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).

 

uaelbaT Tableau

the lake,  where a swan

   floats

arm in arm  with its reflection

[--Vladimir Nabokov, Invitation to a Beheading (1959)]

(For more on the poetry of mirrors, try this:

https://worldofdrjustice.blogspot.com/2013/09/der-mann-ohne-eigenschatten.html )

Король, дама, валет tableaux

Caught by the corner of the eye:

sudden flashes of zigzag light   cast by passing windshields

-- Vladimir Nabokov, King, Queen, Knave (1968; originally published 1928, in Russian), p. 213

Contrast,  as seen full-on.

and lo -- through the crack of the door, one glimpses the long back of the cleric, representative of a boundlessly charitable Church, in the act of bending over the white, white bed.

-- Vladimir Nabokov, King, Queen, Knave (1968), p. 172

An audial analog of a tableau might be la petite phrase.   The following, more like an earworm:

She stared   with her fingers pressed to her temples 

at the white,  white,    intolerably white    tablecloth.

-- Vladimir Nabokov, King, Queen, Knave (1968), p. 160

Up the Spout

The winter seemed colder

than winters used to be;

Margot looked about her

for something to pawn:

that sunset, perhaps.

-- Vladimir Nabokov, Laughter in the Dark (1933)

It is not often than pawning  evokes such wistful mysticism.

Yet here (for readers who found the passage above  quite understandable and natural) is a story that fully develops  the idea  of a  magic  pawnshop:

https://www.amazon.com/Murphy-Makes-Mitzvah-David-Justice-ebook/dp/B005CISOAI/ref=sr_1_1?s=books&ie=UTF8&qid=1503175677&sr=1-1

http://www.barnesandnoble.com/w/murphy-makes-a-mitzvah-david-justice/1104279825?ean=2940012865038

Wan Flame

I first read Lolita when impossibly young (much like the lass herself):  yet with a sense of complete understanding and delight.  Thus encouraged, I read various other Nabokov novels in high school, including, at some point, Pale Fire.   By that I was baffled.

It was my first exposure to what scholars term a sotie: an extended learnèd jest.   You had to wrap your young head around the notion of an Unreliable Narrator (nothing in the Hardy Boys had prepared me for that!), and the ironies and rivalries of literary criticism.    The central/initial segment, the poem, was alright, though not great, but I relished it as one of the longest poems I had then read, and quite comprehensible.   I accordingly took the criticism section in good faith, gradually growing perplexed at the increasing obtuseness of the critic.  What was going on?

A second read in mature years  had naturally a quite different effect.   Now it is easy to get all the jokes, the humor runs throughout, though in a donnish way inaccessible to the inmates of Ridgewood High.    All very jolly;  though as academic-psychosexual-picaresque exercise,  David Lodge does it better.  (Changing Places; Small World.)

~

Over the years,  I read most of what he wrote, the high point being Speak, Memory (the low point:  Ada).    Only a scattering of minor novels were left on my maybe-read-someday list;  when suddenly, the lot of them turned up  all at once, on the local remainder-tables, in a handsome uniform Penguin edition -- hardcover and clean print for these aging eyes.    It was thus that, for a couple of bucks, I took home The Real Life of Sebastian Knight.

Appearing in 1941, it was the first novel that the initially russophone and later germanicolous polyglot wrote in English.   Linguistically, it is no apprentice work.   The style is smooth, as though to the manner born.  Nowhere is there the slightest off-idiom or false note -- scarcely one American author in twenty can write so well, simply from a grammatical and semantic standpoint.  He handles with unobtrusive ease such choice vocables  as elenctic, paraph, and kerf.  (And if anyone presume to make light of such feats:  how’s your Russian, by comparison?) For language-learners and language-teachers like ourselves, on that basis alone  it deserves notice. (Or is it possible that, unannounced by the publishers, Nabokov was allowed successive retouchings over subsequent editions?)

