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Often among young students, or those new to the site in general, we all see questions that are seemingly too trivial to even be asked. Usually, and perhaps unsurprisingly, these types of questions get closed nearly immediately.

I've been thinking about this a lot recently, and I'd like to explain why this hasn't been sitting well with me. I would also like to hear your thoughts too at the end.

I think the following question is a prime example. This will not be a protest to reopen said question, but rather an analysis of it as a question, how it was perceived, and the future of this site.

Is $1/\sinh(4x)$ equal to $\text{csch}(4x)$?

Sorry for the dumb question.

I do know that $\text{csch}(x)=1/\sinh(x)$, but I'm not sure if it applies to $x$ only. I don't know if it's applicable for $4x$ as well, or any other monomial.

"Sorry for the dumb question"

Although a tangent, I would like to point out that this quote, although appealing to emotion, emphasizes that the asker is aware of its triviality. The fact that users feel the need to apologize for their ignorance of a triviality on this site is probably not a good sign.

Lets talk about its triviality

To you and I, the average MathSE user, this question is very trivial. The asker (OP) is clearly in need of some foundational mathematical intuition, as pointed out by a commenter, when they responded to OP by saying

"I think you fundamentally misunderstand how to interpret mathematical identities. For example, (thing+1)-1=thing is true no matter what thing is, so you could say $(x+1)−1=x$ or you could say $(4x+1)−1=4x.$"

Clearly it's obvious what the asker is asking for, there's no issue there. It's a bit of a mystery to me why it was closed, but apparently not obvious to the minimum of 5 users needed to close a question. It seems like it was closed for being too trivial. Even if it weren't, that's how I perceived it.

Perhaps it was closed for lacking research, in which case, I ask this of you. Imagine you are someone with OP's level of mathematical understanding and terminology. What keywords do you search to answer your question?

You might notice, the issue with OP's question comes from a deeper misunderstanding of mathematical identities, rather than the specific nature of the hyperbolic trigonometric functions. A search engine is not going to pick up on this. Thus, their only resource for research is a Q&A site.

The problem

My problem is, trivialities are not trivial at all. For example, it takes months of direct immersion before we humans even understand the concept of object permanence. Plus, the problem of $$f(x)=g(x)\implies f(u(x))=g(u(x)).$$ (which is essentially the problem OP describes), is rather intensive to those first getting familiar with functions, domains, codomains, and ranges. The nature of the equals sign $=$ is even ambiguous. For example, if $f(x)=g(x)$, is this relation true for some solution $x$, or is this an equivalence relation between functions?

These are subtleties, and not trivialities. As I'm sure you're aware, there are so many subtleties in mathematics that one teacher could not cover them all. Hence, all students will eventually find one of these subtleties on their own, obfuscated by seeming triviality, and will have no where else to go, except for a question and answer site such as this one.

From of business point of view, the chances of this user coming back to this site after having their question closed is likely eviscerated due to the psychological consequences of having their thoughts being perceived and deemed too trivial.

This was just one example, of the potentially thousands of unique questions with a similar story. It got closed for not meeting the guidelines, not for being a duplicate.

From my eyes, it is our duty on Math.SE to be an encyclopedia of mathematical questions and answers. Why should we prohibit explaining the subtleties?

