J.W. Dunne gives an example of a painter which (I think) can be appropriated to making a very suggestive incompleteness theorem.
Consider a man who wanted to paint the entire universe. He gets a canvas and starts painting the landscape in front of him, figuring that the rest of the universe will just involve filling in the details. He soon recognizes, however, that he has forgotten to include himself in the landscape. So he adds himself in, only to recognize that he now has to paint himself adding himself in. The regress doesn’t have to go though too many steps before the painter figures out that the picture must always be incomplete; and it is no more or less complete if he draws himself in or not. The mere fact that the painting is produced by someone requires that there must be some reality that it leaves out. But every science and art: metaphysics, physics, philosophy, myth, etc are produced. None of them, or even all taken together, can avoid leaving out some reality – though not just some reality, but a crucial, causative, fundamental one.