# When are questions the same?

This is a rather philosophical question, but reflects the fact that essentially the same question can be asked at different levels of mathematical sophistication and with differing motivation.

Here are three, the last of which has been closed:

Trigonometric equation - solution required

Solving a problem about overlapping circles - help in estimating solution required

Identifying centre of mass of a semicircle - elementary insight required

I'm guessing the answers to the first would not help the person who asked the second very much. So can essentially the same question be different because of the apparent mathematical sophistication of the person who asks it?

• – Aryabhata Jul 1 '11 at 20:05

In the case of the question "Identifying the centre of mass of a semicircle," there is the additional issue that the specific query, about $a-\sin a=\frac{\pi}{2}$, is unconnected with any "best" way, or indeed in any way that I can think of, to tackle the question of the title. Perhaps some attention could have been directed to the title question. In that case the question would have been deemed newer than many.

Some of the people whose question is closed must feel as if they are being shunted off to an answering machine. Certainly if there are very good answers that one knows of, either on this site or on, say, Wikipedia, it is important to give the appropriate references. That is a quite separate matter from closing questions.

As a more general comment, if we automatically close when there is duplication, and the criterion is applied strictly rather than sporadically, a substantial class of questions will be automatically eliminated if the site goes on for an additional year or two.

This means that new users of the site who could contribute answers to questions of a popular kind will not be able to do so.

• I think the right thing to do with duplicates is to merge the old and new into a new question, but the mods aren't doing this. It needs to be merged old->new (not new->old) so that it gets exposed on the new-questions page, not the active page (many folks read only the new vs. active questions). Perhaps we could get the community to help with the merge by having a meta thread devoted to such that gets bumped when merge volunteers are needed. – Bill Dubuque Jul 2 '11 at 16:04
• @Bill: That's also where the discussion on Aryabhata's answer went. If you post the comment as an answer, I'll accept it. – Mark Bennet Jul 2 '11 at 17:23
• @Bill: the reason that I (not speaking for other Mods) am not doing this is that, for the most part, merging is a destructive process. The merged question no longer remains, and their comments also go poof. And unless the questions are word for word identical (including all use of symbols), some of the answer will cease to make sense post merge. I haven't actually seen many good candidates for merges. The few times I did so was when the OP inadvertently posted more than one copy of the same question. – Willie Wong Jul 5 '11 at 23:14
• But if the community is willing to take the time to identify and flag questions that can be merged without those kinds of things becoming issues, I'd be more than happy to oblige. – Willie Wong Jul 5 '11 at 23:15
• @Willie Perhaps we should consider requesting whatever features we would need to make merging satisfy our needs. Is the current merge behavior documented anywhere? – Bill Dubuque Jul 5 '11 at 23:19
• @Bill I don't even know what the current behaviour is, because the last time I tried it made me really reluctant to use it. Let me go see if I can dig up something about what should happen. If we come to some conclusions about precisely what we want and why we want them, I'd be happy to raise the issue over at Meta.SO. – Willie Wong Jul 5 '11 at 23:25
• @Bill Assuming I didn't overlook a more recent post, the merge behaviour should be described by this. Apparently it is not as bad as I remembered: original becomes a stub (like when we migrate to other sites), with answers transferred to the merge target. Comments do get "de-parented", but that's probably no big deal. If you have some candidates in mind, we can try the merge and see how it looks. – Willie Wong Jul 5 '11 at 23:36
• @Willie: This might be a candidate: math.stackexchange.com/questions/51974/…. I and one other user voted to close as duplicate, but no-one else did, and André wrote a beautiful answer to the new question, which in my opinion should preferably have been added as a new answer to the existing question instead. – joriki Jul 17 '11 at 22:17

I would like to vote Bill's suggestion about the way in which answers are merged, but it's only a comment. Something similar emerged in discussion with Aryabhata. The main idea is to merge into the new question, which the moderators might be able to do.

I don't know about the profile of users/vistors - but this might well help to keep common questions reasonably current for new users. On the other hand it might seem repetitive for old hands.

