From metawiki
Escher uses self-reference extensively in his art

The tao that can be described is not the eternal Tao. The name that can be spoken is not the eternal Name -Lao Tzu

Godel's incompleteness theorems are fundamental to understanding the limits of scientific and mathematical knowledge and the power of self-reference. It proves the Taoist saying by demonstrating that we can never fully determine what is true using the language of mathematics.

Gödel, Escher, Bach should be considered required reading for a full understanding of metaculture.

View All References to Self-Reference

Here's a basic explanation of Gödel's incompleteness theorem if such a thing exists.

The Paradox at the Heart of Mathematics: Gödel's Incompleteness Theorem

A free online course from MIT is available to help get the most out of this seminal work.

MIT Godel Escher Bach Lecture Series

Technically this is based on another book by Hofstadter but it does a good job explaining a lot of the concepts of recursion and consciousness that are in GEB.

You Are a Strange Loop

Doug Hofstadter - Reflections on AI

Kirk, Spock, Scotty, and McCoy Outwit the Androids

Bach "Little" Fugue in G Minor