- Assumptions and "background knowledge" are unavoidable, and necessary.
- Always keep "dancing back and forth" between:
- implicit and explicit knowledge,
- syntax and semantics,
- formal and informal,
- abstract and concrete,
- yourself and others,
- theoretical and practical.
- Being aware of:
- what's needed,
- what's missing,
- the surrounding context,
- to which paradigm / modality something belongs,
- self and other-knowledge (see below).
- Make it explicit!
- Play the role of "math lawyer": write a bullet-proof definition.
- Converting one idea / concept / assumption to another, without being aware of it.
- Found in math, programming, and a natural function of our brains.
- which makes it an interesting example of meta-thinking!
- It happens all the time without us noticing.