One way to simplify a problem is to draw a picture.
For example, say you are contemplating rearranging the furniture in your home. If you have a lot of heavy furniture and a complicated layout to your house or apartment, you can save yourself unnecessary grunt work by sketching out your floor plan and penciling in the new arrangements you are thinking about. You could take this a step further by cutting out pieces of paper that represent chairs, couches, and tables and by shifting these scraps around to see how things work out.
If you have drawn an accurate representation, then you can determine—without ever leaving your armchair—which possible arrangement makes sense.
Rocket scientists call such drawings blueprints. They used to draw blueprints by hand, which was a tedious, painstaking task because standard practice required accuracy to within / of an inch. Drafting courses were taught to generations of engineers. I took such a course and hated every minute of it. My impression was, "Here's a hundred-year-old course being taught by a hundred-year-old man." Three views (front, top, and side) which provided three-dimensional information had to be drawn precisely, and labeling had to be done in rigorous block letter form.
Now most drafting is done on computers, consequently the ability of rocket scientists to draw or print legibly has atrophied. But we still use the phrase, "Back to the drawing board" whenever we get bit by Murphy's law and have to redesign a spacecraft or rocket.
It is unfortunate that most rocket scientists can't draw. I think that, in addition to learning computer graphics, students of rocket science should take a course on drawing from the art department. Because we are visual creatures, the ability to make a credible drawing on a piece of paper, a napkin, or a chalkboard is a valuable aid to thinking. Most engineers are visualizers and need pictures to understand the problem they're working on.
In many ways, drawing a picture is a method of simulating and solving a problem. When you sketch your floor plan and consider various furniture arrangements, you are making an analog compu-tation—a simulation. You don't know how things will turn out until you've drawn a picture—and suddenly you see the solution. You've solved the problem, actually computed it, without using any mathematics!
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