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    $\begingroup$ Closure of a question is not to be seen as "your question is not welcome" but rather as "your question needs improvement and therefore try to improve it". The question you link is closed just 4 hours ago and it received a lot of feedback via comments and answers before it was closed. I don't see any response to any of these by the asker $\endgroup$
    – Paramanand Singh Mod
    Dec 24, 2021 at 4:46
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    $\begingroup$ Great contribution. This happened to me and still makes me nervous using this site. For the person asking the question, it is not trivial (otherwise why ask it) so determining if a question is 'trivial' is up to the readers - and we each have own standards as too what is trivial or not based on our knowledge. Remember we were all learning at one stage and probably asked what we now would say are trivial questions. We need to be gracious. As for 'your question needs improvement', this also needs to be handled more gently. Helping guide better questions is preferable than closing them down. $\endgroup$
    – Mari153
    Dec 24, 2021 at 9:15
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    $\begingroup$ I try not to close Questions based on whether they are "trivial". I do try to "enforce quality standards" regarding lack of context, but the amount of context I require is little and I try to engage with the OP by comments suggesting ways, specific to their problem, of how to add context (unless others have done so, in which case I may just upvote their comments). I cannot guarantee my comments will not have "psychological consequences," but I try to frame my remarks in terms of the math, not the person. $\endgroup$
    – hardmath
    Dec 24, 2021 at 19:12
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    $\begingroup$ Gravitron I take seriously the shaming of novice users. But your post is far too full of your opinions, for which you provide not supporting research. Anecdotes of this one question, does not a pattern prove. How can you help inform users, new and old, how to make the best use of this site? And precisely who are to arguing against in your opinion piece? Why do you (often incorrectly) believe that anything you define as trivial, is seen by others as trivial, and why do you believe they are closed for being trivial? You are making many poor assumptions, to create your straw man argument. $\endgroup$
    – amWhy
    Dec 24, 2021 at 19:49
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    $\begingroup$ This is one of the big obstacles to creating the big repository of Q&A on this site: questions like these are important, common, and practically impossible to adapt to the guidelines (even for regulars here, let alone new users). This means we're going to continue to see the same questions, posted over and over again, each one feeling like a duplicate, despite there being no suitable duplicate target. Each time one appears, we're just going to make another asker feel too dumb to contribute to this site, and perpetuate the (what should be a) myth that we punish elementary questions. $\endgroup$ Dec 24, 2021 at 20:48
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    $\begingroup$ On the other hand, if we did manage to let one through, as you point out, searching for it would be basically impossible. If we decided to create an abstract duplicate, such as the $f(x) = g(x) \implies f(u(x)) = g(u(x))$ that you wrote, that wouldn't help any of the people actually asking the question, as the act of synthesising this abstract implication to their specific problem is already an act of mathematical maturity that is out of their grasp. $\endgroup$ Dec 24, 2021 at 20:52
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    $\begingroup$ @amWhy In regards to my "premise [being] uninformed, and misleading," do refer to Mari153's comment, "this happened to me and still makes me nervous using this site." It has, at a the time of writing, the most upvotes on this question. Surely this mutual agreement is a not a hallmark of my spreading of misinformation. It has become quite apparent that SE incubates a system of self-sustaining ego-driven "reputation points" hierarchy. This needs to change. Shifting the conversation from your defense to the season is a red herring, and does not excuse this issue. $\endgroup$
    – Graviton
    Dec 25, 2021 at 3:32
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    $\begingroup$ I second @Graviton. And please guys, in responding to these kinds of questions, let us not forget that we have a Be Nice Policy in place. Too often, I see several (high-reputation) users rudely replying to the OP (in the comments). Please, don't do that. $\endgroup$ Dec 26, 2021 at 5:44
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    $\begingroup$ @Teresa Lisbon - thanks for your considered replies and sensitivity. This issue of nervousness to ask questions applies across different SE subjects - it's not specific to maths. My intention of using this site was to build my knowledge through other people's expertise but its turned out to be a disappointing exercise. I am very well qualified so I can find answers elsewhere if needed but I am concerned for new learners here. There seems to be a real problem with the SE model. While the fixes needed are significant, they are not impossible to make. I will keep those fixes to myself for now. $\endgroup$
    – Mari153
    Dec 27, 2021 at 10:15
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    $\begingroup$ “From my eyes, it is our duty on Math.SE to be an encyclopedia of mathematical questions and answers.” I remember reading the 2020 election questionnaire where the mod got elected enforced the idea that MSE is primarily a repository of knowledge. I don’t know what is the current general view of MSE’s function now. However, if it is a wiki or a repository, then the storage of many trivial questions regarding to “subtleness” seems unproductive.(p.s. This doesn’t mean I am supportive to that idea anyway; +1 for your well-written question.) $\endgroup$
    – fantasie
    Dec 27, 2021 at 13:16
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    $\begingroup$ @rschwieb I concur with your sentiment, but I don't think it's as false of a dilemma as it may seem. Sharing knowledge on SE comes in 2 forms. (1) The direct response to an asker, and (2) keeping record of such response for future askers. What seems to be the consensus is that (2) > (1). I think this is not so different than mindset of "the good of the many outweigh the good of the one." However, I seriously doubt that if we relax closure-conditions, the site will suddenly pile up with rubbish and no one will ever find anything again. $\endgroup$
    – Graviton
    Dec 29, 2021 at 3:48
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    $\begingroup$ @rschwieb To me, the real dilemma is why our community purges "poor questions", instead of answering as much as we can & directing our energy towards having this site be more accessibly searchable. This redirection of moderation would prove beneficial to (1. the individual) and to (2. the many). However, I understand that this is easier said than done. Perhaps my dilemma is naïve, but truly I see great creative potential for different philosophies of moderation here. $\endgroup$
    – Graviton
    Dec 29, 2021 at 3:53
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    $\begingroup$ @Graviton That isn't a dilemma. "Answering as much as we can" is a great way to decrease site quality. I'm not aware of a big queue of good questions going unanswered while we straighten out bad questions, but there is certainly a big queue of bad questions piling up hampering searchability. It is simply easier to ask a poor question than to take care. The program we're undertaking is to put pressure on poor questions to improve. "purging" only happens to the ones that don't improve. $\endgroup$
    – rschwieb
    Dec 29, 2021 at 13:00
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    $\begingroup$ @StinkingBishop, How about 7 days? Would that be enough? Putting a question on hold gives them 7 days to improve the question. In other words, it already does what you are asking for. It puts things on a temporary pause to give the question-asker a chance to improve things. It also prevents posting answers before the question has been improved -- and that turns out to be important, for multiple reasons: (a) to maintain the incentive to improve the question (otherwise, someone will answer crummy questions, teaching people to not bother spending time to improve their questions), and $\endgroup$
    – D.W.
    Dec 29, 2021 at 22:35
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    $\begingroup$ (b) to ensure we have clear requirements and criteria that can be used to judge answers and vote on them (otherwise often it's unclear exactly what is being asked, which can make it more challenging to evaluate answers). $\endgroup$
    – D.W.
    Dec 29, 2021 at 22:35

