A note from Cullen Schaffer:
As a student of Mandarin, I'm fascinated by the fact that the language translates the word 'again' differently in these two cases:
He did it last month and tomorrow he'll do it again (再).
It seems bizarre to me to distinguish repetition in the past and future in this way. Can you or anyone else contributing to Language Log tell me (1) if this feature is unique to Mandarin or if there are parallels in other not-too-closely-related languages (2) how this distinction came to be a part of modern Mandarin?
I recall that, when I began the study of Mandarin back in the 60s, I and all of my classmates were also perplexed by this seeming redundancy, and our teachers spent a lot of time and effort trying to distinguish between yòu 又 and zài 再, both of which are often translated as "again". However, now that I've "been in the business" for so long, yòu 又 and zài 再 seem like completely different adverbs with separate functions that cannot be confused.
It is very common to explain zài 再 as pertaining to the future and yòu 又 as pertaining to the past. See, for example, this page on Chinese Grammar Wiki.
I think that is not the best approach to the problem of how to distinguish between yòu 又 and zài 再.
Mandarin language teachers go to great lengths to show how yòu 又 and zài 再 are used. See, for example, the many explanations given on these web pages.
Yet students go away from the plethora of illustrative sentences confused and without a clear sense for when to use yòu 又 and when to use zài 再.
I suppose that all good teachers have an effective way to communicate the difference between yòu 又 and zài 再 to their students. Here are some of the techniques I use for keeping them straight in my own mind:
yòu 又 basically conveys the sense of "also", "(once) more", "in addition" — the character used to write this word is simple (two strokes); it depicts a hand
zài 再, in contrast, signifies "further", "another time", "still", "anew","repeat", "twice", "second time" — has more strokes (six), suggesting multiplicity, but it is unclear what the oracle bone form is supposed to depict
An ancient, formal term formed with zài 再 is zàibài 再拜 ("to do obeisance again; bow twice; make / perform a double obeisance; an ancient ritual in which one does obeisance, and then does it again, in order to show even more respect"")
Zài 再 forms an enormous number of compound expressions, much like re- in English. See the lengthy list at the bottom of this page. The most common of these is zàijiàn 再见 (lit., "see [you] again", i.e., "good bye"), which is familiar even to those who know no other Mandarin than perhaps nǐ hǎo 你好 ("hello") and xièxiè 谢谢 ("thanks")
Whereas yòu 又 often connotes something unwanted, zài 再 frequently conveys the notion that something is wanted or expected. Thus, yòu láile 又来了 ("[there he / she / it] comes / goes again") and zàilái 再来 ("do it again").
I hope that these notes are helpful in distinguishing between the various usages and nuances of yòu 又 and zài 再. These are merely my own tricks for how to separate the two main words for "again" in Mandarin (there are others! — e.g., chóng 重 and fù 复). Others may have their own tricks for keeping yòu 又 and zài 再 separate. The best way to master them is simply to encounter and use them again and again in context.