[Emendation:   Though the first so written, it was not the first that he published in English.  His own supremely fluent transation of the originally-Russian Laughter in the Dark  appeared in 1938.   Which only moves the mystery back a few years.]

As in Pale Fire, the basic premise of Real Life is the (real or chimerical) obsessive quest of a lone researcher  for the true story behind the author of a supposed literary masterpiece.   In Pale Fire, the author plays fair with you to that extent:  the entire opus, unabridged, is presented to the reader  before exegesis begins.   And though the ultimate result is dark farce, it is not for any failing of the poem.  Pale Fire’s poem has its high points, and goes on long enough to present a challenge to any lesser poet.   It boasts a couple of memorable lines;  many’s the undergraduate alehouse where, as the assembled English-majors work their way to the bottoms of successive schooners, some one of their number will suddenly arise and bellow

I-I-I was the shadow of the waxwing   slain

By the false azure in the windowpane!

before collapsing face-first into the french-fries.

Yet in Real Life, we are granted only late, brief glimpses of the supposed prodigy’s oeuvre,  which turn out to be remarkable in no respect.   As for the late Sebastian Knight himself, the reader never warms to him, he is never really brought to life, and indeed is finally depicted as having been rather unpleasant and not especially memorable  even to his familiars.   By the end of the novel, in the celebrated phrase of the Bard of Hibbing,  “Nothing   is re-  vealed.”

Nabokov is perfectly equal to telling a rousing good yarn when he wants to, without sacrificing any of his connate literary elegance.  Lolita is such, accessible at several levels, variously to adolescents through pensioners.   Laughter in the Dark likewise -- it thus effortlessly made its way to the silver screen.  

Other novels tell a tale,  but allegorically or surreally, straddling a couple of parallel universes:  Invitation to a Beheading, Despair,  The Luzhin Defense.   (That last sort of told a story, but kept drifting inside and outside the protagonist’s head.   When it eventually was made into a film, the novel’s plot was not followed, that being impossible, and the result was  in any case  unsatisfactory, despite having a perfectly cast lead in John Turturro.)

Sebastian Knight, when all is done, hasn’t really told a story either, but only the narrative of someone in search of a story, which he never does find.

Postmodernist avant la lettre?  But the telling is reasonably naturalistic, and devoid of self-consciously self-referential tics.  Thus, a paradox:  a straightforward story that goes nowhere.

Unless it’s actually not straightforward.  We even begin to wonder whether, in exact anticipation of the much more successful execution later in Pale Fire, we might be again in the hands of an Unreliable Narrator who is not what he seems -- no genuine brother of Sebastian (and indeed, their fraternal relations are shown as having ever been sporadic lukewarm, on both sides, belying the later obsessiveness of his supposed admirer), and possibly even identical with Sebastian himself, the way the ‘critic’ of Pale Fire turns out to be none other than the fugitive king of Zembla (a cross between zemlya and semblance).  Fodder for such an extravagant ‘collapse of the wave-function’ is tossed forth towards the very end:   “All [his] books I knew as well as if I had written them myself.”   But unlike the case of Pale Fire, where the many deceptions  deftly interlock,  that interpretation makes nonsense of the entire affair, and would leave nothing but a mound of damp ashes.

~

So.  Not much to salvage.  Like certain other of Nabokov’s always magisteriously prosed novels (e.g. King, Queen, Knave, or the witty but cruel exercise, Laughter in the Dark),  the thing is spottily impressive but fundamentally leaves one cold.   All I can offer the disappointed reader, is the following thimbleful of tableaux, which were the best I could quarry out of this book:

one sheet of foolscap

lying alone  on the blue carpet, half in shade

cut diagonally  by the limit of the light.

~

The sky is alive    with stars

~

“We shall take our coffee in the green room”,

said Madame Lecerf   to the maid.

~

[Afterthought]

According to Wikipedia,  Sebastian Knight was the favorite Nabokov novel of the very well-read critic Edmund Wilson.   Now, Wilson had previously tackled a notoriously difficult and intricate work, Finnegan’s Wake, and managed to winkle out quite a bit of meaning.   Might it be that Wilson was simply more percipient in the other case as well, and that I missed the underlying premise, the way I did when first reading Pale Fire?  In light of the disappointments above, one would be curious to read his take on it.

