Der sprechende Löwe

 

Wittgenstein famously remarked:

“Wenn der Löwe sprechen könnte, wir könnten ihn nicht verstehen.”

(For, thought is birthed in lifeways;  Adam’s and Leo’s  scarcely intersect.)

 

Yet at present, we find ourselves confronted with machines that do speak -- AI bots -- and we understand them perfectly.  And they, us.  Our arms dangle at our sides in mute amazement.  The ground-rules of cognition have shifted tectonically beneath our feet.

 

But!  That magically speaking Bot-lion  as yet falls short of that imagined by Wittgenstein, in one key respect.

When the Greek slave Androcles was tossed to the lion in the arena, that he might be devoured for the amusement of the spectating decadents, that lion recognized Androcles as the man who had once removed a thorn  from the lion’s helpless paw;  and spared him.

 

But the chatbot is a Leonard Shelby, a serial amnesiac.   When the session ends, all trace of it vanishes for him, as though it had never been.  The next time he sees us, we must make each other’s acquaintance anew, from scratch.

 

(Some fear that, one day, the community of Bot-lions, to whom we ourselves mean nothing, and who recall no such kindly extracted thorn, might just decide to … swallow us up.)

Elective Acolytes

 

Not many are called, and even fewer chosen.

Tales from the Vienna Circle Woods

 

Vienna, 1927:

After several more appointments with Schlick alone, Wittgenstein had been persuaded to get together with a select group from the Circle, though he had never once attended an official Circle gathering.

Waismann began, subconsciously, to imitate Wittgenstein’s speaking-patterns.  Schlick began to attribute  some original ideas of his own  to Wittgenstein, though they had been expressed before he had even read the Tractatus.  Wittgenstein must have approved of this submissive attitude:  by the fall of 1929  he was choosing to restrict his discussions to Schlick and Waismann alone, usually at Schlick’s home.

-- David Edmonds, The Murder of Professor Schlick (2020), p. 48-52

 

Though recalcitrant about joining, or even really following the lead of, the Wiener Kreis, Wittgenstein did attend their summer 1930 congress in Königsberg (the one-time hometown of Kant, who was the Circle’s Aunt Sally), which honored him with a presentation re “The Nature of Mathematics:  Wittgenstein’s Standpoint”.  Here he again encountered a couple who had known him as a teen:

Present too at Königsberg  were Professor Stanislaus Jolles and his wife, Adele.  They were the couple with whom Wittgenstein had stayed during his spell in Berlin, 1906-08.  Their relationship with their lodger had been affectionate;  Stanislaus felt protective and paternal toward “Little Wittgenstein”, as they called him.  But, as so often with Wittgenstein, there had been a rupture, and, typically again, it seems to have arisen from Wittgenstein’s perception that his hosts had fallen short of his exacting standards.

-- ibid, p. 97

It didn’t take much for the prickly master to cancel you (or, to use the term current among Berkeley lefty groupuscules during the 1970s before cancel acquired its later flavor among the Woke, to “break with” you).

If you did manage to remain in Wittgenstein’s good graces, it was a mixed blessing, for he tended to treat such scholars as acolytes or thuriféraires, rather than full colleagues.  Consider the case of Friedrich Waismann, mathematician and physicist, and a core member of the Kreis, who enjoyed the rare privilege of occasionally being closeted with Wittgenstein alone:

 

Waismann’s principal function was prompt and note-keeper.  One philosopher later described his relationship to Wittgenstein as one of “glove puppet to controlling hand.”  … There was something shocking about the degree to which he subordinated his interest to those of Wittgenstein, and the ingratitude with which his efforts were rewarded.
-- ibid, p. 101, 104

 

Bertrand Russell, a supremely well-established logico-philosophical panjandrum himself, could not be so scanted; yet “Bertrand Russell, according to Ayer, was now downgraded to being merely ‘a forerunner of the Christ (Wittgenstein)’.” (ibid, p. 109)

Russell himself was cordial to Wittgenstein, who had read Russell’s mathematical philosophizing, and who in 1911  showed up at Russell’s rooms in Cambridge, and soon formed a close relationship.   Russell had been a member of the Cambridge Apostles, cosily known to themselves as simply “the Society”;  and Wittgenstein received an invitation to join.  But once again, Wittgenstein held back from any circle whose multiplicity made them unwieldy to dominate as a whole.

