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I recently proposed an edit to this answer, but my edit was rejected. Can anyone help me understand why my edit was rejected?

The rejection message states "This edit defaces the post in order to promote a product or service, or is deliberately destructive."

My edit absolutely did not deface the post or promote any product or service... so presumably the claim is that it was deliberately destructive? Yet I don't see how a reviewer could come to that conclusion. My edit was not deliberately destructive. It was a good-faith attempt to improve the answer in numerous small ways -- as explained in my edit comment. I thought the original answer had some great ideas, but had some issues that made it harder than necessary to understand those ideas. My edit was an attempt to make those ideas clearer for readers. And, just to be clear, I don't believe my edit changed the meaning of the post or deviated from the author's intent.

So, can anyone help me understand why my edit was rejected? Was the rejection appropriate?

I'm not here to complain. Instead, I'd like to identify what lessons I should learn. I'd be happy to receive any constructive criticisms you might have. Or, if you feel that such edits are not welcome and I should not waste my energy trying to improve answers on this site in this way, that's a fine answer, too. Any and all reactions and constructive advice are welcome.

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    $\begingroup$ "deliberately destructive" is a bit harsh, but deleting the first paragraph of the answer seems to be uncalled-for, and sufficient reason for rejecting the proposed edit. $\endgroup$ – Gerry Myerson Apr 22 '15 at 5:40
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    $\begingroup$ @GerryMyerson, are you familiar with meta.stackexchange.com/q/183267/160917 and meta.stackexchange.com/q/127639/160917? The first paragraph was a meta comment about prior revisions and was something that belongs in the edit summary in the revision comments, not in the answer. Adding "Edit: my previous answer was wrong; I changed it" to an answer is not the right way to use this site; we have revision history so you don't need to do that. Answers should stand on their own. No content was lost in my edit, and no meaning was changed. $\endgroup$ – D.W. Apr 22 '15 at 5:54
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    $\begingroup$ Do you think this might be a case where reviewers weren't familiar with Stack Exchanges guidelines on how to edit your post? Or is it a case where Math.SE has different norms about how to use edits than the rest of the Stack Exchange network? (If the latter is there a link to a Meta.Math.SE post where this is explained?) $\endgroup$ – D.W. Apr 22 '15 at 5:58
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    $\begingroup$ IMHO edits spelling out the errors in the poster's earlier line of thought are useful and educational. The removal of such explanations is not "deliberately destructive", but I, too, find it uncalled for. I don't know about the rest of SE network, but here it is more important to document why an earlier approach did not work rather than simply state that it didn't work. I am not saying that we have a definite policy on this matter, but relying on the edit histories alone to convey this kind of important additions feels suboptimal. Of course, all depending on the details of the case. $\endgroup$ – Jyrki Lahtonen Apr 22 '15 at 6:46
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    $\begingroup$ @JyrkiLahtonen, OK, got it. To see if I understand: if I re-submitted my earlier edit, but added a sentence at the end saying something to the extent of "Previously I had tried using xor instead of modular arithmetic, but this doesn't work because (such-and-such)", then would you consider the edit useful and appropriate? $\endgroup$ – D.W. Apr 22 '15 at 6:49
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    $\begingroup$ But +1 to the question. Your edit was largely fine, so IMHO a reviewer would have done better by improving and bringing this part back. $\endgroup$ – Jyrki Lahtonen Apr 22 '15 at 6:50
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    $\begingroup$ Adding an "edit:" or "added:" to a question or answer when making substantial additions is a question of style (I do it myself sometimes, and I would hate for people to remove it). While it can be seen in the edit history, that does not make it superfluous. $\endgroup$ – Tobias Kildetoft Apr 22 '15 at 7:52
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    $\begingroup$ Not until now, and they did not change my mind about this. The math site has its own slightly different take on a lot of things, and this is one of them. $\endgroup$ – Tobias Kildetoft Apr 22 '15 at 8:03
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    $\begingroup$ @JyrkiLahtonen it seems the current answer is completely different from the earlier one. Thus, what the author should have done, is post a new correct answer and edit the flawed one to say why it is flawed (or just delete it). The current situation is a bit of a mess. $\endgroup$ – quid Apr 22 '15 at 9:53
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    $\begingroup$ The only part of the edit that was a material improvement was the substitution of \bmod for %, and even that isn’t really necessary, since the answerer defined the % notation; certainly in all other respects the answer is quite readable and understandable just as it stands. That being the case, I prefer to let it speak with the answerer’s voice. $\endgroup$ – Brian M. Scott Apr 22 '15 at 21:18
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    $\begingroup$ @D.W.: Your edit did not really do any of those things. $\endgroup$ – Brian M. Scott Apr 22 '15 at 21:40
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    $\begingroup$ For what it's worth, I feel like the review queue puts reviewers in a sort of tunnel. Or like I'm being questioned by a lawyer trying to twist my words. Sometimes none of the options given quite seem to make sense to the case at hand, but to choose "no comment needed" seems worse somehow. $\endgroup$ – Robert Soupe Apr 26 '15 at 17:33
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    $\begingroup$ @RobertSoupe since there is the option to write you own reason for rejecting an edit, I fail to see your point. $\endgroup$ – quid Apr 26 '15 at 19:42
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    $\begingroup$ @RobertSoupe when you chose "reject" you get a list of reasons the final one is "free form", Like "Does harm because [your text]" or something like that; about like "other" in mod-flags. I do not recall the timeline; there was not very long ago, though not recently either, a reworking of these reasons, though. $\endgroup$ – quid Apr 26 '15 at 20:53
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    $\begingroup$ @quid It was September-October 2014 $\endgroup$ – user147263 Apr 27 '15 at 0:21
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The reason your current edit was rejected is very likely the fact that you deleted the first paragraph, as explained by several others.

