All this talk about 2 and 3 dimensions got me thinking again about the book "Flatland", which I read many years ago. Written by the nineteenth century English clergyman Edwin A. Abbot, the book describes the adventures of the two dimensional character A. Square as he makes a visit to the three dimensional world.
I remembered that the book sent me on many trips, imagining what life might be like in more or less dimensions than the three we are used to. Although I never managed to satisfactorily make the leap in my mind's eye, I always felt like there must be a way to use computers to help us effectively simulate life in 2D or 4D.
Then a friend sent me a link to Rob Bryanton's "Imagining the Tenth Dimension". This brilliantly executed Flash site serves as a promotion for the book of the same name, but more importantly provides the clearest visualizations of multiple dimensions that I've ever seen. Although I lose track of things at about the sixth dimension, this site is to me a miracle of clarity for understanding the first five.
Then just the other day, while surfing for kid-friendly games online with my daughter, we came across a little Flash-based game called "N", and suddenly two dimensions came alive in a way I've never seen before. The game summary? "Play as a ninja trapped in a world of well-meaning, inadvertantly homicidal robots".
If you've ever wondering what it might be like to live in 2D, this is the way to find out. Not only is the game an amazing play on physics, level design illustrates exactly the way I always imagined a two dimensional house (or forest, factory, cliff, or vault) would look.
A warning though: although the game has only three controls (right, left, jump) it is extremely addictive and extremely difficult. That said, I can't wait to go back and play more.
Now that I can imagine it so well, I realize that living in 2D is a lot harder than I expected.
(Oh, and those kid-friendly games for my daughter? Well, let's just say that she's better at surviving in two dimensions than I am.)