A criterion for distinguishing between two kinds of questions

Question

Abstract: In which cases must a poster exhibit efforts to answer a question and in which does the content of the question itself suffice to provide context?

---

It is often suggested that a question should be closed because the poster showed no effort to answer it. The reason for that is obvious in cases where it's phrased like a homework question -- for example:

• Prove that if two random variables are independent then their covariance is zero.
• Evaluate the following integral: $\displaystyle\int\cdots\cdots.$
• Solve this differential equation: $\displaystyle\frac{\partial^2 u}{\partial t^2} + \cdots\cdots.$

However, one sometimes sees it stated without qualification that ALL questions for which the poster does not indicate what efforts have been made to find the answer should be closed. I think that statement is being made thoughtlessly because when examples are cited, it will be seen that there are types of questions to which that does not apply. Sometimes the content of the question itself is considered to have shown sufficient effort, as demonstrated by the fact that nobody votes to close the question and lots of people up-vote it. Some examples appear below (all posted by myself since it was easy for me to find those quickly, but plenty of others exist).

So my question is: Has anyone tried to define the difference, i.e. explicitly state the criteria for deciding between (1) cases where some effort to answer the question needs to be explicit, and (2) cases where the content of the question is considered sufficient, as in these examples?

• This one is a less-than-earthshaking example, included because its recentness makes it easy to find: Quotient rule/Quotient rule
• Perhaps a more substantial one: Are there any "other" ways to show a normed space is NOT an inner product space?
• When is proof by well-ordering preferable to proof by induction?
• SAT and proofs in propositional logic
• Are there any natural proofs of irrationality using the decimal characterization?
• Uses of vector spaces over $\mathbb Q$
• Average shape of Voronoi cells in dimension $n\ge 2$?
• I wonder if "effort" is shown by the inclusion of two utterly wild guesses about the answer, both of which are wrong, as in this case with $15$ up-votes?: Rearrangements that never change the value of a sum
• A very short one: Characterizations of the cross-ratio

Answer 1

Let's call a spade a spade and admit that "show your work"/"what have you tried?" in the context of this site are primarily intended to be a less accusatory way to say "no, we will not do your homework for you".

It is, of course, true enough that showing some work will also help answerers tailor their answers to the particular lack of understanding that the asker is suffering for -- but still it seems to be nearly universal that demands for shown work are made exclusively when the question looks like a "do my homework please".

The questions of your own you list do not look like "do my homework". Many of them don't look like something that can reasonably be posed as homework at all -- and those that do still come with a cogent explanation for what makes you wonder about that question other than "my teacher wants me to show I can do it".

In other words, those questions state a context that shows they're not homework questions. This matches why the "we won't do your homework" closing reason masquerades as "missing context or other details" -- showing work is officially relegated to being one kind of "other details" that might be missing.

(For the record, I think that's a horribly confusing close reason, but at least there's some method to its madness).

Answer 2

Most of the questions that I up voted without asking for work by the author are problems where, at first glance, I have no idea what should have been tried (or wouldn't expect the author to know).

Combinatorial problems are an easy example. Yes, you could try to enumerate the options, but the point is to avoid such. Usually the hard part of the answer is that first step in modeling the problem, and then applying some standard formula or trick.

The questions you mention look similar. They are soft, making standard first steps hard to pin down.

Meanwhile, an integral or derivative question has a well known set of standard tools that can be applied. Here I want to see why these can't be used, and why we're being bothered with a problem best answered with "Ask Wolfram."

All of this is pretty subjective, and area dependent. I think it would take significant community work to make concrete conditions for each tag, and probably best managed with up votes as we do now.

Answer 3

In which cases must a poster exhibit efforts to answer a question [...]

As far as I am concerned only when they do not manage to provide enough context to allow for productive answering in a more immediate way. Exhibiting efforts to answer the question is a means to an end (making the problem more clear), not an end in itself. Of course "allow for productive answering" is subjective and vague, but I feel putting it in this way still changes the problem.

