The Ontology of History (updated)

The pageant of all that has happened is, to begin with, a blooming buzzing confusion.   Historically, one aim of the chronicler has been to slice up some of it, and dress it up into a narrative that will be entertaining or edifying for the audience.  More analytically-minded historians (such as Ibn Khaldun and his successors) have set themselves an additional task:  To make sense of it.

ابن خلدون

A wide-ranging comparative historian acknowledges the wealth of data which confront the historiographer, but

The “intelligible fields of study”, the comparable units of history, remain inconveniently few for the application of the scientific technique.

-- Arnold Toynbee, A Study of History (12 volumes; 1934-61; introduction, last paragraph)

One classic move is to organize the ever-mingling, ever-onrushing flow of events  into coherent thematic chunks;  as:  the Dark Ages; the Renaissance; the Reformation;  the Enlightenment.   Others refer to calendric stretches but, if so, normally must modify the defining termini a quo and ante quem  to reflect actual historical development:  thus, “the long nineteenth century” (which lasted into the Edwardian autumn, and winked out forever at Sarajevo), and “the Sixties”,  which  in the good sense  began with JFK’s election, and  in the bad sense  with his assassination;  and then petered out ignobly in the early seventies.

Anyhow, huge subject, won’t treat it here, but merely serve up a couple of quotes specifically related to Islamic historiography -- thus posting at least a place-holder for the topic, in our wildly successful “Ontology of …” series (soon to be featured on bubble-gum cards, suitable for trading).

“Classic” or “classical period” is likewise a construct, all the more obviously so  since it is being borrowed from one phenomenon, Greek and Roman antiquity, and used to somehow periodize another quite different one, Islam.

-- F. E. Peters, preface to A Reader on Classical Islam (1994)

History is a seamless garment;  periodization is a convenience of the historian, not a fact of the historical process.  By choosing carefully, one can slant history without any resort to actual falsehood.  For example, a writer on relations between the United States and Japan can start with Hiroshima, or he can start with Pearl Harbor.

-- Bernard Lewis, “In Defense of History” (1997/1999), reprinted in From Babel to Dragomans (2004), p. 389

He goes on to make an exact parallel with the historiography of the Crusades, of intense current relevance, but too hot to handle in this space;  consult the (excellent) original article.

The essential human unit  in which man’s nature is fully realised  is not the individual, [n]or a voluntary association which can be dissolved or altered or abandoned at will, but  the nation.

--Isaiah Berlin, “Nationalism”, repr. in Against the Current (1979), p. 342

(Cf. individual vs. group selection  in Darwinism.)

[Afternote] We sometimes also find explanatory periodization, not by historians, but by the people themselves:

The Aztecs … sought relief … from the oppressive idea of eternity, by breaking it up into distinct cycles … each of several thousand years’ duration.  There were four of these cycles;  and at the end of each, by the agency of the elements, the human family was swept from the earth, and the sun blotted out from the heavens, to be again rekindled.

-- William Prescott, History of the Conquest of Mexico (1843), p. 53

~

Glanced at above is the internal ontology of historiography -- its structure and staffage.  There is also the matter of its external ontology -- how it fits in with other disciplines.

“History is an art, like the other sciences,” a felicitious paradoxical epigram crafted by Veronica Wedgwood.

--John Lukacs, The Future of History (2011), p. 81

.

On Crunchy Numbers

In the Ike era, we grew up on Wonderbread® :  a sort of Brot ohne Eigenschaften whose edulcorated transmogrification is known as Twinkies.

Since that time, we have learned to abjure, not only such treif, but anything not calling itself wholegrain.   Or, better still, multigrain: some brands boast seven grains, a few claim twelve; disparate mixtures  full of gritty, grainy, crunchy goodness.

 

Now  our local upscale supermarket offers a variety of own-branded bread, that boasts (in large letters) no fewer than

27 GRAINS

That really surprised me.   It’s one of the main points of Jared Diamond’s Guns, Germs, and Steel  that digestible, domesticable, feasibly growable grains  are not to be had for the asking;  there just aren’t that many of them.   The explanation is that, a little lower down and in smaller font, the label reads

AND SEEDS

In other words, this brand of bread is equally at home in the bakery and in the bird-feeder.

Our son, scoffing at this terminological legerdemain, inquired why the market chose “27” of all things.   Unhesitating I replied, “Because it is three to the third power -- the trinitarian pinnacle of the Perfect Cubes”.  -- Said heir and offspring, himself a nascent mathematician, appreciated the point, but doubted that your average shopper was aware of such things.

