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