----- Original Message -----
From: Carolyn Kunin
To: Vladimir Nabokov Forum
Sent: Sunday, September 28, 2003 10:28 AM

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.


> 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? "