Wikipedia:Articles for deletion/Vector quadruple product


 * 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   delete. --  Phantom Steve / talk &#124; contribs \ 16:20, 19 September 2010 (UTC)
 * Following a request for a rationale, here it is: Four editors (including the nominator) suggested that this should be deleted, as there are either no sources, or this is covered elsewhere; 1 editor suggested redirecting, but this was not supported as an option; 2 editors suggested keeping (one suggesting the alternative of a merge, but there was no support for this); and a final editor suggested a merge (implicitly, not explicitly), but again there was no firm support for this idea. As such, the consensus would appear to delete the article. --  Phantom Steve / talk &#124; contribs \ 21:15, 19 September 2010 (UTC)

Vector quadruple product

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Seems to be a neologism. Does not appear in the source (though I could only search it in snippet view) and the Mathworld link where it looks like the name comes from has the name as Lagrange's identity, and that article is a list of identities related only by being products of four vectors. So is a separate article needed, should it be renamed to something more matching the sources; e.g. this gives it as "Lagrange's identity" (though we have such an article), or even to a more WP-ish "List of products of four vectors"? JohnBlackburne wordsdeeds 14:45, 12 September 2010 (UTC)


 * Delete. Article is a good as empty and the subject is hardly notable. Furthermore, according to sources the product (AxB).(CxD) isn't even called a "Vector quadruple product" to begin with. DVdm (talk) 15:12, 12 September 2010 (UTC)


 * Modify and rename, or merge Redirect to Quadruple product. The product is indeed called the vector quadruple product here, although the name is poorly chosen as the result is a scalar, not a vector. As a scalar, a name preferable to vector quadruple product is quadruple scalar product. A more general result that includes this one is known as the Binet–Cauchy identity. The source cited by Wolfram does not appear to use the name vector quadruple product.  The Wolfram article could be better named "vector identities using four vectors" or something similar, and this article would be more notable if it held a list of such identities for four vectors. I suspect that there is already an article that reviews such identities on WP, where this page could be merged. Brews ohare (talk) 16:51, 18 September 2010 (UTC)
 * I'm unable to locate a page listing vector identities. Perhaps this page could be renamed and used to nucleate such a list? Brews ohare (talk) 17:06, 12 September 2010 (UTC)


 * comment. From the history it looks like it was sourced from Wolfram's Mathworld, but though the article there is titled "Vector Quadruple Product" but it is a list of identities, not one: it starts "There are a number of algebraic identities involving sets of four vectors", so there is no product named "vector quadruple product" there. In any case Mathworld is a lot like Wikipedia, so is more a tertiary source than a secondary source and I would always look for other sources as well, and prefer them if they are different from Mathworld. I did not think of this but: merge to where? We have a page Vector calculus identities, a redirect from List of vector identities which already includes these two so there would be little or nothing to merge. while the more notable one is covered at Cross product and Binet–Cauchy identity already.-- JohnBlackburne wordsdeeds 17:17, 12 September 2010 (UTC)
 * Proposal: The subsection here of Vector calculus identities is not appropriate as it doesn't refer to calculus per se. Also, the Binet–Cauchy identity article is a generalization of the quadruple scalar product. Perhaps this article can be renamed as List of vector identities and this subsection moved over? A number of other identities can be added, as per the Wolfram article, and some triple vector product identities added? Brews ohare (talk) 18:22, 12 September 2010 (UTC)
 * Here's a beginning. Brews ohare (talk) 18:38, 12 September 2010 (UTC)


