"Now, here, you see, it takes all the running you can do, to keep in the same place." -The Red Queen

Chess is beautifully and almost infinitely complex.  When you play, you have to visualize where the pieces on the board can move and then extrapolate out, imagining where they might move one, two, three, or more moves down the line.  You have to anticipate where your opponent might move and how you can react.

Usually, this all happens in your head.  But now there's a chess program, Thinking Machine 4, that allows you to see the strength of different moves and the lines of attack and defense as the game unfolds.  It's designed as an art project, but I think it has a lot of potential as a chess training tool.  At the moment, the computer isn't a terribly good player and the abstract pieces are simply annoying.  Still, if you combined the idea with a decent chess program like Shredder you could have a powerful learning tool.

"Thinking Machine 4 explores the invisible, elusive nature of thought. Play chess against a transparent intelligence, its evolving thought process visible on the board before you.

The artwork is an artificial intelligence program, ready to play chess with the viewer. If the viewer confronts the program, the computer's thought process is sketched on screen as it plays. A map is created from the traces of literally thousands of possible futures as the program tries to decide its best move. Those traces become a key to the invisible lines of force in the game as well as a window into the spirit of a thinking machine."