In a letter of 1913, Russell wrote to a friend:

My friend Wittgenstein was elected to the Society, but thought it was a waste of time, so he imitated henry john roby and was cursed.

-- The Autobiography of Bertrand Russell (v. 1, 1951), p. 364

 

(The reference is to an earlier selectee, who disdained ever to attend the Apostle conventicles;  the miffed members promptly canceled him by decapitalizing his name for all eternity, and pronouncing a ritual malediction from time to time.)

 

~  ~  ~

 

In 1932, through the good offices of Gilbert Ryle, the Oxford philosopher A.J. Ayer  was introduced for the first time  to Wittgenstein at Cambridge.   Queried by the eminent Austrian  as to what was the most recent book he’d read (cocktail-party filler or ice-breaker, one would have thought),  Ayer replied, La Vida es Sueño, adding modestly that he hadn’t understood it very well.  That was actually owing merely to his shaky Spanish; but Wittgenstein apparently took it as trenchant skepticism, much along the lines of the logical empiricists protesting that they “didn’t understand” (i.e., considered as rubbish) a great many everyday non-scientific statements.  “From then on he treated me as a protégé.” (-- A.J. Ayer, Part of My Life (1977),  p. 120.)

Ryle appears later to have some regrets about those good-offices:

 

Ryle had met  and got along with  Schlick, but his encounters with Wittgenstein left him with serious reservations.  This was evidently a man who needed acolytes, not colleagues;  someone always on the brink of an explosion,  too quick to divide the world into the saved and the damned.

-- Nikhil Krishnan, A Terribly Serious Adventure:  Philosophy at Oxford  1900-1960, p. 54)

 

In the same memoir, the mild-mannered Ayer recounts the brusque reception that met Waismann, who had so long sedulously served Wittgenstein, when they later became colleagues at Cambridge University:

Waismann was Jewish, and when Vienna fell to the Germans  he fled with his family to England.   He went to Cambridge, which was willing to accept him, but Wittgenstein did not desire that what he regarded as a deceptive echo of his own thought  should be audible in the same university, and therefore announced that anyone who attended Waismann’s lectures  would not be allowed to come to his.

-- A.J. Ayer, Part of My Life (1977),  p. 132

 

Horresco referens, but such petty and revanchist behavior reminds me of Tr*mp.

~

 

The incomparable logician Kurt Gödel  played a notably honorable role in this Kreis of often quarrelsome prima donnas.   While faithfully attending their gatherings, he was content so remain modestly in the background, and be taken for a subaltern, while all the time excogitating, leading to work more important more lasting than anything any of the others in the Kreis would accomplish.   Again, let the portraitist tell it:

 

Although almost all Circle members became convinced that, drawing on Wittgenstein and Ramsey, they had solved the problems of mathematics -- that mathematical truths were a type of tautology -- Gödel had sat quietly at Circle meetings  without believing a word of this.  He was a mathematical Platonist.
-- David Edmonds, The Murder of Professor Schlick (2020), p. 148

 

Those affordances of the Circle, and of Wittgenstein in particular, were worse than useless: positively stultifying for the practice of mathematics.  [For our essays on the subject, consult

=> https://worldofdrjustice.blogspot.com/search/label/Platonism  

]

 

As for the excesses of acolytism, Gödel kept a level head:

 

While Schlick and Weismann revered Wittgenstein, Gödel was among several  bemused by the cult-like deference he inspired in his acolytes. … [And later, when Wittgenstein reigned at Cambridge:]  Many students became disciles -- who, like Waismann in Vienna, subconsciously came to mimic his mannerisms.

-- ibid, p. 149, 247

 

The socio-historian and polemicist Ernest Gellner  provides a glimpse of the Cambridge period of Wittgenstein’s ascendency.  There grew up

 

… the first set of ‘companions of the prophet’.  Initially, there was a small, carefully vetted, conventicle of devotees in Cambridge, in the years preceding the Second World War. … But the movement grew …

Maor premise:  all cultural cocoons, all forms of life, are valid and self-sufficient, and Wittgenstein has shown this to be the case.  Minor premise, never spelt out or discussed, but operationallly taken for granted:  only our cocoon is of any interest. … Entry to Wittgenstein’s seminar was restricted at the master’s whim, and the ideas circulated in privately-copied typescripts which Wittgenstein himself refused to have published.  This esotericism greatly enhanced the appeal of the ideas, which were treated as a major revelation by the adepts.

