Thursday, January 30, 2014

Arnoldian Epigram





            Proofs are to mathematics  what spelling is to poetry.
            -- V.I. Arnold





Wednesday, January 29, 2014

Word of the Day: “thug”


I do not follow sports.  So when I saw this item in the table of contents for this week’s New Yorker -- “Amy Davidson on the Richard Sherman affair” -- it meant nothing to me.   I read it only because it is the lead article in the lead section -- “Talk of the Town”:  a spot that, in recent years, is reserved for weighing-in on matters of wide moment, often written by the editor-in-chief.   (For the first decades of the magazine, which was born in a spirit of cheeky and amiable humor, it was more often some winsome pen-portrait of a walk about town, written from the standpoint of the editorial “we” -- which takes reflexive singular concord:  ourself, not ourselves.  But we have all become so serious since those days…)

It turns out that Richard Sherman is -- Well, but you know that already;  you don’t need old Doctor Justice (peering up behind bifocals, from his dusty books) to tell you about him. 

Anyhow, turns out the fellow is a splendid cornerback who just insured his team’s participation in the Superbowl.   Hero, right?  No, villain, thanks to the magic of Social Media.


The fairly undisputed facts are these:

(1)  A pass was thrown to one Crabtree, that might have saved the game for the other side, and Sherman forced an interception.
(2)  In the NFL equivalent of the traditional sportsmanlike tennis gesture of the winner’s leaping over the net to shake hands with one’s respected colleague who happens not to have won this one, Mr. Sherman went up to Mr. Crabtee with outstretched hand.  (Tennis was formerly a sport of decorum, but has since been subject to the mass fanbase with its Darwinian imperative.)
(3)  Crabtree then shoved him in the facemask -- which, football fans will know, is more serious than it sounds, “Facemask” bringing a particularly severe penalty in play.
(4) Interviewed immediately after that, Mr. Sherman unfortunately followed the example, not of the judicious Nestor, but of Achilles, if not Thersites.
(5) For this he was roundly hounded by the Erinyes of Twitter.

Now, what lifts this from the level of quotidian sports trivia, into something worthy of the lead article in The New Yorker,  is that the incident illustrates the increasingly perturbing power of YouTube and Twitter to serve as the contemporary equivalent of the Salem Witch Trials, though with even less evidence.  The anonymous online audience is like a crowd of cicadas:  Devastate;  devastate;  move on.

Richard Sherman, fleeing the Furies

As Ms. Davidson shows in her excellent essay, Mr.  Sherman may be about as close as you can come (certain exceptions aside), in these debased days, to a Gentleman and Scholar (a Stanford alum, no less) in the NFL.   His autodéfense in the matter of the “epic rant”, is almost poetry:

It was loud,
it was in the moment,
and it was a small part of the person I am.

(Even Achilles, you might recall, was not without his faults.  And I don’t mean just the heel.)  Indeed, as Ms. Davidson reports,

He talked about the switch he has to turn on and off to play “a very barbaric sport”.

And the thing about switches is:  If (like the human soul) the item it regulates has a large capacitor, then turning it On or Off  does not result in an instantaneous change of state.   Mr. Sherman was evidently still in barbarian mode when (among the screams from the stands) some reporter shoved a microphone into his face.

~

Well, so, anyhow.  What business have I, a linguist, to blog about this at all.   The fragile peg I’ll hang it on is simply this:
The word that came up again and again in the Tweets denouncing him (sent from the comfort of a Laz-E-Boy, with chips and a drink ready to hand) was “thug”.  (A semantic bridge was perhaps provided by rappers’ approving use of gangsta.) Mr. Sherman observed that this “bothers me because it seems like it’s the accepted way of calling somebody the N-word nowadays.”   And as someone who closely follows the Vox Populi in the Readers Comments columns, I can attest that this is true;  much as, in an earlier generation, in America, inner city came to be a code-word for ‘obstreperous minorities’;  much as, in our own generation, in France, la banlieue has come to mean the same thing (somewhat ironically, since it literally means ‘the outer cities’ or suburbs;  the connotation is thus the opposite of that for suburbs). 

