The theorem can be likened to a pearl, and the method of proof to an oyster. The pearl is prized for its luster and simplicity; the oyster is a compl… - Douglas Hofstadter

Godel showed how a statement about any mathematical formal system (such as the assertion that Principia Mathematica is contradiction-free) can be translated into a mathematical statement inside number theory (the study of whole numbers). In other words, any metamathematical statement can be imported into mathematics, and in its new guise the statement simply asserts (as do all statements of number theory) that certain whole numbers have certain properties or relationships to each other. But on another level, it also has a vastly different meaning that, on its surface, seems as far removed from a statement of number theory as would be a sentence in a Dostoevsky novel.

The paraphrase of Gödel's Theorem says that for any record player, there are records which it cannot play because they will cause its indirect self-destruction.

And that is also the way the human mind works — by the compounding of old ideas into new structures that become new ideas that can themselves be used in compounds, and round and round endlessly, growing ever more remote from the basic earthbound imagery that is each language’s soil.