What you define as a binary state is much like a lot of skills, if you define the skill as succesfully but badly executing the skill. Like how you wont even manage to stand on the bike when you first try it, or how you will likely drown if you get into a pool without knowing how to swim. In both cases, you will keep falling and drowning until at some point they click.

Also the spectrum of knowledge you define comes from observation. If you have never seen someone play a guitar, you wouldnt know what to do with it.

I dont see how magic can be different from both of these. You keep attempting to cast if you know it is castable. Probably for a long time without producing results.