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.)
(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.