 * comment there was a List of vector identities until a few months ago, but it was decided there's no need for two lists and it was merged into Vector calculus identities. I think that's best: one list where everything can be found rather than two you have to check, or even two and the identity you want is in the list you didn't check. I found it easily enough by typing "List of vec..." into the search box, so although it's not at the place I expected a redirect is there to make it easy to find. As the two identities on this page already appear at Vector calculus identities I think making this a redirect there makes sense; a merge except the content is already there.-- JohnBlackburne wordsdeeds 18:40, 12 September 2010 (UTC)
 * It seems to me awkward to place simple vector identities under the auspices of a more specific and complex subcategory that involves differential operators, namely Vector calculus identities, especially when the simple identities do not depend in any way upon calculus or derivatives. Therefore, the sensible course is to have a separate article. Brews ohare (talk) 19:44, 12 September 2010 (UTC).
 * Books on vector calculus start with simple vector identities, so there is no reason to have two articles. We already have the list of simple vector identities in Vector calculus identities. DVdm (talk) 20:25, 12 September 2010 (UTC)
 * DVdm, help me understand your remarks, which seem counter-intuitive: books start with simple vector identities: OK, that suggests a precedent for an article like this too, no? We have already a misplaced list of simple identities in Vector calculus identities, even though they have no connection with calculus, so this list should be moved to the correct location in a list of simple vector identities, no? Brews ohare (talk) 22:55, 12 September 2010 (UTC)

The list is already at List of vector identities. That's where I found it, the first place I looked, as WP lists usually start with "List of...". Vector identities also redirects there, which might have been the second thing I tried. So there is no problem finding the list using either obvious name. As I noted above the problem with having two lists is that that's twice as many articles to check for an identity. Or there's the chance that someone looking for an identity will check the wrong list. The only way to avoid both of these problems would be to have identical lists, clearly pointless. If you check the histories of the list you'll see this has already been looked at, and the lists were merged, without any problems or objections. As for them having no connection to calculus they are all connected: the vector calculus identities are closely related to the others, so much so it's easiest to remember them all together. -- JohnBlackburne wordsdeeds 23:59, 12 September 2010 (UTC)
 * John: the link List of vector identities is a redirect to Vector calculus identities, which as noted above several times is an inappropriate place to list simple vector identities unrelated to calculus. The notion that a separate list requires checking two lists is a straw man. One could equally say that it's less convenient to have a misfiled list because upon finding one's search redirected to a misnomer one then has to search to see if in fact the redirect is appropriate.
 * More significantly, a separate List of algebraic vector identities (say) could be extended to be quite useful.  Brews ohare (talk) 00:09, 13 September 2010 (UTC)
 * The merge of two lists probably seemed appropriate at that time because the list was a hodge-podge of algebraic and calculus identities. It should have been split up instead of moving both types to the calculus list. Brews ohare (talk) 00:21, 13 September 2010 (UTC)


 * Keep or Merge: I did get a few GBooks hits on "Vector Quadruple Product" and together with the MathWorld entry I think that establishes notability. MathWorld tends to prefer shorter articles than Wikipedia, so I won't claim the article should be kept as a stand alone article, but I don't see a viable candidate for a merge target at the moment and it would better to keep the article until one can be found. A merge with Triple product might work. As far as the name goes, my experience with WP has taught me that names in mathematics are often rather fluid, with different authors using different names for the same subject or writing about a subject without naming it explicitly at all. Creating article names in such cases is a challenge and I don't think deferring to MathWorld should be a problem, even knowing it is notorious for neologisms, unless a consensus among more authoritative sources is found.--RDBury (talk) 06:39, 13 September 2010 (UTC)


 * I'm inclined to avoid the use of the term Vector Quadruple Product as done by Wolfram because this GBook search suggests it most commonly refers to expressions that really are vectors made up of cross products of cross products. Brews ohare (talk) 09:26, 13 September 2010 (UTC)


