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At the moment, Mathematics SE has tags and . However, tag is a synonym for tag . Why?

Motivation

Since tag does not exist, tags and are often used instead, which is unfortunate. Two tags are being corrupted because tag does not exist:

Moreover, there are dozens (if not hundreds) of duplicates of the following question.

Find the gradient of the scalar field $f : \Bbb R^n \to \Bbb R$ defined by $f ({\bf x}) := {\bf x}^\top {\bf A} \, {\bf x}$.

Over the past year, I found some 30 duplicates. There may be many, many more. I suspect it would be easier to find such duplicates if existed as a non-synonym.

Related

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    $\begingroup$ Some previous discussions about (gradient) can be found in Tag management 2019. There were also some related discussions in chat: chat.stackexchange.com/rooms/3740/conversation/the-tag-gradient chat.stackexchange.com/rooms/3740/conversation/… $\endgroup$
    – Martin Sleziak
    Sep 6 '20 at 23:54
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    $\begingroup$ Both in the list of tag synonyms and using SEDE it can be checked that this tag synonym was created in December 2014, $\endgroup$
    – Martin Sleziak
    Sep 6 '20 at 23:57
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    $\begingroup$ (+1) regardless of the fact that there were previous discussions about that, the lack of a gradient tag simply makes no sense to me. $\endgroup$
    – Arnaud Mortier
    Sep 7 '20 at 6:43
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    $\begingroup$ What do users following this discussion think about the tag (grad-curl-div), which was proposed in the post linked above. The post has score 8 - although some of the upvotes might have been cast before it was edited into the current form. (This proposal was also discussed a bit in chat, see the links in the first comment.) $\endgroup$
    – Martin Sleziak
    Sep 7 '20 at 10:50
  • $\begingroup$ @MartinSleziak There are some 27K5 questions with the tag multivariable-calculus. I find minimalism in tagging utterly incomprehensible. Why minimize the number of tags instead of minimizing the time wasted by the members of Math SE? I have answered the same question twice or thrice because I could not quickly find the earlier duplicates. $\endgroup$
    – Rodrigo de Azevedo
    Sep 7 '20 at 11:09
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    $\begingroup$ @MartinSleziak I think that the grad-curl-div idea is perfectly appropriate here, for the reasons mentioned (I'm one of the 8). $\endgroup$
    – Arnaud Mortier
    Sep 7 '20 at 11:58
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    $\begingroup$ @RodrigodeAzevedo There is a limiting factor that one question can have at most five tags. If this is changed, that would also influence the philosophy of creating tags. While there is some limit, I would personally advise to be careful about creating very specific tags. This is only a general comment, I have neither upvoted nor downvoted your post. $\endgroup$
    – Martin Sleziak
    Sep 7 '20 at 11:58
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    $\begingroup$ @RodrigodeAzevedo Only around 500 posts are tagged with Hessian matrix, while a search of "Hessian" returns around 4k hits (even worse for Jacobian). The reality is that most people don't think of using an object to classify their post. I doubt if creating "gradient" would help search questions involving gradients. $\endgroup$
    – Arctic Char
    Sep 7 '20 at 14:06
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    $\begingroup$ @ArcticChar Searching for hessian is:question returns some 2k16 results. Still too ambitious. I would be happy if I could easily and quickly find duplicates amongst the questions I have already answered. Which is why I have started appending a list of tags to some answers of mine. Forget past questions. I would focus on properly tagging future posts, ideally so that many of them can be closed as duplicates. Answering the same question under different guises 100s of times seems quite Sisyphean to me. $\endgroup$
    – Rodrigo de Azevedo
    Sep 7 '20 at 14:23
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    $\begingroup$ I agree and I really hate when I know I have answered the same question but failed to locate it. (On the other hand, trying to re-tag everyday seems equally Sisyphean to me. It is just not sustainable in the long run). $\endgroup$
    – Arctic Char
    Sep 7 '20 at 14:31
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    $\begingroup$ @RodrigodeAzevedo RE: " I would be happy if I could easily and quickly find duplicates amongst the questions I have already answered." You seem to have a similar activity to mine in terms of number of answers. Have you tried using the filter "user:me" in the search? I very easily find answers I want to reread using it and some keywords I remember from the question. $\endgroup$
    – Aloizio Macedo Mod
    Sep 8 '20 at 16:17
  • $\begingroup$ @AloizioMacedo That works well for topics on which I have few posts. However, I have 32 posts on directional derivatives. Unfortunately, my duplicate-finding missions are on the topics on which I have written the most. $\endgroup$
    – Rodrigo de Azevedo
    Sep 8 '20 at 17:39
  • $\begingroup$ What does 27K5 mean? What does 2k16 mean? @Rodrigo $\endgroup$
    – Gerry Myerson
    Sep 15 '20 at 12:58
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    $\begingroup$ @Rodrigo, thanks. What is gained by writing 2k16 instead of 2160? Doesn't it just make readers work harder for the same amount of information, when they have to unpack the notation? $\endgroup$
    – Gerry Myerson
    Sep 15 '20 at 13:03
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    $\begingroup$ @GerryMyerson I borrowed the notation from electronics, where, say, $1\rm{K}2 \,\Omega$ is used for the nominal value of the resistance of a resistor. Why? Because of error. If the actual value can deviate from the nominal value up to $5\%$, saying that the value of the resistance is $1200 \,\Omega$ is a bit dishonest. It would be more honest to write $1200 \pm 60 \,\Omega$, but it's a bit wordy, too. To summarize, $1\rm{K}2$ says that the error is too large to include more digits. $\endgroup$
    – Rodrigo de Azevedo
    Sep 15 '20 at 13:09
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In Tag management 2019 it was suggested to use the tag as an umbrella tag for questions concerning gradient, curl, and divergence. (Currently, is a synonym of , while and exist as separate tag. So the situation for these three notions is not exactly symmetric.) This suggestion was also discussed a bit in chat, namely in November 2019 and in December 2019.