In any event, I wish Mr. Sherman a splendid SuperBowl, just as I do for his worthy opponents.   May that team win, which Fortuna-the-fickle favors.   And may the warriors, en preux chevaliers, embrace one another afterwards, regardless of the outcome, as befits scholars and gentlemen.

~

For an essay on the logic of tournament sports, try this:
       The Badminton Gambit


Stop me if you’ve heard this one!


Jevver hear the one about the Priest, the Rabbi, and the Mother-in-Law, walking into a bar?


-- If not, you never will, if the Féministes of France get their way:


You can still make fun of priests (in fact, that same faction encourages you to), and still make fun of …. we-ll, maybe not rabbis: but imams, for sure [**].   But Mothers-in-Law will be off-limits, by order of the Speech Police.  

[** Footnote:  Actually, that only goes for the United States.  In Europe, the subject is by now completely taboo.]

Mysogyny is to be outlawed;  mysandry … Aber freilich;  be my guest.


[Mehr zum Thema:  La chasse aux hommes.]

Monday, January 27, 2014

Mathematical hamsters


The following hamsters are mathematical:

Fluffy




Fuzzy




The proof is left as an exercise.

For extra credit:  Show that Fluffy and Fuzzy constitute an orthonormal vector basis for the entire mathematical hamsterspace.
[Hint:  Sad;  Happy;  get it?]


Sunday, January 26, 2014

A menace to penguins


We interrupt your weekend merry-making  with a red alert:

Let us imagine a planet covered with calm water. If you drop a large rock into the water at the North Pole, a wave will propagate out  in a circle of ever-increasing radius.  In due course, however, this circle will reach the equator, after which it will start [inexorably] to shrink,  until eventually the whole wave raches the South Pole at once, in a sudden burst of energy.
-- “Manifolds and Differential Geometry”, in Timothy Gowers, ed., The Princeton Companion to Mathematics (2008), p. 44

Moral of the story:  DO NOT DROP A LARGE ROCK INTO THE WATER AT THE NORTH POLE !  It would swamp the penguins!

[Note for connoisseurs:  This effect is an analog of what S|G|NTers call "antip*dal recepti*n", one variety of the 'whispering-gallery' phenomenon.]

Incidentally -- For an example of a manifold in the form of a differentiable penguin, click here.

Saturday, January 25, 2014

On Movies and Moral Anchors


(Reflections on “The Wolf of Wall Street”.)

I am comfortable with complexity,
and I think I’m pretty good at keeping my moral compass
while recognizing that I am a product of original sin.
-- President Barack Obama (quoted in the current New Yorker)

Had it been merely up to me, I would not have gone and seen the movie, based upon David Denby’s review in The New Yorker, and a general lack of interest in watching Wall Street sharks on the screen.   (In this respect, they are classed with serial killers, boxers, and baseball players on my personal cinematic to-avoid list.)   The blandishments of glitz and drugs are among those I happen to be immune to.   And, had I been watching it alone, rather than in the company of a Named U.S. Spouseperson who (a stone Di Caprio fan) was loving every minute of it, I would have walked out after half an hour.   My appetite for cinematic depravity is extremely limited;  for a time, I actually used to dial up the minute-long recorded reviews provided telephonically by the Catholic Church, for some guidance as to what to see.   Yet, having stayed, I found much to enjoy, principally the comedy, both physical and verbal.

We went, knowing that the film was controversial.   My companion had been perturbed that people had been denouncing the film by saying that the villain doesn’t get his comeuppance.   After  we had seen the actual movie, she wondered which movie the others had seen.  She rather thought that losing your wife, your kids, your house, your car, your bank balance, and going to jail,  does count as a comeuppance of some sort.
However, what makes a movie moral  is by no means that the ultimate verdict of Judgment Day shall be anticipated here in this life -- as it so manifestly is not, despite the hype and come-ons from certain motivational evangelists outside the discipline of the Historical Church.   It is probably a good thing that movies aimed at children do mete out such punishments and rewards on-screen, by way of gently shepherding the development of Just Deserts, to be followed later by that of Right and Wrong, ultimately to be heightened and quite transformed in the fullness of Christian understanding.    Hollywood habitually panders to the childish desires of its audience in this regard, as the Historical Church notably does not;  but we cannot fault Mr Scorcese for refraining from regressing to that level.  Moreover, he was closely following the perpetrator’s memoirs in his narration:  the actual scamster was not sent to prison for life, nor was he struck down by a thunderbolt from the blue, nor (as the Erinyes would have it)  gobbled up by gerbils, beginning with the genitals;  sorry, it didn’t happen.

