Saturday, June 29, 2013

Ideas: the case of Induction

[We continue with our survey of leading Ideas, begun here.]

(3) Induction

            There are logical problems with practical induction, notorious since Hume.  That we nonetheless freely (and even over-freely) constantly make use of it, might suggest that it reflects merely an innate disposition, reinforced because often successful (the world being, contingently, the way it is), thus logically on a par with the inveterate conviction of salmon that they need to swim upstream and spawn – which also usually works.  So let me creep up on it genetically, via something at least similar to the notion of induction, which I did not always take for granted (hence its eventual attainment may count, albeit marginally, as an Idea).
            For Parents Night, our third-grade teacher put samples on the blackboard  of multiplication problems  mastered by her class.  Everyone in the class could multiply a one-digit number by a one-digit number, she explained; eighty percent could multiply a two-digit number by a two-digit number, and one pupil (unnamed, but in fact your correspondant) could multiply a three-digit number by a three-digit number.  Not unnaturally proud of this accomplishment – which already was my first glimmering of an idea  not widespread in the lowest-common-denominator society of primary school, viz. that individual abilities might differ – I jauntily asked my father, How many digits can *you* multiply?
            The response I expected was something like “five” (he being an adult), or even “seven” (he being a scientist), or maybe even “ten” (what a special Dad!).  Instead he looked puzzled, even embarrassed.  It was not, he said, a well-defined question.  Multiplying numbers of *any* length was just a small homogeneous step up from multiplying slightly shorter numbers.  In practice you might become confused, and have to carefully write things down and check your work (indeed there *is* an individually varying limit as to how formidable a pair of numbers one can multiply in one’s *head*, but that was not the ability under discussion); yet in principle there was no limit to it, just as there wasn’t any highest number one could count to:  if you make it as far as n, you can get to n + 1.
            Now, he didn’t explain it quite as clearly as that, I imagine, but whatever it was he did say  triggered a flash of insight in my small head.  From that moment on  I had a completely different attitude to arithmetic as taught, to school as conducted, even a different attitude towards knowledge and education in general.  The teacher, from being an oracle, shrank to a small frail figure indeed.  And the problems on the blackboard were no longer confined to their chalky two dimensions, but bored outward, into the void.

            So far, there’s been no demonstration of an Idea beyond what we were born with, merely the application of same to phenomena initially conceived to be beyond its reach.  That is, the child began by conceiving the multiplication of two-digit numbers and the multiplication of four-digit numbers  to be as distinct as bipeds and quadrupeds, and we do not conceive six-legged insects and eight-legged spiders and octopuses to be some sort of inductive continuation of these.  But by the time we have arrived at mathematical induction, there does seem to be something new under the sun.  Given (by demonstration or observation) the truth of F(0), and proving that F(k) implies F(k+1), we suddenly, by these two little finite exercises, have access to an infinitity of truths, down to uncharted reaches of the sample space.

And lest you consider that elementary anecdote  a mere trifle of childhood, the smooth and indefinite extensibility of multiplication being obvious to any mature mind,
consider this, from John von Neumann:

In an analogy machine [what we now call an analogical computer, when we call it anything at all, since these have largely fallen by the wayside -- ed.],  a precision of 1 in 10^3 is easy to achieve; 1 in 10^4 somewhat difficult; ... 1 in 10^6 impossible …
In a digital machine, the above precisions mean merely that one builds the machine to 3,4,5, 6 decimal places … The transition .. gets actually  easier …
--- quoted in  James R. Newman, ed. World of Mathematics (1956), p. 2077

Compare further this parable:

[Continued here.]

Friday, June 28, 2013

A Simple Explanation

Q:  Why do bunnies have long ears?
A:  So they’ll be easy for children to draw.

Bunny, hearkening to the Music of the Spheres (too high for you to hear)

[For further fascinating totally-true fact-checked and verified Natural History revelations,
click here:
When Penguins Ruled the Earth .

For more wonderful bunnyfun, here. ]

Tuesday, June 25, 2013

Les dernières nouvelles dans la chasse aux hommes (mises à jour)

Prefatory anecdote:
Recalling his days as a prisoner in San Quentin, Jan Valtin writes, in Bend in the River (1942), p. 89:

He and the others played ball for a half hour each day  in a small concrete yard  wedged between the garden and Death Row, while  from a nearby balcony,  smartly dressed women, young and old and armed with opera glasses, looked on.  These women came day after day  from near and far  to pay the prison treasury a half dollar for the privilege of watching men doomed to be hanged  play ball.


For some reason, the following story has not yet been reported in the anglophone press, so here you go.   U heard it here first …

Gentlemen are requested to be seated

Un député suédois va défendre cette semaine une loi obligeant les hommes à uriner assis. Objectif selon lui : améliorer l'hygiène, renforcer l'égalité homme-femme. Cette obligation permettrait aussi, selon les tenants de cette proposition, de renforcer l'égalité des sexes, un thème cher aux Suédois, en mettant les hommes et les femmes... au même niveau.
Et depuis l'an dernier, le dictionnaire compte un nouveau mot: «Hen», un pronom neutre entre le «il» et le «elle».

