Coping with *abstract* duplicate questions.

Any longtime reader cannot help but notice that we get many abstract duplicate questions, e.g. this recent question on partial fraction computation, which is not essentially different from many other questions of the same shape, e.g. this question. Once you know how to solve one of these problems you can solve them all. There are many classes of problems that frequently arise in reparametrized variants, e.g. divisibility problems using Fermat's little theorem, proving basic properties of gcds, etc. Does it make sense to try to try to prevent these minor variations from swamping the site? In a couple years time we could well have many hundreds of variants of such questions that are all essentially the same except for minor variation of parameters. Among other detrimental consequences, this greatly obfuscates search results. Certainly our user community has the expertise to appropriately classify and eliminate these "abstract" duplicates. Perhaps with a little ad-hoc add-on infrastructure, and with moderator support, we could address these issues before they get out of hand. Thoughts?

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Maybe we add a new close reason: "Minor Variant". – Aryabhata Mar 10 '11 at 5:37
+1 for raising the issue. I think that trying to keep track of minor variants (I like that terminology better than "abstract" duplicate question) is both something that would be very valuable for the site and something that would require significant time and diligence on the part of moderators and experienced users. So, if others agree that this is a worthy goal, we should brainstorm about strategies to try to do this in an efficient and minimally time-consuming way. – Pete L. Clark Mar 10 '11 at 5:44
@Moron: But that doesn't help remove hundreds of closed minor variants that litter search results. It's a vicious cycle: question poser can't find an answer by searching because there are too many variations or closed threads littering the search results, so they post yet another minor variant. – Bill Dubuque Mar 10 '11 at 5:44
@Bill: It is one of the many things we would need to do... – Aryabhata Mar 10 '11 at 5:46
@Pete, @All: Generally speaking, it's probably a good idea. It would require the "survivor variant" to have answers that address both the general strategy (so as to be useful for future minor variants) and specific application to the question at hand (which shows how the general strategy applies to a specific problem). – Arturo Magidin Mar 10 '11 at 16:40
How about at least linking all the minor variants together, so once someone finds one they can find them all without much trouble. This would save a lot of time, and it would be easier to refer between posts. – Eric Naslund Mar 10 '11 at 21:05
To me the art of answering a question is as valuable as asking a question. Why not accept that such a website will keep going over the same things and let the constant flow of newcomers deal with repeated questions? This will allow the natural flow of people to get their hands on at answering these widely recurrent questions. Trying to create permanent solutions isn't the point of a forum, people can collaborate on the wiki-proof project for that. So if we desire to keep this place young and vibrant, we'll have to accept re-runs of popular questions. – David Kohler Mar 31 '11 at 8:05
I read this thread and then ran into an example almost right away, so I was inspired to create this: math.stackexchange.com/questions/1583883/… Maybe we could have a special tag for such posts? – Stella Biderman Dec 21 '15 at 0:08

The current thinking is that subtly different variants of the same question be closed as duplicates of a more canonical, more general question and answer pair:

http://blog.stackoverflow.com/2011/01/the-wikipedia-of-long-tail-programming-questions/

If you keep seeing the same form of questions, whether it’s mod_rewrite rules on Server Fault, freezing computers on Super User, or how to use regular expressions to parse HTML, write a great, canonical answer, once and for all. Make it community wiki so that as many other people as possible can make it great. Work really hard on writing something that is clear, concise, and understandable by as wide an audience as possible.

Personally, I would express this sentiment as "old-timers are tired of answering what is essentially the same question in millions of tiny different varations".

Whenever you feel that is happening, I recommend approaching it as per the above.

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I would suggest that:

• if there is a sufficiently-general form of the question, new variants should be closed as duplicate, but not deleted—this provides a way for someone searching for that variant to get to the more general result;
• if there is not a sufficiently-general form of the question, ask the general form of the question so that it can be answered in the general case (remember, you're allowed to ask and answer your own question as doing so provides valuable content) and future variants can be closed as duplicates, as above.
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Are closed question deleted in general now? – draks ... Apr 7 '12 at 11:00
@draks: I don't know, nor have I been around enough lately to have an idea. Perhaps it would be best to ask that as its own question here on meta. – Isaac Apr 7 '12 at 18:02
For the second point: maybe quoting (linking to) the specific variant that inspired the general form of the question as an example of application would be nice. I would not like the idea that the poster of the specific variant has his/her question closed and be redirected to a general question that he/she cannot understand because too general. – Taladris Mar 12 '15 at 7:29

(too long for comment)

I agree. It is not clear what should be done. Sometimes the problem can be fixed if the most general solution was posted. As an example, the following three threads are conceptually identical:

Limit of algebraic function avoiding l'Hopital's rule

Limit of algebraic function $\ \lim_{x\to\infty} \sqrt[5]{x^5 - 3x^4 + 17} - x$

But here, the question can be generalized and solved. That is for polynomials we can show: $$\lim_{x\rightarrow\infty}\sqrt[n]{x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0}}-x=\frac{a_{n-1}}{n}$$

Should they be merged? I definitely think so. The proof techniques in the answers of each post are exactly the same.

A harder question is what to do with all the Fermat's little theorem problems They are all so similar, but different enough that there is no "universal case" that can be proven.

