[zeroego]

"The word school derives from Greek σχολή (scholē), originally meaning "leisure" and also "that in which leisure is employed", but later "a group to whom lectures were given, school"."

https://en.wikipedia.org/wiki/School

I remember I had Philosophy professor tell me this, back in the day. I think part of his point was that up until very recently, getting an education was a privilege that only the elite got to enjoy. Also, I imagine he was trying to say that compared to the back breaking manual labor almost everyone was expected to participate in back then, learning must've actually been leisurely.

More specific to your comment, I feel like what you're describing is sort of the idea behind things like the pomodoro technique. Take a timed break, let your mind wander, and come back (sometimes) with a solution. To digress one final time, this idea also reminds me a of practicing a musical instrument. I can't tell you how many times I've struggled with a piece of music, only to stop for a few hours or maybe a day, just to come back and "magically" be able to play it.

[genericone]

Taking that philosophy to be true, maybe the word 'leisure' has taken on the role of 'diversion' in the modern day. Is there an ancient Greek/Roman/Eastern take on 'diversionary' activities?

[zeroego]

Not that I'm familiar with. I know various sports were big in Ancient Greece, but I couldn't say if they were seen as a 'diversion' from a cultural standpoint.