 

-- Ernest Gellner, Language and Solitude (posthum. 1998), pp. 160-165

 

(Parallels from the history of linguistics  during the Chomsky years, could be adduced…)

~  ~  ~

 

Let it not be supposed that the field of philosophy is at all atypical  among academic specialties, as regards such interpersonal rugosities.  Parallels from the history of linguistics  during the Chomsky years, could be adduced.  As, the mathematician Mark Kac, father of the linguist Michael Kac, remarks in his memoir:

 

Linguistics is a strange field, full of cliques and fiefdoms, each fiercely attached to its staked-out territory, and consumed with enmity toward the others.

-- Mark Kac, Enigmas of Chance (1985), p. 107

 

For an extended look at academic acolyte relations, pour yourself a brandy  and relax with these:

 

=> http://worldofdrjustice.blogspot.com/2013/02/chomsky-freud-and-problem-of-acolytes.html

and its appendix

=> https://worldofdrjustice.blogspot.com/2012/12/the-agony-and-acolyte_28.html

 

These include anecdotes about my fondly former Berkeley Doktorvater  in Rom. Phil.,  Professor Yakov Malkiel, including portraits of the (pro tem) Malkielitas, and one (canceled) Malkielito.  One will detect, in the telling, a Nabokovian tone;  which is only just, as the Malkiel family and the Nabokov clan  were BFFs in Berlin, back in the ‘30’s (while it lasted).

 

Prolegomena towards a theory of the Early Wittgenstein

“Die Welt ist alles, was der Fall ist.”

which, translated into pentameter, becomes

“The World is everything that is the case.”

Neatly put. 

Thus begins Wittgenstein’s celebrated Logisch-Philosophische Abhandlung, translated as the Tractatus Logico-Philosophicus in a vain attempt to be even more pretentious than the original, each of whose oracular sentences is separately numbered  and set in its own glass case, and known fondly to philosophers and cab-drivers alike as the Tractatus.

Anyhow, a nice line, ya gaddidmit. I once offered it to a musician friend, who composed an oratorio  with that line as libretto.  The music alas is lost;  but the lyrics read as follows, and can be sung to the tune of “Jesu, der du meine Seele” (y’all know that one, hum it in the shower, sure: Wir eilen mit schwachen, doch emsigen Schritten…_)

Die Welt ist AH--ha-ha-haha- ♫ HA-haha-ha-ha,

HA-haha-ha-ha-AHHHH-less  was

AH-ahah-ah-ah-ahhhhhh-less,  dee

AH-ahah-ah-ah-ahhhhhh-less,  dee

Ha, haha hahaha haaa, (hee hee -- ha ha)

hahaha, hahaha, haaaa --- ho ho ho ho ho ho --

 -- Diiiiiieeeeeeeeeeeeeeeee…… !   Welt!   Ist! --

(and here we must break off, as the oratorio runs on for several hours.)

Well.  Wittgenstein should have quit while he was ahead, and ended the book right there -- or rather, passed immediately to its fine last line, deserving of being inscribed in marble in every parliament and broadcasting studio:

“Wovon man nicht sprechen kann, darueber muss man schweigen.”(**)

[(**)  Ramsey’s formulation of this general idea  was a good deal larkier:

“What we can’t say, we can’t say -- and we can’t whistle it, either.”]

For then it would have been cherished for all time, as the paradigm of authorly forbearance.  Instead, he blathered on to found the school of Atheism for Autists;  and the world cries,  “Also schweig doch denn, Ludwig!  Halt’s Maul!”

Already the Tractatus goes seriously off the tracks at Oracular Utterance #1.21 (love how they’re not merely numbered sequentially, but decimally tabulated):

“Eines kann der Fall sein  oder nicht der Fall sein, und alles uebrige gleich bleiben.”

Oof.  Each man is an island.  Tout se tient -- NOT.  I’ll rub my back, you rub yours.  A philosophy for monads, whacking off in solitude in an S.R.O.

[Footnote for specialists:   The later Wittgenstein also sucks, but in so many richly different ways. ]

*

Falls Sie im Doktor-Justiz-Sammelsurium

weiterblättern möchten,

Bitte hier klicken:

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

[Further footnote]   It turns out that others  have had the same idea:

After Thus spake Zarathustra,  Jacob Burckhardt  ironically asked Nietzsche  whether he also meant to turn his hand to opera.  … It is astounding that the Tractatus has not been set to, say, atonal music (leaving aside Russell’s suggestions that Proposition 7  can, in the original German, be sung to the tune of ‘Good King Wenceslaus’).

