Actually, I didn't even have to peek--I knew that trick, though from another context: as a bookkeeper. A transposed number's difference is always equally divisible by nine. (Not quite the same method, but the same result.) Someone showed me that oh, lo, these many years ago; a truly nifty and quick error-finder.
Anyway, back to the subject.
> To analyze a work of art requires me to make a conscious effort, and I can lapse into - in fact, I default to - uncritical enjoyment without any effort. <
I think the dividing line comes about when one is actively studying something, making the effort to train one's mind to absorb the knowledge to the point of it becoming second nature. The inability to "throw the switch" lies somewhere between the active study and the full absorption: One is too aware of the new knowledge, and thus tends to mentally trip over it. Eventually, one can dampen down that effect to a simple awareness, tucked in the background--the concurrent whisper.
With me, what drove me highest up the wall was viewpoint. I found it relatively easy to grasp in principle, but struggled mightily with the smooth execution of it. However, once I'd worked with it long enough myself (grumbling all the way, early on), I actually began to see it in all its glorious nuance--and usages, and advantages, and, and, and...! Wonderful bit of mechanics, viewpoint. But....
Then I could not escape noticing it, painfully so. VP errors threw me "out of the story" so hard I felt for bruises. Even just awkward shifts--not true error, but merely not well done--disconnected me from what I read. I actually complained to my friend/editor/writing-coach that this had "ruined" my enjoyment of reading! She, wisely, assured me that this, too, would pass. And it did, as did the over-processed, over-awareness of most of the other writing mechanics I learned at that time. A blatant typo or technical flaw will still make me twitch; it just no longer stops me dead. Well, usually, anyway.
Learning some of this foundational stuff (I emphasize some!) did give me a deeper regard for good work, with the ability to notice particularly well done turns, though. Knowing why something is really, really good is a kick and a half; the flip-side of cringing at error is the appreciative gasp at the exceptional.
> What I know [of music analysis], I've learned from (a few) books and from (much) listening, <
Self-guided study is probably easier to back away from than formal technical study, I would think. The ability to "default to uncritical enjoyment" may be more likely, IOW, when the point of heightened awareness is a search for enhanced enjoyment as an end in and of itself. You choose to focus more intently on listening at times, and it's simply a matter of choosing (again) at other times to relax the intensity, soften the focus, and return to a lighter level of listening.
> And so the question becomes: would I sacrifice the ability to appreciate that proof to regain the pleasure I took in that first trick, so many years ago? <
I'm in complete agreement with you--Not on your life! I say that, though, from the perspective of having learned how to choose, and therefore control, the level at which I read. Had I been unable to gag-order the Inner Editor, I'd have been one highly unhappy student of the craft of writing.
Before I had sufficient knowledge of technique and craft and such, I do think I had a good instinct, a decent radar for quality--and certainly, a driving curiosity for the why and how of it, which is why I pursued the further understanding. It's not as if I now can somehow "un-know" what I learned; I do still know it. Perhaps it's akin to just choosing not to allow it to demand the forefront of the focus, when I'm reading with the "switch" OFF. The awareness is still there, it's simply relegated to secondary notice, and not primary.
Nine!
Anyway, back to the subject.
> To analyze a work of art requires me to make a conscious effort, and I can lapse into - in fact, I default to - uncritical enjoyment without any effort. <
I think the dividing line comes about when one is actively studying something, making the effort to train one's mind to absorb the knowledge to the point of it becoming second nature. The inability to "throw the switch" lies somewhere between the active study and the full absorption: One is too aware of the new knowledge, and thus tends to mentally trip over it. Eventually, one can dampen down that effect to a simple awareness, tucked in the background--the concurrent whisper.
With me, what drove me highest up the wall was viewpoint. I found it relatively easy to grasp in principle, but struggled mightily with the smooth execution of it. However, once I'd worked with it long enough myself (grumbling all the way, early on), I actually began to see it in all its glorious nuance--and usages, and advantages, and, and, and...! Wonderful bit of mechanics, viewpoint. But....
Then I could not escape noticing it, painfully so. VP errors threw me "out of the story" so hard I felt for bruises. Even just awkward shifts--not true error, but merely not well done--disconnected me from what I read. I actually complained to my friend/editor/writing-coach that this had "ruined" my enjoyment of reading! She, wisely, assured me that this, too, would pass. And it did, as did the over-processed, over-awareness of most of the other writing mechanics I learned at that time. A blatant typo or technical flaw will still make me twitch; it just no longer stops me dead. Well, usually, anyway.
Learning some of this foundational stuff (I emphasize some!) did give me a deeper regard for good work, with the ability to notice particularly well done turns, though. Knowing why something is really, really good is a kick and a half; the flip-side of cringing at error is the appreciative gasp at the exceptional.
> What I know [of music analysis], I've learned from (a few) books and from (much) listening, <
Self-guided study is probably easier to back away from than formal technical study, I would think. The ability to "default to uncritical enjoyment" may be more likely, IOW, when the point of heightened awareness is a search for enhanced enjoyment as an end in and of itself. You choose to focus more intently on listening at times, and it's simply a matter of choosing (again) at other times to relax the intensity, soften the focus, and return to a lighter level of listening.
> And so the question becomes: would I sacrifice the ability to appreciate that proof to regain the pleasure I took in that first trick, so many years ago? <
I'm in complete agreement with you--Not on your life! I say that, though, from the perspective of having learned how to choose, and therefore control, the level at which I read. Had I been unable to gag-order the Inner Editor, I'd have been one highly unhappy student of the craft of writing.
Before I had sufficient knowledge of technique and craft and such, I do think I had a good instinct, a decent radar for quality--and certainly, a driving curiosity for the why and how of it, which is why I pursued the further understanding. It's not as if I now can somehow "un-know" what I learned; I do still know it. Perhaps it's akin to just choosing not to allow it to demand the forefront of the focus, when I'm reading with the "switch" OFF. The awareness is still there, it's simply relegated to secondary notice, and not primary.