Vladimir Nabokov

NABOKV-L post 0008702, Sat, 4 Oct 2003 09:51:58 -0700

Fw: Bernoulli lemniscate (Pale Fire)
From: Dmtir Nabokov

I have a couple of brief comments in reply to Carolyn and to Phil Wren. It is very unlikely that VN came across "lemniscate" in either of the two dictionaries he used most: Webster's New International, 2nd edition, unabridged; or the more voluminous thirteen-tome OED. He would have had to be searching for it specifically, or else to have happened upon the term by pure luck just when he needed it but while he was searching for something quite different in the neighborhood. A thesaurus is an even less likely source, since neither of the two thesauri he used contains the word.

It is true that he was not a mathematician, but, when he needed precise information, he researched any number of subjects thoroughly. Nor (to return to a sensitive point) did he display his skill with words gratuitously. Then again, the threshold of one's need to search in dictionaries depends on the level and variety of his culture and his vocabulary.

"Lemniscate" has various meanings and various relatives. The two definitions that interest us are 1) the Bernoullian lemniscate and 2) the Boothian lemniscate which is a generalization of the Bernoullian. I have the precise formulae for both but shall not overload this posting with math. Suffice it to say that the Bernoullian variety is neither simply an eight snoozing on its side nor the infinity symbol. If one examines it carefully one will notice that part of the central section (roughly from NE to SW) is thicker than the rest of the figure. This may be interpreted as the zone where the track was thickened by the imperfect overlap of two bicycle tires, which just might have been what Nabokov intended to convey by his choice of the word. The skater's joy Phil mentions is exemplified by a poem of my father's -- which I have translated for my collection and shall post as soon as it has come out in Aretè -- in which a deft blade can even design a flower. So maybe we should set lemnicycling aside and instead lemniskate.