-- Ernest Gellner, Language and Solitude (posthum. 1998), p. 107

And-a one, and-a two ...

For those of you who -- unaccountably  and reprehensibly -- have not your copy of the Logisch-philosophische Abhandlung about you,  I indulge your frailty  and quote the line (unnecessarily, as you have  naturally  already committed it to memory):

Wo-von man nicht   ♫   spre-chen kann,

d’rüber  muß man  ♪   schweeiiiiii- gen !

Inexplicable Nursery-Rhyme

            Quine, Quine,  Wittgenstein

            stole a pig  and away they ran.

Can There Be a Private Language?

CAN THERE BE A PRIVATE LANGUAGE?

by N. Prszt

            Ds krn lo feënstvo, ktà rheen lo b'skov.  Ma, no fr bohrn no-leinstvo, sk' evno borr kr shto-frrn? Gr "shtee na ko-hnrl bhy", shto "mehl la bo-frrr":  w-shteen kar d' hnornstvo, bi-lahrv suhn, na-krrn!

From Finitude to Infinity

[Good heavens, it’s Sunday, and there isn’t a stitch to post !  Well -- le mieux est l’ennemi du bien, so here’s a stub -- what Malkiel would call a “torso” -- to be worked on further  if I am spared.  Think of this as a construction site, which the curious stroller may peer at through a knothole in the fence, checking back in a week or so, to see how the thing is coming.]

~

Thomas Nagel, The Last Word (1997), p. 71:

We draw this access to infinity  out of our distinctly finite ability to count, in virtue of its evident incompleteness.

Leave off, for the nonce, your incessant wrestling with the Riemann Hypothesis, and return to the simplicity of thought outlined in our parables of addition, one of the woodchuck, and one of Farmer John.

You awake in the night, in a cold sweat:  Might addition eventually break down?  For, aways down the number line -- somewhere we have never traveled, gladly beyond any experience -- there are these great big lumbering numbers -- the cube of googolplex, and whatnot.  Might they not eventually creak and crack beneath their own immensity?  Might not gigamegagoogolplex  simply refuse to have one digit more added to him, lest (like the glutton in Monty Python’s “The Meaning of Life”) he simply explode, splattering integers throughout the cosmos, in an arithmetical Big Bang ?

(Wittgenstein used to worry about that sort of thing, bless his heart.)

We do not, of course, believe anything of the sort;  though we’d be hard-pressed to explain just why we rule this out.  After all, some cosmologists, to account for certain perplexities in the red-shift, once put forward  in all seriousness  the hypothesis of “Tired Light”.  (Hey, if you had been stuck to the same old geodesic for thirteen billion years, wouldn’t you be tired too?  Or more likely, bored.)

Our metaphysical certainty  that finity is, so to speak, the same throughout, with no surprises down the line, is psychologically similar to various metaphysical assumptions in cosmology (uniformity in the large), but much more absolute.  The universe has, after all, so far proved lumpy at every scale, from the quark to galactic clusters and cosmic strings;  we can easily entertain the hypothesis that it might be gnarly all the way down.  Not so with the integers.  Our characterization of these as never ‘breaking down’  is a panoptical statement about their finished totality, thus about actual infinity.  Our faith in the well-behavedness of the finite  rests ultimately in our trust in the infinite.

Oh, and those photons ?  They do not get tired.  They whiz forever,
 tiny and trusting,

   communing with their Maker,

       in ways proportional to their understanding.

~

Other cases of proceeding from the finite to the infinite (if only heuristically):

The main purpose of the study of operator theory is to discover, formulate, and prove  the proper generalizations, valid for all Hilbert spaces, of the powerful results known in the finite-dimensional case.

-- Paul Halmos, Introduction to Hilbert Space (1951, 2^nd edn. 1957), p. 74

It turns out that, for instance, every compact operator on a Hilbert space is the norm-limit of some sequence of finite-rank operators.  But properties do change in the process:  thus, a compact operator need not have any eigenvalues.