Mannekin Pis --  Soon to be illegal in politicalcorrectness-stan

As usual, the readers have better sense than the Scandinavian PC-fanatics:

L'hygiène au contraire, exige au contraire à ne jamais s'asseoir dans des toilettes publiques ! pour ces pauvres suédois, et en vertu du respect de l'égalité, on pourrait mettre les hommes en jupe puisque nous avons pris leurs pantalons !
On attend impatiemment les solutions des féministes pour réduire la durée de vie des femmes, une inégalité scandaleuse d'après leur logique.
A quand une loi pour le sens du rouleau de PQ ? parce que ça aussi c'est pénible ! 1 an de prison en cas de récidive !
Et pourquoi ne pas obliger les femmes à uriner debout ???? Il existe des accessoires utilisés en navigation maritime qui le permette.....
Les hommes devront-ils aussi utiliser des soutifs et des tampons, par souci d'égalité?

Si cela vous parle,
savourez la série noire
en argot authentique d’Amérique :

[Update 9 June 2013]   And now this:

Sweden male train drivers wear skirts after shorts row

At this rate, skirts may become not merely optional but mandatory for Swedish men, for ease of squatting at micturition.

[Update 12 Sept 2013]  Good Lord, manskirts now at the University of Cambridge as well:

[Update 22 June 2013]  And now this, Gawwd help us:

Dans un pays, où la lutte pour l'égalité entre les sexes fait rage, un nouveau mot a fait son apparition : hen. C'est un pronom neutre appelé à remplacer «il» et «elle». Cette coquetterie grammaticale, encouragée par les militants de la théorie du genre, a même fait son apparition dans un livre pour enfants.
Dans le monde idéal des livres publiés par Olika en Suède, tous les pères font la cuisine, certains refusent d'aller travailler pour rester à la maison et ils pleurent sans qu'on les traite de mauviette. S'ils ne peuvent encore allaiter, ils savent tous préparer le biberon. C'est nécessaire surtout lorsqu'ils sont deux pères à élever leur enfant. Les filles postulent pour des postes de scientifiques, les garçons, des emplois de sage-femme et un petit gars peut porter des baskets à paillettes à l'école. Les enfants ne se moqueront pas de lui. Dans ce monde, on imagine même gommer le sexe de l'enfant pour éviter que des stéréotypes d'un autre âge ne brident son évolution et n'entachent son épanouissement.

Mais ils deviennent fous, ces suédois!

[Update 25 June 2013]  From Sweden, we let our camera lens turn to Italy,  where an all-female three-judge panel has just condemned former premier Silvio Berlusconi to seven days in jail for having consorted with a prostitute who lied (quite plausibly, judging by her photos) about her age:  none other than this delicate maiden, this paragon of virginal virtue:

The Virgin Ruby

No wait -- not seven days, seven weeks.
No wait -- seven months.  No… uh-oh … (can this be correct? for consorting with a whore?)
Seven years.

I hold no brief whatsoever for Berlusconi, no more than for Al Capone:  a crook, a clown, a blot upon all Italia.  But the verdict of this troika of harpies  leaves a sour taste …

As usual, the reportage and commentary in Le Figaro  does not disappoint.  We offer a generous selection (as much for the benefit of students of French, as anything -- several fine idioms here):

Une nouvelle condamnation au palmarès du «Cavaliere». Au terme de sept heures de délibérations, le tribunal de Milan a condamné lundi Silvio Berlusconi à 7 ans de prison et à une peine d'inéligibilité à vie dans la sulfureuse affaire du «Rubygate». L'ancien président du Conseil italien était poursuivi pour incitation à la prostitution de mineure et pour abus de pouvoir: il a été reconnu coupable dans ces deux volets de l'affaire.

Ce verdict, résultat d'une procédure de deux ans, est plus sévère que les six ans de prison réclamés lors des réquisitions. «Il Cavaliere», âgé de 76 ans et sénateur depuis les élections de février, est condamné pour avoir eu des relations sexuelles tarifées avec la danseuse marocaine Karima El Mahroug, alias «Ruby la voleuse de cœurs», alors que celle-ci était encore mineure. Les faits se seraient notamment déroulés lors des fameuses soirées orgiaques dites «bunga bunga», organisées par Berlusconi dans sa villa d'Arcore, près de Milan, entre février et mai 2010. La condamnation pour abus de pouvoir concerne une affaire distincte, dans laquelle Berlusconi était accusé d'avoir fait libérer la jeune femme en mai 2010, alors qu'elle était au commissariat pour le vol d'un bracelet d'une valeur de 3000 euros.
[Readers’ comments:]
Il est vrai que lorsqu’on voit la jeune personne de la photo, nul doute qu’il s’agit d’un « détournement de mineure ». Les juges italiens … en l’occurrence les « femmes juges italiennes » qui ont condamné le Cavaliere ont tout à fait la tête de l’emploi… des moches et frustrées de la vie. Pas du tout dans le genre de cette magnifique Ruby que personne, en tant qu’homme, ne saurait dédaigner ! Ils ont perdu la cervelle les justiciers (ères) d’outre-alpes.
Pouet-pouetique la RUBY, on s'en occuperait avec plaisir....
J'aimerai assez que les juges mettent autant de zèle à condamner les jeunes prostituées mineures qu'ile mettent à condamner les clients !
Une prostituée mineure qui ment *volontairement* sur son âge devrait être considérée comme adulte.
Au-delà du fait qui lui est reproché , je note que comme en France chaque fois qu'il s'agit de tribunaux jugeant des faits de société , comme les divorces ou les histoires de moeurs les juges sont essentiellement des femmes .On peut avoir quelques doutes sur l'impartialité .La parité est réclamée à gauche mais seulement aus endroits choisis .

il faut qu il arrete les liftings, on dirait une vieille dame
Dans l'entreprise où je travaillais fin des années 80, on a diffusé aux cadres en réunion un petit film pour illustrer la "réussite" des entrepreneurs chéris du président Mitterrand. On y voyait le président remettre la légion d'honneur à 3 personnages,Berlusconi, Tapie, et Carlo de Benedetti.
Un an après, les 3 étaient en prison pour des affaires d'argent. La cassette a disparu comme par magie.

