Friday, March 18, 2016

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.



  1. It's as lovely to read a second time as it was the first. It was a pleasure to help set this post loose.

  2. Fun! I do like the Twain quote, and I also like thinking about "drilling down" in all directions. But why do you think consciousness will be "snuffed out"? Isn't that part of the Indestructible?