I wonder: is it better to aim for "impossibly hard", or simply "implausibly hard"? That is, it's obviously good to be challenged, but if you're in it for the learning experience, is it better to do something so hard that you can't possibly succeed, or is it better to set the bar so that there's some small, but nonzero chance of success? This is disregarding the fact that constantly failing will discourage you emotionally from proceeding, as it is assumed that the learning itself is considered the success.
To put it another way: would students learn better/faster in school, if every assignment was designed to be impossible to complete? (Obviously, the assignments would thus go un-graded, but frequent micro-examinations would be inserted to assert the learning derived from all the failure.) As an interesting side-effect, in such a curriculum, any student that succeeded on an assignment could be immediately skipped ahead to the stuff they can't do.
Pushing against a brick wall won't move the wall -- but if you do it long enough, it'll make you stronger.
The point is that it's good to reach beyond your grasp every once in a while. And when you're trying, you can't always tell if the thing you're grasping for is too far away. You just reach.
no. Learning and difficulty is not linear where the most impossible teaches the most. After a certain challenging level you learn less. Like in weight training, piano, math, etc. Learning a piano piece you cant play wont make you a good piano player.
Doesn't sound like fun for the crowd or the teacher...