In part this is also, as far as I understand, the historical reason for this request. It can be seen as a compromise between:

• Let us not simply provide solutions on 'assigned problem' posts.

• It is unreasonable to expect a learner to be able to contextualize their problem in a meaningful way.

The point of the attempt is not, at least not mainly, or at the very least not only, to check if the poster is a hardworking individual that thus deserves our help, but rather to be able to understand where they are coming from. This is nicely explained in the comments by hardmath and dxiv (reproduced, if ever there should be a more comprehensive comment purge):

The short answer is that "what you tried" is not the only way to provide context. The purpose of adding context, beyond what might otherwise be a textbook or coursework exercise, is to put the OP's understanding into perspective alongside the problem statement. It sometimes turns out that the OP is not familiar with the terms used in such a problem statement, so that a direct attack on the problem does not further their learning until the basics are revisited. I can elaborate as Answer if it would be helpful, but these points have been rehearsed in posts linked above, inter alia. – hardmath

@hardmath Context is also important as to what answers are expected. It happens all the time that an otherwise valid answer elicits a comment from the OP "but I don't know complex numbers, or generating functions, or asymptotic analysis etc". Framing the question in the right context helps getting better focused answers, and can sometimes save the question from being closed as a duplicate altogether. – dxiv

In a different direction, to take an example from the posts you mentioned as not showing efforts to answer the question:

Uses of vector spaces over $\mathbb Q$

I know of two applications of vector spaces over $\mathbb Q$ to problems posed by people not specifically interested in vector spaces over $\mathbb Q$:

• Hilbert's third problem; and
• The Buckingham pi theorem.

What others are there?

The inclusion of the two examples you know about, contrary to what you suggest, one could just as well see this as "exhibit[ing] efforts to answer the question" (you started out to compile the list you seek). And, I feel these examples are really important to making this a good question. Not because otherwise I would think: "Wow, Michael Hardy is such a lazy guy, just dumps his question here without documenting efforts. There I'll teach him some manners. I'll close it down."

But rather because without them I would have had a hard time, or at least a harder time, to see what you mean with "problems posed by people not specifically interested in vector spaces over $\mathbb Q$."

Conversely, I for one do not need an actual attempt at at solution to go with "Prove that if two random variables are independent then their covariance is zero." What I do want though is an explication what OP wants and needs specifically. As mentioned in a comment I quoted, in such a case OP might well not know what independent even means or what the covariance is, they also might know this just fine. Both is in a way a reasonable state of affairs, but it does significantly influence what type of answer is required.

Answer 4

While I advocate for closing, I am fairly conservative (by my standards) in regards to actually doing so — early on I realized most of the benefit could be gained from closing just the most egregious examples.

In particular, I mainly only close in the "most obvious cases" of posts in the form of an exercise.

Skimming over your list of posts, the main distinguishing feature is that they aren't in the form of an exercise.

---

For someone writing a new post, I think that is the most important point — you want to ask a question about mathematics, not assign a problem to mse, so write your post to reflect that!

Answer 5

I agree with this.

I think the pattern is the difference between the "simplicity of the question vs answer", not in the "actual context".

This is very subjective. For some people, a problem could be boring and for other not, which would be reflected in the comments and|or the answers.

1. When a question is simple to ask and simple to answer, it got several answers without asking for context.

   • Typically elementary and first years college problems, "fun" | "fast" to answer,
   • In this cases the question is just given, maybe not one, but several, maybe because it is gratifying to expose our self confidence in one specific topic,
   • And also, just to gain easy fast points.

2. When a question is simple to ask and difficult to answer, context is requested.

   • Typically college problems, which require more than a couple of lines, "boring" to answer,
   • Do an integral by parts require a context? No, it is simply because the difference between Q&A is noticeable and one don't want to make all the job alone,
   • And after all that work, you maybe will not get the rep points, hence you view negatively the question.

3. When a question is difficult to ask, and which normally also are difficult to answer, again normally no context is requested.

   • typically last year college, thesis work, research. "interesting" to answer.