Why should "trivial" questions not meet the guidelines?

Question

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?

Answer 1

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!

Answer 2

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.

2. 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.

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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.