivering in his Cave of Retreat, at last is confronted with an Archangel, who (after some preliminaries which it would delicious to retell, but which space does not permit), says:  Iqra’! (“Read!” -- or rather, “Recite!” or “Repeat after me!”)  and reveals the Qur’an.  

Likewise the future Saint Augustine.  He led a misspent youth, at one point sinking to the actual infamy of stealing pears (!);  until one day, a unseen voice cried out: 

Tolle, lege!

(‘Pick up [the Bible] and read!’)

After these interventions, it is pretty much smooth sailing for our Chosen Ones (one of the epithets of Muhammad,  Mustafa, means precisely ‘chosen’), who never look back.

~

And now we come to the intellectual autobiography -- specifically, the mathematical memoir -- of Edward Frenkel (Френкель, Эдвард, de son vrai nom):  Love and Math.

He too grew up in somewhat unpromising circumstances, well outside of Moscow, which for a Soviet of the time  was as cruel a fate as living far from Paris, for the French.  Jewish to boot, which meant that, so far from being called (here in a secular sense summoned, rather than that of ‘having a calling’), he was actually turned away at the gate, and later (not taking nyet for an answer) had literally to scale a fence and sneak past armed guards to reach the seminar rooms of that sanctum sanctorum, Moscow State University.
(There is some takeaway here for idealistic educators:  You can paint the classrooms with colors as bright as you like, but ultimately it comes down to student capability, and motivation.)

Now, all that high adventure is fine preparation for an actor, or a novelist, or a revolutionary, but is not especially helpful to gain a grounding in the principles and arcana of contemporary mathematics:  a path that has risen at an ever-increasing pitch, since antiquity, and branched into perplexing byways, before the blessed consilience  of synthesis, such as Cartesian geometry, the Erlangen Program, and latterly the Langlands Program, forged new anastomoses, reknitting the whole thing.  Yet at the age of sixteen, when most of us are just learning to shave (or looking forward to needing to -- meanwhile, these pesky pimples), he somehow comes to the attention of a world-class mathematician, who refers him to the special care of one of the archangels of the field, Prof. Dmitry Fuchs.  Fuchs hands him an article from the forefront of breaking research, and says:  Tolle, lege.  (Or, one supposes, принять! читать!)   And the next thing you know, our shaveling is attending the legendary evening seminars of that god among men, I.M. Gelfand -- the Wiener Kreis of Soviet mathematics --  understanding everything, and swiftly publishing a research breakthrough of his own.  By the time he is twenty-one (barely old enough to vote, when I was that age), he has been summoned to Harvard.

(For anecdotal evidence about how hard this stuff is, even for people who have been doing math their whole life, try this:  Oligophrenia mathematica.)

~

Now, if you have never yourself grappled with research-forefront mathematics, you will have no idea how extraordinary, almost preposterous, that account is.  The epiphany-stories of Muhammad and of Augustine, which theophobes will dismiss out of hand as «miraculous» (as though the presence of a miracle itself suffices to spoil the tale, like a fly in the soup), are humdrum by comparison.

For, both those chosen were presented with texts in a language they already knew (Arabic and Latin respectively), and which  moreover  had been composed specifically to be received by the masses (with imperfect understanding, it may be, but getting the gist and the uplift).  The Qur'an, indeed, helpfully mentions that it has been revealed «in plain Arabic».   Whereas the Fuchsian manuscript presupposes millennia of progressively more successful wrestling, with abstruse insights, by the finest minds on earth.
So:  Either Professor Frenkel is embellishing just a bit, or rather compressing, in retrospect, or else this scene indeed was:  a miracle.  For, for anyone else, that manuscript would have been a book  of seven times seven seals.

~

Frenkel's heart is in the right place.   He has joined with such popularizers as Stanislas Dehaene, in suggesting that more or less everyone has la bosse des maths,  the little darlings need merely be placed into the right pot and watered, and they will bud and blossom.   The invariant come-on is a pointing to results «beautiful and elegant».   On the very first page of his book, attempting to explain the public indifference or actual aversion to what they imagine to constitute math, Frenkel writes:

What if at school  you had to take an 'art class' in which you were only taught how to paint a fence? ... While the paintings of the great masters are readily available, the math of the great masters  is locked away.

True, and nicely observed. But such beauty and such elegance are perceptible only to the mind prepared -- otherwise it is like playing Bach to a baby.

The suggestion that one can chug one's way to the top of this particular ethereal Parnassus, simply with hard work and the right attitude (I think I can, I think I can), fits in well with the myth of the Little Engine that Could, that I and my playmates were brought up on, pluckily chugging uphill.  Whereas in practice, the brave little engine makes it only as far as the first false-peak, never ascending the Ladder of Abstraction that lies beyond; while one of your company  suddenly sprouts wings, and is halfway up the slope.

The position that we are all Gausses in nuce, if only we were given half a  chance, likewise fits in well with the anti-innatist, doggedly/dogmatically environmentalist political-correctitudes of our own day.   Yet I am here not really plunking for either side of that false dichotomy.   Yes, both are necessary, sweat-equity and the right genes;  but beyond that, something mysterious ... Call it Grace.

Well;  bless him.  May his infinite series never fail to converge, may his commutators ever commute.  For the rest of us, we must be content with a Pisgah-glimpse.  And to reconcile ourselves to the following refractory, diamond-hard truth:

Not that many are even called,

and precious few are chosen.

~     ~     ~

[A note to my readers, puzzled  perhaps  by a sudden change in punctuation-style.   My word-processor, for reasons best known to itself, between the hour at which I posted the beginning of this essay, and a moment ago when I posted the rest, has suddenly and inexplicably switched from American-style quotation-marks  to the angled version favored in France (or, in reverse order, in Germany).  Apparently the software has been favored with some sort of epiphany, to which I myself am not privy.
Perhaps, as the day wears on, the keyboard will begin printing in Cyrillic.  And yea, I shall be baffled thereby, and sore afraid.
Then strange symbols, and equations, will begin creeping in:  and I shall shake, in fear and trembling.
But then a voice from on high rings out --

TOLLE -- LEGE !

And all will be well.]

~

Further reading:

Beauty as a criterion of truth in math and science.

Mathematical autobiography: 

            André Weil

            Neal Koblitz

Psychologia mathematica:  Invention and Insight 

Chess Challenge (updated)

Updated here/ Mise à jour ici / Hier auf den neuesten Stand gebracht:

http://worldofdrjustice.blogspot.com/2013/11/chess-challenge-further-updated.html