The reason why this specific reason was chosen is a bit less clear, it might be that the reviewers just thought it fitted relatively best (I'd disagree but this is a detail) or they just saw a relatively big delete and did not check more carefully what was the precise nature of the edit. This is however tangential, I think.

This leaves us with the issue if the edit should have been rejected. This is a bit more subtle. I think clues to what changed in a post can be useful, especially in a context were one writes for readers that likely saw the initial (or earlier) versions, as opposed to working towards an "optimal" version. The former idea is more prevalent here than on some other sites.

However, I believe some resources you linked to make good suggestion how one can better balance the two goals, and you yourself proposed here to move that opening paragraph to the end, which I think can be a good idea. Indeed, in the very specific situation, as mentioned in a comment, I tend to agree that this opening paragraph feels a bit pointless (and definitely should not be that prominent) as it does not really high-light a change in the current version but rather refers to a completely different answer (that happens to have been given in the same post); if one really wants to follow up on this one would have to consult an earlier revision anyway.

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Personally, if someone made such an edit to one of my answers, I would have rejected it. You deleted one paragraph, and you substantially altered parts of the proof. Even if the edits are correct, and the edited post is equivalent to the initial one, I would not want someone to change the notations and formulations used in my answers.

I think that it is better to leave a comment suggesting the edit instead of editing large parts of an answer or question.

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I don't know why this edit was rejected, but I have some small qualms about changing $a\,\%\, b$ to $a\bmod b$. The notation introduced in about the year 1800 by Carl Gauss is that $(a\equiv b)\pmod c$ means that $a$ and $b$ both leave the same remainder on division by $c$, and that notation is still in widespread use by mathematicians. Computer scientists, probably in about 1950 or '60 I suspect, introduced a different notation, in which $a\bmod c$ means the remainder when $a$ is divided by $c$, and I think today that is also often used. But some who prefer to distinguish between the two senses write $a\,\%\,b$ for the latter sense. In particular, this posted answer seems to use the "mod" notation in the sense in which Gauss used it.

(And notice that I've coded $a\,\%\,b$ by manually adding a small space between $\%$ and the letters before and after it. And now I've corrected the notation in the posted answer by doing the same there. That's not needed when writing something like $a+b$, which you'll notice looks different from $a{+}b$.)

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    $\begingroup$ Re: last paragraph, there is a command \mathbin to tell latex (or mathjax) that something is a binary operator. It will space everything correctly, even in subscripts etc. (though the difference is probably very small in main text). Compare: $a\,\%\,b$, $a \mathbin{\%} b$, $X_{a\,\%\,b}$, $X_{a \mathbin{\%} b}$. Similarly there's a \mathrel command for relations (eg. $=$, $<$...) that gives a slightly larger spacing. See this: tex.stackexchange.com/q/38982 It might not be super important here, but I think it's good practice and makes a real difference when writing in latex. $\endgroup$ – Najib Idrissi Apr 27 '15 at 12:42
  • $\begingroup$ I see no conflict between the use of mod in the relation $a\equiv b\pmod m$ and as the binary operator in $a\bmod b$; syntax completely distinguishes them. In a purely mathematical (i.e., non-programmin) context I find the $%$ notation extremely annoying. If it appeared in a question that I was editing for other reasons, I would very likely change it. $\endgroup$ – Brian M. Scott Apr 30 '15 at 4:14

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