NABOKV-L post 0018418, Wed, 1 Jul 2009 13:53:17 -0300

[NABOKOV-L] Nabokov sighting through S.K-Bootle and some Math
Here are news from Stan and Nabokoviana:

May 18, 2009

One Peut-Être, Two Peut-Être, Three Peut-Être, More Puns and allusions
Stan Kelly-Bootle, Author
"One is always loath to explain a joke. In face-to-face badinage, the joker can judge the comprehension of the jokees from their immediate reactions [...] Returning to my title, I'm forced to admit that beyond what might seem to be an obvious pun, requiring a little French (peut-Être means "perhaps, maybe") and knowledge of the children's game of counting potatoes, at which point the title at least sounds funny-there, I've already broken my rule against over-explicating a joke-you may still not grasp the full import of my waspish wit and unbounded, but lightly worn, erudition. Reluctantly, and risking your jealous scorn, I first remind you of Rabelais' lament, "Je m'en vais chercher le grand peut-Être" ("I'll be looking out for the big maybe"). Nothing to laugh at yet, considering that the poet is speaking of death, the big unknown, the big perhaps. Move on to Vladimir Nabokov (1899-1977) and his baffling masterpiece Pale Fire (a quote from Shakespeare indicating the moon's poor reflection of the sun), where we find the poet John Shade also pondering his mortality, but fighting back with dark humor:

L'if, lifeless tree! You great Maybe, Rabelais
The grand potato
I.P.H, a lay
Institute (I) of Preparation (P)
for the Hereafter (H) or If, as we
Called it-a big if-engaged for one term
To speak on death...

There's no end of chuckles for the word-sleuths here, and Nabokovians come to blows chasing their allusions. Amusingly, Nabokov himself was fond of rejecting many of the scholars' claimed solutions, saying that so-and-so was a brilliant interpretation, and he wished he had thought of it at the time of writing.

To quickly note the puns and allusions: l'if is French for the yew tree, of ancient Celtic significance for both death and long life (which just shows how usefully flexible mythology can be); l'if can also be read as "the IF," well known to programmers who need to branch (trees again) conditionally to remote parts of the coding forest. To play the allusion game you must be bold enough to spot that we have been "learning tree languages from positive examples and membership queries." This also

happens to be the title of a famous paper on algorithmic learning theory by Jérôme Besombesa and Jean-Yves Marion, in Theoretical Computer Science (Vol. 382, Issue 3), published the very week I moved back to England from the United States. Spooky beyond mere coincidence.

Nabokovians are obsessed by, and have a rare pet name for, spooky dates: fatidic. Look it up before complaining. Rabelais we've already met with his big peut-étre/potato, perhaps the biggest "maybe" we mortals face. Nabokov loved, analyzed, and lectured on James Joyce's Ulysses but couldn't stand Finnegans Wake (far too cryptic). Perhaps there's a clue here, an echo of the Big Potato Famine that devastated Ireland in the 1840s. There they sang, "Oh the praties they are small and we dig them in the fall, and we eat them roots and all, over here." We now have three Frenchmen: the authors Jérôme and Jean-Yves plus Rabelais; why not a fourth, Pascal, whose Wager tests our deathbed faith in salvation?

We then transliterate IF to the Greek IPH, giving us the Institute of Preparation for the Hereafter. We can pause briefly to recall that IPHigenia, daughter of Agamemnon, had a close dice with death until saved by the virgin goddess ARTemis. The theme of art bestowing a form of immortality via the survival of your artistic corpus runs through the work of Russian poets such as Derzhavin and Nabokov. That noble image is abruptly (deliberately?) tarnished by the close positioning of the word preparation and the letter H. Yet the sequence IF, maybe, suppose, suppository confirms our linkages.

Undismayed by Nabokov's teasing denials of the wilder conjectures, dozens of Pale Fire exegetes have published conflicting readings (Google Pale Fire and try the fine Wiki main article for starters). It's something of a literary FLT (Fermat's Last Theorem or Mrs. Fermat's divine lettuce and tomato sandwich) with some significant differences. First, it's not quite clear what the puzzle is and whether a unique solution, if such there be, would stand out as unique. Next, the setter and adjudicator-nastily known as Vlad the Impaler by the many butterflies he pinned down (spreading, I think, is the in-name) as a leading lepidopterist-is no longer with us to vet (and denounce) solutions.

It was certainly sound book-commerce to keep the puzzle open as long as possible. I know of only two positive, off-the-cuff, extra-textual hints made by Nabokov during his lifetime: he confirmed that Botkin (a near-Russian-anagram for "nobody") was indeed a Russian national lecturing at New Wye; and that Charles Kinbote (alias the deposed King of Zembla, and yet another near-anagram), the apparently deranged annotator of Shade's cantos, ended up committing suicide, outside the novel itself, as it were. So, finally, compared with FLT, there are several Andrew Wileses (he who finally proved the 300-year-old conjecture), each of whom is convinced he knows what the novel is all about.

There's more money to be made solving the P = NP conjecture (or its converse, the Clifford $1 million is unclaimed as I go to press my trousers), but a Pale Fire breakthrough could bring you lasting fame and headlines in the TLS or NYRB. It's not without its computational aspects-namely, carefully constructing hypertext "allusional" graphs not unlike the ones devised by El Don Knuth to illustrate who was sharing carriages and information with whom on Agatha Christie's Orient Express. Even minor Pale Fire discoveries have titillated the Nabokovian world, proving how easy it is to be dis-allusioned. A reference to Edsel Ford was for years taken to be Henry's son or the eponymous, infamous, ill-fated motor car. Matt Roth, a Pale Fire expert, uncovered the shocking coincidence that there was indeed a rather obscure poet born and christened Edsel Ford (1928-70), although, of course, not at all obscure to those who know of him. Indeed, among those who knew him was that omnivore Vladimir Nabokov, who quotes two lines from Ford's sonnet "The Image of Desire" in the novel Pale Fire.

