再
zài
再 faces forward: one more step you haven't taken
The picture Placing one more footprint ahead of you, on ground you haven't stepped on yet. 再 puts the footprint ahead, on ground not yet walked; 又 presses it onto one already there.
Where the picture shows up in 再
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one more, up ahead
请再说一遍。
qǐng zài shuō yí biàn
Could you say that again?
Holding out an open palm at the point where the words broke off, asking for it from the top.
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again, next time
我明天再来。
wǒ míng tiān zài lái
I'll come back tomorrow.
Stepping out the door while tapping tomorrow's square on the calendar.
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and only then
吃完饭再走吧。
chī wán fàn zài zǒu ba
Finish your meal first, then go.
Turning toward the shoe rack only after the empty bowl has been set down.
A 完 再 B means 'do B only after finishing A'. This 再 orders the steps in time.
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push one notch further
再便宜一点吧。
zài pián yi yì diǎn ba
Come on, knock a bit more off the price.
Pushing the number on the price tag down one more notch with a finger.
All of it in one picture
再 faces forward, not back. The open palm at the break asks for 'one more time'; the finger on tomorrow's square is 'again, next time'; turning to the shoes only after the bowl is down is 'and only then'. Pushing the price tag one notch lower is 'a bit further still'. The footprint always lands ahead of you, and that is why 再 lives in requests, promises and next steps.