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 floor…(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, ‘Rain Forest’): 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 frames’ 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.
You’ll all know the American-Indian version of Pythagoras’ Theorem:
“The squaw on the hippopotamus hide is equal to the sum of the squaws on the other two hides?”
Tepe or not tepe?
I take this opportunity to CONFIRM VN’s 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 “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 had explained logarithms to me much too early, and I had read (in a British publication, the Boy’s 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)”
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 VN’s reported digits are remarkably, blindingly EXACT. As Dmitri noted recently, some minds (esp. synaesthetes’) 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. Woody’s on-going research is not yet conclusive:
“I 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.”
I’ve 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. (There’s 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 COLOURS?
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