I have been jumping back and forth between practicing string, wind, and keyboard instruments a lot lately, and have consequently been thinking about music, movement, and vision.
String playing requires a lot of functional body movement, but, when playing the flute or the recorder, functional body movement is restricted to the breathing mechanism in the horizontal and vertical center of the body, the mouth cavity (also central), and the fingers. In the case of the recorder (or I guess with any wind or brass instrument) the hands, arms, and fingers oppose one another in a relatively still position at the center of the body. Wind players have the luxury of reading music head-on, so the music is always in the center of a wind player's physical field of vision.
The flute is different from other wind instruments because the hands and arms are off to one side, though their function is pretty much the same. The mind's eye of a flutist has to be taught to visualize to the right, because that's where the fingers of both hands contact the keys. The hands and fingers are "over there," and they are impossible to actually see them when you are playing. All wind players must use their inner vision to pay attention to the inside of their mouths and the interior components of their breathing mechanisms. Nobody can really see that stuff without fancy imaging equipment.
Both hands function the same way when a musician plays a wind instrument. The fingers of both hands work like levers, and ideally make the same motions, rising to and dropping from the same height, and landing in various combinations at the same time. Sometimes the little fingers and thumbs work actual levers, but that doesn't change the basic function of the fingers. The hands stay still, and they make sure the fingers function efficiently.
A string player's fingers and hands do different things while being totally interdependent. The fingers of the left hand work like levers, and the left thumb works like a flexible fulcrum. The left hand fingers, powered by the arms, generate some elements of expression, and that expression is generated by constant efficient motion. The right hand fingers are both firm and flexible, and the thumb acts like a stable fulcrum, but the joint still bends when it needs to bend. The fingers sometimes pull and push the bow, and are sometimes pushed and pulled by the arm. They do millions of unseen and impossible-to-articulate unconscious things (not unlike the ideomotor phenomenon) that unlocks the subconscious mind.
Unlike wind playing, there is no actual physical contact between the components that set the musical vibrations into motion. String players have to feel the music through sticks, hair, and wire (or gut). The music we make exists outside of the body, yet we cradle the instrument in the most intimate part of our neck (or lap) and use the bow to make the instrument feel like it vibrates the way a voice vibrates. We sometimes have the mental illusion that we are singing when we are playing.
How the left hand looks has a huge amount to do with playing efficiently, and how the right hand steers the bow in order to keep parallel to the bridge and make efficient string crossings has everything to do with the sound. Violinists and violists have to constantly visualize left, right, and center, paying constant attention to all parts of that semi-circle we occupy. We have to use our inner eyes the way we use our peripheral vision while driving (but, thank goodness, we don't need to know what's happening directly behind us).
My flute-mind "training" has taught me to visualize right when I am looking at music, so I can easily look at music and "see" my bow hand. But there is a whole world of "left" that violinists and violist also have to keep in the mind's eye. The mind's eye has to be taught to visualize a full 180 degrees (and even more, considering the fact that the tip of the bow extends another 20 degrees when playing up-bow on one of the lower strings) in addition to looking at the music. The violinist's or violist's mind's eye has to imagine a wider span than a pianist's mind's eye.
Visualizing the whole half circle (and more) is always a challenge for me. I understand the challenge more acutely when I spend time practicing the recorder, which is like a vacation from peripheral visualization. Even practicing the piano involves less than 180 degrees of vision (even at the extremes of the keyboard, I can see both hands). Practicing with a mirror (or two) is really useful, but once you take the mirror away the mind's eye is on its own.
I always enjoy sitting to the right when I share a music stand because my real vision is "aiming" to the left, and my left hand can be "visually louder" (by physical default) than my right hand. The conductor is also easily in view at the center. This orchestral season I will be sitting on the left side of the stand, so I will have to work harder at left-side awareness because I will be looking at the music towards the right. I'm looking forward (right and left) to the challenge.