I'm not the only one who has been thinking about visualizing mathematical concepts!
At roughly the same time I was writing my previous post, Math Blog was posting thought-provoking mathematical videos. The videos that were chosen are very effective at making hard-to-imagine concepts easier to understand. Do you think you can understand 10 dimensions, or how to turn a sphere inside out with poking a hole in it?
The idea of making mathematical and scientific concepts easy to visualize isn't just a passing fancy, either. The National Science Foundation has hosted the Science and Engineering Visualization Challenge since 2003. Interesting past winners include Still Life: Five Glass Surfaces on a Tabletop (seen in the graphic above) and Flight Patterns.
Planetary Motion from Eudoxus to Copernicus, which only made honorable mention, is especially interesting. It's a visualization over time of how humanity pictured the universe. Planetary Motion reminds me a little of James Burke's documentaries (Connections and The Day The Universe Changed).
Speaking of TV shows, there aren't that many shows today, other than Numb3rs, that regularly feature mathematical visualizations. I remember a PBS show called Square One TV that used to teach an amazing variety of mathematical skits to hit the point home. As an example, how do you make the summation of positive and negative numbers visual? Here's Square One's approach:
You might think it would be hard to visualize would be Einstein's Theory of Relativity. If that's true, the people who created Al's Relativistic Adventures have proved that wrong. This is an interactive Flash demonstration that takes you step by step through the numerous principles involved in relativity, and even quizzes you to make sure you're following along.
It's a shame that math isn't taught to both the left brain and the right brain. As a final thought on this matter, I suggest reading If We Taught English the Way We Teach Math.