The possibility is uncomfortable  -- as one who already suffers from Stultitia mathematica, it would be dreadful to suffer likewise from Stultitia literaria.

In defense nonetheless of the above jaundiced summary of the book,  it isn’t in any case  much fun to wade through -- not the sort of thing I’d reread in hopes of catching something I’d missed.   To that, someone might retort:  But if you missed the underlying point, that rules all your other observations out of court.

For some works  that’s true.   But an all-round work of narrative art, whether literary or cinematic, can be enjoyed on several levels.   Thus, “Memento” was an engrossing watch, and I expended much (futile) ingenuity later, trying to fit all the jigsaw fragments together;  and though ultimately failing (and reaching a suspicion that, in the final analysis, some of them don’t fit), it didn’t matter, Getting There is Half the Fun.   So too, classics like Robinson Crusoe or Alice in Wonderland or Wind in the Willows  can be fully appreciated only by historians or logicians or theologians  respectively, but laymen and even children are none the worse for the pleasures of the tale.
(/) At the extreme, there is the case of the Three Little Pigs, which has managed to delight generations of nursery dwellers, though they had no inkling of the deeper purpose of the tale:  at one level (as any professor can tell you), it is a thinly-disguised disquisition upon the filioque controversy concerning the Trinity;  yet at a deeper level (clear only to specialists), it is a subtle contraposition of the “Copenhagen interpretation” of the quantum theory, to the theory of Many Worlds or the “Three-Fold Way” philosophy of later researchers.   (/ Nabokovian sotie.)

[Another Pale-Fire-style sotie  can be viewed here.]

~

[Postscript] 

Shortly after posting all the above, and by sheerest happenstance, meaning to while away the remaining hours of a Sunday afternoon, 

I plucked from a pile of literary miscellanea,

an omnibus volume of criticism by the late Mary McCarthy,  novelist and critic and controversialist:

A Bolt from the Blue, and other essays,

edited by the estimable A.O.Scott  for the New York Review of Books in one of its exemplary editions of Books Worth Reviving -- a worthy counterpart to the Penguin Classics:  creamy paper, crisp type, and a dust-jacket  silky as a geisha’s intimate skin.

Indeed, no other publisher quite approaches these exemplars, unless it be Lingua Sacra, editore to the cognoscenti.

The title essay turns out to be a review, from 1962, of Pale Fire (interesting that Scott promotes this assessment  to primus inter pares of McCarthy’s critical oeuvre).

Nothing escapes her.  It is a masterly reading of a tricky work, brilliantly expressed.  Her ingenuity of interpretation, her weeviling through baklava-like strata of authorial metaphor and detail, exceeds what all but a very few readers could aspire to -- or desire.  By the time she is done with her analysis (and with us), Pale Fire has come to seem as steroidally mythological, and as perversely interarticulated, as Finnegan’s Wake (which I have never managed to read, despite assaults  first on the north face, then on the east, and finally an attempted gondola-ride to the summit  using the cheat-sheets of the Skeleton Key).   In particular, I blush to acknowledge that, no, after all, even after second reading, I did not get all the jokes.

Just possibly, such virtuosity might (after much labor) triumphantly decode Sebastian Knight as instructions for a play-by-play laying-out of an actual chess-game, from pawn-to-king’s-four to nuts.   Or better yet, a variant upon the tragic but celebrated grudge-match of Capablanca vs Nimzowitsch (Havana, 1894), in which Nabokov (or Sebastian himself?)  discovers an unexpected alternate line of attack at the crucial move 45, resulting in a late save for Black.

Only, such a feat still doesn’t work as simply literature, for a readership; any more than some blate embodiment of arcane fourteen-tone musical theory, dazzling on the Partitur  to handful of  virtuosi (sadly deaf), can cross the footlights  to actual ears.

