Say, for instance, that your character wants to learn a new chemical formula from a textbook he has received. What does the character do? He picks up the textbook and starts reading, and after a couple hours starts an experiment to prove the results, and once the indicated process happens correctly, he's learned how to make that chemical.
The problem? Where does the player come into this? Surely the player can't be expected to know the chemical ingredients for every single chemical recipe in his/her character's mind, and the exact processes needed to produce that chemical reliably -- after all, it's not a chemical-making game, it's a roleplaying game. But because it takes time to read and prove results, the player is left staring at the computer screen while his/her character is on a voyage of intellectual discovery.
Puzzle Pirates has a good solution; passive occupations, like repairing your ship or pumping out water that has swamped the boat, are done through unique never-ending puzzles which the player does in real time. The better the puzzles are performed, the faster the work is done. Even with terrible work a little work is done, so no matter what, at least you're giving an effort to involve yourself.
But if you have a roleplaying game, obviously puzzles aren't an ideal solution... any ideas on how to involve the player in the process of learning (or in any other passive tasks -- this is just for sake of example) without actually needing to learn the actual methods him/herself?