And indeed, there is a larger point.   For number-theorists like Ramanujan, each integer has its own flavor, its own biography and backstory -- cf. the famous incident of the taxicab numbers (in which G.H. Hardy plays the straight-man or fall-guy).  But for ordinary folks, like rocket scientists (who deal with contingent analogue quantities, rather than integral transcendent entities) or English professors (surrounded by a midge-cloud of  pre- or sub-arithmetical post-modernists), all but a very few -- small -- integers  will be featureless.   Some will be visually familiar:  3 and 4 (the triangle, the square), 5 (the quincunx on dice), 6 (boxcars, ditto),  7 (a “lucky” number for the superstitious) or 23 (ditto, for the more cerebral), 10 (count your fingers), 20 (with its portrait of Jackson).   Some will be familiar for incidental, non-mathematical reasons, like 100 and 1000 (which owe their prominence to the accident of base-10 notation -- a case of decimal fetishism).   --  Those associations are widely shared;  but there may be others  more individual;  as, (mostly for girls), “sweet sixteen” (or in Latin America, la quinceañera).   Indeed,  any integer small enough that you have lived that number of years (particularly those for which you still kept track of your birthdays).    As, the poem(-collection) “Now We Are Six” (by A.A. Milne), an anniversary in memory still green (and which I teach to the neighborhood children when they reach that delightful threshold).  Or…. 27;  which, even before I had attained that age, always seemed numinous (probably, indeed, for its prime-power nature), and which was ratified as such by my marrying at exactly that age, quite close to my birthday.    Whereas, for most folks, a number like 81 (pourtant a perfect square, as well as  3^2^2, to boot) tells no tale, sings no melody.

~

The preceding remarks are of psychological or anthropological interest, but of no moment for mathematics itself:  They present an external, human-centered view of the integers.  But further considerations suggest a subtle distinction between two ways a given integer may be “interesting” (a more bloodless equivalent of our anthropomorphic term crunchy).   We might dub these internal and external:  both times internal to mathematics as a whole, but in one case only, internal to number theory in its most elementary sense.

Thus, consider 5.  Number-theoretically, it’s a prime and that is pretty much that; but in the geometry of three-space, it is the number of Platonic solids.  Or 17:  Number-theoretically it is both a prime and a Fermat number; but in the geometry of two-space, it is the number of crystallographic planar symmetries.  

https://en.wikipedia.org/wiki/Wallpaper_group

Or: 230, the number of space groups.

Here, the integer in question is not a creature or crystal considered distinct and in itself, but a stopping-point one arrives at by calculating and counting.  There might have turned out to be, say, 18 plane symmetry groups, without upending the world; but the internal structures of 17 and 18 are unrelated.

~

This dichotomy of internal versus external interest  chez the integers, represents ideal poles, which are not exhaustive, but bookend a spectrum.  As, probably intermediate: the “crunchiness” of natural numbers as viewed by students of finite groups.    (Here the masticatory metaphor  returns unbidden, for I always imagine finite groups along the lines of a wrinkly-surfaced walnut.  Finite simple groups -- those for which no homomorphism can split out any subchunk as its “kernel” -- the hardest nuts, the ones you can’t crack.)  Simon Norton seems to have had such an intimate gustatory appreciation of individual finite groups, before he Threw It All Away and went off to ride the bus.

~

In light of our training, we know at least one thing to do, should we ever be given an unfamiliar integer and locked in a room, with no other toys to play with.  Namely, we can probe for primality.  (An activity that becomes, indeed, crucial, for cryptographers.)

But now imagine that instead we had been handed some fraction like

      (2 +  √137) /4081

Untrained, we react with dismay.

Yet later, learning of the Golden Section, (1 + √5)/2, and its many remarkable properties -- not the least of these being that it can be represented as the infinite continued fraction consisting of nothing but ones -- we conclude that the critter is crunchy indeed;  and that there are more things in heaven and earth, than are dreamt of here below, and that we must anticipate the afterlife, before we could begin to embrace them.

~

Our treatment focused on what the innumerate are missing, much like what the Daltonist, unbeknownst, lacks of the hues.   But there is such a thing as unearned crunchiness --  a bogus significance assigned to certain numinous numbers, like 19 among the Baha’i’s; the “23 enigma”; 666; 1000 AD as the Millennium; the mumbo-jumbo numbers in “Lost” and "Touch"; for all which, cf. Wikipedia on apophenia.   In the face of such things (which have snared some otherwise rational people -- a close friend of mine, critically brilliant but unmathematical, fell for the “23” business), we are inclined to say, along with Nulla  extra ecclesiam  salus,  that  Nulla  extra mathematicam  ratio.

~

For a rather recondite example of crunchiness, consider the ‘amicable numbers’  (  الآعداد المتحابة) reported by the medieval historian Ibn-Khaldun in his Muqaddima .   Apparently only two of these were known to the Arabic medievals (or: they are the only two numbers characterized by a theorem of Thabit ibn Qurra), and they are not much to look at:  220 and 284;  but they meant something to contemporary practitionars of the talismanic art.

The modern view is summarized here:

https://en.wikipedia.org/wiki/Amicable_numbers

My apologies to M. le Président

I know of no sadder sight  than a commander who has little of command but the name.