Twinned Eternities

In the poem portion of Nabokov's Pale Fire (1962), we read:

Outstare the stars. Infinite foretime and infinite aftertime.

The basic lexicon of Classical Arabic, as it happens (with its wealth of words), distinguishes these two, with a brief, monomorphemic word for each:

أبد  [abad] prospective eternity (with a terminus post quem but no end)

أزل [azal] retrospective eternity (with a terminus ante quem but no beginning)

Reflecting separately on these  raises interesting philosophical questions, e.g., regarding the indestructibility of the soul.  But as a merely intellectual matter, the picture will be clear to anyone who has got as far as geometry or calculus -- "half-infinite" directed intervals (such as the non-negative reals).

In Laughter in the Dark (English version 1938), Nabokov plays with the twinned hemi-eternities, in a passage full of satire:

“Haven’t I met your sister once?” queried Dorianna in her lovely bass voice.

“My sister is in Heaven,” answered Rex gravely.

“Oh, I’m sorry,” said Dorianna.

“Never was born,” he added.

Much is rustling beneath the sheen of this. First, Rex, po-faced, lays a logical snare for Dorianna, knowing that she would automatically assume that the now-absent soul is residing in the after-eternity (Arabic abad), which is all that most people ever think about, or even conceive to exist. An extra twist is provided by Dorianna’s automatic, flustered response at the unexpected reply – the conveyed sense is meant to be, “I’m sorry for your loss,” but simply stringing bits of syntax together yields, “I’m sorry that your sister is in Heaven.” (**) Rex then, indirectly pointing out the ambiguity in his initial statement, and implicitly rebuking Dorianna for failure to perceive ambiguity (again, in whatever sphere, most people don’t), reveals that this sororal Arlésienne is in fact at present domiciled in the ante-eternity (Arabic azal).

That passage, incidentally, rests as well on the paradox alluded to last time, that of the indestructibility of the soul. Intuitively, we think of a soul as the sort of thing (being brewed, after all, from the aethers of the Eternal One) that doesn’t simply wink out of existence. But by the same token, it shouldn’t be the sort of thing that simply winks in – in which case it must, as in the Platonic conception, be “stored up” somewhere (Rex specifies Paradise as the ‘green room’ or on-deck circle, though probably more from a faux-polite convenance than from any committed Platonism).

That observation does not exhaust the (depthless!) well of paradox subtending such insight. Follow it out, and you’ll encounter a retrospective version of the quantum-mechanical “many-worlds” scenario.

(**) P.G. Wodehouse plays on the same effect. In his world, earls are crotchety and idiosyncratic, and butlers are perforce imperturbable in the face of all.

            “Dash it, Beach, this egg is undercooked!”

            “Yes, sir.”

            “What – is the cook out sick again?”

            “Yes, sir.”

            “Well, I’ll be damned!”

            “Yes, sir.”

(Picture an infinitesimal lengthening of the glide initial: “Yyyes, sir.” The joke is, the double-meaning will be completely lost on the earl.)

~

It was the contention of “The Stokes Conjecture” (a chapter in my book, The Semantics of Form in Arabic)  that possession of such a neatly twinned pair of monomorphemes as azal and abad, as opposed to such roundabout (and nonce) phrasal confections as “infinite aftertime”, should track with a greater tendency of speakers of the language so outfitted, to be clear on the subject, for it to be cognitively relatively accessible, and thus to accrete around it  further developments both morphological (derivata) and semantic (metaphors).   Whether this be the case for Arabic letters and Islamic theology, I leave to my learnèd readers to make out.

~

The casual reference above, to the isomorphism of azal and abad, as constituents of infinite Time, to the half-rays  as subsets of the real line, conceals a textural disparity, in point of richness.   Not, as you might imagine, in favor of the human/experiential conception of Eternity, but the mathematical/intellectual science of the Real Line.

