Motivations for studying computation and its limits:
- Useful to know what problems are not solvable, so you don't waste your time and so you know to seek alternate formulations.
- Sometimes hard problems are useful (e.g. Cryptography - decrypting should be a hard problem).
- Historical / Cultural - in the last 50 years, people have spent lots of time thinking about the subject. What did they come up with? How did the computer come about?
Guiding principles for theory:
- Models should be widely applicable across time and in many domains.
- Models should be practically relevant or at least informative.
- Build up a coherent body of knowledge over generations.