2 Answers 2

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TL;DR

This post has many upvotes now, but I'd like to make sure everyone is talking about the same thing. I think it's natural that many of those votes are probably fueled by the sentiment "I support even trivial question askers" but I would dispute the ones that were cast with the sentiment "yeah, this closing of trivial questions has to stop" because I think this latter position is tilting at windmills.

Are we reading this meta post right?

The title

Why should "trivial" questions not meet the guidelines?

presupposes that questions are closed because they are "too simple", but I believe this supposition to be unwarranted. There has never been, as far as I know, any major antipathy to questions that are simplistic.

Firstly, it is a subjective line to draw about what is too simple, and secondly I think everyone here has had the experience of learning something new and having these sorts of questions, and finally, we pretty clearly lay out in our guidelines that we anticipate questions from beginners:

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

It is not unreasonable to extrapolate that this would require us to be tolerant of simple questions from the lower levels that we welcome.

What is a more likely reason for the closure?

It probably is the case that there is a correlation between low level questions and questions which do not conform well to the quality guidelines. There are many quality-based reasons to close a question, but triviality is not among those reasons. It is also totally understandable that a first time asker has not yet encountered the quality guidelines, isn't very good at seeking answers in the first place, etc. That's why closure exists, to signal that something needs to be done to turn things around. If closure didn't exist between "open" and "deleted" then we would have a lot of problems indeed.

On the flip-side, it is probably easy in the case of a short post containing a lot of confusion for a reviewer to feel like the context requirement is not met. I think that is probably the case for the example given. Sometimes in such cases it is possible to glean what the user's misconception is and to return with a great answer that addresses it. It could be that the post gains merit this way and lives on.

The survival of these questions is best left to the moderation process. There is no need to take it as an indication that all such questions are unwelcome and to take to meta to rally people against closing them, just as there is no need to take open questions like it as an indication all such questions are welcome and we should rally support to make sure they get closed.

Closure: not necessarily the end

I mention in the comments that there is a widespread misunderstanding, mainly among newer users, that closure is some sort of death sentence or black eye for a post, whereas we're striving to use it as a sort of soft lock and signal that the post needs improvement before it can be answered.

It could be that they bring this conception from other stackexchange sites, or it may simply be an affront to their dignity that their first attempt was not accepted. Either way, we need to do better explaining the actual meaning of closure to them in our community, and to be ready with the reopen votes when closure spurs improvement.

Actually, I found the old meta post where I wanted to start a conversation about this: Reforming closure's reputation: ideas to make closure more useful, less scary and more likely to be undone. It's been a long time... worth revisiting!