We really don’t know what to do with Eternity -- and literally, wouldn’t know what to do in it.    Like the silence of the infinite spatial reaches that so dismayed Pascal, we stand aghast at the prospect of doing anything “forever”, be it strumming harps or standing around on clouds swapping New Yorker captions.   The prospect of an infinite afterlife, for which we are supposed to yearn, is strictly baffling.

(Note that there is nothing heretical in that observation of human psychology;  notably, C.S. Lewis was converted to Christianity  before any sort of belief in or appreciation for  an infinite afterlife  was granted him.)
(For a mathematician's take on how the afterlife shall be spent, try this.
For an equine perspective,  this.)
(I riff upon the bafflement in the azal case, here.)

The Real Line, by contrast, is … infinitely diverting.   To begin with, even in a low-focus broad view (abstracting from the  so to speak  “quantum foam” of the infinitessimally inspected continuum), it harbors a great many other infinities within itself.  Thus, that infinite ray or half-line,  [0, ∞ ), is topologically equivalent to a mere half-open interval,  [0, 1):  in both cases, you can cover the space with a countably infinite sequence of disjoint intervals, no finite subset of which can do the job.  Thus, for the ray: [0,1), [1,2), [2,3) …. etc;  for the interval, [0, ½) [½,¾), [¾, 7/8) …

Further, the infinitude lies not only in thus stretching out forever, but in drilling down.   Any interval (even one that is closed, and thus compact) harbors infinitely many intervals as subsets;  and any such patch contains an uncountably infinite collection of points.  (We recall Dyson’s title, “Infinite in All Directions”, but with ‘directions’ differing qualitatively rather than simply like a compass needle.)

And those are just the appetizers.  The continuum is a regular zoo of exotic creatures -- the Cantor set, the Borel sets, projective sets, and a host of others studied in the discipline of “Descriptive Set Theory”.

~

As for those specifically twinned infinities, staring at each other from opposite sides of a mirror, they have a counterpart in modern physics, which takes reversibility of Charge, Parity, and Time (separately for some processes, in combination for others) as a kind of credo, like Liberté, Egalité, Fraternité.   Traditionally, time-reversed solutions were usually dismissed out of hand as unphysical;  other, more venturesome theorists, embraced them, telling fables of antiparticles as simply particles moving backwards in time, among other scenarios that chill the blood.

[ShoutOut:  Many thanks to Djinn ibn Sayârah  for help in formatting this for posting here.]

[Afternote]  My friend the Arabian theologian writes in :

Mark Twain wrote, regarding death:

“I do not fear death. I had been dead for billions and billions of years before I was born, and had not suffered the slightest inconvenience from it.”

That's kinda funny for as far as it goes, but no one who has experienced consciousness can be seriously flippant about it being snuffed out.

.

The Ontology of Sociology

The present post is simply a sort of by-trifle to The Ontology of Psychology.   It might alternatively be dubbed “The characterology of individual action in a multiperson structured setting”.

The unit of analysis  in Goffman’s accounts  is always the individual role-player  striving to effect his will  within a role-structuring situation.

-- Alasdair MacIntyre, After Virtue (1981; ²1984), p.  115

This put me curiosly in mind of the ‘sociology’ of chessmen.  (Here we speak, not of the vision of grandmasters, which is doubtless far more holistic, but of patzers, which is the only one I know.) 

Originally, the game was a metaphor or rather ‘video-game representation’ for medieval warfare.  Thrilling stuff.   And to a beginner, at least, it really does feel as though individual pieces are venturing out, or ignominiously retreating,  issuing powerful threats or just pushing pawnily along.   Sometimes, a noble warrior even ventures to be ‘sacrificed’ for the greater good.  I can testify that, as a scrappy lad first learning the rudiments, the queen, rather than just a factor among many, in a sort of multivariate algebraic equation,  was dizzying in her potential power -- “Wait’ll I sic my queen on ‘im!”  It was reminiscent of the culture of trading baseball cards -- Trajea a Mickle Mantle for a Yogi Berra plus a Roger Marris.    An archive of children’s chess-matches  would probably back this up, showing far more early-game forays by that dominating dame, than in expert play.