 * Draft of alternate article: This article could be replaced by the article Vector algebra relations recently posted. The list of algebraic identities in this subsection then can then be replaced by a link. Brews ohare (talk) 08:36, 13 September 2010 (UTC)
 * comment That's not a draft; once an article is posted in main space it's a live article. Creating such article both preempts the result of this AfD—before the discussion is ended you have decided that the article should be kept and so created one under a different name to replace it—and effectively undoes the perfectly good merge done earlier between List of vector identities and Vector calculus identities and so recreates the same problem of multiple articles serving the same purpose. Please remove it from mainspace until this AfD is concluded.-- JohnBlackburne wordsdeeds 16:49, 13 September 2010 (UTC)
 * Yes, I didn't express this well: the idea was that it is a first attempt at the kind of general presentation I was suggesting. It is independent of of this AfD, inasmuch as the article here Vector quadruple product is a very specific case, and can stand or fall on its own quite independent of Vector algebra relations. The impact Vector algebra relations has upon Vector quadruple product is to provide all its identities save one dubious unsourced identity, which might remove the need for this article except possibly as a redirect.
 * The article Vector algebra relations, as explained further on Talk:Vector algebra relations does not duplicate anything. It does provide an opportunity to move the misfiled vector algebra identities that have nothing to do with calculus or differentiation out of Vector calculus identities to a properly named article.
 * The "perfectly good merge" you mention was nothing of the kind, as it mixed together distinctly different types of vector relations. Brews ohare (talk) 17:07, 13 September 2010 (UTC)
 * I'd suggest at this point that to save the article Vector quadruple product it should be renamed as Quadruple vector products (by analogy with Triple product) and that it be expanded to do more than present the identities by also discussing their implications and applications. Brews ohare (talk) 18:02, 13 September 2010 (UTC)


 * comment again please remove it from mainspace. You have prejudged the outcome of this discussion by carrying out your own recommendation before this discussion is concluded. Further now we have two lists of vector identities, one at Vector identities one at Vector algebra relations, creating exactly the problem the earlier uncontentious merge fixed.-- JohnBlackburne wordsdeeds 18:55, 13 September 2010 (UTC)
 * Blackburne: The introduction of the article Vector algebra relations does not prejudge the outcome of this AfD. All it does is introduce a new article listing a large number of properties of vectors in 3-D, considerably beyond the scope of Vector quadruple product. The article under discussion here Vector quadruple product should be constructed as a parallel to Triple product, that is, as a stand-alone article providing full details of quadruple products, including perhaps the connection to Geometric algebra and other applications. Thus, this AfD is in no way pre-empted by the general listing of vector relations in Vector algebra relations, which article is the analogue of Vector calculus identities for relations that involve only algebra and no differentiations. Unfortunately, as other editors have commented, including yourself, the article Vector quadruple product at present is both misnamed and holds little content. Brews ohare (talk) 19:11, 13 September 2010 (UTC)


 * Delete. Unsourced (it says something very different from what's at the MathWorld link, turning an identity into a definition), and redundant, given the new article. -- Radagast 3 (talk) 22:01, 13 September 2010 (UTC)
 * Note: This debate has been included in the list of Science-related deletion discussions.  -- • Gene93k (talk) 02:00, 14 September 2010 (UTC)
 * Delete - already covered in Binet–Cauchy identity; doesn't merit a separate article. Gandalf61 (talk) 09:37, 14 September 2010 (UTC)
 * Keep and clean-up -- The problem is that the MathWorld article is weirdly garbled, and gets it wrong. The vector quadruple product is the cross-product of the cross-products.  The formula here is the scalar quadruple product.  Honestly, neither of these strike me as particularly interesting, but they're both real terms, and thus should have pages.  People linked to some Google Books references above, but here are lecture notes from MIT's calculus class that mention both terms, and here are lecture notes from an engineering course from Oxford that talks about vector quadruple products.  Maybe it doesn't deserve a stand-alone article and should just redirect somewhere else, but it's not a neologism but a real term. -- Walt Pohl (talk) 11:55, 15 September 2010 (UTC)
 * To be fair to MathWorld ("though Arthur didn't see any need, beyond the sheer mental exercise of it"), the MW article does not actually say that the expression given is the vector quadruple product. Its article is called "vector quadruple product", a name that it never mentions again, until you get to "CITE THIS AS".  Then it lists some identities, the first of which is for the scalar quadruple product.  Maybe not great writing, but not quite blatantly erroneous.
 * As a general rule, though, WP should not rely on MW for anything, most especially naming. It's too given to neologisms, even if this particular one is not.  It's very unfortunate that MW was apparently used as a source of topics to put in Missing science topics.   --Trovatore (talk) 00:41, 16 September 2010 (UTC)
 * The source mit cited by Walt Pohl correctly names its section Quadruple products and then correctly identifies the scalar quadruple product and the vector quadruple product. That is quite distinct from this article called Vector quadruple product that proceeds to describe the scalar product incorrectly as a vector product and then proceeds to describe an identity of dubious origin regarding a vector product. Beyond these erroneous statements, and a source that does not support the material at all, the statement of the correct identities in this article are already provided, without the garbage, in Vector algebra relations. Brews ohare (talk) 15:27, 16 September 2010 (UTC)
 * But my more important point was Wikipedia should not rely on MathWorld for anything, most especially naming. --Trovatore (talk) 18:04, 16 September 2010 (UTC)
 * Trovatore: Good enough; now that it exists, would you favor a redirect of Vector quadruple product to Quadruple product, the analog of the article Triple product, as supported by [this Google link? [[User:Brews ohare|Brews ohare]] (talk) 15:00, 19 September 2010 (UTC)

