According to the tag description, the is:

For question[sic] regarding the notion of orientation both in topology and in global analysis.

There is no further information in the tag wiki. A quick perusal of the first page of questions tagged with (of which there are only 214) indicates that a fairly nontrivial percentage of them are not related to the orientation of manifolds or global analysis. For example:

  • Questions about the orientation of the boundary in Stoke's theorem: e.g. [1], [2], [3]
  • Questions about the orientation of vectors and othe related questions: e.g. [1], [2], [3], [4]
  • A question about graph theory

Since the tag lacks a decent description and seems likely to cause confusion rather than lend clarity, I would like to propose that this tag be gotten rid of. If it has any use, it is perhaps as a synonym of .

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    $\begingroup$ It seems "orientablity" is a much better term. I searched "orientability" and it seems a lot of questions are highly related (but most of them are not tagged "orientation") $\endgroup$ – user99914 Feb 22 '18 at 5:46
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    $\begingroup$ Is the orientation of the boundary in Stokes's theorem really not related to the orientation of manifolds or global analysis? $\endgroup$ – Michael Hardy Feb 23 '18 at 5:50
  • $\begingroup$ @MichaelHardy The tag description is not clear (which is a big part of the problem), but it seems to me that the intention of the tag was to explicitly highlight topological notions of orientation and orientabiliy. These notions may play a role in Stoke's theorem, but the linked questions certainly have nothing to do with higher level difficulties concerning topological orientation. Moreover, if the tag really is meant to be so inclusive as to encompass all of the above, then I don't think it is a useful tag, in that it doesn't help to filter questions in a meaningful way. $\endgroup$ – Xander Henderson Feb 23 '18 at 15:10
  • $\begingroup$ This tag is indeed not well-defined. However, it seems to me a better description would be better suited than removing it altogether. Indeed, much like you indicated, this tag is used to address questions related to a fundamental notion of differential geometry. $\endgroup$ – niko Feb 23 '18 at 22:33
  • $\begingroup$ Orientation is important for the domains of integration in vector calculus, which is a subject taken by a great number of students. (I even teach it, and I teach at a community college that is not known for teaching advanced math.) Questions about Stokes's Theorem are likely to be about this, and that topic bleeds into orientability of manifolds (per Michael Hardy's comment). But the majority of these students are not going to know the word ‘manifold’. $\endgroup$ – Toby Bartels Feb 24 '18 at 8:15
  • $\begingroup$ Looking more at the offered examples, I'd say that they're all about the topic in the tag description, except for the graph-theory example and example [3] from the vectors list (the one about Euler angles and cell phones). There's a progression of sophistication from orientation of vector spaces to orientation of flats (linear or affine subspaces of vector spaces) to orientation of parametrized submanifolds (the topic in vector calculus) to orientation of abstract manifolds and bundles (the topic in topology and global analysis). $\endgroup$ – Toby Bartels Feb 24 '18 at 8:29
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    $\begingroup$ @TobyBartels (and others) Perhaps, but I think that this is more or less the same as arguing that a question from a freshman level calculus class should appropriately be tagged [real analysis]. That being said, I'm open to the idea that the tag could (or even should) be more inclusive, and perhaps the real problem is that the tag is not well-described. Does someone with a better background than myself feel like writing a better tag-wiki? (If not, I contend that the correct action is burnination.) $\endgroup$ – Xander Henderson Feb 24 '18 at 16:38
  • $\begingroup$ How else would the freshman tag it? If we didn't have the term "calculus", then "real analysis" would be overrun by freshmen questions. What is the equivalent term that we can redirect the freshmen to in this case? $\endgroup$ – Toby Bartels Feb 26 '18 at 21:28
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    $\begingroup$ @TobyBartels Well, the stokes-theorem deals with most of the first set of questions, since they are really asking about a confusion in the details of a computation. I'm not sure that the orientation tag adds any filterability or clarity to those questions. That being, said, as I have repeated often, I think that the big problem is that the tag is not well described, and is currently being used in different, somewhat orthogonal, ways. I'm open to a better description. I just don't have the expertise to write one. $\endgroup$ – Xander Henderson Feb 27 '18 at 0:57
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    $\begingroup$ Moreover, as John Ma points out, there are a lot of posts that actually probably fit the (minimal) tag description which are not tagged orientation. If the tagged posts don't quite fit the current description, and there are other posts that do fit the description but are untagged, how is the tag helping people to search the site and find what they are looking for? What reason is there for keeping it? $\endgroup$ – Xander Henderson Feb 27 '18 at 1:01
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    $\begingroup$ It seems that Stokes theorem is the only place where one deals with orientation in calculus level class. So I agree that the "Stokes theorem" tag is good enough. $\endgroup$ – user99914 Feb 27 '18 at 1:17
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    $\begingroup$ Related: there's a non-orientable surface tag created recently. $\endgroup$ – user99914 Feb 27 '18 at 1:18
  • $\begingroup$ Perhaps the "orientation" tag should be renamed to "orientable-surfaces" or "orientation-of-surfaces" (these seem narrow, as higher dimensional manifolds can be orientable...) or "topological-orientation" or some such? In any even it still needs a better description... $\endgroup$ – Xander Henderson Feb 27 '18 at 1:25
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    $\begingroup$ @XanderHenderson : A tag called orientable-surfaces is still going to attract people asking about Stokes's Theorem, I'd expect. $\endgroup$ – Toby Bartels Feb 28 '18 at 13:19
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    $\begingroup$ I could write a description of this tag that should make it clear that it includes every linked example except for the graph theory example and vector example #3. (Perhaps I should put that as an answer.) I think that that would be preferable to getting rid of it. (On the other hand, if someone wants to preserve this tag but use it only for high-level stuff as implied in the original description, then the name should probably be changed to something that Calculus students wouldn't think to use, and I don't have any suggestions about that.) $\endgroup$ – Toby Bartels Feb 28 '18 at 13:28

The tag should be kept, but it requires a better description.

After two years, this question has attracted 8 upvotes and no downvotes (which seems to indicate a moderate consensus towards keeping the tag , I guess?). In the comments, it was suggested that the real issue might be that the tag description is unclear. Yet no one has come forward to write a better description (again, I fee that I am unqualified to write this description).

Can someone qualified please step forward and take action to clarify the tag description?

  • $\begingroup$ I didn't know the tag existed. I hope it is kept, because I've been taking a sporadic interest in a series of papers by Lino Gutierrez Novoa on the topic of $n$-ordered sets, for which the tag order-theory does not seem to be appropriate. I agree the tag description is unclear. I agree with those who say the remedy is to clarify the description. Sadly, I'm not qualified to do that. I hope you're right about what the 8 upvotes may indicate about the consensus, but the opposite interpretation also seems possible! It could be that those 8 people agree with you that the tag should be got rid of. $\endgroup$ – Calum Gilhooley Jun 8 '20 at 12:51
  • $\begingroup$ @CalumGilhooley The headline question is "Is the tag useful?" and the discussion seems to indicate "yes, the tag is useful". I'm going with the interpretation that others want to keep the tag, hence this answer. ;) $\endgroup$ – Xander Henderson Jun 8 '20 at 13:35

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