Those of you whose classical education deals easily with a reference to “harpies”, are ready for the next step:

So kommt es, wenn die Erynen, die Rachegöttinnen des olympischen Götterhimmels, die Hybris eines Machos und Staatsmannes bestrafen, der von unterhalb der Gürtellinie gesteuert wird und darob den Kopf verliert.

[Update 18 VII 2014] Overturned on appeal:

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

 For another notable example of a prominent European politician (and scoundrel) pursued for the wrong reasons, by a judicial system gone mad:


[Update 9 November 2013]  The latest madness from Sweden:

Gravity échoue au test féministe suédois
Harry Potter, Le Seigneur des Anneaux et d'autres blockbusters ont failli au test de Bechdel, mis en place par quatre cinémas scandinaves et censé déterminer le degré de sexisme des longs-métrages.
Chez les champions de la parité homme-femme, les films sont soumis à une nouvelle cote. Désormais, en Suède, les fictions sont bien sûr classées selon leur niveau de violence ou d'érotisme, mais aussi en fonction de leur degré de machisme! C'est parce qu'elle jugeait la place des femmes trop marginale au cinéma que Alison Bechdel, auteur américaine de BD, a imaginé ce test dans une de ses œuvres, Les Lesbiennes à suivre (1985). Selon une planche de la bande dessinée, un film noté «A» réunit trois critères: au moins deux personnages féminins sont présents dans l'intrigue, elles doivent se parler entre elles, et aborder d'autres sujets que les hommes. Quatre cinéma suédois ont décidé d'appliquer ce test.

Sur l'année 2012- 2013, seuls Hunger Games, Blue Jasmine, Man of Steel ont réussi le test de Bechdel. Qui sont les mauvais élèves? Majoritairement des blockbusters. «La trilogie du Seigneur des anneaux, tous les Harry Potter sauf un, Star Wars, The Social Network, Pulp Fiction», énumère Ellen Tejle, directrice du cinéma Bio Rio à Stockholm. Plus surprenant, Gravity a lui aussi échoué. Le film de science-fiction d'Alfonso Cuarón fait pourtant la part belle au courage féminin. Sandra Bullock porte le film à elle seule et fait preuve d'un instinct de survie que peu d'hommes pourraient revendiquer. Mais l'actrice est la seule femme à l'écran et peut donc difficilement parler à un personnage du même sexe.
Hollywood semble séduit par le test de Bechdel. «Une notation féministe? C'est tellement intéressant, s'est exclamé l'actrice et productrice Jada Pinkett Smith, lors d'un dîner caritatif pour l'égalité homme-femme. «Voyons si cela fonctionne!» Mais le système compte aussi ses premiers détracteurs. «S'ils veulent plus de femmes dans les films, ils ont qu'à les produire eux-mêmes plutôt que pointer du doigt les réalisateurs», proteste la physicienne Tanja Bergkvist sur son blog consacré à la «folie du féminisme».

[Update 27 Aug 2014] More re Swedish political-correctnes:
now with a new relevance, given this:

[Update 14 Oct 2014] 

Sunday, June 23, 2013

A Subcontinental Platonist

It is not only Europeans, or Christians, or inheritors of the Greek tradition, or those philosophically schooled, who have arrived (semi-independently) at a position of Realism in mathematics.
This, from a most engaging biography of the Indian number-theorist Ramanujan:

In the West, there was an old debate as to whether mathematical reality was made by mathematicians  or, existing independently, was merely discovered by them.  Ramanujan was squarely in the latter camp:  for him, numbers and their mathematical relationships  fairly threw off clues to how the universe fit together.  Each new theorem was one more piece of the Infinite unfathomed.  He told a friend:  “An  equation for me has no meaning unless it expresses a thought of God.”
-- Robert Kanigel, The Man who Knew Infinity (1991), p. 66

For more on the theme, click here:

[Footnote:  To Kanigel's credit, he has a section towards the end which examines even-handedly the possible influences of Ramanujan's spirituality upon his style of math.  The account is neither credulous nor dismissive -- that is all we ever ask.]

Thursday, June 20, 2013

Syria: Logic vs. Victimology Porn

For many years, I subscribed to NPR.  For certain reasons, I no longer do;  but I still sometimes listen to their news broadcasts.   And a staple of their reporting over recent months has been tragical stories from refugee camps, recounting the woeful tales of the women and children.   The locations vary -- neighboring Sudan, or Somalia, or Iraq, or wherever, the details doubtless soon vanishing like mist from the listeners’ minds -- but always with one theme that, with repeated repetition, is reinforced rather than overwritten:   that the victims are women (and children;  but more prominently women, since it is they, rather than the children, who get interviewed). 
And one day it occurred to me:  Where are all the men, who are seldom if ever mentioned.   Off playing golf, or dining off room-service in some five-star hotel?  -- Given where folks have been fleeing from, more likely slain, or imprisoned and tortured.   But their fate, whatever it might be, does not excite the interest of NPR.

[Update Saturday, 15 June 2013, 12:07 p.m. EST]
Disclaimer:  There are indeed atrocities, particularly in that part of the world, which specifically target women;  the following being just the latest, which just now broke into the news:

Gunmen have attacked a hospital in the western Pakistani city of Quetta, hours after an explosion on a bus killed at least 11 female university students.