~

The critical reactions to this film have been all over the map.
The Guardian reviewer complains (with what passes  in these times  for the equity of Solomon) that, while much pussy is on display, we do not likewise get to set lots ‘n’ lots ‘n’  lots  of cocks, and the one they did show he found (apparently a connoisseur) personally disappointing (duly noted;  "More cocks for the gentleman in aisle three, please")  And he objects, with great Correctitude, that “With a couple of notable exceptions, the women here are all wives, girlfriends and sex-workers.”  (The complete absence of nuns,  woman Supreme Court justices, or female astronaut-cum-brain-surgeon-cum-rocket-scientists from the trading floor  is indeed inexplicable other than by imputations of sexism.)  Though also (as he does not note):  with (as we shall argue) only one notable exception, there are no admirable men.  --  Folks:  If you want positive role-models for women, do not go to Wall Street, neither in the movie-house or on lower Manhattan.  (Cf. further the excellent memoir Liar’s Poker in this regard.)   And if you want to see your favorite identity-group  glowingly portrayed upon the silver screen -- women, or Hispanics, or plumbers, or meteorologists, or Pacific Islanders -- then make a movie; don’t kibbitz the one that other people have made. 
Actually, as the Telegraph reviewer pointed out, the movie does make an extra-textual concession to current sensibilities:

Scorsese includes a sensational scene that echoes the moment in The Public Enemy where Cagney vengefully pushes half a grapefruit into the face of his lover. Here, though, it is Belfort’s outraged trophy wife Naomi, played by Margot Robbie, who hurls a first, second, then third glass of water in her husband’s face, while he throws a spluttering tantrum.

That is very much in line with the current fashion, in movies and especially on television, of depicting men as schlumpfs (an emasculated Cagney) being easily pushed around by superwomen.  Maybe that’s an improvement, matter of taste;  but surely we have seen enough of that.
(There are other scenes of Belfort being masochistically abused:  One  by wife  as he crawls on the floor, the whole thing watched on a hidden camera; and one by a somewhat homely dominatrix -- an unpleasant scene (mercifully brief), but which ends with a very funny line:  “Wolfie, Wolfie!” he yelps, as the hot wax becomes too much;  yet she continues the torture.  “Hey, that’s my Safe Word!” he objects, in the jargon of that sad trade.  Fuck your safe-word” she retorts, and keeps on abusing him .)

~

And what of that lone male exception to the general depravity, which I mentioned earlier?
“Down these mean streets, there must walk a man, who is not himself mean.” (The credo of PI Phillip Marlowe.)   In this movie, in a brief and understated role, that upright man is Denham, the FBI investigator (based, we are told, upon the real agent Gregory Coleman, whom we here salute).   The small but crucial role is played with great patience and self-effacement by Kyle Chandler, whose visage in repose  says more than words.   The virtues of such dogged self-restraint recall those we praised in our review of Argo,  concerning the role taken up by actor/director Ben Affleck.

Among the most poignant and elegiac moments in movies, come towards the very end of the weary road traveled, and occur without words.  Such is the silent and solitary walk beneath the falling leaves, that culminates “The Third Man”;  such, the blowing leaves across the lawn, as a single shot rings out in the distance, in the second “Godfather”;  and such, here, the agent’s lonely ride on the New York subway, after another wearying day at work, as he silently beholds the care-worn faces of the strangers around him, whom he is sworn to protect.

Roger Ebert:

Belfort chides the prosecutor Denham for living what Henry Hill would have called the goody-two-shoes life, and in a scene near the end, as Denham rides the subway home, we can see that the taunt stuck in his craw.

(He’s not a prosecutor, he’s an FBI investigator, but anyway.)

