You know, this is actually the main reason why I went back to college. I had to find a way to feed my mind something technical and difficult enough for it to STFU. It worked, too. 
My dad says that when he was doing his PhD work, his mind would work on things and solve parts of the puzzle while he was sleeping. I always thought that was cool.
I don’t know if there are any practical benefits to just thinking, but it’s my favorite hobby.
“To be stupid, and selfish, and to have good health are the three requirements for happiness; though if stupidity is lacking, the others are useless.”
Gustav Flaubert, letter to Louise Colet, August 3, 1846
Google “cognitive resilience alzheimer’s”. Use it or lose it.