I'm awake about 17 hours a day. Of those I'm being productive maybe 10 hours a day.
My working definition of productive is in the direction of: "things that I expect I will be glad I did once I've done them"[1].
Things that I personally find productive include
- Chores
- Work
- Eating
- Cooking
- Reading a good book
- Watching TV with my Wife/Kids
- Playing with the kids
- Socialising with friends
But not
- Doomscrolling
- Watching TV alone
- Playing most computer games
- Sitting on the couch doing nothing
- Reading a book I'm not particularly interested in
etc.
If we could find a magic pill which allowed me to do productive things 17 hours a day instead of 10 without any side effects, that would be approximately equally as valuable as a commensurate increase in life expectancy. Yet the first seems much easier to solve than the second - we already have some drugs which get pretty close (caffeine, amphetamines).[2]
Now obviously the correct thing to do is both, but in the same way as we want a Manhattan project for anti-aging, we should also advocate for a Manhattan project for focusing/willpower.
Your examples sound familiar to me too, but after rereading your comment and mine, maybe it all can be generalized in a different way. Namely, that internal motivation leads to a low level of effort: reading some textbooks now and then, solving some exercises, producing some small things. It still feels a bit like staying in place. Whereas it takes external motivation to actually move forward with math, or art, or whatever - to spend lots of effort and try to raise my level every day. That's how it feels for me. Maybe some people can do it without external motivation, or maybe they lucked into getting external motivation in the right way, I don't know.