Determining the OP's background when answering questions

Question

I've been running into a lot of situations like this:

OP asks how to find a solution to an elementary equation (in the sense of being written in elementary functions), but without an answer that can really be given in an exact form, something like solving $3^{x} + \frac{x}{5} = 2.7^{x}$, something that cannot be solved explicitly, but can be solved numerically. Somebody responds by suggesting that one finagle it a bit, and then appeal to Banach's fixed point theorem. This is of course a sound method, and will work (assuming such finagling is possible), but it doesn't strike me as very appropriate, because the question strikes me as a homework-type problem, or at least one that was encountered in or inspired by a class. I see this problem and think, "This cat's going through a pre-calc, college algebra course," so it seems sensible that a good answer would use the tools the student has at her disposal, and though I cannot speak for everybody when I say this, it was my understanding that something like Banach's fixed point theorem would not be encountered until a good bit later in a math education (for better or worse). Of course, the OP could look up "Banach fixed point theorem" and see what it says, maybe even understand the proof, but it would not be of much aid in the actual class.

It reminds me somewhat of a calculus class I took, and we were given a test covering Taylor expansions, and we'd been told to derive the Taylor expansion for $\exp$. I said that we could do this by understanding $\exp$ as the unique solution to the differential equation given by $f' = f, f(0) = 1$. I got no credit, and when I asked him about it after the fact, he asked (and probably rightly so) how I knew those conditions had only one solution, to which I mumbled something along the lines of, "Because you said so once." Obviously I could not answer his inquiry satisfactorily, and so I did not get credit on the exam. But even if I had given a complete proof that my answer worked, going through to show that any two solutions to $f' = f$ could only differ by a multiplicative constant, it still would've missed the point, because the goal of the question was to test my familiarity with Taylor expansions, and my method didn't do it.

Similarly, using Banach to answer a pre-calc question sounds not only like overkill, but moreover sounds like taking a foreign and undiscussed result/method that the student may very likely not really grasp, and missing the goal of working some other more elementary technique, and so to say, "Appeal to Banach" might be a sound and workable method, it doesn't meet the OP's needs.

So my question is, does MSE etiquette have a mechanism for this? Is there a way to determine the appropriate amount of "technology" for a problem? Is there a way to express to another answer that you think their answer is inappropriate for the OP and their needs? Perhaps should there be?

Answer 1

I sometimes write answers to questions using techniques that are likely too advanced for OP. If I'm aware I'm doing it, I try to add a note at the beginning, something like:

This is an advanced answer.

or,

This is a more abstract approach.

or, probably best,

If you know the Banach Fixed Point theorem, ...

An answer is a written communication. It should anticipate to whom it is communicating. If you start with algebraic manipulations, without any preparation for the fact that you are about to make an appeal to some high-power theorem, it can be an irritating experience for the reader. It will feel like an appeal to a higher power - "Then, a miracle occurred." If you think OP, or anybody with a similar question, is unlikely to understand this answer, you are wasting that person's time by not warning him in advance.

As a general rule, I want readers to know what kind of answer they are getting before they start.

That said, any time there is a question asking to prove there are infinitely many primes of the form $4k+1$ or $6k+1$ or $30k+1$, some smart-@$$ writes in an answer that the result is a direct result of Dirichlet, which is hardly useful.

Answer 2

So my question is, does MSE etiquette have a mechanism for this? Is there a way to determine the appropriate amount of "technology" for a problem?

It is requested from users asking question to provide context for their problem. Their background is such context. It is alright to ask for this background. Once determined, one can make a reasonable judgment.

Is there a way to express to another answer that you think their answer is inappropriate for the OP and their needs? Perhaps should there be?

A way to do this is a comment. Note though that not everyone will react positively to such remarks. In extreme cases you can consider casting a down-vote too (if you are convinced the answer is not useful in a strong sense.) It should however be kept in mind that absent any context what you think is appropriate level is your opinion and the answerer might just have a different one.

In my opinion to ask the questioner to make clear what type of answer they are looking for is the way to go.

Answer 3

Thanks to OP for bringing up this topic. +1 for the same. I believe that an answer given on MSE has two purposes:

1) Help the OP get the answer to his question. This means that it is always a good idea to guess the level of OP (either from context of the question or by asking OP directly). If OP is not satisfied with an answer (just because it is at a different level) and faces similar instances multiple times probably he will be less inclined to use MSE. MSE thus loses one user (and probably a host of potential nice questions). Hence there should be some effort from users to provide an answer at a level suitable for OP and this kind of behavior should be encouraged.

2) Help others apart from OP get answer to the question posted. If an answer is on a different level compared to what is expected by OP then it may not be so useful to OP at that moment (and OP can indicate this by not voting/accepting it, or by a comment) but at the same time it may be useful to others who can comprehend the answer. This way it adds to the knowledge base of MSE and hence this behavior should not be discouraged by users of MSE.

I think MSE's mechanism of voting/accepting/commenting takes care of such answers in most appropriate manner. At least I never felt that answers at an advanced level are a problem for me. I can ignore them at that moment and perhaps return to them when my level has increased somewhat.

On the other hand I have seen that most of the answers which use advanced tools and techniques often get more votes (because of their small size) and answers which are based on simple ideas and elementary techniques are kind of treated as just another answer. I don't want to complain here, but I kind of follow "simpler is better" policy especially when dealing with maths and apply it during voting/giving an answer.

Answer 4

When answering questions, I think it goes beyond considering the complexity level of the answer or even alternative approaches to getting the same answer.

For example when I see answers that show how to fit a curve to some data and the resulting answer gives fitted curve goes through the cloud of points appropriately and adequately which answers the question, I also will consider if the residuals are what should be expected given the particular curve fitting method and what might be done with the estimates of the coefficients. Even if the fit has a good appearance, if the objective is to compare coefficients of different datasets, careful consideration of the residuals is imperative to believing one has appropriate standard errors for the coefficients. That kind of assessment for curve fitting seems to be rare in these forums. (And I'm likely to hear a lot of pushback about that.)

My point is that one shouldn't always just answer the question (at whatever level of complexity or approach) but also consider what might be done with that answer - even if it is just asking "Have you considered these consequences?" That's where I see the biggest advantage to all of the experience available in these forums.

To get to the original question: I don't think that there's a particular etiquette. It has to vary by the individual's expertise, experience, and time available. And when one oversteps with an answer, this crowd is not shy in stating opinions.