I've rather enjoyed your insight into VN'w work and I hope I can help. I've had
a few graduate classes in quantum mechanics, cosmology, and elementary
particles, so I've had some background in the topic.
The
area of mathematics that you and, I believe VN are referring to is a specific
problem in mathematical topology. Although I read Ada earlier this year, I don't
recall the exact reference in which Van "solves the Euler problem," but it makes
perfect sense in my understanding of the "intercepting/overlapping worlds of
art" described in Ada. Topology in mathematics refers to the nature of the
"surfaces" in a particular problem (where "surface" can, and usually more than
two-dimensions, if three dimensions, then it is a "world" or "space", or
SU(3)/SU(2) × U(1) space). I found a nice description of the original Euler
problem at http://mathforum.org/isaac/problems/bridges1.html . Although the
original problem came from trying to figure out if someone could walk across a
set of bridges without recrossing the same bridge, it has become the basis for
understanding the fundamental nature of complex topologies, such as described in
the recent Nova program on string theory. An example question in topology is
there a "hole" in a surface. There is no hole for people who live on a flat
plate or sphere, such as earth (terra), but there would be for someone living on
the surface of a donut. String theory asks if the sting open ended or closed.
Cosmologists ask if our Universe is flat or curved. If curved, what is its
shape? If we travel in a "straight" line in one direction, would we return to
our starting point, or go on forever? If we came back to the same point in
space, would going in another direction be a longer or shorter route? What is
its topology?
My
understanding of the universe described in Ada comes from what VN said in "Good
Readers, Good Writers" (or do I have that switched) in the introduction to his
"Lectures in Literature." He said a novelist creates a world in which characters
are created, occupy and interact. This world is not the "real" world, but a
wholly, self-contained universe. A "good" artist creates an interesting world
with self-consistent rules. He warns us not to look for historical understanding
of pre-Revolutionary sociology of Russia in Tolstoy, but rather to read Tolstoy
for the new worlds that he has created. The "world" of Antiterra is indeed
complex because an artist in the world of Terra (our world) created it, in this
instance, by VN himself. Other artists have created other Antiterra worlds that
overlap Van's world by the degree of their artistic relatedness. This degree of
this artistic relatedness is the Euler problem. By solving this problem, Van
then understands that his world is not "closed," but rather has holes to other
artistic worlds, and eventually to our "real" world. Worlds created by other
artists intersect and influence Van's world, just as other artists have
influenced VN's artistic world. The magic and novelty of Ada is that VN
literally takes the "good reader" idea and stands it on its head. While a "good
reader" is exploring the world of Ada, a character in Ada is trying to explore
the reader's world. This begs the question - is Van a "good" reader? We can only
explore his world only through the porthole of the author, and Van discovers he,
to, is limited to seeing and understanding our world.
I
know I'm not the first to express this theory, and I'm sure others, including
you, have done it better. Reading, and trying to understand VN's wonderfully
complex stories and novels are a simple past time constantly interrupted by
children, dishes, and work. Thank you for your continued literary research. Much
of it, unfortunately, is totally beyond my comprehension.