Actually, it turns out that even this superficially straightforward story  has layers.  Hearing this story the way it was reported on NPR (it was the top item, just moments  ago), listeners will naturally assume that this was an attack upon women students as such, in objection to female higher education;  such attacks have indeed been the practice of the Afghan Taliban (or at least reported to be so).  But the article goes on:

An extremist Sunni militant group, Laskar-e-Jhangvi, told the BBC it carried out both attacks.   A man calling himself spokesman for the group said they were a revenge for an earlier raid by security forces against the group in which a woman and children were killed.

So who knows what the real story is.  In any case, our point in this post  has nothing to do with the details of this tragedy or that, but with the way the media packages and spins the news, typically to specs that will serve the desired pre-existing narrative.


Today’s big story has been the report that just came out, estimating the cumulative number of dead in Syria’s civil war  as 93 thousand -- “most of them,” NPR assures us, “civilians”, and many of them children; including "more than" so&so-many children under the age of whatever; including cute winsome towsel-haired dollie-clutching girlchildren.
These headlines were repeated throughout the day;  until, this evening, happening to flip the radio on towards the end of an hour’s broadcast, where some stories go into more detail, I heard the following.  The dead in that conflict are … 80% male.  To repeat:  eighty percent male.
The anchorwoman, not pausing for the bat of a mascara’d eyelash to digest this statement, which undermines the thrust (or rather spin) of their whole story as packaged for American p.c. consumption, rushed on to query the gal reporterperson about the percentages of children among the victims.  This elicited a bit of hemming and hawing, at which point I shut the receiver off in disgust.

Their slant is thus arithmetically impossible.  The warriors are almost a hundred percent male;  the civilians, therefore, fewer than fifty percent male (how much less -- call it X -- depends on the percentage of warfighters in the population).   If one hundred percent of the deaths were civilian, the percentage of male deaths would therefore be X -- less than half.   Plug in whatever numbers you like, you can’t get a majority of civilian deaths with 80 percent of the actual victims being male.


The impulse to post this was purely logical, just one instance of the importance of statistical literacy for policy decisions.  (American Scientist has run some excellent articles on this theme, e.g. as regards the assessment of school performance.)  But there is indeed an invidious gender dimension to this story, all too characteristic of the way the world has turned in the past several decades.   For more, click here:

Medical scandal:  Women are dying like flies !!  (again with a statistical twist, and an NPR focus)
Gentlemen are requested to be seated  (you must be over 18 to click on this)

Yet though what caught our eye was an arithmetical fallacy, the principle noxious effect of the NPR propaganda concerns neither statistical literacy nor the gender wars, but international politics.   For the point of the story was to add to the chorus calling for US arming the anti-Assad forces, or “rebels” as they are (to American tastes) comfortably known.  (Contrast “insurgents”, which means the same thing but has quite different connotations.)   The point was reinforced by a companion story, revealing that Washington has now concurred with France and Britain that Syria has used chemical weapons -- an action which the President had rather imprudently called a “red line”, so the obvious question now is, Whatcha gonna do about it?

For some time now, the noisy John McCain, his appetite for war against Muslim governments  still not slaked by Afghanistan, Iraq, and Libya, has been calling for just that.    Well and good;  but it is essential, before blundering in to yet another morass, to the sounds of drums and trumpets, to cast a cool eye on the facts, so far as these are known.

Nota bene:  I bear no brief either for or against President Assad;  and even if I did, this would not motivate my comments here, since  -- for very good reasons -- no-one cares about my political opinions (indeed, being vastly fallible contingencies relating to this transient world here below, they scarcely interest even me).  Accordingly, as per the WDJ Guidebook, I shall emphasize logical and statistical considerations, independent of party fervor.

And so to work.

(1)  A logical point.
The following allegation has garnered a fairish concensus:

   (a) Chemical weapons have been used in Syria

There are some forensic problems here, but  for present purposes  we can set those aside.  Note only that (a) is not logically equivalent to the following proposition, which is however, the one that pops into every American’s mind when he hears (a):

   (b) Chemical weapons have been used by the Syrian government

Nor, if true, does (b) logically entail (c):

   (c)  Chemical weapons have not been used by the Syrian opposition.

Yet, absent the truth of (c), calls for intervention based purely upon the alleged transgression of that “red line”  rest upon sand.
Some investigators have in fact concluded to the falsity of (c);  but that is an empirical question best left to the experts.  (And you internauts can find the reports more expertly than I.)  I here make merely a logico-rhetorical point, concerning implicit assumptions.

(2) A statistical point.
What percentage of those 93,000 deaths  do you suppose are due to chemical weapons?  Again, let us ignore the forensic difficulties (tests not being performed on the actual battlefield immediately subsequent to the alleged use, but on samples provided by one side or the other, which can be doctored), and just consider the numbers.  The maximum figure so far alleged, out of those 93 thousand, is …
… (check your own assumptions before scrolling down)
… …
somewhere upwards of a hundred.
Why then is sarin a red line, whereas indiscriminate bombardment of population centers is, say, pinkish?

(3)  The next point is neither logical nor statistical;  yet still apolitical and basic.

In addition to all the numbers being tossed around, there is a qualitative side to all this.  For, although empirically the conflict pits pro-government forces against anti-government forces (and even that is a simplification, since much “pro”-government sentiment is really anti-antigovernment), the texture, the flavor, cannot be captured by such a dichotomy.  And it is by no means simply that of Tyranny versus Democracy.  De facto, the war is increasingly confessional -- sectarian.
And what might these sects and confessions be?  Well, on one side, we have Shiites and Christians (and perhaps Kurds);  on the other Sunnis.   So, simply on that basis, which would Americans wish to support?  Which side would John McCain presumably support?
[Think I’ll pause here.  Check your own assumptions, and later scroll to the exciting conclusion.]

