Assuming good faith for naïve questions

Question

It's standard practice here to close questions that are too elementary to be considered "research-level". But I think people have been too quick to label some questions as "too elementary", when in fact they describe very real research-level questions. For example:

• How are lower bounds for computational complexity proved?

• Roots of a polynomial

In both cases, there is an undergraduate-level "textbook" answer. (For the first question: Sorting requires $\Omega(n\log n)$ comparisons. For the second question: Hilbert's 10th is undecidable.) But if we look past those easy answers, these are legitimate research-level questions in theoretical computer science.

• Okay, but then how does one prove lower bounds for problems that can't be solved by comparison trees? Or lower bounds bigger than $\Omega(n\log n)$ for problems solvable in polynomial time? Or exponential lower bounds for NP-hard problems?

• Okay, but then how does one actually find integer roots of polynomials in practice? Are there effective algorithms for broad and interesting classes of polynomials? Are there algorithms with provable approximation guarantees (for interesting classes of polynomials)?

In both cases, the deeper question is likely not what the original poster intended. (But StackExchange answers are for the entire community, not just for the original poster. And why should we shy away from blowing the original poster's mind?) And even if it were, the posts would require significant editing to bring the deeper question to the fore. (But editing good questions is generally preferred to closing them.)

Should we really close such questions? Or am I just being a smartass?

Answer 1

I read the first question, and it does appear to me that there's an excellent CW (or not) answer waiting to be written for it. The question is certainly broad, but I wouldn't speculate on the motives or expertise level of the questioner. It's likely that they don't have much background, but so what ? I face this kind of question in my graduate algorithms class all the time, and as JeffE points out, it's really a tricky question with very different answers.

In fact, the very idea that you need to fix a model to even talk about lower bounds is not at all obvious to students who haven't been steeped in theory for a while. It's possible to go through an undergraduate degree in CS at a reasonable place, learn that "sorting takes n log n time", and never really confront what this means until you hit grad school.

In short, there are questions where the questioner has little background and the answer is quite trivial. But then there are questions where the questioner has little background and the answer is highly nontrivial. I agree with JeffE that this is a good chance to "blow the questioner's mind" with some truly deep ideas that theoreticians have developed over the years, as well as create a general reference answer that others will be able to Google.

One issue that might have been raised with this is "well, let's let it go on cs.SE and it can be answered there". While that's something that we could do, I'm more inclined to define our scope broadly rather than narrowly (as the SE overlords have said in the past regarding the SE system in general). In other words, the fact that this question could be answered in some form on cs.SE shouldn't disqualify it from being answered here, and in fact for this particular question I think we are the more appropriate forum for expert answers.

Answer 2

Jeff, I generally don't vote to close unless there are several close votes. But I think it should not be problematics to comment and say this looks off-topic when I think so. I usually try to even phrase such comments carefully and conditionally so the OP can reply and clarify that I misunderstood and that would be fine with me.

I think I have expressed the following before (probably as a reply to Peter in some meta discussion). I agree that there are some very knowledgeable users on cstheory who can write very deep and interesting answers even to very simple questions. I don't have an issue with this by itself and I even enjoy reading such answers. But I think you would agree with me that we have to draw a line somewhere for separating on-topic from off-topic (it doesn't need to be very rigid and black and white but it should be clear when some questions is really off-topic).

It seems to me that following what you are suggesting we should not close any question, even very basic ones, because someone might be able to write a very deep answer (independent of what its author was looking for). I am not sure if even very simple standard undergraduate textbook exercises can be closed then as I am not sure that no one can write a deep answer to such questions.

To put it in another way, my issue is this: where do we draw the line? You or some other user might like a question and might want to write or read a deep answer to it, but I can't read minds or future. I need something more concrete that I can base decisions on. I can't tell a user whose question is closed that another similar question is left open because someone wanted to write a deep answer to it although it has similar level. I don't mind if we relax where we draw the line, but I need it to be reasonably clear to be able act based on it and also categorize as off-topic those questions which others consider to be really off-topic here.

ps: if you or someone else edits an off-topic question and makes it on-topic that can be fine. However, IIRC, we had a discussion about this long time ago and the result was that if someone has a related interesting question they should post it as a new question. I personally don't edit such question except in very special cases for two reasons: 1. I don't think it is good to edit someone else's question so much that it is not what its author is looking for. 2. I feel that this might open the door for more similar off-topic questions.