Let's imagine a 2-D world in which everything is, naturally, a 2-D object. We have squares, circles, triangles, and other less regular shapes that live in this 2-D world. The view of all 2-D objects by other 2-D objects, everything there is, is left-right and forward-backward. That's all 2-D objects can see because that's where they live. A 2-D object cannot see anything in the 3rd dimension because it doesn't live in 3-D space.
Now, let's imagine a 3-D object, say a sphere, poised above the 2-D world described above. All 2-D objects cannot see this 3-D object because the sphere lives outside the 2-D world. The 3-D object, on the other hand, has a very different view of the 2-D world. The sphere can see all of the objects in the 2-D world, simultaneously. The sphere sees the circle, the square the triangles and all other objects in the 2-D world at a glance, even those objects which may be hidden to a 2-D viewer. To see why this is so, suppose you hold up a piece of paper in front of you. You can see all points on the sheet of paper at the same time, can you not? If you are a square placed between a circle and a triangle on the page, the circle cannot see all of the triangle because the square is blocking its view. So, you might think of this sphere's 3-D view as x-ray vision of the 2-D world because the sphere can see the circle, square and triangle simultaneously.
What if the sphere speaks to a 2-D object? The 2-D object might think of the sphere as a spirit because it can't see the sphere in its world. Suppose, now, the sphere wants to make contact with a circle in the 2-D world. So the sphere moves downward into the 2-D space. What the 2-D object, the circle in this case, sees is only a cross-section of the sphere. As the sphere proceeds downward into the circle's space, at first the circle sees only a point, followed by a circle of increasing size, then a circle of decreasing size and finally a point until he sees nothing as the sphere passes below his 2-D world. For a while, then, the circle in 2-D space sees the sphere which has been communicating with him from afar, but the circle never fully appreciates the sphere because he never sees it in its entirety. In other words, the circle never really knows what a sphere is based on what it has seen of it.
What if the sphere communicates with the circle once again, but this time the sphere makes contact with the circle in a big way. Imagine that as the sphere moves downward through the 2-D world it touches and then nudges the circle out of its 2-D world into the 3rd dimension. Now, the displaced circle has entered another dimension that wasn't possible for it before. What does the 2-D object see? You're right! The circle can now see the sphere for what it is, a sphere! This is because the circle now lives in the 3-D world where it can see other 3-D objects. The 2-D circle also has acquired the ability to see all of its 2-D friends simultaneously. But, none of the circle's friends can see him now. The circle has acquired an x-ray vision of its former 2-D world.
What implications does this discussion have for 3-D objects as viewed from the 4th dimension? That is the subject of chapter two.