: At what point in editing / revising does one poem become another poem? Many writing journals say they will not publish previously published poems. But if I revise a previously published poem,

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Assumed you only regard changes of words within a text, f.i.., a poem. And each word should at most be changed once. Then the number of changes you could possibly make is equal to the number of words.

Say w is the number of words and
say c is the number of word changes
(so 0<=c<=w)

The change rate r shall be equal to c/w
(so 0<=r<= 1).

Now intuitively if r is very small (near to 0) you might want to consider the texts being the same and in case r is big (almost 1) you will tend to consider the revised text to be new. When r is neither near to 0 nor near to 1 you could justify both, i.e., to call it a new text or to call it the same.

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I doubt that there is a hard and fast line. I suppose a publication might say, "If the revised poem has at least 50% of the words changed it is acceptable". But I doubt they do.

One could, of course, play games with this sort of thing. You could take a completely original poem and cry, "Look! It includes the phrases 'undying love' and 'made for each other', just like this other poem over here! Obviously a copy." At the other extreme, I can't imagine that any editor would accept that changing one word in a five-page poem makes it a new poem.

Any standard is likely to be subjective. Does it "sound like" the other poem? Etc.

I have to wonder: Why do you ask? Did you write a poem, get it published, and now you want to publish it again? Or are you contemplating taking a book of poems by Shakespeare or Poe, changing a couple of words here and there, and submitting them as your own?

I suppose if you wrote some poem that you consider your master work, that you are not confidant that you will ever be able to create something of this quality again, and you had it published in some obscure literary journal that six people read and you are now frustrated because you can't get it out to a wider audience ... well, I'd talk to the editor about that and explain your position. Otherwise, I think you'd be better to just write new poems rather than try to tinker with someone else's. Well, other than to produce a parody, like your example above is obviously a parody on Road Not Taken.

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Happily since this is a practical question, one does not need to solve Theseus' Paradox to provide an answer. The intent behind the rule is to provide distinctive work, i.e., no reader will think "I have read this before." To determine whether a new work is too similar to a previous work, one should consider whether a reader would think the work had been read before from fallible memory of perhaps a year earlier.

Trying to play lawyer with the definitions of "same work" and "previously published" will not endear one to editors. In fact, being upfront about the relationship — while also demonstrating that one is familiar with the submission guidelines and does not expect special treatment — may slightly increase the chance of publication.

On the practical matter, if I were an editor, I would consider such minor changes to be revisions and quickly reject the submission (if I knew the previous work had been published). The two works are sufficiently similar that a reader who had read one a year after the other could easily think them the same. Both use substantially the same form, both have the same tone, both use the same imagery, and both cover the same subject (in this case made more obvious by the reference to "The Road Not Taken", which would make those aspects more memorable).

Note that the rule about previously published is subject to the editor's discretion. For example, a mediocre work published in a poetry magazine with very low standards (e.g., some college poetry magazines) that was substantially refined such that it would be eagerly accepted for publication if it had not be previously published would typically be considered as if it had not been previously published. A typical reader would not think them the same work from memory (even if all the above mentioned traits were the same); in fact, a reader presented with both would likely think the earlier work a weak imitation of the latter. Furthermore, the obscurity of the earlier publication would make the editor feel that readers would be even more likely to appreciate the work as new.

If one has some juvenilia that was "published" in a high school poetry magazine, one might be able to refine such works into what would be accepted as new by a poetry magazine with high standards. Similarly, if one took a well-written and previously published Shakespearean sonnet and revised it into a Petrarchan sonnet of the same or better quality, the modest difference in form and presumed changes in images and tone (a Shakespearean sonnet traditionally has a two line "conclusion", while a Petrarchan sonnet has a turn after the first eight lines) might be sufficient to be considered new. In that case, an editor might appreciate being exposed to both version (and might even desire to republish the earlier version to highlight the contrast).

In general, it is not a good idea to submit a revision of work that has been previously published when the publisher requires that submissions not be previously published.

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