"For the mathematically inclined reader we note that a Calabi-Yau manifold is a complex Kahler manifold with vanishing first Chern class."
"For the mathematically inclined reader we note that this particular Calabi-Yau space is a real three dimensional slice through the quintic hypersurface in complex projective four-space."
From the footnotes to Chapter 8 in Brian Greene's The Elegant Universe.
Whew! What was that all about?
I like to read science books from time to time. I try to understand within the limits of my meager education and experience what I am reading about. Mostly I enjoy these books because they often spark my imagination and I get ideas for science fiction stories that I will someday hopefully write. The text in these books is often easy to follow with excellent examples from everyday life used to illustrate very complex theories. I usually don't check the footnotes. This time I did and I found myself drowning in a pool of mathematical jargon. Figuring this would be a chance for me to learn more I plugged into Wikipedia and began looking up the vocabulary unfamiliar to me. I soon found myself drowning in a sea of jargon. It was like having taken a beginner course in another language and then being given a legal document in that language to decipher. However, I made some discoveries of how this world of algebraic geometry and theoretical physics had found its way into pop-culture.
First I should explain that as far as my comprehension ability had permitted me to understand, a Calabi-Yau manifold is a geometrical representation in two or three dimensional space of a complex geometry in six dimensional space. The designs created on computer are rather pretty and resemble certain things I have seen living in the sea and even a certain species of cactus (found a photo on the Net of a "Calabi-Yau" cactus). Check out the wiki link to learn more.
Whenever science introduces such a concept that can be represented by a pretty design or has excellent implications for science fiction writing it quickly finds its way into the world of pop-culture. Doing a search for images of Calabi-Yau manifolds or Calabi-Yau space I found that there is a rock band called Calabi-Yau and also an album entitled Calabi-Yau Space by Dopplereffekt. Wikipedia also lists various instances where Calabi-Yau space is used in science fiction stories and dramas. The most intriguing of these I found to be in issue #15 of Ms. Marvel where items can be hidden in plain sight using Calabi-Yau space. Imagine that! How tidy our rooms could be if we could just shove everything into a six-dimensional contorted space. I can just imagine, however, the horror of having to retrieve those items at a later date. The worst attics and basements would seem user-friendly compared with a Calabi-Yau space closet. I am sure the infomercials would be worth watching. Maybe we already have Calabi-Yau space closets and don't know it. That might explain where all the missing left socks go! (Ren and Stimpy reference there)
Doctor Who also makes mention of Calabi-Yau space and introduces creatures called Chronovores. Now there's an interesting concept. If you have any unpleasant memories in your life you can just feed the experience to a pet Chronovore. Be careful not to overfeed. "My Chronovore ate my life!" I feel another sequel to The Hitchiker's Guide to the Galaxy coming on. Too bad about Douglas Adams.
The most amusing thing I read, however, was that in an episode of Numb3rs, there is a plush toy of a Calabi-Yau manifold. I actually would like one but on the other hand I think such an item is made popular by people who, like myself, don't fully grasp the concept or mathematical implications of Calabi-Yau manifolds. Like E=mc² and the Mandelbrot set, Calabi-Yau manifolds will be nothing more than a novelty item to the masses who wish in vein to be associated with a much higher level of intellect. However, if we can make a model to hang over cribs for babies of Calabi-Yau manifolds, Mandelbrot sets, other fractal designs, tesseracts and Buckminsterfullerene models then maybe we can hope to raise a child that will take interest in and study those things and be able to explain them to us, the poor parents who missed out on physics and advanced calculus classes but like to pretend we know something about that world in order to appear plausibly intelligent.
Science aside, Calabi-Yau manifolds and fractals do make for pretty designs.
At ArtWanted.com there are some artists who work with fractal programs. Thea Walstra does a lot of them.
I wonder if there are now programs for creating Calabi-Yau manifolds...