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    $\begingroup$ I also took a look at the closed queue to glean patterns in the kinds of questions we "usually" close. It's really a lot of textbook exercises, where there's definitely a rift of thought between what the OP has presented (often nothing i.e. PSQ) and what the actual answer is. Given that most questions incoming are certainly "non-trivial", if the exercise is non-trivial, then for the question to be "trivial" the poster must have made an attempt till they were stuck, which becomes context. That just makes questions like the one attached rarer, and therefore to be dealt with carefully. $\endgroup$ Jan 5 at 20:44
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    $\begingroup$ By "carefully", I'll look back at the guidelines and can say with some confidence that "triviality" + "low" level/disposition of OP of a question implies the smaller number of options they can present as context. Ruling out motivation/attempt obviously, and background because users can be embarrassed (statements such as "this may be dumb, but..." form evidence) , that leaves source+ definitions as the only context. That narrowing of options means that we should certainly moderate such threads with some care. tl;dr : such Qs are rare and special, so must be handled with care. $\endgroup$ Jan 5 at 20:54
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    $\begingroup$ "It could be that they bring this conception from other stackexchange sites, or it may simply be an affront to their dignity that their first attempt was not accepted." Or it's a completely natural assumption from common usages of the word "closed". If I open a support ticket, they help me, and I'm satisfied, the ticket is then "closed" (which means both parties are done with it, not that my specification of my problem is insufficient). If a police investigation is "closed", it doesn't require further input from the victim. I don't think the fragile dignities of users are at fault here. $\endgroup$ Jan 6 at 3:51
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    $\begingroup$ It also can be scary to post to a Stack Exchange site for the first time, which might make it more likely a new user cuts and runs. I myself have experienced much trepidation before engaging in other sites. Once, in 2019, I spoke to students about MSE, and they (somewhat nervously) told me that it was a good site for help, "so long as your question isn't too basic". This is a misconception, to be sure, but if the correlation is sufficiently strong, it won't matter one way or another. $\endgroup$ Jan 6 at 4:01
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    $\begingroup$ @TheoBendit Or it's a completely natural assumption from common usages of the word "closed" That's exactly what I was intending to say when I said "other stackexchange sites". I meant that they assumed it meant the same thing it meant to them elsewhere. So this isn't a new observation. $\endgroup$
    – rschwieb
    Jan 6 at 14:54
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    $\begingroup$ @TheoBendit I can understand some apprehension when posting online, but I don't understand what it has to do with this topic. We can't prevent people from feeling that. If a person feels apprehension when undertaking something at virtually zero cost and risk and has no material consequence to them, it's not a problem we can solve. Can you elaborate on the bearing on the topic that you want to convey? $\endgroup$
    – rschwieb
    Jan 6 at 14:56
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    $\begingroup$ @rschwieb I bring up the apprehension as a possible explanation as to why closure so often means death. This is something that is well within our power, as a community, to change, and I have long been in favour of doing so. I didn't interpret the "other stackexchange sites" thing so broadly; we'll chalk that up to a misunderstanding. $\endgroup$ Jan 6 at 17:06
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    $\begingroup$ @TheoBendit Yes well i think we're on the same page so far as "we can change the perception closure means death," which is what I'm hearing. $\endgroup$
    – rschwieb
    Jan 6 at 18:49
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    $\begingroup$ I thought I remembered having the discussion before, and somewhat surprisingly it's been already like 8 or 9 years: math.meta.stackexchange.com/q/10852/29335 $\endgroup$
    – rschwieb
    Jan 6 at 18:51
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    $\begingroup$ @SarveshRavichandranIyer It is not at all clear to me what you mean in your comments. You are free to encourage askers on how to improve questions, as are those who want to answer PSQs. Whether arithmetic questions, or algebraic geometry questions. The problem is not "trivial vs. sophisticated", as gravitron seems to insist. It is quality standards all askers are expected to follow. $\endgroup$
    – amWhy
    Jan 6 at 22:24
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    $\begingroup$ @amWhy I am arguing that there are quality(worth keeping in a repository) questions that OPs cannot fit under the guidelines easily. A newbie OP asking an elementary "trivial" question will not be able to provide you attempt/motivation for sure, and background out of potential embarrassment (particularly if phrases such as "I know this is dumb" is present). That leaves source + definitions, at the most. All I'm saying is that reviewing should acknowledge these lack of options and see the quality in such questions. That MSE discriminates against such questions is blatantly false, no doubt. $\endgroup$ Jan 7 at 4:05
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    $\begingroup$ We have no intention of removing questions that are "trivial" : for sure, and by all means I encourage posters asking for background : it's obvious that it would help them provide a more precise answer, and help others see the connection between what they answer and where OP is coming from. We do, however, have an intention of removing questions that don't follow the guidelines, and all I'm saying is that a "lack of quality" isn't equal to the set "doesn't follow guidelines" : as the above question and my justification attempts to show. $\endgroup$ Jan 7 at 4:09
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This is to augment rschwieb's answer (which I agree with) by the following observation:

While there is no causation between (perceived) "triviality" of questions and their closure at MSE (see rschwieb's answer), nevertheless, there is some correlation between the two.