[Clock ticks;  time passes accordingly …]


*     *     *
~ Commercial break ~
Relief for beleaguered Nook lovers!
We now return you to your regularly scheduled essay.

*     *     *

Okay, the answer you’ve all been waiting for:  The government faction is largely Shiite and Christian.  So McCain is calling for support for the side that, should they win, are most likely to start slitting the throats of Christians.  (Witness Iraq, Egypt, and Boko Haram.)
Yet again nota bene:  I am not here  myself indulging in any sort of victimology porn -- I make no assumptions that a dead Christian is any more a tragedy than a dead Sunni or Shiite or whatever you wish.   The point is simply that, in ululating for intervention, most of John McCain’s partisans do not know what they are about.

Additionally, quite apart from the sectarian affiliations of either side, consider that the rebel forces have been significantly swelled by non-Syrian Salafi/takfiri carpetbaggers, largely organized by al-Qaeda in Iraq:  these currently constitute the ginger group.  However, recently the government side has been augmented by Hizbollah carpetbaggers from Lebanon, who have already proved their military might, man-for-man.  So from that aspect, it’s kind of a wash.

(4)  A logico-statistical point:

Given the caveats that have been raised about whether both sides may have used chemical weapons, an analogous question logically presents itself as regards that blood-curdling figure of 93,000 killed.
The way this story is spun leads unreflective members of the audience to assume that most or all of that total were killed by government forces.   To take just one story at random (this one from the Washington Post):

Nearly 93,000 people have been confirmed killed in the conflict in Syria, the United Nations said Thursday, as it warned that more bloodshed could be imminent in the northern city of Aleppo, where government troops have massed.

Note the artful juxtaposition of two independent facts, suggesting a causal connection.
But then -- What have the rebels been up to, those we propose further to arm?  Apparently just distributing chewing-gum to children, and tossing flowers at government troops.
Again, I’m not arguing for one side or the other;  merely pointing out that this obvious question is typically not even posed.

(5)  Another logico-statistical point.

Let us bracket all the caveats above, and assume that, from an American perspective, a rebel victory in Syria is a consummation devoutly to be wished.  What follows from this?
Well, before you answer, “Barge in with both barrels blazing!”, consider than there are thousands if not millions of situations around the world in which we might fervently desire outcome X over outcome Y.   Yet  we do not always and everywhere  violently intervene, in part because (again bracketing the disasters that often follow good intentions, and the basic validity of meddling in other nations’ affairs) our resources are limited.   To justify the cost of intervening in venue Z (again assuming that we have a perfect right to do anything we please in the world, whenever it strikes our fancy), one criterion is essential:  a reasonable likelihood of success.
Now, the likely eventual success of the Syrian rebels (or rather, the anti-government forces in Syria, consisting of both Syrians and of foreign soldiers-of-fortune)  has long been paraded in the media as a given:  like the elusive Higgs boson, it is always just around the corner, and yet (like the procrastinating Monsieur Godot) never quite arriving.  Now, the London Review of Books this week has an interesting article by Patrick Cockburn on just this issue, which I commend to your attention,
pointing out an essential asymmetry in the YouTube wars.   Draw your own conclusions;  the matter, being empirical, is no part of our brief here.  Our only point is that such considerations matter.

(6)  One final observation, before I retire to my couch, for a night of blameless repose  and dreamless sleep -- and here we must stray far from our proper province of purely logical commentary, and wade into the swamps of subjectivity and geopolitical Fingerspitzengefühl:

Out of all the woes of this world, why would John “Bomb bomb bomb, bomb bomb Iran” McCain  choose to focus on this one? 
(I am here channeling Humphrey Bogart’s similar question in “Casablanca”.  For more on the slippery  “bomb-bomb” faction, click here:
Anyone who has been following events over the last couple of decades -- or indeed, over the last hundred years -- has leave to doubt that the prime motivation here is the politically colorblind mission of promoting and spreading “Democracy”.   And even if you believe that such was indeed the motivation from Wilson down to Dubya, the actual results of our recent nation-building adventures in Afghanistan and Iraq  should give anyone pause, to say nothing of other venues of the Arab Spring.
Nay more -- democracy-transplants aside, it is not even apodictic that all these motions and maneuverings on the part of the interventionists  primarily concern Syria.   Recall the neocon watchword back in 2003:  Everyone wants to go to Baghad;  real men want to go to Tehran.”   Refresh your memory with the equation:  Assad … Iran… Hizbollah … Shiites …  And consider (and here we definitely stray from anything simply logical or in any way uncontested) in whose interest our Mideast foreign policy has been conducted for many years … from the USS Liberty through Iran-Contra down to the bogus case against Iraq (long prepared by tools like William Safire) … and consider, coolly from the standpoint of Realpolitik, in whose primary interest it lies  to combat Assad, and Iran, and Hizbollah … ?

Falls Sie im Doktor-Justiz-Sammelsurium
weiterblättern möchten,
Bitte hier klicken:

[Flash update, 15 June 2013]  It turns out this whole “red line” thing was just smoke ‘n’ mirrors, a tour de passe-passe in the Société du spectacle:

So funny.  -- In particular, we now are pleased to gallantly retract our earlier characterization of President Obama’s earlier “red line” remarks as “incautious”:  instead, they were cannily calculated.   While seemingly painting the Administration into a box (see our essay on pre-commitment), in actual fact it was a box they had already decided to occupy:  Rook to Knight’s Five!