What this article should be; See Quadruple product, which would be the appropriate article with more work on the section Interpretation and the addition of a section on the connection to Geometric algebra. Such an article would be the parallel to Triple product. Brews ohare (talk) 17:41, 16 September 2010 (UTC)
 * For the second time in days, you have created a new article as your "solution" to the problem, preempting the outcome of the discussion and causing extra work for everyone. The new article is largely the same as this, except with some working, mostly trivial except where it's incorrect. The title is misleading as there is no such "quadruple product" in maths, and such a title just raises the question "product of what?" It could be numbers, matrices, almost anything. The link for the reference is broken, so it's not possible to check but it seems unlikely that the source defines the "quadruple product".
 * The way to fix the article is directly: editors are allowed and encouraged to work on the article while it's under AfD, to can fix the problems have triggered the deletion discussion. Creating another article on the same topic just creates extra work for everyone, as if the changes would have saved this article then the deletion and recreation could have been avoided. If even with the changes it does not justify a separate article then both articles need deleting. So please remove the new article and consider making any changes to the article under discussion.-- JohnBlackburne wordsdeeds 16:45, 17 September 2010 (UTC)
 * The article Vector quadruple product under discussion here is named incorrectly, and is a mess. It seemed easier to start a new article that has the name Quadruple product selected by analogy with the existing article Triple product and it uses the same outline of topics. The term "quadruple product" is not less appropriate than triple product and is used by Gibbs among others. Creation of the article quadruple product means the present article Vector quadruple product simply can be deleted, as its content is corrected and put into the new article, which parallels the existing article triple product. The new article is intended to be a more extensive treatment of its topic than, for example, Vector algebra relations, which is simply a listing of useful relations without any explanations or applications. I've invited Blackburne to contribute to the geometric algebra aspects of the page quadruple product. Brews ohare (talk) 20:02, 17 September 2010 (UTC)
 * While triple product is a well known name in mathematics for a particular product "quadruple product" isn't. Search for it and the first three hits are Wolfram, this article and the new one, after which there's no clear pattern. I don't see any corrections in that article: since I wrote the above you've fixed one error and introduced another, but it's still adds only trivial working to this one, and a long section on geometric algebra which isn't related to the vector products except in trivial ways (as all vector products can be re-written using geometric algebra). And I can't help you with it as there is no "quadruple product" in geometric algebra, at least that I know of.-- JohnBlackburne wordsdeeds 20:20, 17 September 2010 (UTC)
 * The article triple product immediately devolves to scalar triple product and vector triple product, and as this link shows, exactly the same is true for quadruple product: there are scalar quadruple product and the vector quadruple product. If you like that better, the article could be named "scalar & vector quadruple product" and likewise the article Triple product can be renamed for parallelism Scalar & vector triple product. It all sounds like hair splitting to me. If you like, Scalar quarduple product can be redirected to Quadruple product if you think that is a likely access point.
 * Of course, in the sense of "quadruple product" meaning products of four vectors in various ways, geometric algebra has abcd a∧b∧c∧d, a∧b·c∧dand every permutation and combination of these products of four vectors. Brews ohare (talk) 21:00, 17 September 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.