NABOKV-L post 0014446, Tue, 19 Dec 2006 19:47:08 +0000

Re: Query: interesting association
On 18/12/06 11:12, "jansymello" <jansy@AETERN.US> wrote:

> Another associations I recently set down:
> And Pythagoras was drawing the shadows of the window frames on the bright
> polished floorŠ(page 145, Bend Sinister)...
> I almost felt here the flitting shadow of the waxwing slain from Shade's
> poem...

Jansy-in-the-Jungle (or, as we say in Greenspeak, ŒRain Forest¹): I take the
more direct track (geodesic!) to Pythagoras the Geometer (more a School than
a single Chap). The shadows cast by rectangular window frames (lattices!)
suggest many interesting ideas in Projective Geometry which, in fact,
POSTdates Pythagoras by some 800 years. Mathematicians would prefer to
attribute the frames¹ right-angles to Pythagoras and their shadows (in
general non-rectilinear) to the later, greater Greek Pappus. The well-known
Theorem of Pythagoras really belongs to Euclid, by the way.

You¹ll all know the American-Indian version of Pythagoras¹ Theorem:
³The squaw on the hippopotamus hide is equal to the sum of the squaws on the
other two hides?²
Tepe or not tepe?

I take this opportunity to CONFIRM VN¹s arithmetic in Speak Memory! I remind
you of the passage, and APOLOGIZE if others have already checked the sums
(my archive searches were nullish). If my findings are original, I claim 2nd
prize after the EDSEL FORD discovery!!

* In Speak Memory [pp 36-7], VN recalls losing his early ³abnormal 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 had explained logarithms to me much too early,
and I had read (in a British publication, the Boy¹s Own Paper, I believe)
about a certain Hindu calculator who in exactly two seconds could find the
seventeenth root of, say,
3529471145760275132301897342055866171392 (I am not sure if I have got this
right; anyway the root was 212)²

With help from Number Theorist and Crank-debunker Prof Underwood (Woody)
Dudley (he has an Erdo:s number ONE which should impress the impressible),
we can now say that VN¹s reported digits are remarkably, blindingly EXACT.
As Dmitri noted recently, some minds (esp. synaesthetes¹) have a remarkable
capacity for recalling long numbers ‹ so theory A is that VN correctly
recalled the above result from boyhood. Theory B is that VN is playing his
mischievous tricks. I keep an open mind. Woody¹s on-going research is not
yet conclusive:

³I don't know who the Hindu calculator referred to in _Speak,
Memory_ could have been. The definitive work (so far) on calculating
prodigies, _The Great Mental Calculators_ by Steven B. Smith (Columbia
U. Press, 1983), mentions only two Indian specimens of the breed, and
they flourished long after Nabokov's youth. Smith says that finding
n-th roots of integers is easy, if the answer is an integer, and the
BIGGER n is, the EASIER it is. Finding seventeenth roots is as nothing
compared to, say, multiplying two eight-digit numbers mentally.²

I¹ve attended sessions where Prof Arthur Benjamin (Harvey Mudd College, CA)
beats us (we armed with electronic gadgets) in all kinds of horrendous
calculations. Unlike the trad, Idiot Savant, who achieves similar feats
without knowing how (and has no other mathematical talents) Benjamin (and
others, such as Johnny von Neumann) are real mathematicians willing to
reveal their methods. (There¹s an MAA book by just out by Benjamin ‹ title
eludes me). One of the mnemonic tricks is to associate SOUNDS or IMAGES to
each of the digits ‹ which VN could well exploit with the addition of

Interestingly, one of the greatest mathematicians of the 20th century was
the Hindu RAMANUJAN whom G H Hardy invited to Cambridge. Well worth a Wiki
or google.

Stan Kelly-Bootle

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