(I thought of putting a link to this post in the Comments section of that WaPo article, but that bull(shitt)y pulpit of vox populi is already so bloated with idiotic repetitious fact-free Obama-bashing unrelated to the facts of the Syrian situation, and barely even nodding towards the ten-second hand-puppet popular version of events (since the conclusion to be reached is present in advance:  that Muslim Kenyan socialist in the Black House is the pits), that it would be worse than pointless.   Anyone relishing that loose-stool stream of inexpert invective, would scarce find himself at home in our own austere and ivied halls.)

~ Celebrity Endorsement ~
“I -- Vladimir Putin.  I say, is all booolsheet.
You want read good truthy “pravda” stuff,
you read this instead:”
Murphy and the Magic Pawnshop

The New York Times puts a slightly different spin on the story,

All this must, like the Watergate hearings, (lest we lose our reason) simply be enjoyed as public theatre.  And here, from that article,  the culturally au-courant  telling detail:

His ambivalence about the decision seemed evident even in the way it was announced. Mr. Obama left it to a deputy national security adviser, Benjamin J. Rhodes, to declare Thursday evening that the president’s “red line” on chemical weapons had been crossed and that support to the opposition would be increased. At the time, Mr. Obama was addressing a gay pride event in the East Room.

O tempora, O fagedabouddit.


~ ~ Посмертный Одобрение

"Если бы я был жив сегодня, и в настроении для тайны,

это то, что я хотел бы читать: "

Я не делаю случае развода

Мерфи на горе.

Иосиф Сталин, и я одобрил это сообщение.)

~ ~

[Update 20 June 2013] 

Despite months of laboratory testing and scrutiny by top U.S. scientists, the Obama administration’s case for arming Syria’s rebels rests on unverifiable claims that the Syrian government used chemical weapons against its own people, according to diplomats and experts.

[Update 21 June 2013]  Yet another indication that the “red line” was political theatre:

CIA operatives and U.S. special operations troops have been secretly training Syrian rebels with anti-tank and anti-aircraft weapons since late last year. The covert U.S. training at bases in Jordan and Turkey began months before President Obama approved plans to begin directly arming the opposition.

 And a sobering thought:
In the first months of the conflict, it seemed to be going well for the rebels, particularly given some high-level defections from the Assad regime -- if the rats were deserting, the ship must be sinking, it seemed.   Yet lately the tide seems to have turned.   So, why would we go in now?
There are innocent possible explanations for this.  But a more meta, more geopolitical, more Realpolitik calculation suggests itself as well.   Rather than let the insurgency collapse, give them just enough to keep going, without actually winning -- a strategy of “A plague on both your houses” and “Let’s you and him fight.”

[Update 13 July 2013]  He said / she said:

[Update November 2015]  Canada:  Rescue the women, leave the men to die.

"Canada's exclusion of single male refugees may exacerbate Syrian conflict"
Die neue kanadische Regierung will bis zum Ende des Jahres 25.000 syrische Flüchtlinge aufnehmen, junge Männer dabei aber ausschließen.
Guardian vom 24.11.2015

[Update New Year's Day, 2016]  Authoritative casualty figures have just been released.  The number of Syrian war dead during 2015  tops 55,000, including 30,000 women and over 40,000 children.
The number of victims of color  had not been determined at press time.

Tuesday, June 18, 2013

Recent developments in the Riemann Conspiracy

A little-noticed news item:

Journalist who ended Gen. McChrystal's career dies in crash
Michael Hastings, best known for a Rolling Stone feature that led to the resignation of Gen. Stanley McChrystal, died early Tuesday in a car crash in Los Angeles

The sting against McChrystal was a bigger deal, really, than people realized, given what a key role he played in our nation’s geopolitico-military strategy, and how trumped-up was the entrapment (gotcha-journalism strikes again) that brought him down.   Still, this fait-divers of the LA police blotter  would not excite our interest, but for the following detail, buried in that account:

Coroner's officials said they could not immediately identify the victim, saying the body was burned beyond recognition. Without identification or next of kin, neither the LAPD nor the coroner's department could officially identify the body found in the vehicle.

Immediately, the seasoned observer of the dark doings known generically as the “Riemann Conspiracy”, involving (at a minimum) :  the Vatican, the Illuminati, the Freemasons, Skull & Bones, the Bilderberg Group, the Red Orchestra, the “Four Just Men”, and the Junior Rotarians Auxiliary Society of Cedar Rapids Iowa (some in league with each other, some only pretending to be in league, and some sworn enemies  to the knife), detect the tell-tale ear-marks and thumbprints.   Where Hastings may have been whisked off to -- and whether voluntarily or not -- we have no idea.   But They will find him.  They will find him. 
They always do.

[Warning:  Simply by reading this post, you have opened your computer, and all your personal communications and private movements, to surveillance.  Log out, destroy your PC, buy a brand-new one, set up a fake account and log on, and  -- using TOR, of course, plus encryption -- follow the following thread -- wherever it may lead!

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

For those conoisseurs among you,  interested in the extremely obscure and uncertain “Iowa” connection, click here:
[Update 14 July 2013]  This just in --  Fragment scribbled on a napkin, clutched in Agent Kaplan’s cold dead hand:

When Ralph saw Ortcutt  in his brown hat  behaving suspiciously, I think Ralph came to believe of Ortcutt that he was a spy, and this despite the fact that he didn’t know, in any helpful way, who Ortcutt was.

