GEB Ch3 - Figure, Ground, and Formal Systems: An Exploration

This chapter 3 of GEB explores the concept of figure and ground in various domains, starting with formal systems where rules define theorems (the "figure") and non-theorems form the "ground." It introduces the tq-system as an example of representing multiplication typographically and discusses the challenges of typographically capturing the concept of prime numbers. The text then broadens the analogy to art and music, illustrating how foreground and background can interact and how recognizable patterns can exist in both. Finally, it touches upon the mathematical notions of recursively enumerable and recursive sets, linking them to the figure and ground distinction and hinting at the limitations of formal systems, before concluding with a dialogue that playfully introduces concepts related to self-reference and hidden meanings, exemplified by Bach's music and linguistic devices like acrostics