David Thomson agrees:
When he tells the FBI man who has been tracking him for years that on his lowly government salary the agent will still be riding home on a hot, slow subway watching the lost faces he’s supposed to be protecting, this could be the bravado of a crook on the run. But then the movie depicts that glum moment and Mr. FBI looks like a stooge who realizes every Belfort boast was gold.

That might well be the director’s intention;  I don’t know, I saw it through my own lenses, with a vision entirely different, tutored and clarified is it has been  by the example of Father Brown.   As Denham’s eyes beheld the tired and decent subway-riders at the end of another workday, to me it felt like a return to sanity.  Here were the people that Belfort had fleeced:  and -- thanks to Denham’s tireless efforts -- Belfort (as we are reminded in the next shot, surely a hint at what was in Denham’s mind as well at that moment)  was heading off for a stretch in the slammer. 

The perspective I have in mind  is difficult to convey in a few lines;  but I shall try, simply by way of pointing to a short work which, all in itself, is worth a dozen of the films of Mr. Scorcese:  G.K. Chesterton’s “The Queer Feet”, featuring the portly bespectacled detective-priest, Father Brown.   In this tale, Brown is obliged by circumstances to undo a swindle being perpetrated upon “The Twelve True Fishermen” (the name is an irony), these being a group as select and wealthy as the money-men of Wall Street:

Since it is immeasurably unlikely that you will ever rise high enough in the social world  to find “The Twelve True Fishermen”, or that you will ever sink low enough among slums and criminals to find Father Brown, I fear you will never hear the story at all  unless you hear it from me.

The key to solving the mystery, which Father Brown, even more immured than Nero Wolfe, solves purely by listening to footsteps, from within the confines of a cloakroom, lies in something just a bit off about the rhythm,  just as, in the classic story “The Wrong Shape”, it turns upon a subtle corruption of shape.

Father Brown recovers the silver loot and returns it to its (improper) owners, while recovering (how far more precious a treasure) the thief to Grace.  (Though, in a merely physical sense, he lets him go.)

“Did you catch this man?” asked the colonel, frowning.
Father Brown looked him  full in his frowning face.   “Yes,” he said, “I caught him, with an unseen hook  and an invisible line  which is long enough to let him wander to the ends of the world, and still to bring him back with a twitch upon the thread.”

Laus deo!

And then, his work there done (though never understood or properly appreciated),  Father Brown must end his workday.

And saying “Good evening,”  he pushed upon the heavy doors of that palace of pleasures.  The golden gates closed behind him, and he went at a brisk walk through the damp, dark streets,  in search of a penny omnibus.

~

Thus far have faith and philosophy had their say.   What of the actual human viewer?   Consider the response of my companion, who watched the whole thing enthralled.
At one point, as the Bureau’s investigation inexorably progressed, she remarked (the first thing she had said in the course of the movie): “It’s too bad he’s doing things that are illegal.”
I turned and stared.  “Um, honey, even apart from that:  he is not a good man….”
Her attitude (which I report with reticence) flowed by no means from generalized moral obtuseness, but from a specific scotoma supplied from the collective unconscious, from the psychic substrate from which we grow:  She sees in Di Caprio the visual image of her former suitor and her current son.  (This insight was originally supplied to me by someone who knows us both.)  Do not scoff at this;  it is because of such instincts that mothers put up with us at all.


~

A.O. Scott begins and ends his review with a question;  respectively,

Does it offer a sustained and compelling diagnosis of the terminal pathology that afflicts us, or is it an especially florid symptom of the disease?
and
Does “The Wolf of Wall Street” condemn or celebrate?

Answer (respectively):  “Neither”;  and “Both”.

It’s not important to “get this movie right”;  it is not an important movie.   One good friend hated it;  my wife loved it;  de gustibus.   The bacchanalia quickly fades;  eternal things remain.


