The mathematician's sense of tension is intimately related to his sense of beauty, and is what makes mathematics worthwhile doing. - Douglas Hofstadter

The "Strange Loop" phenomenon occurs whenever, by moving upwards (or downwards) through levels of some hierarchial system, we unexpectedly find ourselves right back where we started.

"There can be conceptual skeletons on several different levels of abstraction. For instance, the "isomorphism" between Bongard problems 70 and 71, already pointed out, involves higher-level conceptual skeleton than that needed to solve either problem in isolation."

Relying on words to lead you to the truth is like relying on an incomplete formal system to lead you to the truth. A formal system will give you some truths, but as we shall soon see, a formal system, no matter how powerful—cannot lead to all truths.