The Magnetic Resonance Imaging figure on page 38 does remind me how important predictability is in slicing. In medicine, predictability is paramount: it is how deformities and abnormalities are diagnosed. When we can see by shadow or color or shape that something is different, for example in brain tissue, the patient can be given the appropriate therapy for their problem. It could be a tumor, or a hemorrhage, or swelling from an injury. These are all treated differently, so the texture and shape on the MRI point the doctor in the right direction for diagnosis.
These different views also made me think of cooking, and the ways in which layering or marbling can change the presentation of a food. A fruit layer tart, for example, may be all one fruit from the overhead view, but when sliced can reveal a rainbow of different colors from other fruits. A marbled vanilla and chocolate cake is made by either putting one layer on top of the other or one layer concentrically inside the other. The chef then draws a knife through both layers, so that one cuts into the other. Then when the cake is sliced, the dough looks as if it has been mixed in a marble style.
I was trying to tell a friend about the higher dimensions we've been trying to visualize and he could not seem to grasp the idea of a spatial fourth dimension. Then I realized that we were sitting in front of a beautiful hardwood table. The grain in the wood provided a great analogy for us looking in on a "flatland". I got him to imagine the tree as a whole, and that now that it was sliced, we could see it in the second dimension. Then we extrapolated to creatures who are in a higher dimension than we are, and he understood that they would look at us as if we were sliced. His response was, "Ooooooooooooh. ...WEIRD!!".
To exercise those brain cells that were showing up on the MRI, look at a contour map of your area or a favorite hiking spot. Does it make sense to you? Now, put your non-dominant hand on a writing surface and make a contour map of it with your writing hand. Use only one color, so you don't get too confused. Curve your fingers in different ways, or make a fist, to make the map more interesting.