잘
jal
Not 'excellently' — 'without snagging'
The picture Gears turning without catching anywhere. A person, a machine, a sound — if it runs without snagging, that's 잘. 잘 is running without snagging; 못 is stopping against a wall. So 잘해요 and 못해요 are not grades of skill — they are rolling versus catching.
Where the picture shows up in 잘
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time that rolled by without trouble
그동안 잘 지내셨어요?
geu-dong-an jal ji-nae-syeo-sseo-yo
How have you been?
All those days rolling past without the gears catching even once.
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not coming through smoothly
소리가 잘 안 들려요.
so-ri-ga jal an deul-lyeo-yo
I can't hear you well.
The gear halfway along the sound's path catching, so the voice arrives in broken pieces.
Not about bad ears — the sound isn't arriving smoothly.
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a skill that runs smooth
한국말을 참 잘하시네요.
han-gung-ma-reul cham jal-ha-si-ne-yo
Your Korean is really good.
Korean running out of your mouth without snagging anywhere.
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a frozen set phrase
잘 먹겠습니다.
jal meok-get-seum-ni-da
Thank you for the meal.
One gear frozen in place, making the same sound at the same moment every time before you pick up the spoon.
Said before eating; nobody is literally promising to eat 'excellently'.
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before a negative: 'not exactly'
저도 잘 모르겠어요.
jeo-do jal mo-reu-ge-sseo-yo
I don't really know either.
Set before I do not know: you cannot even put a finger on where the gear caught, so you let go.
잘 몰라요 is closer to 'I'm not sure' than to 'I have no idea'.
All of it in one picture
잘 is one picture: gears turning without catching. Days that rolled past without catching make it a greeting; a gear caught along the sound's path makes it I cannot hear you well; Korean coming out of a mouth without snagging makes it praise; a gear frozen at the same spot before every meal makes it a set phrase. Before I do not know, it means you cannot even locate where the catch is. Read 잘 as excellently and these five fly apart; read it as without snagging and they hold together as one.