[I am not trying to address here the inherently subjective nature of the word "trivial". I am adopting the "eye of the beholder" attitude to the word "trivial."]

  1. Users who ask "trivial" questions tend to be newbies, for most of them, this is the first (and only) question they ever ask at MSE (regardless of what answer they receive!). Accordingly, they have not read Meta guidelines for asking a good question (and, likely, they do not even know about the existence of Meta). Accordingly, their questions tend to suffer from a variety of issues such as (I am not trying to give a complete list here):

(i) Not using Mathjax to render math formulae.

(ii) Asking a question in the title and not in the body of the post. Asking a question where the question in the title is different from the one in the body of the post.

(iii) Not responding to hints/remarks in comments that attempt to direct OP to answering their own questions or explain their level of mathematical maturity.

(iv) And then comes "lack of context", "lack of clarity," and so on....

All of these, especially in combination, are conducive to a closure.

  1. At the opposite extreme, many users are intimidated by "high-level" questions which are hard to understand for somebody outside of the appropriate area of mathematics, hence, do not even look at such questions, let alone, vote to close. Examples abound: Questions in Model Theory (a subarea in Mathematical Logic), in Algebraic Geometry, advanced Algebraic Topology, hard-core Nonlinear PDEs,... (One more thing: Occasionally, such questions are asked by famous mathematicians, who, for whatever reason, decided to post here and not on Mathoverflow. I will refrain from naming names.)

Personally, I never vote to close questions where I am completely out of my depth and would not be able to figure out if the sufficient context is provided even if there is some explanation. But this is my personal preference, others have different attitude and I have no problem with this, see the discussion of this meta question.

Such "advanced" questions do get closed for lack of context or clarity, but less often than the "trivial" ones, (in particular) for the reasons I just explained. Personally, if I see such a question closed and it is in "my area" of math, then, I might edit to add the additional context and post a request to reopen on Meta here.


Edit. For the record: There are Stack Exchange sites where "trivial questions" are indeed not allowed, however Math Stack Exchange is not one of these. For instance, at History Stack Exchange, there is a long-standing tradition of closing questions which can be answered simply by reading an appropriate Wikipedia article. The standards of what is acceptable vary greatly from site to site in the Stack Exchange network and its a good thing.

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    $\begingroup$ Absence of MathJaxing is something I can cope with. Shooting from hip, I'd say most of the votes to close are induced by a "solve my homework for me" attitude. And it's definitely not because one is a beginner in math. It's a general attitude problem. There are also beginner level students who clearly put effort in their assignments. I am much more motivated to help those that are willing to work. $\endgroup$
    – AlvinL
    Jan 6 at 11:35
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    $\begingroup$ @AlvinL The problem is that the question spoken of here doesn't look like a "solve it for me". It's "trivial", but in a manner as explained in the post. That immediately rules out effort/motivation etc. from being presented for such problems. We can't discard the "human" element if that is the primary reason behind why certain context isn't presented ,which leads to the loss of "quality" questions as evidenced above. The problem is that SE itself chooses to put its(and not many others') definition of quality over the "human" element with its close reasons. So we need to be careful. $\endgroup$ Jan 6 at 12:27
  • $\begingroup$ @AlvinL: I agree with you in general, but I made my "list" (putting items (i)-(iii) ahead of (iv)) with the specific question in mind (the one mentioned by Graviton). Just take a look at that question and also read the sentence I wrote immediate after my list (cumulative effect). $\endgroup$ Jan 6 at 14:14
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    $\begingroup$ @SarveshRavichandranIyer The OP is claiming that questions seemingly trivial, are not allowed. That is patently false. Only rschwieb and Moishe have pointed that out. $\endgroup$
    – amWhy
    Jan 6 at 20:18

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