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Yes, in fact there are general algorithms for computing limits for wide classes of elementary functions. (In fact I had the pleasure of discovering the first known such limit algorithm, e.g. see here.) The problem is choosing the appropriate level of generality when unifying questions - how far to abstract past minor variations. Since we welcome all levels of math here we can only go so far without losing some folks in abstraction. – Bill Dubuque Mar 10 '11 at 6:14
There is also the practical issue of merging: non-abstract answers given to such questions cannot be reasonably merged under one thread. I would say just closing (and possibly deleting) would be better than merging. – Willie Wong Mar 10 '11 at 12:26
@Bill: I guess you are right, since the askers of those questions were certainly first year calc students wanting to understand the simplest possible approach. – Eric Naslund Mar 10 '11 at 21:02
@BillDubuque: the desired level of abstraction is such that the solution (or, rather, the principle of solving) remains easy to understand for the target demographic. In other words, the answer must remain highly practical. – ivan_pozdeev Sep 25 '14 at 2:34

At least so far, I don't see this as a problem. It would be nice if a search turned up the earlier variants, but I don't know how to do that and the evidence is that the posters of these problems don't search anyway. I would support a relaxation of the wording of "exact duplicate" to "if you read this you should be able to figure it out", but the volume is not too bad. If I can find the previous answer I post a link, but often I can't.

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A request for comment:

Perhaps it will be worthwhile to have a two-pronged approach:

• Maintain a list of FAQ This is not an FAQ in the sense of how to use the site. But actually a list of Frequently Asked Questions. This could be implemented as a Meta Thread (and to be incorporated in/linked to from the FAQ on how to use this website), or perhaps as a tag (though for the latter it'd be much more reasonable for this to be a "restricted" tag, with a reputation limit before one can tag a question as such). To this list (or a separate one) we can also add all those silly puzzle questions that crop up every now and then, and those inevitable questions about 0.999999... = 1.
• Aggressively closing and possibly deleting such minor variants and duplicates. If I am not mistaken, 10K+ users (of which there are quite a few now on this site) can vote to have an already closed question deleted. So with a bit of help from the community we can certainly clean up the clutter.

To populate the list of FAQ, each question in the FAQ should be a good CW, abstract question/answer to a canonical form of the question that often appears. And ideally we should also link to, in that question should be included links to some less abstract examples that has already appeared on this forum. So we address the abstract and the practical in one go.

Of course, this will require a lot of work from the community.

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I thought this is what tag-wiki/faq is for. – Asaf Karagila Mar 10 '11 at 19:44
Why not just post the general questions on the regular site (not meta) but with the faq tag? (Each question separately, but tagged instead of one long hard to navigate thread) In any case, I feel this is a great suggestion. – Eric Naslund Mar 11 '11 at 1:29

One of the reasons we get the same question over and over is people who are learning new concepts cannot tell if two problems are essentially the same. In a sense, what they are asking us is "what type of problem is this and how do I know it is that type?"

Deleting what looks, to trained eyes, to be "minor" variations will not stem the flow of questions... but grouping a large number of similar examples together just might.

Is there any way that we could do this?

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Closing does not mean deleting. Once closed, the question asker can look at the linked section of the parent and see all the variations, if we ensure we usually choose the same parent everytime... – Aryabhata Mar 3 '12 at 16:45

This brings up a good point. I frequent [Combinatorics] which is always flooded with minor variations of the same question. For example,

1. How many ways can George give 6 apples to his 2 kids John and Rebecca?
2. How many ways can Alice give 8 apples to her 3 kids Jimmy, Mary, and Susan?
3. How many ways can you place 8 unlabelled balls into 3 labelled urns?
4. How many ways can you place $n$ unlabelled balls into $m$ labelled urns?
5. How many ways can you place $n$ balls into $m$ urns?

Do we close both (1),(2),(3) as duplicates of (4)? Will the person asking question (1) be able to tell how their question relates to (4)? Do we close (4) as a duplicate of (5)?

I honestly think "duplicates" by itself is completely inadequate for organizational purposes. We need an easier way to navigate the hierarchy of generalizations. Being able to tag one post as a generalization of another would go a long way. Then each question could have four links attached at the bottom: specializations / variations / generalizations / duplicates. The questions above can be linked (1) ~ (2)=(3) < (3) < (4). A few issues:

• Since a question can often be generalized in many different ways, how do we define (variations).

• Do we allow generalizations between vastly different areas of mathematics. Do I really want (5) in measure theory terms? How do [tags] play a role?

• If (a)<(b)<(c), then when you click the (generalizations) link on (a), should (c) be listed?

• etc.

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I don't know what the moderator features are on the site, but it might be possible to merge the specific questions into the thread of the more general one under a category of "examples".

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There is a lot of value to having multiple (if similar) examples of a certain type of question. Grouping them would be much better than deleting. – futurebird Mar 3 '12 at 5:27

I'm curious if we can somehow combine the tools of wolfram with some sort of language comprehenser program, and an AI which is fed the whole of Math.SE as test data.

Then theoretically if someone posts a question there will immediately be an answer from the computer which will answer the question correctly if it indeed is 'minor' enough of a variant

leaving the only questions that were not instantaneously answered correctly as new questions which need to be answered by the community.

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It's far fetched but I imagine a good number of mathematicians on this site are capable of programming and it could make a cool open source project that also solves the current issue at hand – frogeyedpeas Jun 18 '14 at 1:20
It would need a step by step solution, otherwise it wouldn't be any different than (the free version of) w. Alpha. – Squirtle Jun 21 '14 at 4:35