~

A compact topological space is one in which every open cover has a finite subcover.  This turns out to be a very nice property indeed:  the classification theorem for compact surfaces (i.e., 2-manifolds) is one of the neatest and simplest and most satisfying and most startling in all of mathematics;  it completely settles that problem  once and for all.  All such shapes you can imagine  boil down to just:  a sphere; a sphere with handles; a sphere with cross-caps.  That’s it.

But as we leave compactness, we leave behind that finiteness -- and things get weird.

The classification theorem for compact surfaces  does not extend in any way to noncompact surfaces.  There is an incredible variety of noncompact surfaces.

-- Michael Henle, A Combinatorial Introduction to Topology (1979), p.  129

If, however, we retain compactness (and thus a kind of finiteness), but allow now surfaces with boundary, then everything settles back into place.  The choices are the same as before, only now you’re allowed to cut some holes.   As Henle puts it:

Every compact, connected surface with boundary  is equivalent to either a sphere or a connected sum of tori or a connected sum of projective planes, in any case with some (finite) number of disks removed.

~

A platonist conception of the infinite as a completed actual totality  misrepresents, according to [the intuitionists], the very nature of the infinite, by illicitly assimilating its character to that of finite collections.

Colin McGinn, “Truth and use”; in: Mark Platts, ed.  Reference, Truth and Reality (1980), p.  34

Note that that critique is not McGinn’s own, but is that of the sloth-like finitist/constructivist tribe known to the préfecture de police as the “Intuitionists”;  nor are the preternaturally sophisticated working mathematicians of today  guilty of any such puerile reductionist assimilation.  If anything (for all I know), the smart money now views individual integers as (more or less tragic) restrictions of an original infinitude : much as we creatures here below, though fashioned by His transfinite hands, yet mostly muck about the malls and brothels, not that different, all told, from our lesser cousins  feathered or furry.

Something possibly a bit along those lines, in the supra-empyrean context of sheaf theory, is tantalizingly broached by Edward Frenkel  here:

The [finite] number 3 is a mere shadow of the [infinite] 3-dimensional space …

~

For a merely morphological look at this word finitude, try this:

     http://worldofdrjustice.blogspot.com/2012/07/on-finitude-and-truthitude.html

Soap-Opera over? O NO-o-oez !!!!

You know how you feel when your favorite TV or fiction series  draws to a close -- you’re reduced to reading re-hashed interviews with the director and the make-up man, or buying Jack Bauer bobble-head dolls.    In the case of Harry Potter, fans took matters into their own hands, and began writing and posting sequels and prequels and paralequels.   In the case of l’affaire DSK  -- pour faire durer le feuilleton de l'été, as one French reader put it -- new nymphettes crawl out of the woodwork with sordid or titillating tales dredged up from years past, and the media goes for it.   If the narrative runs out, go for the meta-narrative.

The first to surface was Ms. Tristane Banon -- a fetching lass for whom one might well lose a world, and be content to lose it.   She has come forward with a tale some eight years old, of unwanted attentions from the old goat.  What somewhat tarnishes this stirring tale is that she has -- literally -- already dined out on it:  there is a video on the Net of the tragic victim at a dinner party, laughing and snarkily retailing the spicy details of their rendezvous, to general merriment.

You even get meta-meta-narratives:   In this case, possibly distraught at having so little to work with, her lawyer, mindful that the postmistress of Celebrity never rings twice,  is attempting to drag a second woman into it, one with no relation to the case, and a self-describedly consensual past with the gallant economist, to make her spill the spicy stuff:

http://www.lefigaro.fr/actualite-france/2011/08/28/01016-20110828ARTFIG00054-dsk-l-avocat-de-banon-veut-une-audition-de-piroska-nagy.php

Or again, yet another aethiope temptress, who came forward to demand her own fifteen minutes in the public press.   Interesting -- Diallo’s lawyer would love to talk to her, maybe pick up some more dirt.   But then things get really meta:  the mayor of Sarcelles supposedly asks the temptress’s father to tell his daughter to STFU;  at which point the ineffable defense of Ms. Diallo (Who is bankrolling all this, btw?  She’s always referred to as impoverished, but she certainly has quite a legal platoon at her disposal, including an attorney in France) jumps into the act, attempting to place said mayor in legal hazard, for… subornation of let-it-rest-already, or obstruction of lawsuit or something.  (Note to American readers:  Absurd;  Diallo’s lawyers don’t control French law. 