Wednesday, January 22, 2014

The Yellow Card Man


For Christmas, our son gave me Stephen King’s recent novel, 11/22/63.  (He might have chosen a more mellifluous and less mouth-filling a title, I must say;  mais passons.)  A quite intriguing minor character is the “Yellow-Card Man”.  What he is up to, I cannot yet say;  but consider this predecessor, from a century before:


And this, where he appears with a different symbol, other than the yellow card:

     The Umbrella man in Dealey Plaza

Tuesday, January 21, 2014

Definition, Description, Delimitation


One of the signal developments in semantic theory during my lifetime  has been an increased appreciation for the role of prototypes in organizing our knowledge.  To introduce or elucidate a concept, don’t try to define -- to delimit -- the whole domain, which can get fuzzy around the periphery:  give a central, typical, illuminating example.  Thus

sparrows, and animals like that

clams and the like

are not-half-bad characterizations of the idea of ‘bird’ or ‘mollusc’.  You might need to learn a bit more become earning your doctorate in zoology, but for ordinary folks, for everyday purposes, that is pretty much what we mean by bird and mollusc. 

There are tons of such structures in mathematics, where the prototype literally came first and then was generalized.   Thus, the integers are the prototype for ring theory;  although, as a matter of idiom, mathematicians usually do not say “prototype”, but motivating example.  

(For further examples, and a vigorous defense in principle, from some leading Russian mathematicians, of the wisdom of motivating-examples for mathematical pedagogy -- and indeed, even for mature cognition -- try this:  Abstraction and Generality.)


Now, this procedure works only if the prototype is antecedently known.  Thus, to revert to zoology, suppose you run across the term Chelicerata and ask your naturalist friend what that means.  Casually he replies, “Oh, that’s like harvestmen and solifugae, and all that sort of thing.”  You’d probably be pretty much where you started out.

Such was my experience, while trying to learn what is meant by "vertex operator algebra", upon meeting this helpful hint:

“Chiral algebras are the prototypical examples of a vertex operator algebra.”

So profound is my ignorance of anything touching on the subject,  so stygian is the blackness of my nescience, that it got me no further forward.

~

The status of “What is …?” questions  differs pragmatically -- subtly but importantly -- depending upon circumstances, in particular what field fills in the blank.   Thus, suppose you ask, “What is exobiology?”, already knowing the sense of exo- and biology but being unclear as to what these parts mean in conjunction (sort of like the opposite of “internal medicine”, perhaps?  Like dermatology, or the study of scales and fur?).  Upon being told that, no, it means the study of extraterrestrial life (should any such exist), you have been told all you need to know. 

Take it a step further:  “What is etymology, as opposed to entomology?”  (a question which, as a licensed etymologist, I have indeed many times met).   In this case you’ll be enlightened merely by “Word-origins versus insects”.  For here your semantic Wissbegierde is probably minimal, and may be actually zero as regards one or other of the paronyms:  you simply want to be set straight about an easily confusable pair.  In this case, clarification happened via verbal signs;  but it need not.  The case shades into those in which no intension is involved at all, but merely extension -- reference.    As, “Which of the Wilson twins is Bobby?”   A satisfactory answer might be simply pointing;  the questioner is not asking, “Who is Bobby Wilson really -- as a person?”
We may say that, in this case, we have definition not as description, but as delimitation.   Such a style of defining is called ostensive definition.

(Note:  Such a duality between interior/intension and boundary/delimitation  may remind adepts  of that jewel in the crown of the higher calculus, the generalized Stokes Theorem, displayed in all its refulgence here.   However, the analogy is superficial.)

A similar case from the vocabulary of mathematics.   I ask, “What is a semigroup, as opposed to a quasigroup?”  Without the second phrase, I might be asking for a concise but contentful thumbnail, such as “like a group but lacking inverses”.  But perhaps I simply stumbled across both terms on the back of a cereal box.   Now my friend admonishes:  “Semigroups are the things we met briefly back in undergraduate algebra, remember?  Quasigroups are fancy new items which, if you can’t even recall the definition of a semigroup, you really oughtn’t to go bothering your head about.”

O-oh, so-o-o … Do we feel patronized by that?  Okay, here you go, an actual definition, quoted from Wikipedia:

A quasigroup (Q, *, \, /) is a type (2,2,2) algebra satisfying the identities:
  • y = x * (x \ y) ;
  • y = x \ (x * y) ;
  • y = (y / x) * x ;
  • y = (y * x) / x .