A tentative identification has since been made.  See:

            The Man in the Brown Hat

Sunday, June 16, 2013

The “Idea” Idea (with an excursus on ideation and subvocalisation)

Much of the most important and vital work done in the last half-century  depends [not upon experiment or brute calculation, but] upon new ideas;  and new ideas are notoriously exceedingly difficult to grasp.
-- Louis J. Mordell, Reflections of a Mathematician (1959), p. 11

We previously stated that mathematics is best characterized as the science, not of number, but of structure (or of pattern -- at this level of generality, either term will do).   As MacLane phrases it:

This chapter introduces the idea of the formal  in terms of certain basic structures:  Set, transformation, group, order, and topology.  With Bourbaki, we hold that Mathematics deals with such “mother structures”.  Against the historical order, we hold that they arise directly from the basic stuff of Mathematics.
Saunders MacLane,  Mathematics:  Form and Function (1986), p. 7

That last bit, you will note, is unabashedly Platonist, counterposing contingent human praxis  to transcendent time-independent Truth.  (We discuss this contraposition here.)

Voilà  le hic

But beyond that, or rather as an animating force within it,  and distinguishing mathematics from such structure- or pattern-centered enterprises as architecture or the plastic arts, is the central role of ideas. 

MacLane puts the matter well.  Re the derivation of Hamilton’s equations from Lagrange’s:

What appears as a trick is in fact an idea -- an idea which must have been clear to Hamilton when he did it.  But we claim that in general  most of the formal tricks appearing in Mathematics  are really ideas in disguise -- ideas presented as manipulations  because the manipulations can be made explicit, while the ideas are a bit nebulous.
-- Saunders MacLane,  Mathematics:  Form and Function (1986), p. 284

In a previous series of essays, we put forward certain particular “mother ideas”.  Here we reserve a meditation-space  for musing about “Ideas -- the very idea”.


Hadamard comments on Rodin’s testimony that, throughout the process of sculpting, he must keep the “global idea” in mind, even while working on the smallest details;  and that “this cannot be done without a very severe strain of thought.”

I do not feel that I have understood [a mathematical argument] as long as I do not succeed in grasping it in one global idea; and, unhappily, as with Rodin, this often requires a more or less painful exertion of thought.
-- Jacques Hadamard, The Psychology of Invention in the Mathematical Field (1945), p. 65

Hadamard scoffs at the account given by Souriau in his Théorie de l’Invention:  “Does the algebraist know what becomes of his ideas when he introduces them, in the form of signs, into his formulae?  Undoubtedly not,”  but just turns the crank of mechanical calculation.  Apparently Souriau never consulted an actual mathematician, says Hadamard:  the mathematician trusts his idea, his insight, his intuition, more than he does his calculations, which after all are not infrequently in error  (Hadamard confesses that he, like Poincaré, was but an indifferent numerical calculator):  If these clash, you first redo the calculations, before tossing overboard the Idea that motivated the whole thing.


Ideation and subvocalisation

Hadamard then makes an excursus  rather off the path our our principle inquiry;  yet we shall follow him a little ways.  He confronts the question of whether language be the key to thought;   and waxes indignant at those who, like Max Müller, dogmatically assert that, without language, thought itself must needs collapse:

I had a first hint of this when I read in Le Temps (1911):  “The idea cannot be conceived otherwise than through the word, and only exists by the word.”  My feeling was that the ideas of the man who wrote that  were of a poor quality.
-- -- Jacques Hadamard, The Psychology of Invention in the Mathematical Field (1945), p. 66

Likewise, the behaviorist J.B. Watson says somewhere that “thinking is nothing but our talking to ourselves”.
The devotees of this position  point to the dual meaning of the early Greek word logos -- ‘word, language’ and ‘reason, thought’;  and would by implication deny that our diminutive and prickly friend, the humble hedgehog, could really know One Big Thing or even a little weentsy one.

Hadamard, by contrast, is virtually a militant in the opposite camp:  “I fully agree with Schopenhauer when he writes, ‘Thoughts die  the moment they are embodied in words.”  This even applies to algebraic symbolism:  too cumbersome to actually think with;  you mostly only use them when checking your work.

The Dutch Intuitionist mathematician L.E.J. Brouwer is of similar mind:

De woorden van uw wiskundig  betoog zijn slechts de begeleiding van een woordloos wiskundig bouwen …
(Caption quotation from Dennis Hesseling, Gnomes in the Fog:  The Reception of Brower’s Intuitionism in the 1920s (2003), p. 38.)

The Neothomist philosopher Etienne Gilson  seconds the opinion of his countryman:

Si un linguiste me dit que c’est notre langue qui modèle d’abord  le monde que nous pensons,  je sais qu’il ne me parle pas en linguiste, mais en philosophe, qui se dispenserait d’ailleurs de me donner aucune justification philosophique de son opinion.  Non seulement je ne sais pas si elle est vraie, mais je ne sais même pas pourquoi elle lui semble vraie.
-- Etienne Gilson, Linguistique et philosophie (1969), p. 51

A noted Freudian psychiatrist agrees:

Every single thought, before formulation, has gone through a prior wordless state.
-- Otto Fenichel,  The Psychoanalytic Theory of Neurosis (1945), p. 46

A contemporary philosopher goes even further:  some ideas may be not only pre-linguistic, but even pre-conscious:

We may not be aware of our ideas.  An idea  in this sense  is a tendency to accept routes of thought .. that we may not recognize in ourselves, or even be able to articulate.
-- Simon Blackburn, Being Good (2001), p. 3.

