The concept of the fourth dimension is usually surrounded by mystery and suspicion. How dare we, creatures of length, height, and width, speak of four-dimensional space? Is it possible by using all our three-dimensional intelligence to imagine a superspace of four dimensions? And what would a four-dimensional cube or sphere look like? When we say "imagine a giant dragon with a long scaled tail and flame streaming from his nostrils, or a super-airliner with a swimming pool and a couple of tennis courts on its wings, you are actually drawing a mental picture of the way it would look were it to appear suddenly in front of you. And you draw that picture against the background of the familiar three-dimensional space in which all ordinary objects, including yourself, are located. If this is the meaning of the word "imagine," then it is just as impossible to imagine a four-dimensional figure against the background of ordinary three-dimensional space, as it is impossible to squeeze a three-dimensional body into a plane. But wait a moment. We do, in a certain sense, squeeze three-dimensional bodies into a plane by drawing a picture of them. In all these cases, however, we do not of course use a hydraulic press or any other physical force to do the job, but apply the method known as geometrical "projection" or shadow building.
George Gamow, One Two Three...Infinity: Facts and Speculations of Science