Nun, alles klar?
~


Sometimes to be met with in the practice of math (the praxis, rather than the pre-existing body of truth), and scarcely outside it, is the dialectical definition:  Posit, analyze, refute, sublate;  repeat until golden brown.    Lakatos’ Proofs and Refutations illustrates the process.  (For an example of such a “working, preliminary definition”, click here.)


~


Further illustration of the vocabulary, with concrete examples:

Just as Euclidean space can be thought of as the model Riemannian manifold, Minkowski space  with the flat Minkowski metric is the model Lorentzian manifold.
-- http://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold

This is not “model” in the sense of mathematical “model theory”;  it is an informal term equivalent to the linguists’ prototypical.   The latter is occasionally also used;  as here, by algebraic topologist Raoul Bott, speaking pedagogically in the introduction to a text:

We use the de Rham theory as the prototype of all cohomology.

~

For further considerations, focusing mainly on math, try this:


For the lexicography of mathematics proper, this:

    What is Mathematics?”

Appendix to "la quenelle" : the "Rabi`ah"



[Update Jan 2014]   There is a ludic, aesthetic dimension to this, which you notice immediately in the case of the ungainly quenelle (at least you do if you are not humor-impaired, like Valls and Hollande), along with a certain modest pride in coming up with a gesture that never previously existed.   Here is a somewhat subtler case:






This gesture is new to the global political landscape, and could only have been born in Arabic, in particular in Egypt.   For it depends upon an Arabic double-pun.

The hand is holding up four fingers (thus the visual pun in "R4BIA").  The reference is to Râbi`ah Square in Cairo, where protests against the military coup that overthew the elected President Mursi were held.  The square is so named after a medieval saint,


رابعة العدوية


“Huh?” you say.   Well, although Râbi`ah was her name, like many names in Arabic  it has a literal dictionary meaning:  in this case, the feminine form of the adjective meaning ‘fourth’.   Reinforcing the four-ness of it all is the fact that Râbi`ah Square, unlike its more famous Cairene sister Tahrîr, a large, roughly round arena,  is a quadrangle, fed by four streets, in which the demonstrators massed.   So something of a pun.
Or actually, a double one, or else none at all, depending upon whether you think the next link in the etymology reinforces or reverses the sense of word-play.  For the saint herself was named, not by randomly selecting a girl’s-name out of a hat, but because she was the fourth born in order.


[Update]  The Director of the Latin Divison at the World of Dr Justice (headquarters:  Geneva), Dr Keith A. Massey,  weighs in with this:

Romans also named their children by ordinal numbers, hence things like Julia Secunda, Quintus, etc.

Somehow, to our present perspective, that seems sort of impersonal.  But -- autre temps, autre moeurs.


[Update 2]  For a tendentious piece, but with lots of intriguing information, try this:




[Update 3]
It is a  matter of current debate, to what extent this Rabiah symbol, born in a broad-based protest, has been hijacked by extremist jihadi groups.   The matter is not entirely academic;  it could affect actual choices in CT.
My hunch is that, simply as a matter of psycho-geometry, the symbol is ill-suited to serve Salafists, let alone out-and-out takfiris.   It is too inclusive, like those four streets all leading into the square, as though from all four corners of the Earth.  Quadruplicity, as we know from Russell, drinks procrastination;  it does not quaff Hotspur.  (Inside joke, folks, you get it or you don’t;  moving along.)   And if Jung is correct (which he probably is not), this implication common among Westerners  should be universal.   


Indeed, if any number were to be a symbol for Muslims, it would have to be one, since Muslims are such rigorous monotheists.  As, accordingly, the finger-gesture:

Kamal asked, “When is he going to forgive you?”
The mother gestured upward with her index finger and murmured, “Forgiveness comes from God.”
-- Naguib Mahfouz, Palace Walk (transl. of Bayn al-Qasrayn, 1956), 1990, p. 210

(That gesture has also been common in recent years  among evangelical Christians.)