The epigram "We may not be aware of our ideas" is deliberately paradoxical.  Blackburn means "idea", not in the sense of the completely conscious  "I have an idea, let's...", but of something like the often tacit metaphysical underpinnings of mentation and investigation, which we treated of earlier.  -- Blackburn extends this notion (in a way reminiscent of, but antedating, Freud):  "A permanent strand in Christian thought  is that we have no insight, or even lie to ourselves, about our heart's desires." (id., p. 30)
We close this excursus with an epigram of William Hamilton  which Hadamard quotes:

Speech is thus not the mother,
but the godmother of knowledge.


The reason such musings lie off our main track, is that we are largely uninterested in psychology, or thought-processes, or any of the hunches & hiccups that fallen Man is heir to  as he struggles to comprehend all that His hand hath made.  With Hadamard, we conceive that there are cognitive activities for which vocalization is neither required nor especially helpful:  say, playing Go, or basketball.  

There is an epigram, variously ascribed, that has always fascinated me:

“How can I know what I think
 until I see what I say ?”

On the face of it, this would appear to be anecdotal evidence for the thought-needs-language thesis.  But upon nearer inspection, it might argue rather the opposite:  That thought rose from some wordless region of the self, and only became an object to critical consciousness after having been concretized by transformation into words.

For us, the key question is to what extent an Idea -- one worthy of the majuscule -- can even be adequately expressed in our language.   Certainly the higher mathematics cannot be expressed in ordinary human language.  It has invented for itself a more or less arcane system of signs, obeying no human syntax;  you may, if you like, par abus de langage, call that too a “language”, but it is no natural human language, but rather an aide-mémoire cobbled together to express ideas that observe their own semantics, call that language or not.   Hadamard himself attests that human language does not serve him especially well, when he must express mathematical ideas.  Whenever he must hold forth on a mathematical topic, even one of his own devising and thus, to him, abstractly clear as a bell, he must write out the text of his lecture beforehand, lest he be left gasping and groping for words.

There is another old adage, current among linguistic philosophers:

“Whatever can be meant
can be expressed.”

At this point we hear the shade of that crusty critic of Le Temps, growling:  All that you mean, maybe. 


Let us put the point even more starkly.  Ask Not  (we channel Kennedy here) whether our (necessarily human versions of) ideas  could be adequately communicated to some other rational species.  Ask whether the Idea, as pre-existent in Platonic paradise, has been adequately incarnated in us.

(There now swims within my vision  the image of a category-theoretic Universal Object, with arrows slanting downwards  this way and that, as in Blake’s great painting.)


This is becoming interesting.  Hoping that your appetite has been whetted as well, we link to a couple of math-related installments of the “Any Ideas?” series:


We have tried to outline a capitalized or pregnant sense of the everyday word idea, which in most contexts certainly does not bear such freight.  (“I’ve got an idea, let’s go get pizza.”)  There is, however, another sense, which is still scientific/intellectual, yet which bears no Platonic or foundational flavor:  what is sometimes called a “bright idea”.   A bright idea is what causes a light-bulb to appear over the cartoon character’s head.  And it does represent some genuine cleverness, though its success is by no means guaranteed (and in the case of Donald Duck, will almost certainly come to grief.)

This more powerful form of inductive construction  can be deduced rather simply from the older form.  The trick is to construct, not the sequence of values, but the sequence of partial functions…
-- Andrew Gleason,  Fundamentals of Abstract Analysis (1966), p. 145

A “trick” is to an idea  as tactics is to strategy. 

We could prove the inequality by a limit argument from the known inequality for finite sums, but the following reasoning involves a very interesting technical device.
-- Andrew Gleason,  Fundamentals of Abstract Analysis (1966), p. 195


We have noted before  that, once you set out to focus on Ideas per se, you keep winding up back in mathematics -- if only because there are so many of them there.  Yet more:  In our own lifetime, math itself has spawned a subfield  whose task, it would seem, is precisely the study and development of Ideas -- for their own sake, almost, and beyond such practicalities as computing the area of the field of Farmer Brown (or rather, Farmer Enkidu, since this concern goes back to Babylonia and beyond) or even its offspring, geometry, or the handmaiden of that, the calculus, or …  This field is called Category Theory, which (as faithful readers of this tragic blog will already know)  I do not personally understand:  but do note, that a recent introduction to same (subtitled “A first introduction to categories” -- the style of the title is that of children’s books;  and God willing, someday toddlers will study this stuff), by Lawvere & Schanuel, is titled:

Conceptual Mathematics

C’est un titre astutieux.  For again (this is a phenomenon which we have treated, in these essays, under the label “faux-naïf”), on the surface this might seem to be one of those liberal-feelgood substitutions for the actual hard work of thought, meant to bolster the self-esteem of slow-learners;  whereas in actual fact, it points at concepts -- what underlies such relatively superficial activities as real analysis, point-set topology, algebraic geometry (you with me, kids?), and all the rest.

[Excelsior]   There is a vast philosophical literature (and a smaller, but still substantial, linguistic literature) concerning the relations between language and thought.   To rehearse this would be pointless;  to attempt to enrich it, quixotic.   Still we may feel our way forwards, and conceivably (eventually) contribute some minim of value, by taking as our paradigm area of Thought -- mathematics, rather than cats being on mats, and that sort of thing.   And Language as comprising, not only natural human languages, but any attempt at symbolic and communicable representation of Thought. 
(For this quest, I request:  God’s guidance and Grace.  Since, sine qua, non.)

An initial linguistic bridge is provided by our remarks above about the notion idea in the sense of ‘bright idea’.   A bright idea is no mere clothing of a perception;  it is closer to an invention.   And the key term it brings us up next to is:  insight.

[TBC?  Solâ gratiâ … ]