Contributed by
Fusun Akman
The topics change
from the Titanic to a giant octopus but a central one is the
Mandelbrot set. We are introduced to mathematiciancumcomputer
wizard Edith Craig who invents software to fix the Y2K problem and
later loses her mind staring at the depths of the Mset. Hubby Donald
is also in the same business but he is sane. Their nineyear old,
Ada, gives lectures to their visitors on the properties of the
Mset. Needless to say, they have a pond shaped like the Mset in
their castle.

I was very disappointed by Clarke's very long and poetic, but ultimately
wrong and insulting description of the Mandelbrot set. This description
occurs twice (once in the story as told by little Ada and again in an
appendix in Clarke's own voice). His description is wrong because it
involves only the distance of a point in the plane to the origin (the
absolute value, if you are thinking of the plane as the complex numbers).
If that was true, the Mandelbrot set would be symmetrical around the
origin, which it obviously is not. I could be generous and say that he is
trying to avoid introducing the complex numbers because he doesn't want to
scare the readers, but it actually seems to me as if he himself doesn't
understand what he is saying. (It would have been possible to avoid
introducing the idea of complex numbers without being wrong by defining the map (x,y) >
(x^2y^2,2xy) which is the same as squaring the complex number x+yi.) And, mostly, I am
offended on behalf of my friends in complex dynamics who investigate the
Mandelbrot set and other geometric consequences of chaotic dynamics by
Clarke's implication that all there is to do with the Mset is look at it
on a computer. Like many other areas of math research, computers are
useful for providing clues as to what might be true, but in the end it is a
human mind which must analyze and explicitly prove the claims in
mathematical terms. A good deal was known about complex dynamics before
Mandelbrot noticed this set on a computer, and much more is known since
from the really deep work of these mathematicians (not at all something
that would have been easily done "as soon as man learned to count" as
Clarke claims in a completely ridiculous example of hyperbole.)
For a better view of the Mandelbrot set, I suggest you look at Boston University's
interactive description. 