Note further that, for those using the gesture, it is not simply “holding up your open hand” (as opposed, say, to a militant fist), as it might strike a Westerner;  it quite definitely contrasts with a five-finger symbol that antedates it by centuries in the Mediterranean region:

To ward off the evil eye, Khadija spread her fingers apart  and held up her hand with the palm facing Yasin, reciting “And from the evil of the envious person in his envy.” (Qur’an 113:5)
-- Naguib Mahfouz, Palace of Desire (transl. of Qasr al-Shawq, 1957), 1991, p. 34


If someone flashed you that symbol, it would be an insult;  much as the Quaker/hippie two-fingered “Peace” sign, if performed palm-in and in England, means something very bad.   And, just as with that last example, if you turn the palm inward for the Muslim five-finger gesture, it changes the meaning, in this case from hostile to friendly:

He spread his hand across his chest to express his thanks.
-- Naguib Mahfouz, Palace of Desire (transl. of Qasr al-Shawq, 1957), 1991, p. 138

For more on the khamsa  خمسة‎, see


[Afterpiece]

Let us dwell a bit upon the semiology of gesture in the Arab world.

Some gestures are apparently instinctual, and hence seem transparent, and probably universal.  As:

… flogging the ground with his camel-stick  to give emphasis to his words
-- Wilfred Thesiger,  Arabian Sands (1959; repr. 1990), p. 160

He shook his head rather forcefully  as if to expel these thoughts.
-- Naguib Mahfouz, Sugar Street (transl. of al-Sukkariyya, 1957), 1992, p. 30

Others are clearly more culturally conditioned:

We squatted down to drink, for no Arab drinks standing.
-- Wilfred Thesiger,  Arabian Sands (1959; repr. 1990), p. 165

She held her hand out to him  after wrapping it in a corner of her cloth, so she would not nullify his state of ritual cleanliness.
-- Naguib Mahfouz, Palace Walk (transl. of Bayn al-Qasrayn, 1956), 1990, p.

I once put my hand on the back of bin Kabina’s neck, and he turned on me and asked furiously if I took him for a slave.
-- Wilfred Thesiger,  Arabian Sands (1959; repr. 1990), p.  163

Ibn Sa’oud had ridden up to his enemy’s tent, and laid his hand upon the tent pole  so that the prince of the Shammar had no choice but to let him enter.
-- Gertrude Bell, The Desert and the Sown (1907, repr. 2001), p. 47

Antiquity breathes through such gestures.   Intrigued, I queried the official Latin and Theological authority of this site, whether there were any parallels from Roman history, and received this reply:

Roman citizens always reclined to eat or drink. The slaves always stood.
In fact, one of the accepted rituals for manumission was to ask the slave to recline and join you at table. If you did this in the presence of witnesses, you had de facto set the slave free.

It is for this reason that the default stance at Liturgy in the Historical Church has always been standing. At Liturgy we are hoi douloi tou Theou, the servants of God, standing ready to serve him.

Early on, people began to feel that, at particularly "high" moments of Liturgy, the reading of the Gospel, the Consecration of the Eucharist, the Lord's Prayer, they wanted to kneel.
The Fathers of the Church were so concerned at this incorrect impulse that they passed a Canon at the 1st Council of Nicaea, banning kneeling on Sunday, period.
When people persisted in violating this Canon, St. John Chrysostom wrote into the Liturgy the correction:

"Let us stand upright and listen to the words of the Holy Gospel."

And yet, in most Orthodox Churches you will still see people drop to their knees, precisely when the Liturgy reminds them that they are forbidden to do so.

Rome has recently also waged a war on this point, reminding the faithful that the only stance that is always correct in Liturgy is standing.


For further thoughts on psychogeometry, in a mathematical/theological context, try this:
On Symbols.

[Update 13 Sept 2014] Another visual Muslim symbol, this one banned in Germany:

http://worldofdrjustice.blogspot.com/2014/09/flagge-verbot.html


 [Update 3 Oct 14]  For a lovely gallery of recent political hand-gestures, now this:





http://www.washingtonpost.com/blogs/worldviews/wp/2014/10/02/hong-kongs-crossed-arms-and-other-hand-gestures-of-defiance-around-the-world/?tid=hpModule_04941f10-8a79-11e2-98d9-3012c1cd8d1e

One might add the "one-finger" gesture of ISIL, but that is not so much protest as triumphalism.