Difficulty: What's it mean to you?
 

I was having this interesting conversation earlier today with someone about the definition of difficulty.

I always believed something was harder if it meant that the next tier of things you learn require more skills and require you to learn more things.

He believed that diffculty meant that the next tier required a better mastery of earlier ideas, so any problems you had with earlier material would eventually catch up with you, and as a result would make the next tier impossible to master.

For example: if you were learning math, he believes that an earlier tier, such as learning division, would create huge problems later if you had trouble learning it then. So when you did algebraic divison, it would catch up with you.

I always believed it meant that the next tier, IE calculus would require more skills,and better insight in order to comprehend it.

What do you guys think? How do you define something hard?

That is roughly the definition of the word difficult, isn't it?

Errm, well if something requires comprehension of something you don't fully understand then of course it will be difficult to understand. Its only logical. Although I try to replace the word difficult into something more appealing like challenging or interesting. Tends to motivate a person more than saying this so-and-so task is very difficult.

easy: everything i can do
hard: everything i can barely do
impossible: everything i can't do

There, that was easy.

I do see the difference in definitions, but the difference is so (for lack of a better word) abstract/trivial, that I can't see the discussion of difference. Maybe you can give us more to work with?

I'd say difficulty is used in the developement of skill, the matter of difficulty are the degrees between your current skill in an area and how much more skill it would require to master a task you're not yet able to master without doing some effort.
Therefore difficulty is the matter of effort you'll have to do finishing a task compared to the ideal effort which would be the smaller amount of effort it would take for someone who "completely" (which is a rather idealistic belief) masters finishing the task.
For example: It is more difficult for a pianist who's at a lower level to play Liszt's Hungarian Rhapsody no. 2 than someone who's already at a higher level of skill and is playing far more difficult pieces (of whom would probably easier again for someone who's even more skillfull in that area).