This is a little excerpt from Michio Kaku's book Hyperspace. I thought it was a simple yet brilliant analogy so I decided to share it. I highly recommend this book to anyone who is interested in learning about the theories of higher dimensions. The content (as far as I've read, at least) is laid out in very simple ways where anyone should be able to understand it. Kaku seems to use a lot of analogies, much like this one, to help get ideas across.

Traveling Through Space and Time


The hyperspace theory has also reopened the question of whether hyperspace can be used to travel through space and time. To understand this concept, imagine a race of tiny flatworms living on the surface of a large apple. It's obvious to these worms that their world, which they call Appleworld, is flat and two dimensional, like themselves. One worm, however, named Columbus, is obsessed by the notion that Appleworld is somehow finite and curved in something he calls the third dimension. He even invents two new words, up and down, to describe motion in this invisible third dimension. His friends, however, call him a fool for believing that Appleworld could be bent in some unseen dimension that no one can see or feel. One day, Columbus sets out on a long and arduous journey and disappears over the horizon. Eventually, he returns to his starting point, proving that the world is actually curved in the unseen third dimension. His journey proves that Appleworld is curved in a higher unseen dimension, the third dimension. Although weary from his travels, Columbus discovers that there is yet another way to travel between distant points on the apple: By burrowing into the apple, he can carve a tunnel, creating a convenient shortcut to distant lands. These tunnels, which considerably reduce the time and discomfort of a long journey, he calls wormholes. They demonstrate that the shortest path between two points is not necessarily a straight line, as he's been taught, but a wormhole.

One strange effect discovered by Columbus is that when he enters one of these tunnels and exits at the other end, he finds himself back in the past. Apparently, these wormholes connect parts of the apple where time beats at different rates. Some of the worms even claim that these wormholes can be molded into a workable time machine.

Later, Columbus makes an even more momentous discovery--his Appleworld is actually not the only one in the universe. It is but one apple in a large apple orchard. His apple, he finds out, coexists with hundreds of others, some with worms like themselves, and some without worms. Under certain rare circumstances, he conjectures, it may even be possible to journey between the different apples in the orchard.

We human beings are like the flatworms. Common sense tells us that our world, like their apple, is flat and three dimensional. No matter where we go with our rocket ships, the universe seems flat. However, the fact that our universe, like Appleworld, is curved in an unseen dimension beyond our spatial comprehension has been experimentally verified by a number of rigorous experiments. These experiments, performed on the path of light beams, show that starlight is bent as it moves across the universe.