in 1940, master sci-fi author robert heinlein wrote the short story "and he built a crooked house." in the story, our hero builds his home from an unfolded four-dimensional hypercube. when an earthquake strikes, the house folds up, creating the world's first four-dimensional house, where occupants can look down a hallway and see their own backs. dimension is one of the most important and intriguing ideas in mathematics. we move in three dimensions of space, we live in four dimensions of space...and time, but mathematicians and increasingly scientists of all flavors, from statisticians to biologists, are finding that they need to understand and work in worlds of hundreds and even thousands of dimensions, worlds that reach well beyond human sensory experience. when we start asking questions such as "when did our universe begin, and how will it end?" many scientists believe the answers will involve 10, 11, 12, or even more dimensions. but what do we really mean by the word "dimension"? generally speaking, the dimension of space or a problem is simply the number of numbers that we need