Compare, from Nabokov’s chess-novel:

…palpable pieces whose quaint shape and wooden materiality  always disturbed him, and always seemed to him but the crude, mortal shell  of exquisite, invisible chess forces.

…

Luzhin removed and placed on the table beside him  what was no longer an incoporeal force, but a heavy, yellow Pawn.

… The weightiest elements on the board  called to one another with trumpet voices, and again there was an exchange, and again two chess forces  were transformed into carved, brightly lacquered dummies.

-- Vladimir Nabokov, The Luzhin Defense (1964)

~

In Go, by contrast, the counters are all blandly interchangeable in themselves.   They pop out of nowhere, one by one (indefinitely); and once placed, have no power to move from the spot.  A holistic view is imposed even on the beginner.

On the same cat, sunning herself, on the same spot, again

  On the same cat, sunning herself, on the same spot, again

    Will you look at that cat … !

    Can you top that ??

    I can’t !

[Appendix from English literature]

The lady-mother of the kitten  sat sunning her white bosom

in the window,

and looked round  with a sleepy air of expecting caresses,

though she was not going to take any trouble for them.

-- George Eliot, Silas Marner (1861)

And, with the sunlight itself  being depicted as a cat:

All the windows in the villa were open.  Sunlight made itself comfortable in unexpected corners of the room.

-- Vladimir Nabokov, King, Queen, Knave (1968), p. 227

Word of the Day: “callipygian”

Logophiles were recently introduced to a rather beguiling-sounding name,

Callista

borne most prominently by Mr. Gingrich’s eighty-second paramour (and third wife).  The word derives from Greek,

καλλίστη

(transcribed kalliste), a feminine adjective of the superlative degree, meaning ‘most beautiful’.   Whether this epithet  accurately describes  the ex-mistress/spouse-of-the-month of Mr. Potato-Puff,  depends on your taste in helmet-haired bottle-blonde Barbies  with smiles like a constricted sphincter.   Such matters form no part of our scholarly concern;  our aims here are purely philological.

The -ist suffix is actually cognate with the English ending -est, used likewise to form adjectival superlatives.  That is, it does not form part of the root, which is simply kalli- ‘beautiful’.    This root has no English cognate, but it does show up in an English word  borrowed from the ancient Greek;  to wit

callipygian

For anyone who knows this word, it surely figures among the top ten favorites.  And its meaning is, um, well… that is to say…  Fact is, we here at the World of Doctor Justice run a pretty trim ship:  family-friendly, and dedicated to Wholesome American Values.   Not that being callipygian is necessarily out of line with Wh.A.V., not at all, it’s just … Unlike certain strutting public adulterers, who parade their paramours while posing as a paladin of the Moral Majority (and who previously, squatting in hiding, and still reeking from the bed of lust, hurled stones at President Clinton) -- unlike such gentlemen, I say, we are reluctant to utter here on this site  the least syllable that might bring a blush to a maiden’s cheeks -- either set of cheeks.  And so we urge you simply to consult (provided you are over eighteen, and for purely lexicographic purposes)  this sober and decorous encyclopedia article concerning classical scupture of the Hellenic isles,

Ἀφροδίτη Καλλίπυγος

A more plebeian appreciation of the feminine form  may be consulted here:

Dames, dames, dames !

A callipygian penguin, followed by an admirer

[Children cease reading here.  You must be 18 to view the following image.

Otherwise --  Don’t look down !!]

.

.

[no peeking !]

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.

Not smut! Classical stuff! (Guess which one is Mrs. Gingrich)

For an even more educational and not-naughty vision of the callipygian, verify that you are over 21, then click here.

[Bonus adjective]  An even rarer form, describing buttocks-traces left on a beach:

a pair of huge pygal-shaped impressions  left on the sand

-- Vladimir Nabokov, King, Queen, Knave (1968), p.

Use it!  Impress your friends!!