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-allu-sioned. 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 ...