My own Pale Fire solutions include the far-fetched idea that Pale should be pronounced Pally as in Palearctic, the very eco-zone in which every single butterfly nabbed [sic] and classified by Nabokov is to be found. This pale- prefix is a common contraction of paleo- meaning ancient or Old World. When we go a-llusioning, all things are possible. We now have not only pally or friendly fire (or amicide to increase your word-power-why buy Reader's Digest?) in our chain, but productive hints of Promethean fire and unbounded links to Aeschylus, Shelley, and that crowd.

And here we return to mathematics, computer science, and veer toward John Playfair's notion of a porism: "A proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate or capable of innumerable solutions."

Loosely (the word has been through many mangles since Euclid was a lad), we can think of a poristic equation as having either NO solutions or an INFINITE set of solutions. In England, we have the weaker Omnibus Existence Theorem: either NO bus comes to your bus stop or suddenly THREE arrive together. This is Brit Whine 2, after the Weather Whinge but ahead of the Cricket Test Match Results Shock. The poristic situation seems bizarre: you'll know that many existence proofs rely on reaching a contradiction after assuming that no solution exists. This familiar reductio ad absurdum (or law of the excluded muddle!) is known as a nonconstructivist approach, in that you may have proved the existence of a solution (at least one) without actually producing any actual solution(s). The limited choice between NO solution and a whole bleeding INFINITY of the buggers is not fair play, my dear Playfair.

I've no evidence that Nabokov ever used the word porism, but it's the sort of arcane word that would delight him. He does use many mathematical terms such as surd and lemniscate (both as the butterfly shape and as infinity on its side). He is acquainted with the higher dimensions of Einstein's space-time (which he attacks without showing a deep understanding of relativity) and speaks of bringing his "expanding universe back to a Newtonian norm." In The Real Life of Sebastian Knight (another cryptic masterpiece devoted to confused identities), he does a bit of Peano by having a character in the novel, closely identified with Nabokov himself, declare that "ONE is the only real number, and everything else comes from addition."Mathematicians would avoid the ambiguity between "real" (actual) and "real" (as in the real number system of which the integers derivable from 1 and + are but a tiny drop in the numerical bucket).

In addition to being an aficionado of butterflies, Nabokov was a skilled chess-problemist, adding to the notion that his literary puzzles might inherit the same challenge of "finding the unique winning solution," as in, "White to play and force mate in three moves." Extending that to the Pale Fire problem is, of course, much more complex. Hence my guess that we are in poristic territory: there may be no solution, but if we do find one, an indefinite number of rivals will have to be accepted.

In his memoir Speak, Memory (ranked in the top 10 of the world's nonfiction!), we can see what a great mathematician Nabokov might have become:

"As a little boy, I showed an abnormal aptitude for mathematics, which I completely lost in my singularly talentless youth. This gift played a horrible part in tussles with quinsy or scarlet fever, when I felt enormous spheres and huge numbers swell relentlessly in my aching brain. A foolish tutor [Nabokov enjoyed a wealthy, multilingual upbringing in Tsarist St. Petersburg] had explained logarithms to me much too early and I had read (in ... The Boy's Own Paper, I believe) about a certain Hindu calculator who in exactly two seconds could find the seventeenth root of, say [here follows a 40-decimal-digit number] (I am not sure if I have got this right; anyway the root was 212.)"

The remarkable thing here is that the numbers are correct: the 40-digit number is indeed (212)^17. More remarkable is that Nabokov claims to have remembered the numbers from a fleeting childhood event some 40 years previously. (In passing, Underwood Dudley, who knows some of the tricks of the calculating prodigies, tells me that knowing in advance that a given number is in fact the exact 17th power of some integer really simplifies finding its 17th root! You readily estimate the range of x from log (x^17) = 17logx = log(N). But that leaves the amazing task for most of us to mentally calculate 17 powers.) Nabokov is not claiming to have calculated anything, but had he lied he need only have remembered 212 and 17 and then computed 212^17 for his memoirs. This is most unlikely, as is the possibility that his copy of Boy's Own Paper survived the 1917 Revolution and the Nabokov family's subsequent odysseys in Germany, France, and England.

And yet, the more I learn of his life, works, and remarkable brain, the less inclined am I to doubt his word. He suffered (or enjoyed) synesthesia, so he "saw" words, letters, and numbers as colored images. He composed his novels on index cards, and at a certain point had the complete work fixed in his mind. So, if your exposure to Nabokov has been limited to his controversial Lolita (or the movies "they dared not make!"), perhaps the Pale Fire mystery might help widen your horizons. It may perhaps improve your IT career opportunities by sharpening your deductive and word power. Maybe not! Who cares? We'll all be on the dole until the recession ends at 6:12 a.m. GMT on September 15, 2014 (you read it here first).

As that most annoying of adverts says, "Make the Most of NOW!" (I can never recall the product. I just rush at time's moving target, missing one NOW after the next.) Relax with Pale Fire. It's full of laughs, just like my title! As Jeremy Paxman says on the UK game show, University Challenge, "Here's your starter for 10. Which unfinished 999-line poem begins:

"I was the shadow of the waxwing slain
By the false azure in the windowpane"?

No conferring!

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