People back then had miles to walk and no phones to stare at or tvs to watch. There was plenty of time to think.
It's easy to think of ideas that others have had (interpolate). Much harder to synthesize new ideas (extrapolate), or at least those of significance. Probably related to P NP problem.
Edit: yes, verifying would be P and synthesizing would be NP. And with this new intuition I suppose encryption will probably be safe!
P vs NP is more about verifying correctness of a solution compared to the hardness of finding a good one. I don’t think interpolation/extrapolation fits very well.
However, what fits better is understanding existing ideas and verifying they indeed solve a problem, compared to the hardness of finding a “best solution” to a given problem. This is still only a rough parallel. You are right that many (probably most) complexity theorists believe that hardness separation in this case is a fundamental principle reflective of real life.
Depends where you're walking how free your mind is to wander - if you're walking through woodlands, on rough tracks, in country with wild animals then you could have no cognitive overhead available for pondering.
I walk, pandemic aside, 45mins each way to work as it's on quiet pavements I can walk without thinking which is a different experience to walking in rough country when one needs to focus on the walking itself.
For me I come up with a couple of inventions/innovations every week (ideas are cheap as everyone says, which is rubbish for me as ideas are about my only differentiator) but unfortunately I don't have facilities or time (nor probably the skills) to develop them.
> saying she was too busy with courtly life to follow his instructions
That's because his instructions were totally extreme even by today's standards. This says nothing about averages and ultimately as a noble she simply did not want to.
>And exercise, the other thing that's nicer for thinking behind doing nothing besides warm water, was also not really a thing for women then
Are you implying that women just sat around not thinking all the time? Because I am too, but for different reasons, and not just men.
The vast majority of people are not interested in thinking beyond the bare minimum. Otherwise we'd have more than a tiny fraction of the population purposefully self learning.
It's easy to think of ideas that others have had (interpolate). Much harder to synthesize new ideas (extrapolate), or at least those of significance. Probably related to P NP problem.
Edit: yes, verifying would be P and synthesizing would be NP. And with this new intuition I suppose encryption will probably be safe!