Mary Krimmel is correct -- Mandelbrot did coin the term
"fractal." First published appearance of the word is 1975, so far as I know
without further research. Mandelbrot however did teach at Harvard. I have not
yet found out exactly when, but will try to do so. He is still alive by the way
and affiliated with Yale.
VN may have known about fractals even without
any personal relationship with Mandelbrot. The idea goes back earlier in the
20th century to another Polish mathematician named Sierpinski and before that,
as Jansy asks, it is definitely related to the logarithmic spiral. Like other
fractals, the spiral continues unchanged no matter how closely you look at it.
It recedes infinitely at the same level of detail. I am not describing it very
well, but if you are familiar with the phenomenon you will know what I am trying
to say.
I have seen the frac-tail reference, and there does not appear to
be any mathematical allusion there. Jansy's find may be an optical illusion, but
it has turned out to be one with interesting repercussions. I intend to
look into the possibility (planted in my memory of Tom Stoppard's play
Arcadia) that Byron's mathematical daughter Ada may have conjectured in
this field of geometry. This may have implications for VN's novel of that
name.
Also interesting to find that a Summer workshop on Fractals
included literary examples of fractals drawn from two works of VN's, The
Eye, and Ultima Thule.
Carolyn
> EDNOTE.
NABOKV-L thanks Mary Krimmel for her discriminating and informative >
note. > ----- Original Message ----- > From: Mary Krimmel >
Message requiring your approval (29 lines) ------------------ Benoit >
Mandelbrot claims the coining of the term "fractal" for a collection of >
certain mathematical sets. He explains this in "Fractals: Form, Chance, and
> Dimension", published in 1977, a "much modified and augmented second
version > of 'Les objets fractals:'.. (1975)". No one disputes his claim.
> > The explosive interest in and development of the topic
depended much on the > development of computer technology. So VN could
not have known about fractals > when he wrote Pale Fire, first published
in 1962.. Surely he must have known > something of the name and
reputation of J. Bernoulli and of "Math", but > putting the golden
rectangles into the collection of connotations of the > lemniscate of
line 137 is too much of a stretch. > > The rectangles are not
related to the findings about fractals - at least not > in any but the
most distant way. > > Mary Krimmel > > Jansy
asked: > > "In the Post-Script that VN added to "Lolita" he speaks
about enchanters and > he uses the word "fractails". I wonder if he
could also be making a reference > there to the modern mathematical
discoveries concerning 'fractals' ? > "Would those 'smaller
and smaller golden rectangles' of Bernouilli´s > logarithmic spiral
-brought up by C. Kunin - be in any way related to the > findings
about fractals? Would VN be familiar with Math, Bernouilli and >
Fractal theory? " > >