Wikipedia:Articles for deletion/Nine-dimensional space


 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review).  No further edits should be made to this page.

The result was   redirect to n-dimensional space. Tim Song (talk) 04:07, 8 June 2010 (UTC)

Nine-dimensional space

 * – ( View AfD View log  •  )

The page is following the same template as seven-dimensional space and eight-dimensional space, but unlike those pages does not contain any special-case applications. It would serve better as a redirect to n-dimensional space. ~  Keiji (iNVERTED)  ( Talk )  19:31, 31 May 2010 (UTC)
 * delete These were created at the same time as copies of Six-dimensional space at the end of last year, I assume with hope they'd be expanded with relevant applications, but it seems there are none in nine dimensions: the polytopes are covered at 9-polytope and there's nothing else here of worth, and the series of articles should stop at eight. If in future an editor finds something of interest that would make a worthwhile article it could be recreated, again from one of the lower dimensions.-- JohnBlackburne wordsdeeds 21:28, 31 May 2010 (UTC)
 * Comment - significant coverage here - (snippets only) and there's another paper concerning 9-dimensional space at . Also, a few applications exist - conductivity theory: ,dynamics  and also in string theory -  and . I'm not sure what the notability guidelines for mathematical constructions and so forth are, but it seems to have applications, if that's an indicator of notability. Claritas §  09:02, 1 June 2010 (UTC)
 * A detailed analysis of each reference:
 * Difficult to tell, because "9-dimensional" only occurs a few times, but probably a result which wouldn't be suitable for the article if it did exist.
 * Not clear, as only the first page of the paper is available, but doesn't seem to be suitable for inclusion even if there were an article. It has to do with 3-vectors over C9, and 9-dimensional space only relates to R9.
 * Appears to be about a specific quantum-mechanical system which has 16 states, which can possibly be reduced to 9 by symmetry considerations. It also seems to be a complex 9-dimensional space.
 * Nothing there at all. It's 4n+9-dimensional space.
 * There might be something in string theory. I seem to recall that most string theory lives in 10- and 11- dimensional space, so this might refer to a 9-dimensional manifold in 11-space.  However, this paper refers to an artificial 9-dimensional space consisting of the tensor product of 2 3-dimensional spaces.
 * Definitely a specific 9-variable problem, not a general question about 9-dimensional space.
 * — Arthur Rubin (talk) 16:27, 1 June 2010 (UTC)
 * Note: This debate has been included in the list of Science-related deletion discussions.  -- • Gene93k (talk) 14:05, 1 June 2010 (UTC)
 * Delete. If something comes up, it could be recreated, but there's nothing there now.  — Arthur Rubin  (talk) 16:28, 1 June 2010 (UTC)
 * Delete and possible Transwiki to commons, currently nothing more than an image gallery and there is no suggestion that this special case is particularly notable. Paul Carpenter (talk) 17:10, 1 June 2010 (UTC)
 * Delete. Unless and until something emerges that gives the case n=9 in "n-dimensional space" any special significance, this article will remain totally ridiculous. No notability whatsoever. As the discussion above shows, the search for "9-dimensional" has only brought up incidental mentions, so actually confirmed this. Hans Adler 06:41, 2 June 2010 (UTC)
 * Delete. This article came about as the result of a campaign by a single editor of "copy, paste, and add one".  See  this thread.  Ultimately, User:Arthur Rubin arrived at the current compromise solution, presumably in the hopes that User:4, the only apparent supporter of this campaign, would add enough content to the article to make it worth having.  Well, that was in December, and so far the article has not progressed from its copy-pasted state, except (during the course of this AfD) to include some formulas that are already in the n-sphere article, and images of 9-dimensional polytopes.  As already suggested above, if article-worthy content surfaces, then the article can always be recreated by copying one of the lower dimensions again.   Sławomir Biały  (talk) 11:15, 2 June 2010 (UTC)
 * Delete and redirect to n-dimensional space. There is nothing here that is not an explicit example of an n-dimensional phenomenon. TimothyRias (talk) 11:49, 2 June 2010 (UTC)
 * Redirect per TimothyRias and WP:CHEAP. Bearian (talk) 17:34, 2 June 2010 (UTC)
 * If its the same as n-dimensional space then redirect it. Otherwise Keep.  Clicking on Google news and Google books and Google scholar show all results for all of them, this an actual thing.   D r e a m Focus  06:36, 3 June 2010 (UTC)
 * Weak Keep or Redirect References have been added to establish notability. Its strange how even elite subjects get put up for deletion when theyre related to engineering.  I recall the squad had to completely re-write the related and excellent Plastic deformation in solids article to save it from deletion.  Please ask editor Logger9 or administrator materialscientist if you require confirmation of this topics importance to structural engineering. Sources covering the applicability to  string theory are abundant.  PS - I hope no one feels bad that they've missed these key applications, its a normal feature of accademic immersion in this area to loose perspective of geometries outside your area of study.  FeydHuxtable (talk) 19:14, 3 June 2010 (UTC)
 * Comment. The string theory reference is almost plausible.  The material deformation is not.  The 9-dimensional "space" is the image of the tensor product of 2 three-dimensional spaces, as is reference 5 above.  (It's not clear to me whether the 3-dimensional spaces relate contravariently or covariently, making it unclear whether the space divides into 3- and 6-dimensional spaces, or 1- and 8-dimensional spaces.)  It's topologically 9-dimensional, but not Euclidian.  — Arthur Rubin  (talk) 21:09, 3 June 2010 (UTC)
 * Comment. Even if FeydHuxtable's additions were notable, those parts of the 2-paragraphs which are accurate should be trimmed to sentences and merged into a subsection of "Applications", such as:
 * 9-dimensional space is used in superstring theory[1] and material science.[2]disputed
 * 10-dimensional space is used in m-theory[3]. 10-dimensional space-time is used in superstring theory.[1]
 * 11-dimensional space-time is used in m-theory.[3]
 * 24-dimensional space is the first dimension in which an irregular packing is known to be better than any regular packing.[4] (Or whatever is true of the Leech lattice.)
 * — Arthur Rubin (talk) 21:34, 3 June 2010 (UTC)
 * — Arthur Rubin (talk) 21:34, 3 June 2010 (UTC)


