I find Turf3's views amusing, in a condescending way. There is a presumption that everyone in the world is a visually acute person who thinks, learns, reacts, and navigates the world in the same way that he does. Well, it's just not true. I started to learn to read and play music (piano) at 6 years old and continued to learn to play woodwind instruments for many years after that. However I was never a great reader. It was only when I took up singing (and was a professional) that I found that I could make music come alive. This translated back to the woodwinds and being able to play by ear (as one always sings by ear, even if you're reading music). If you can't hear the note you can't sing it! I play sax the same way, I hear what I want to play and it comes out of the horn, no reading or theory required. Can I read music? Yes, but struggle and don't play effectively. It's the opposite of what Turf3 says. Reading hampers my ability to play. It's stiff and lifeless. I spent more than a decade trying to master reading so that I could be proficient, but was only able to be barely adequate. However playing by ear comes easily. There is no visually remembering notes, I can hear what I'm playing. When I was a singer I remembered heaps of songs and could hum all of them. What I needed the sheet music for was the words!
Here's a test: How many songs can you hum or sing? Probably hundreds if hearing them on the radio (sing along). Could you after a few notes turn off the radio and continue singing the whole thing? Maybe? Could you play all of those on your horn even if given the first few notes? Not likely, however an experienced ear player can and in any key. If you can hear it you can play it. What's more you could improvise on it as it's still just a matter of what you hear, not what you see or are tying to interpret visually or mentally via chords/changes and then translate into sound. You're connected to your instrument and can play what you hear. The creativity of your improvisation is a matter of individuality and one's internal library of sound.
Can some visual players develop this ability? Sure, but an extremely visual learner may find it very difficult. They want/need to have a visual or conceptual clue that works as the pathway for their fingers to play the right notes. Does jazz theory teach one how to become one with their instrument where you play what you hear? Nope! The sad reality is that the people who are very auditory learners/thinkers have to find this for themselves as the majority (like Tur3) happily promote strictly visual learning and playing as the only way to master an instrument.
We are not all the same. The projections of a majority who are visual learners is not an absolute. I'm very happy to be in the minority who don't need to play cut and paste riffs and arpeggios and call it improvisation. The world of music is big enough for all sorts. Is there only one way to learn or make music? The dichotomy or multifaceted ways of learning and expressing ourselves is a reality.