There are game design gurus like Raph Koster and Jonathan Blow who would point out the connection between fun and learning.
I don't know if playing Dungeons and Dragons (which was, from my perspective, mostly carefully reading books filled with charts and rules in anticipation of play, rather than playing) taught me to be able to study API documentation; but it might have. Playing with Hypercard and Cosmic Osmo and Myst might have taught me something about the simplicity of the secret text behind the world. Maybe people who play a lot of SpaceChem will do better in multithreaded programming. Maybe people who play a lot of FoldIt will do better in nanotech design.
What I'm trying to say is the premise of "fun is what we do to recover from work" might not be the best place to start thinking about this.
If you consider that the utility generated by working is much greater than the utility directly generated by having fun, then the main thing that you're going to optimizing when you have fun is how much motivation the memory of having that fun increases your working capabilities. This is distinctly different from optimizing for the direct preference fulfillment generated by the fun, even if the same activities are optimal for both utility functions.
The same model works for any action A such that the utility generated by the effect of that action on another action is much greater than the utility generated by the action itself. This probably applies to most maintainance actions, such as doing laundry, sleeping, eating, but this is more obvious to us -- we usually don't see laundry as an end unto itself, but we often do pursue fun for it's own sake. I'm not advocating that we shouldn't have fun, but that we (or at least I) seem to be optimizing for the wrong thing -- direct preference fulfillment, rather than motivation.
This feels like a significant insight, but I tend to get a significant number of false positives. Any ideas on how we might use this?