In the previous post you can find also proposal for the tag-info for this tag. The linked post in the tag management thread has currently score 8.

This would be a compromise solution between users who want as a separate tag and the users who would consider this as having too many narrow tags. (Which is sometimes a problem, considering that there are only five slots for tags on a question.)

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  • $\begingroup$ Personally, I am not really sure which possibility would be better. (Three separate tags or one common tags.) Probably users who often answer questions in vector analysis could be able to give a reasonable advice on this. I have posted this as an answer for two reasons: 1. In this way, other users can comment on this specific suggestion or at least upvote/downvote it to show what are they preference. 2. This suggestion was previously discussed and gained some support, so it probably should be at least mentioned in this new discussion. $\endgroup$
    – Martin Sleziak
    Sep 8 '20 at 7:27
  • $\begingroup$ There are 100s of questions on computing gradients of scalar fields. I have answered 10s of them. Lacking tag gradient, one often finds them with tag derivatives. I find this utterly incomprehensible. Search for gradient? What about tag gradient-descent? Those who claim that the tag is not needed are probably not editing such questions. The 5-tag limit is not that much of a problem if the question is focused enough. If it's not focused enough, perhaps it should be split into 2 or 3 questions. $\endgroup$
    – Rodrigo de Azevedo
    Sep 8 '20 at 9:13
  • $\begingroup$ @RodrigodeAzevedo Why not posting an answer with more detailed explanation why you consider separated tag for gradient useful. In that way, other users could upvoted/downvote the answer to show whether or not they agree with that assessment. (Or maybe you can find somebody else who could volunteer to post an answer.) $\endgroup$
    – Martin Sleziak
    Sep 8 '20 at 12:49
  • $\begingroup$ Indeed, I could do that. However, I am not sure that popularity contests on Meta are the way to go. This approach — let the infinitely wise Cardinals on Meta re-read the holy scriptures, then vote on it — is Medieval. Competition between conflicting viewpoints is won via popularity contests, rather than experimentation. The people who actually need the tag may be 18-year-olds taking multivariable calculus and who have never and will never visit Meta. $\endgroup$
    – Rodrigo de Azevedo
    Sep 8 '20 at 13:08
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    $\begingroup$ @RodrigodeAzevedo Then disregard the "popularity contest" aspect and just elaborate your opinion, which is useful in itself. $\endgroup$
    – Aloizio Macedo Mod
    Sep 8 '20 at 15:57
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    $\begingroup$ I think div-grad-curl is a perfectly acceptable alternative. The mechanics of each are fairly similar and the tag is unique enough that it shouldn't attract a lot of oddball questions. Furthermore, often times there are multiple part questions that involve calculating each. $\endgroup$
    – Cameron Williams
    Sep 17 '20 at 15:06

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