-- Melville, Benito Cereno (1855)

Certain passages over the course of these essays (here, and here), might have been construed as suggesting that the French President, M. F. Hollande, is a bumbling, shambling, mealy-mouthed crowd-courting doofus;  a lackwit wazzock;  a waddling dumpling, a toddling butterball upon the world stage, upon which Fortuna has improvidently cast him.  Nothing, it turns out, could be further from the truth, if we are to credit the testimonies of the following lucid-skinned, diamond-eyed hottie:

Il fait chic, dans mon sac!

Let the French newspaper of record tell it:

La rumeur court depuis des mois mais Closer dit en avoir la preuve. Le magazine people affirme que François Hollande entretiendrait une liaison avec la comédienne française Julie Gayet. Vers 23 heures jeudi, le magazine a annoncé sur son site une édition spéciale pour le lendemain «révélant dans un dossier spécial de 7 pages les photos de la relation entre le chef de l'État et la comédienne». L'Élysée a réagi dès 7 heures vendredi matin. François Hollande «déplore profondément les atteintes au respect de la vie privée auquel il a droit comme tout citoyen» et «examine les suites, y compris judiciaires, à apporter à cette parution».

La une de Closer titre sur «L'amour secret du président: il passe ses nuits avec elle à deux pas de l'Élysée». «Autour du jour de l'An, le chef de l'État, casque sur la tête, rejoint à scooter la comédienne dans son pied-à-terre où le président a pris l'habitude de passer la nuit», écrit Closer sur son site . D'après l'hebdomadaire, «ces rendez-vous secrets» auraient commencé en juin 2013.

«Des photos étonnantes, poursuit l'hebdomadaire, qui pose aussi la question de la sécurité du président. Le chef de l'État est accompagné d'un seul garde du corps qui protège le secret de ces rencontres avec la comédienne et apporte même les croissants!»

http://www.lefigaro.fr/politique/2014/01/10/01002-20140110ARTFIG00264-rumeurs-sur-sa-vie-privee-hollande-envisage-des-suites-judiciaires.php

It is that detail of the bodyguard supplying the croissants for these trysts -- that objective correlative, as Eliot would put it -- which lifts this saga from the level of the sordid, to the realm of the sublime.

Having already shown his iron resolve by threatening prosecution of the comedian who invented the gesture of the “quenelle” (La justice interdit le spectacle de Dieudonné ), M. Hollande, with perfect conséquence, is thus threatening the newspaper as well.

~

The magazine promised photographs, but none were actually of the Président and his paramour in flagrante.   Rather (in the manner of that Monty Python spoof of tabloid television blackmailing highly placed men with a secret, initially showing only blurry and ambiguous images, while the cost of hush-money keeps rising as the film advances) they presented a photo of two helmeted figures on a Vespa, on which the President riding bitch.  (A perfect metaphor for his domestic policy.)

~

For further sober, high-toned, scientific examinations (suitable for use in the classroom, to supplement Civics texts) of Sex and the Hegagon, try these:

http://worldofdrjustice.blogspot.com/2012/08/juicy-french-sex-scandal.html

http://worldofdrjustice.blogspot.com/2012/09/une-affaire-grave-updated.html

~

[Update 11 January 2014]

Some caviling commenter with a sketchy display-name (vide infra) kvetches that this post lacks gravitas.   We-ell --  You want gravitas, we got vats of it !  Simply turn on the tap.

Ahem.  This whole affaire, from quenelle to the bit-o’-jam, well illustrates the Cyclic Theory of History.

Was it not the great historian Ibn-Khaldun who said… something quite relevant, one feels sure, but which at present escapes me.   In any case, Hegel then went on to say that “History repeats itself”;  to which Marx remarked,  “Hegel forgot to mention:  the first time as tragedy -- the second time as farce!”

To which now Dr Justice appends [epigram ©2014, all rights reserved, y compris en URSS and in Taleban-controlled areas of Afghanistan]:  “… and the third time as French politics !” ® ^TM    (Or alors ça, c’est bien un bon mot.)

[Update 18 January 2014]  Pour préciser. 

In further defense of the much-maligned Président, who has presided  like a toad squatting on a stone  over the further deline of France, allow me to object, contra to his various detractors, that his sordid moped-borne nocturnal trysts  do not//NOT  constitute actual “adultery”,  since  wife  has he none.   Rather, they were an infidelity (if you can even call it that, for someone with no conception of faith) vis-à-vis his current (and easily disposible) concubine (a different hetaira, whose name is here -- and elsewhere -- of no consequence).   Hollande himself has always denounced the sacrament of marriage as a “bourgeois institution”, and can in no way be criticized for demeaning something of which he has not the slightest understanding:  any more than a garden slug, having (which God forfend) somehow slimed its way up onto the communion table, could possibly desecrate the consecrated Host.  

[Update 27 mars 2014]   Anthony Lane, reviewing the new Tavernier film “Quai d'Orsay” (the title which Wiki gives it in English as well, though apparently it has recently been dumbed down for American audiences as “The French Minister”, rather the way the first Harry Potter book, “The Philosopher’s Stone”, had to become “The Sorcerer’s Stone” to cross the Atlantic), highlights the femme fatale character:

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

-- The New Yorker, 31 March 2014

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