• We should probably start a new discussion thread to hammer out the policies for mergers. There are a few possible difficulties that comes to mind: what if the old question already has an accepted answer? What if the notations are slightly different? What if there were good comments made in the question statement of the old question? (The merge available in software, the last time I checked, essentially takes the answers from one question, sticks to the other, and redirects all links to the old question to the new one.) – Willie Wong Jul 5 '11 at 23:19
• What's also important is to have users help in maintaining the list of common questions. Aryabhata has been helping out lots with flagging for possible dupes; we need more people like him or like Bill who keeps good track of what has been discussed before to keep the list current and populated. – Willie Wong Jul 5 '11 at 23:22
• Apparently the "last time I checked" may be a while back. According to this post question merge is not (as) destructive any more. – Willie Wong Jul 5 '11 at 23:38
• @Willie Thanks for the thoughtful comments - I'm sure these things are never as easy as they can seem in theory. – Mark Bennet Jul 6 '11 at 8:50

In this case, the motivation is irrelevant, as they all want a solution to $a - \sin a = \frac{\pi}{2}$, which the answers to the first show, can be found in an elementary fashion in terms of the root of $\cos x = x$ and hence applicable to all three, no matter what the sophistication of the asker.

In general, the motivation could matter, for example consider these two:

Finding the limit of $\frac {n}{\sqrt[n]{n!}}$

Power Series with the coefficients $n!/(n^n)$

These are essentially the same question, but since one of them specifically disallows the use of Stirling's formula, one could argue that they are not duplicates. If you look at the answers, there is duplication, so maybe it is not such a good example.

• I think the second question of my three asks for a way of estimating the solution. Expressing the answer in terms of a root of $\cos x = x$ simply shifts the problem to estimating the answer to a different equation. It is perhaps material that the third was closed as a duplicate of the first. However the third question did reveal that an integral method was available to solve the equation (to identify a centre of mass), hence mathematical insight. I was surprised to see the same equation three times. – Mark Bennet Jul 1 '11 at 20:07
• @Mark: There are estimates for the Dottie number (the root of $\cos x = x$) available on the web and the links given. Suppose I asked a question asking for an estimate of the root of an equation and the root turned out to be 1. Now if someone says the answer is 1, have they not provided an estimate? How is it different? – Aryabhata Jul 1 '11 at 20:10
• but suppose the question is given as an open-ended investigation exercise for students to explore possible strategies for estimating. Knowing about the Dottie number doesn't advance that. Amongst other techniques to explore are graphical, iteration and series expansion: which is best? How does one get an intuition about that? – Mark Bennet Jul 1 '11 at 20:29
• @Mark: If you want, you can ask a question yourself, asking how one can estimate (physically or otherwise) the Dottie Number. Note, here you are looking for an algorithm to calculate, which is different from what the questions have asked so far. In that case, I agree it won't be a dupe. "What is the solution?" is different from "What are some techniques to calculate the solution?". – Aryabhata Jul 1 '11 at 20:34
• @Mark: FYI: Please also note that this is not an open discussion/math exploration forum. Please see the FAQ, in particular, this section: What not to ask. – Aryabhata Jul 1 '11 at 20:50
• The second question I linked asks for help in estimating as you suggest, and has now been closed as a duplicate. I don't think the distinction is necessarily as clear as you suggest, though it may be necessary to cut through ambiguity to manage the discussion in a sensible way. Also calling something "The Dottie Number" tells me it might have wider significance than a particular problem, but it doesn't actually convey much about what that significance is, though it suggests where to look. – Mark Bennet Jul 1 '11 at 21:06
• @Mark: The distinction is really dependent on what the OP wants and in this case, based on the comments, it seems that they were looking for an approximate number, rather than an algorithm to estimate the number. I do hope you agree that there is a distinction. For instance, solution is $\pi$ versus how to estimate $\pi$. I guess one reason it is not that clear is that the number is not a well known constant... – Aryabhata Jul 1 '11 at 21:17
• @Mark: btw, we could always reopen the question (after editing to make the intent clearer), and if it does turn out the OP was looking for a method, I agree with you that we probably should. – Aryabhata Jul 1 '11 at 21:33
• I'm sure there are many areas in Mathematics where the same mathematical $content$ (in terms of equations, constructions etc) turns up in different $contexts$ - in fact that seems to be one of the ways in which mathematics develops. so maybe there is sometimes a case for merging discussions to bring the contexts together (I thought I saw this could be done)? Then there is a continuing open question and all the information about it is in one place. – Mark Bennet Jul 2 '11 at 9:47
• @Aryabhata let us continue this discussion in chat – Mark Bennet Jul 2 '11 at 9:48