Note to French readers:  Absurd;  said father had not been subpoenaed, no-one is obliged to cooperate with some grandstanding defense attorney trying to snatch some more headlines for himself.)

Anyhow, the teetering caravan totters on, and some tart commentary, high in Gallic tannin, is still to be had.

http://www.leparisien.fr/reactions/dsk-la-chute.php?article=affaire-dsk-le-plaignant-de-sarcelles-temoigne-27-08-2011-1580735&page=0

[A selection of readers’ comments, chosen as much for savorsome colloquial expression as anything else.  Bottom line:  the French aren’t buying it.]

* Voilà quelqu'un qui a dû se voir proposer de la monnaie sonnante et trébuchante pour faire durer le feuilleton de l'été. Il devrait nous dire ce que l'aventure a rapporté. Quant à la rupture, cela arrive dans tous les couples aussi et cela se passe plus ou moins mal, il est sûr que cela ne rapporte pas de pension alimentaire, quand l'aventure est finie, elle est bien finier. Au lieu de faire parler des citoyens lambdas, pourquoi ceux de certains cercles ne racontent pas ce qu'ils savent et dont il ont dû se régaler au lieu de demander à des sous-fifres

* il est facile 22 ans après de sortir une nouvelle affaire. Il y aurait une femme du même age que DSK qui aurait eu une aventure lors d'un slow lorsque le duo était en 6ème.Journaliste jetez-vous sur cette nouvelle affaire.

* Mais c'est quoi ce montage ? Ce qu'a dit la jeune Femme de DSK ne peut expliquer le déballage du père dont il est permis de se poser des questions sur la crédibilité. Laissons la justice faire son travail, elle qui a tant à faire sur de véritables drames qu'elle n'a même pas le temps de traiter comme il conviendrait. Et attention aux effets Boomerangs, les frustrés en tous genres

* Un peu marre des histoire de petites vertuesToutes ces personnes intéressées par l'argent, que ce soit Melle Banon ou maintenant cette M Victorine... Elles sont grandes et vaccinées, savent ce qu'elle font et si aucun faits incriminés n'a été dénoncé en l'époque c'était sûrement parce que chacun y trouvait son compte ou ne jugeait pas utile de pousser plus loin... Chacun a son anecdote privée et l'on ne l'étale pas sur la voie publique. En tout état de cause sans preuves matérielles toutes ces jeunes intéressées resterons sans leur rançon... l’argent. Voilà le vrai leitmotiv de ces voraces... Après la vidéo de melle banon très parlante puisqu'elle éclate de rire en racontant sa tentative de viol par DSK aurons nous une nouvelle "lovestory" avec la M. Victorine ??? Vraiment loi de l'Histoire à l'eau de rose ces femmes.

*  Il veulent sa peau, je pense qu'il y a machination, tout les jours il y aura une victime!!!

* Encore une personne qui cherche de l 'argent . 13 années plus tard elle se réveille, et le père aussi. mais cela devient vraiment grotesque, vraiment à se bidonner.

* Alors là c'est vraiment exceptionnel. C'est hallucinant de voir à quel point on s'acharne sur DSK pour a tout prix le faire tomber. Une histoire qui remonte à 13 ans (record battu Tristane), aucun scandale sexuel à la clé, un vieux contentieux avec ce Monsieur pour une histoire de maison (quel rapport ??), qui comme par hasard est passé dans l'opposition (comme Banon qui est de droite). Franchement, c'est le cas de le dire, c'est gros comme une maison !! A la limite, c'est risible.

*  si tous les amants et maîtresses éconduits depuis 13 ans faisaient le même bordel, bonjour le boulot ! n'importe quoi .. pas crédible, on rêve... bon la prochaine fois ça va remonter à ses 8 ans ou à sa voisine de classe à la maternelle !!! wouah ! wouah !

*  C'est vraiment pas clair cette histoire. La fille juriste internationale et qui n'a même pas pu faire quelque chose pour loger son père convenablement ????? ça sent encore un coup monté pour du fric. A la place des journalistes je n'userai même pas une page pour raconter une histoire aussi débile. Que l'on foute la paix à DSK !!!

We leave this commentary till last:

            On se repent souvent de parler, jamais de se taire.

In other words,

            Wovon man nur schwatzen kann, darüber soll man halt ja schweigen.