 * On the first point: The spaces are covariant, and in fact it is only the symmetric (6-dimensional) part that is relevant, I think. But the fact that tensors of various dimensions are used does not mean that this can be a serious source for the notability of this article.  The Riemann tensor in 4 dimensions has 20 independent components&mdash;does this suddenly mean that the hypothetical article 20-dimensional space is notable because of the existence of a tensor with this many components?  No, of course not (even though there is a natural "Euclidean structure" on such tensors).  The chief concern here as I see it is one of WP:OR.  Without sources that treat 9-dimensional space as a specific topic in its own right, attempts to gather and catalog various objects that happen to be 9-dimensional will inevitably be an unpublished synthesis.  One the second point, regarding the specific applications in string theory, this would seem to be content more suitable for an article that specifically discusses the significance of the various dimensions appearing in string theory rather than an article on nine-dimensional space.  That would seem to be a much more sensible way to organize this kind of information.   Sławomir Biały  (talk) 14:12, 4 June 2010 (UTC)

Sorry about the strong keep. I usually take the view that redirecting is as bad as deletion but I guess if even the legendary dreamFocus and Bearian can accept a redirect its churlish to stand in the way of consensus, especially as what youre suggesting above seems a good way to improve the n-dimensional article.

Im just going to talk about the two references cos it would be a shame to have any merged content marred with unsightly tags.

For strings the reference seemed to be ideal for notability: its Oxford University Press so near the summit of our RS hierarchy, its a secondary source and as the author doesnt have a horse in the race its totally independent of the subject. The fact that string theory posits 6 extra spatial dimensions shouldnt be controversial. This was common to all five leading flavours. The primary literature is somewhat opaque and some of the best secondary articles in journals or reliable periodicals like New scientist are behind pay walls. But one can confirm this from countless popular science books, see this one by Cambridge 's Gibbons or this one by arch simplifier physicist David McMahon With strings the common view was there are 9 spatial dimensions plus time. After Witten unified the contradictions between the leading versions of string theory by positing an extra spatial dimension the main stream view is that there are 10 spatial dimension + the temporal. Admittedly there is a sizeable minority view that sees all the dimensions above the 3rd as having a partially temporal character. Theres even an interesting fringe view that there are in fact only 10 dimensions, with time being only one direction in the 4th dimension. But I think the summary in the article is an acceptable simplification and as you concede its totally supported by the reference.

For deformation, Im going to try to put this in simple terms for the benefit of anyone trying to follow this discussion without mathematical training. When you say 9D space isnt Euclidian i guess youre using the word as a synonym for spatial which is common usage among some mathematicians, but for most Euclidian refers to the 3D geometry where the 5th postulate holds true – the space of visual experience. To understand 9D space as its used for deformation one needs to liberate oneself from optical limits. Here 9D space it totally different from the reality imagined for strings and modes of thought from that field aren 't helpful, most especially not trying to visualise the extra dimensions in the manner of Rob Bryanton. Start by considering a regular point in 3D, defined by 3 coordinates. But then instead of thinking of the coordinates as positions along the 3 visual dimensions, just think of them as 3 independent numbers. Then theres no reason why a point cant be defined by n separate numbers, for our purposes nine. Its in this simple but abstract way that we use 9D space for deformation. Unlike with strings there is no significant qualitative difference between the 6 higher dimensions and first 3 (admittedly the typical math only sees vectors being assigned values on 6 out of the 9 dimensions, but this is only due to symmetry between the stress and strain tensors)  As dream focus says, it exists. This is totally mainstream, weve been using higher dimension number systems since the early 17th century, and 9D space for work on deformation for almost 100 years. As per the article "Abstract nine-dimensional space occurs frequently in mathematics, and is a perfectly legitimate construct."

Its good to encounter delete voters who know what theyre talking about for a change. As the material seems to be in good hands ill bow out of this discussion. I hope the tags wont be added back, and to be honest Id rather my additions were totally deleted rather than tagged, but whatever you decide. FeydHuxtable (talk) 12:15, 4 June 2010 (UTC)


 * Material science section removed, by request. By "Euclidian", I actually meant a Riemannian manifold (or locally Euclidian manifold.)  In string theory, that's a given, but there's no natural local inner product in the "materials science" section.  — Arthur Rubin  (talk) 15:04, 4 June 2010 (UTC)


 * Delete or Redirect to n-dimensional space. No claim of mathematical notability whatsoever, source given for superstring theory is about modeling superstring theory, and 9-dimensional space is depreciated by that source. Abductive  (reasoning) 03:35, 8 June 2010 (UTC)
 * Redirect per User:Abductive. RussianReversal (talk) 04:06, 8 June 2010 (UTC)
 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.