1. Strange Loops
2. Formal Systems
3. Self-Reference

A Strange Loop is a cyclic structure that goes through several levels in a hierarchical system. It arises when, by moving only upwards or downwards through the system, one finds oneself back where one started.

Gödel's Incompleteness Theorem states that for any consistent formal system complex enough to represent basic arithmetic, there will always be statements that are true within the system but cannot be proven within the system.

Escher's art often features paradoxical and self-referential structures, visually representing the concept of Strange Loops. His works illustrate ideas of recursion, infinity, and the blending of different levels of reality.

Bach's music, particularly his canons and fugues, demonstrates formal systems, self-reference, and complex patterns. His compositions often feature intricate structures and mathematical relationships, reflecting the book's themes of recursion and emergence.

Zen koans in GEB serve as examples of paradoxical and self-referential statements. They illustrate the limits of formal logical systems and the complexities of meaning and interpretation.

GEB explores the nature of intelligence, consciousness, and the question of whether machines can think. It discusses the challenges and possibilities of creating AI, relating concepts of formal systems and self-reference to the complexities of human cognition.

Recursion is a process where a function calls itself as a subroutine. In GEB, recursion is explored as a fundamental concept in mathematics, language, and cognition, often tied to the idea of Strange Loops and self-reference.

Formal systems in GEB are rule-based structures used to manipulate symbols without regard to their meaning. They are used to explore ideas in logic, mathematics, and language, and to discuss the limits of formal representation and reasoning.

GEB examines how meaning emerges from formal systems and symbols. It explores how complex meanings can arise from simple rules and how the interpretation of symbols can lead to multiple levels of understanding and self-reference.