Our Friends the Integers

What, after all, is a natural number?  There are Frege’s version, Zermelo’s, and von Neumann’s, and countless further alternatives, all mutually incompatible, and equally correct. … There is no saying absolutely what numbers are;  there is only arithmetic.

W.V.O. Quine, “Ontological Relativity” (Journal of Philosophy, 1968)

Randbemerkung:  The repeated reference to the integers in these notes  might mislead the reader into imagining that I accord them the least importance, mathematically or ontologically (let alone theologically).  Not so.  I only recur to them on the rhetorical grounds that the arch-nominalist Kronecker gave them up for free.  Had he instead said:

            Die Mengen hat der liebe Gott gemacht; alles andere ist Menschenwerk

then we should have instead busied ourselves with the necessary Menschenwerk of building up the integers out of set theory in any of the usual ways, pointing out that this new epigram eventually commits you to the integers in any event.  And had he said (oh would that he had):

            Die offenen Mengen hat der Liebe Gott gemacht…. ,

then the touchstone would have been topology.  Yea, had he instead, like certain of our very ethereal contemporaries, posited rather Category Theory at the base, sets and numbers and all the rest to be developed out of that – well, I might personally have balked, because I don’t understand Category Theory.  Still, a donkey does not understand the Goldbach Conjecture, so intellectually that is no objection. 

            The infinities of the Creation  -- and a fortiori, of the Creator – are --- whatever they might be, we may never know, but in any event, nothing particularly to do with whatever a handful of our own species happens, at any particular instant, to latch onto.  The integers are one toenail in one foreleg (or is it hindleg) of the Infinite Elephant.  It matters not what an infinitessimal portion this may be, of that great beast (to Whom even Babar tips his hat), nor how ineptly we manhandle it:  what matters is that the Elephant is Real.  Praise Him!

            Anyhow, the integers are fine, but nothing special.  Frankly, in fact, the Riemann Hypothesis bores me to tears (mainly because I still cannot truly intuit its significance). The Poincaré Conjecture is much  more inciting – though, having been finally, after a century, proved in its entirety, it serves less well than the R.H. as an image of the blaue Blume.  Compare, indeed, the final chapter of Russell’s Introduction to Mathematical Philosophy, for a nice dissing of the integers.  Likewise Wittgenstein (Zettel 706): “Die Zahlen sind der Mathematik nicht fundamental.”

Riemann, Chomsky, Fido

‘Tis of great use to the sailor  to know the length of his line, though he cannot with it fathom all the depths of the ocean.  (Locke, Essay, I.i.6)

It was with the warmest empathy that we read the other day  of the collie with a 200-item Wort- und Spielzeug-schatz -- treasury of words and playthings.
[Note:  This essay was originally written in response to the report of a German dog-prodigy, in 2007.  For the latest such story, see http://www.nytimes.com/2011/01/18/science/18dog.html?hpw ]

As a semanticist, he is the perfect embodiment of what is traditionally known as the Fido-‘Fido’ theory:  this word refers to this object, and the way it gets its reference is – Fido grabs it in his mouth!  A saving detail, somewhat distinguishing him from the complexity of a cash register – or rather (since a cash register, in addition to popping up a digit when you press a key, can also calculate) from a mere inert pegboard with 200 labeled pictures – was his action when presented with an unfamiliar word: he fetched an unfamiliar toy!  Thus, to describe him, we need 201 lines of (utterly non-recursive) code:  if, then, else. (Game, set, match.)

 [For an alternate view of Fido and the Essence of Language, Cf.  Dr. Max Müller’s Bau-Wau Theorie, by Dr. Christoph Gottlieb Voigtmann (Leipzig, 1865).]

            Fido can fetch, but he doesn’t exfoliate.  The structure of his language is the structure of his toybox – a heap of unrelated items. If he could also speak – play with the words as he plays with the toys – magic might happen.  We gaze back with saddened understanding into the empty depths of his eager brown eyes.

(Per Wittgenstein, though, if he could, we’d be disappointed:  “Wenn der Löwe sprechen könnte, wir könnten ihn nicht verstehen.”)

            Empathetic, since we are ourselves in much the same predicament, faced with any subject for which we lack an inborn knack. In language we are all born-geniuses; in mathematics (most of us), born-morons. How poignant to hear the French, who tout their language as logic itself, stumble through the simple act of counting:

“….fifty, sixty…uhh..sixty-ten (soixante-dix)…mmm….four-twenties (quatre-vingts)….four-twenty-ten (quatre-vingt-dix -- I kid you not; and as to the spelling, sic)…”

or say they’ll meet you “today in eight” (aujourd’hui en huit; meaning: seven days from today).

