I've played various musical instruments for nearly 40 years now, but some simple things remain beyond my grasp. Most frustrating is sight reading while playing piano. Though I've tried for years, I can't read bass and treble clef at the same time. To sight-read piano music, when you see this:
you need your right hand to read it as C D E F, but your left hand to read it as E F G A. To this day, I can't do it, and I can only learn piano music by learning the treble and bass clef parts separately to the point where I don't rely on the score for more than reminders, then playing them together.
Transposing is also approximately impossible for me. The musical scale is drawn as a linear scale, but it isn't linear. There are missing steps between B and C and between E and F; B# = C and E# = F . So C D E F, transposed into the key of B, becomes B C# D# E . Transposing music that uses notes outside the scale is significantly worse. The only way I can transpose (badly) is to not look at the music and not think about the names of the notes.
I've blamed myself for lacking some ability that would enable me to do these things. But my conversations with (a few) people who can do these things have been peculiar. They don't have any suggestions for my problem, because they never saw them as problems in the first place. When I talked about the inconsistency of trying to use separate notations for the left and right hand, they stared at me uncomprehendingly. The idea that notations should be consistent seemed never to have occurred to them.
So I've decided to blame them instead. The problem is that my mind is too highly trained.
No, seriously. I realize this is probably an unhelpful, self-defeating attitude. But is it correct?
It seems to me that if you're in the habit of working with things on linear scales, that's going to be a hindrance when you try to transpose music. Your brain latches onto the notes marked on the score and automatically constructs an internal representation that is wrong. Likewise, if you're in the habit of looking for consistent interpretations of data and compressing what you observe, your mind will keep trying to reduce the two clef notations down to one.
The system of sharps and flats is efficient in some ways; you just have to remember the order they always occur in, plus one number per scale (the number of sharps and flats), to construct that scale. You organize the music into concepts like "scale" and "chord", and map those into new keys. It's great if you're playing scales and simple chords, and if your music sticks to a few basic keys plus their minors. But it sucks when you move beyond that.
The notations developed for music work best if you don't aggressively systematize data, so that you can instead learn an orders-of-magnitude-less-efficient mechanism for memorizing note-to-note mappings for every note and every pair of keys , and so that your brain doesn't try to let your left know what your right hand is doing.
(A) If you can transpose music on the fly, have you got the note-to-note mappings memorized? Can you say without thinking what B flat is when transposed from the key of F to the key of C? Of A flat?
(B) Do you think this is plausible--that a very general ability or learned skill can make it more difficult to learn some things, either in this particular example, or in general?
(C) If so, are there any natural systems (not notations devised by humans) which are harder to work with for people with more mental talent or training? Idiot savants come to mind.
(D) Is part of the perceived gulf between art and science due to artists developing notations, theories, and conventions that make art more difficult for scientists?
 Yes, I know they're not really equal in most historical intonations, blah blah etc.
 Yes, I know you musicians think that's easy. That's because you're saying "scale" and "key of B" and constructing a new scale in that key, which is a pretty efficient representation for scales and simple chords, but gets messy for music going beyond that.
 Or mapping the pattern being played into some scale or chord or other construct, translating that into the new key, and recreating it in that key. That seems unlikely, or to require forming concepts for most of the 220+495 possible 3 and 4-note "chords", since even with simple church music musicians often can't say what chord is being played. (komponisto has an explanation for that, saying that what is being played is not chords, but temporal sequences moving between chords. But most musicians don't think of harmony that way.)