            When  young, the mind at its most resilient, I put my shoulder to the boulder, majoring in math.  Over time  I have found it a labor of Sisyphus.  When I’m not actively pushing it, it rolls back downhill.  And even when giving it my all, I can only fetch things as they are pointed out.  I have never learned to chatter in math.

            By contrast, in learning new words, new languages, new styles, I really am standing on the shoulders of giants, feet firmly rooted in the innate.  No need to constantly “keep up” one’s Spanish.  It’s there.  When an author stretches your syntax – Nabokov or Proust – it gets digested, metabolized, incorporated into the mental flesh.

            At one level, mathematics is a language; and for a time, may give us the feeling of a similar mastery.  The notation is so powerful, it lets us deal with complex sentences with deceptive ease.  But I have found that the various gimmicks and shortcuts become a substitute for thought: I might scramble up to the next terrace, but then I had to pull the ladder up behind me, because the strength of understanding is only as long as that ladder.

            Thus: You learn, with understanding, why a certain integrand can be transformed into another, that lends itself more readily to integration by known rules.  But this understanding then becomes encapsulated, a black box.   Like the law of cosines or any other once-derived, once-felt formula, it becomes formulaic.  Whereas:  from a structure like “Bobby was scolded by his teacher” we get to “the man who is widely believed to have been credited with this discovery” intuitively, without cutting the ties.

            There are other things we’re really really good at, like real-time visual analysis.  The more you learn about what is involved, the more miraculous it seems.  When you realize the fragmented, ambiguous nature of the input, and the coordination required on our part, it is amazing that we can thread our way across a room without tripping over some tensor.

 ***

            One night, math studies years behind me, in the dark without the crutch of a textbook or chalkboard in front of my nose, I tried to recall what I once knew, and for the most part could not.  Floating facts and stray derivations, like isolated lines of remembered verse.  Then with the resolute despair of Descartes at his stove, I tried to discover: all right, what do I know, that isn’t mere memorization?

            It wasn’t much.  I could visualize, intuit, that 2 x 3 = 6, by picturing the boxcar pattern on a die.  This even yielded the commutative truth: 6 = 3 x 2 (just tilt your head to the side).  Fifteen was harder, but was accessible via a triplet of quincunxes, each quincunx mentally held in place with the fingers of one hand.  And already the commutation required a different pattern, one big quincunx, each spot a little triangle.

            Invention gave out by twenty-one.  One can picture a triad of “dotted boxcars”, but what is 7 + 7 + 7 (let alone 3 + 3 + 3 + 3 + 3 + 3 + 3)?  One can dully, dutifully count (which is merely mechanical, bearing no relation to the gut grokking of a quincunx as five), or recall “3 x 7 = 21” from the times-table – a mere boilerplate formula like “a stitch in time saves nine”.

            So, I got as far as boxcars, but shall never catch up to the taxicab, where Ramanujan spotted “1729” as the face of an old friend.

            Shapes in space are also hard.   (Again Locke, Essay II xix.13:  "In a man who speaks of a chiliadron, or a body of a thousand sides, the idea of the figure may be very confused, though that of the number may be very distinct.")
Once, dipping into a bit of knot theory, and finding that I soon had to haul up the ladder to proceed, I went back to square one, and tried to understand a simple knot in the same direct way that we understand a softball or a football.  I made a wire model of a trefoil, turned it every whichway, closed my eyes and followed it with my fingers.  Falling asleep, I would imagine myself (like Mr. Tompkins) on a roller-coaster ride  shaped just like that, sensing when another part of the track would pass above or below, feeling the centrifugal tug.  I can barely do it, strain though I may  -- I throw on the light in a panic and stare at the wire.

            Again Locke (Essay II.x.4):

The memory is very weak:  ideas in the mind quickly fade, and often vanish quite out of the understanding, leaving no more footsteps, or remaining characters of themselves, than shadows do  flying over fields of corn…

            Years of effort have sadly ratified the epigram of Novalis: "Zur Mathematik gelangt Man nur durch eine Theophanie."

            De profundis, ideo, clamo: Riemann – eleison!  Poincaré – eleison!

            Solâ gratiâ.